Climate Response to Pulse versus Sustained Stratospheric Aerosol Forcing

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1 Geophysical Research Letters

Supporting Information for

Climate Response to Pulse versus Sustained Stratospheric Aerosol Forcing

Lei Duan^1,3, Long Cao^1*, Govindasamy Bala², and Ken Caldeira³

1Department of Atmospheric Sciences, School of Earth Sciences, Zhejiang University, Hangzhou, China.

2Center for Atmospheric and Oceanic Sciences, Indian Institute of Science, Bangalore, India.

3Department of Global Ecology, Carnegie Institution, Stanford, California, USA.

*correspondence: [email protected]

Contents of this file Text S1

Figures S1 to S10 Tables S1 to S5

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2 Text S1. Linear responses of the climate system to stratospheric aerosol forcing MacMartin and Kravitz (2016) has shown that the climate response to changes in atmospheric CO2 and solar forcing can be predicted using the impulse response function under the assumption that climate responses to these external forcings are sufficiently linear and time-invariant (LTI). The linear response assumption has been used in previous works to calculate the temperature and precipitation changes to CO2 increase and stratospheric aerosol geoengineering (e.g., Caldeira & Myhrvold, 2013; MacMartin et al., 2019). In this section, we briefly discuss linear responses of the climate system to additional stratospheric aerosol forcing applied in our simulations.

To calculate the impulse function for both the global mean temperature and precipitation responses, we first assume that additional stratospheric sulfate aerosols with the same spatial distribution, added at different months of a year, would produce similar time- dependent changes in global temperature and precipitation. This assumption, though not realistic, is used here because we only have one simulation results with a step-function increase in stratospheric aerosols (the sustained case). We fit an exponential curve to the monthly mean results in the form of:

∆𝑉(𝑡) = ∆V₍𝑒^*+,^* (1)

where ∆V is the time-dependent change in temperature or precipitation and t represents the time step. ∆V0 and tau are both derived from the fitting process. The fitting curves for temperature and precipitation over globe, land, and ocean are shown in Figure S8. The impulse response functions are then derived from the derivative of the exponential curve (not shown).

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3 Using the impulse response function calculated from the Sustained simulation, we re- construct time series changes in the global mean temperature and precipitation in the Pulse case using the convolution integral (e.g., MacMartin & Kravitz, 2016):

∆𝑉(𝜏) = ∫ ℎ₍⁴ ₀(𝜏)𝑓(𝑡 − 𝜏)𝑑𝜏 (2) where ℎ₀(𝑡) is the impulse response function derived from Eq.(1) and 𝑓(𝑡) is the time- dependent sulfate aerosol burden. In practice, we use the ratio of total additional sulfate aerosol amounts between the Pulse and Sustained cases at each month as 𝑓(𝑡). Reconstructed temperature and precipitation changes are shown in Figure S9. Our results show that the impulse function derived from the Sustained case can be used to reproduce the climate response from the Pulse case, despite the fact that we assume stratospheric aerosol forcing added at different months of a year have the same effects on the climate response and that results from only one simulation case is used. Therefore, we conclude that the linear and time-invariant hypothesis holds for our simulations as well.

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4 Figure S1: Initial zonal distributions of additional sulfate aerosol concentrations for the Pulse case. The same zonal distribution of the additional aerosol concentrations is applied in all longitude bands. This pattern is also applied (but at different magnitude) in the Sustained case.

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5 Figure S2: Time series of changes in the Pulse case in the first simulation year after the introduction of additional aerosols in the stratosphere: (a) surface temperature, (b) land minus ocean temperature, (c) precipitation, and (d) land runoff.

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6 Figure S3: Zonal distributions of change in temperature and precipitation over globe, land, and ocean for Pulse and Sustained cases. The first-year annual mean results from the Pulse case and equilibrium state results from the Sustained case are compared. Shaded areas are uncertainties represented by one standard error from the Control case.

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7 Figure S4: Distributions of the change in temperature and precipitation over ocean regions for the Pulse case (red), Sustained case (blue), and overlaps between Pulse and Sustained cases. The first-year annual mean results from the Pulse case and corresponding equilibrium state results from the Sustained case are compared. The x-axis shows the interval of changes in temperature and precipitation and the y-axis shows the fraction of ocean areas for corresponding changes. The left-most (right-most) bins show all areas less (larger) than minimum (maximum) value shown on the x-axis. The data for this figure is presented in numerical form in Table S3 and S4.

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8 Figure S5: (a) Changes in vertical velocity over land for Pulse and Sustained cases relative to the Control case and (b) model-simulated vertical velocity over land for the Control case. For panel (a), the first-year annual mean results from the Pulse case and equilibrium state results from the Sustained case are compared. The positive values represent descending motion and the negative values represent ascending motion. Results are interpolated from hybrid sigma-pressure levels to pressure coordinates before averaging.

