On the Additivity of Climate Responses to the Volcanic and Solar Forcing in the Early 19 th Century

. The early 19th century was the coldest period over the past 500 years, when strong tropical volcanic events and a solar minimum coincided. The 1809 unidentified eruption and the 1815 Tambora eruption happened consecutively during the Dalton minimum of solar irradiance; however, the relative role of the two forcings (volcano and solar) agents is still unclear. In this study, we examine the responses from a set of early 19th century simulations with combined and separated volcanic 10 and solar forcing agents, as suggested in the protocol for the past1000 experiment of the Paleoclimate Modelling Intercomparison Project - Phase 4 (PMIP4). From 20-member ensemble simulations with the Max Planck Institute Earth System Model (MPI-ESM1.2-LR), we find that the volcano- and solar-induced surface cooling is additive in the global mean/large scale, regardless of combining or separating the forcing agents. The two solar reconstructions (SATIRE and PMOD) contribute on a cooling before and after 1815 of ~0.05 K and ~0.15 K monthly average near-surface air cooling, 15 respectively, indicating a limited solar contribution to the early 19th century cold period. The volcanic events provide the main cooling contributions, inducing a surface cooling that peaks at ~0.82 K for the 1809 event and ~1.35 K for Tambora. After the Tambora eruption, the temperature in most regions increases toward climatology largely within 5 years, along with the reduction of volcanic forcing. In the northern extratropical oceans, the temperature increases slowly at a constant rate until 1830, which is related to the reduction of seasonality and the concurrent changes in Arctic sea-ice extent. The albedo feedback 20 of Arctic sea ice is found to be the main contributor to the Arctic amplification of the cooling signal.


Introduction 30
Being the coldest period over the past 500 years, the early 19th century is a crucial period for studying the climate impacts from natural external forcing such as volcanoes and solar irradiance (Cole-Dai et al., 2009;Brönnimann et al., 2019). With limited impacts from anthropogenic greenhouse gas, the on-average low temperature in the early 19th century is believed to be caused mainly by the coincidental existence of strong tropical eruptions (the unidentified 1809 and the 1815 Tambora eruptions; Self et al. 2004;Cole-Dai et al., 2009) and the lower solar irradiance (Dalton minimum from 1790-1830; Usoskin 35 et al. 2002;Silverman and Hayakawa, 2021). Studies have investigated the climate impacts from the 1809 unidentified  and the 1815 Tambora eruptions (Raible et al., 2016;Schurer et al., 2019;Zanchettin et al., 2019), and the Dalton minimum (Anet et al., 2014). For example, Zanchettin et al. (2019) examined how different strengths of the unidentified 1809 eruption could have altered the cooling caused by the following 1815 Tambora eruption. However, studies on the interplay between the solar-and volcanic-induced climate responses in the early 19th century are rare. Wagner and 40 Zorita (2005) found that volcanoes are the main contribution to the winter surface cooling in the early 19th century, but no winter cooling is found with the solar-only simulations. On the other hand, Anet et al. (2014) argued that the volcanic forcing alone cannot reproduce the long-lasting cooling found in the reconstructions and the solar forcing is essential for the postvolcanic cooling. Both modeling studies considered only three ensemble members, resulting in not only the lack of quantification of the individual contributions from volcanic and solar forcing but also an inability to identify potential non-45 additive responses when combining both forcing.
For the quantification of the solar and volcanic forcing in the early 19th century, the uncertainty of the reconstructions used for forcing agents is a challenge. For instance, reconstructions of total solar irradiance (TSI) and spectral solar irradiance (SSI) can be calculated by various proxies, such as the sunspot number, solar modulation potential, and cosmogenic isotope concentrations of 14 C and 10 Be from tree rings and ice cores (Usoskin, 2017). Depending on the method, the estimated 50 ultraviolet irradiance can differ by up to 15% (Shapiro et al., 2011). As a result, two solar reconstructions and one volcano forcing are recommended in the protocol of the experiments covering the Common Era (Jungclaus et al., 2017) in the Paleoclimate Modelling Intercomparison Project -Phase 4 (PMIP4; Kageyama et al., 2018). This protocol provides a more consistent way for quantifying the early 19th century climates and further examining the interplay between the volcanic and solar forcing. The two solar reconstructions, SATIRE (the updated Spectral and Total Irradiance REconstruction-Millennia 55 model; Vieira et al., 2011;Wu et al., 2018) and PMOD (Physikalisch-Meteorologisches Observatorium Davos; Shapiro et al., 2011;Egorova et al., 2018) may allow estimating possible boundaries of how much the solar forcing may contribute to the past climates as PMOD has a larger variability and can be considered as an upper limit for the reduction of solar radiation (Schmidt et al., 2012;Jungclaus et al., 2017).
The interplay of volcano-and solar-induced impacts may not be straightforward since both volcanic aerosol and lower solar 60 irradiance can induce surface temperature changes along two pathways: bottom-up and top-down. The bottom-up processes caused by the two forcing agents cool the surface temperature with the reduction of incoming solar radiation at the surface due to the lower solar irradiance (Meehl et al., 2009;Misios and Schmidt, 2012) and the blocking of incoming solar radiation from the volcanic aerosols (Robock, 2000;Timmreck, 2012;Swingedouw et al., 2017). In contrast, the top-down processes for the two forcings are opposite: the reduced solar radiation can cool the lower stratosphere, reduce the meridional temperature 65 gradient, and weaken the polar vortex (Scaife et al., 2013;Maycock et al., 2015), while the volcanic aerosols can warm the lower tropical stratosphere causing a strengthening of the polar vortex (Robock, 2000;Timmreck, 2012;Swingedouw et al., 2017). These opposite polar vortex responses may result in distinct regional and seasonal surface responses, especially at highlatitudes. A question is, when both solar and volcanic forcing are included in the system, can the top-down and bottom-up processes of both forcings be simply additive? And how will the surface temperature cooling respond to the combination of 70 both forcings and both processes?
Besides, Arctic Amplification (AA) is a possible factor creating the latitudinal difference of surface air cooling on Earth as AA is well-known for the latitudinal difference of warming (Graversen et al., 2008;Serreze et al., 2009;Previdi et al., 2021).
Under global warming, the Arctic region is observed and expected to warm faster than other regions and to reduce the seasonality due to a stronger AA in winter. In fact, AA may also exist when the system undergoes a surface cooling. For 75 example, Stjern et al. (2019) show that solar irradiance change has a similar AA strength as other drivers (such as CO2). Liu et al. (2018) state that no volcano-induced AA is found due to the large temperature changes in the tropics, while others have found that the northern extra-tropics encounter a larger cooling a few years after eruptions . This means that the extent of AA for volcanic and solar forcing is not well understood and the combination of both has not yet been studied.
The paper is structured as follows: Section 2 discusses the data, method, and experiment design; Section 3 describes the impacts 80 from solar and volcano forcing separately; Section 4 investigates the additivity between the volcanic and solar signals at the surface, atmosphere, and ocean; Section 5 studies the AA during the solar-and volcanic-forced cooling with a feedback separation; and Section 6 summarizes the paper and discusses potential follow-up studies.