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9 Figure S6: Spatial pattern of changes in annual mean evaporation for the Pulse, Sustained, and Pulse minus Sustained cases. The first-year annual mean results from the Pulse case and equilibrium state results from the Sustained case are compared. Hatching indicates regions where differences are not significant under Welch’s t-test with a 5% significant level.

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10 Figure S7: Changes in global and annual mean vertical (a) temperature and (b) specific humidity for the Pulse and Sustained cases relative to the Control case. The first-year annual mean results from the Pulse case and equilibrium state results from the Sustained case are compared.

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11 Figure S8: Monthly mean changes in (left) temperature and (right) precipitation in the Sustained case relative to the Control case (black lines) over globe (top panels), land (middle panels), and ocean (bottom panels). The red lines show exponential fits to the monthly mean results using Eq. (1).

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12 Figure S9: First 10-year changes in (left) temperature and (right) precipitation for the Pulse case relative to the Control case over globe (top panels), land (middle panels), and ocean (bottom panels). The black line represents the model ensemble mean and the grey lines show changes for each ensemble member. Results re-constructed from the impulse response function is represented by the blue line. Changes in temperature and precipitation in the Pulse case are well reproduced except for the land precipitation. Understanding the underlying reasons for this mismatch requires further explorations with specific experiment designs to account for the seasonal variations and more ensemble members.

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13 Figure S10: Time series of changes in the first 10-year annual average temperature (left column) and precipitation (right column) over globe (top panels), land (middle panels), and ocean (bottom panels) for the Pulse and Sustained cases. Our simulations show that for the Pulse case, the magnitude of the temperature response over globe, land, and ocean first increases and then decreases due to reductions in stratospheric sulfate aerosol amounts.

Global and ocean mean precipitation show similar trends with temperature changes, whereas land mean precipitation reaches the maximum in the first year due to the land minus ocean temperature change as mentioned in the main context. For the Sustained case, because the stratospheric sulfate aerosol layer stays persistently, simulated changes in temperature and precipitation show persistent reduction over globe, land, and ocean. The magnitude of the first-year annual average response in the Sustained case is smaller than that in the Pulse case, mainly due to smaller aerosol amounts added in the stratosphere for the Sustained case.

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14 Table S1: The amount of total additional stratospheric sulfate aerosol resident in the stratosphere in the first two years in the Pulse case. After month 24, the amount of additional stratospheric sulfate aerosol is set to zero .

Month of simulation Aerosol amount (Mt S) Month of simulation Aerosol amount (Mt S)

1 8.05 13 3.44

2 7.34 14 3.14

3 6.76 15 2.83

4 6.28 16 2.53

5 5.89 17 2.26

6 5.59 18 2.00

7 5.26 19 1.81

8 5.00 20 1.57

9 4.80 21 1.35

10 4.58 22 1.14

11 4.15 23 0.93

12 3.77 24 0.73

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15 Table S2: Values of key climate variables in the Control case and changes in the Pulse and Sustained cases relative to the Control case. For ΔPulse, we show the first-year annual mean results from the Pulse case minus the mean of the Control simulation. For ΔSustained, we calculate the mean of the last 60-year of total 100-year simulation from the Sustained case minus the mean of the Control case. The ITCZ location is defined as the latitude where the median of the zonal mean area-weighted precipitation between 20º S and 20º N occurs. Uncertainty is reported as one standard error that is computed based on 36 first-year Pulse results and 60-year Sustained results.

Control ΔPulse ΔSustained ΔPulse/ΔSustained

Temperature (K)

Global 287.03 (±0.01) -0.70 (±0.01) -0.69 (±0.01) 1.01 (±0.03) Land 282.18 (±0.02) -0.95 (±0.03) -0.76 (±0.02) 1.25 (±0.05) Ocean 289.73 (±0.01) -0.55 (±0.01) -0.65 (±0.01) 0.85 (±0.02) Land minus ocean T (K) -7.55 (±0.01) -0.40 (±0.03) -0.11 (±0.01) 3.66 (±0.49) Precipitation (mm day^-1)

Global 2.88 (±0.00) -0.04 (±0.00) -0.05 (±0.00) 0.82 (±0.03)

Land 2.40 (±0.00) -0.07 (±0.00) -0.04 (±0.00) 1.57 (±0.16)

Ocean 3.15 (±0.00) -0.03 (±0.00) -0.06 (±0.00) 0.50 (±0.05)

Land runoff 0.74 (±0.00) -0.03 (±0.00) -0.01 (±0.00) 2.31 (±0.42)

ITCZ (°) -1.44 -0.17 0.03 -5.67

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16 Table S3: Distribution of changes in temperature over land and ocean for first-year Pulse and equilibrium state Sustained cases relative to the Control case. Intervals of the temperature response are consistent with the color scale shown in Figure 3. The data listed in this table is illustrated as bar charts in Figure 4 and S3.

Pulse minus Control Sustained minus Control

Interval (K) Land area (%) Ocean area (%) Land area (%) Ocean area (%)

∆<-1.5 3.69 1.90 0.19 0.84

-1.5≤∆<-1.3 13.45 1.12 2.22 2.61

-1.3≤∆<-1.1 17.34 1.73 5.49 5.67

-1.1≤∆<-0.9 19.44 3.22 16.95 9.84

-0.9≤∆<-0.7 20.23 10.89 29.46 12.34

-0.7≤∆<-0.5 19.82 42.41 35.22 27.99

-0.5≤∆<-0.3 4.55 27.21 10.15 40.43

-0.3≤∆<-0.1 1.02 7.07 0.32 0.28

-0.1≤∆<0.1 0.29 2.09 0.00 0.00

0.1≤∆<0.3 0.10 1.53 0.00 0.00

0.3≤∆<0.5 0.04 0.58 0.00 0.00

0.5≤∆<0.7 0.00 0.21 0.00 0.00

0.7≤∆<0.9 0.02 0.02 0.00 0.00

0.9≤∆<1.1 0.01 0.00 0.00 0.00

1.1≤∆<1.3 0.0 0.00 0.00 0.00

1.3≤∆<1.5 0.0 0.00 0.00 0.00

1.5≤∆ 0.0 0.00 0.00 0.00

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17 Table S4: Distribution of changes in precipitation over land and ocean for first-year Pulse and equilibrium state Sustained cases relative to the Control case. Intervals of the precipitation response are consistent with the color scale shown in Figure 3. The data listed in this table is illustrated as bar charts in Figure 4 and S3.

Pulse minus Control Sustained minus Control

Interval (mm day^-1) Land area (%) Ocean area (%) Land area (%) Ocean area (%)

∆<-0.45 2.70 4.03 0.00 0.69

-0.45≤∆<-0.39 1.47 1.33 0.03 0.61

-0.39≤∆<-0.33 1.86 1.75 0.22 0.89

-0.33≤∆<-0.27 3.10 2.41 0.61 1.89

-0.27≤∆<-0.21 4.66 3.07 2.54 4.64

-0.21≤∆<-0.15 7.89 5.08 6.32 7.65

-0.15≤∆<-0.09 12.28 11.39 14.99 17.47

-0.09≤∆<-0.03 21.92 18.81 31.05 23.96

-0.03≤∆<0.03 25.65 21.17 30.91 24.14

0.03≤∆<0.09 8.92 11.94 6.90 10.18

0.09≤∆<0.15 4.13 7.56 3.64 4.05

0.15≤∆<0.21 2.57 3.40 1.33 2.21

0.21≤∆<0.27 1.27 1.71 0.75 0.77

0.27≤∆<0.33 0.33 1.39 0.25 0.64

0.33 ≤∆<0.39 0.33 1.10 0.24 0.19

0.39≤∆<0.45 0.28 0.86 0.13 0.02

0.45<∆ 0.65 3.01 0.09 0.00

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18 Table S5: Distribution of land runoff changes for first-year Pulse and equilibrium state Sustained cases relative to the Control case. Intervals of the runoff response are consistent with the color scale shown in Figure 3. The data listed in this table is illustrated as bar charts in Figure 4.

Interval (mm day^-1) Pulse minus Control (%) Sustained minus Control (%)

∆<-0.45 2.02 0.15

-0.45≤∆<-0.39 1.03 0.15

-0.39≤∆<-0.33 0.99 0.13

-0.33≤∆<-0.27 2.17 0.26

-0.27≤∆<-0.21 2.59 1.04

-0.21≤∆<-0.15 4.00 2.24

-0.15≤∆<-0.09 6.24 6.29

-0.09≤∆<-0.03 11.60 18.14

-0.03≤∆<0.03 50.88 57.90

0.03≤∆<0.09 10.17 8.49

0.09≤∆<0.15 4.59 2.98

0.15≤∆<0.21 1.56 1.12

0.21≤∆<0.27 0.96 0.50

0.27≤∆<0.33 0.36 0.22

0.33 ≤∆<0.39 0.22 0.25

0.39≤∆<0.45 0.21 0.07

0.45<∆ 0.42 0.06