Datasets and methods
In this study, the Max Planck Institute for Meteorology Earth System Model version 1.2 at low resolution (MPI-ESM1.2-LR), 85 which is the CMIP6/PMIP4 version of MPI-ESM (Mauritsen et al., 2019), is used for our simulations. The MPI-ESM1.2-LR is a state-of-art climate model composed by the ECHAM6.3 atmospheric model, JSBACH3.2 land model, the MPIOM1.6 ocean model, the HAMOCC6 ocean biogeochemistry model, and the OASIS3-MCT coupler. The atmospheric component is using the T63 Atmospheric triangular truncation (~200 km horizontal resolution) with 47 vertical levels (0.01 hPa or 80 km on average for the top) and the ocean grid is the GR1.5 grid (~150 km nominal horizontal resolution) with 40 vertical levels. 90 For solar forcing, the SSI is interpolated to 14 wavelength bands with the lowest bound at 120 nm. The stratospheric aerosol forcing is prescribed with monthly zonal mean aerosol optical properties and without interactive chemistry. It is noted that the quasi-biennial oscillation (QBO) is not simulated in this version of MPI-ESM due to the relatively low vertical resolution (Krismer et al., 2013). This may impact our results as the QBO is known to affect the Arctic oscillation (Holten and Tan 1980; the 1991 Pinatubo eruption tends to weaken the polar vortex, while the westerly phase of QBO in 1992-1993 can enhance the aerosol effect on the AO. Four sets of ensemble experiments, each consisting of 20 members, are conducted in this study (Table 1). All experiments are carried out from the year 1791 to year 1830 for 40 years. The 20 ensemble members are created by perturbing the atmosphere with slight changes (0.99990 to 1.00009) in the stratospheric horizontal diffusion during 1771 from the past2k run (van Dijk 100 et al., 2021;Fang et al., 2021) and simulations are run from 1771-1790 to obtain distinct ocean states (Fig. 1a). Besides the volcanic aerosol and solar activity (including the ozone concentration in the upper atmosphere), all other boundary conditions of the experiments are the same as in the past2k simulation.
The first two experiments, Basic and SolarStrong, are simulated with the SATIRE-14C (Usoskin et al., 2016) and the PMOD-14C (Shapiro et al., 2011;Egorova et al., 2018) solar reconstructions formulated in the PMIP4 past1000 protocol (Jungclaus 105 et al., 2017). The reason to use two solar reconstructions is because no prior research, to our knowledge, has quantified the possible range of solar impacts in the early 19 th century with two different reconstructions along with volcano eruptions. The PMOD reconstruction has a larger variability with lower solar radiation in the early 19 th century than the SATIRE reconstruction ( Fig. 1b) due to their distinct assumptions of the proxy, the solar modulation potential and the photospheric magnetic field changes, respectively. This entails why the PMIP4 protocol provides two reconstructions since the PMOD 110 reconstruction can be considered as an upper limit of the possible secular variability as it shows larger long-term changes in solar irradiance than other reconstructions (Schmidt et al., 2012;Jungclaus et al., 2017). Specifically, we use the 14 C version of the reconstructions calculated from the cosmogenic isotope concentrations of 14 C. The prescribed ozone concentration is calculated based on solar irradiance (not including the volcanic impacts) following the PMIP past1000 protocol (Jungclaus et al., 2017;Matthes et al., 2017), as the solar irradiance can alter the stratospheric and mesospheric ozone concentration (Haigh, 115 1994). For instance, the zonal average ozone concentration in the stratosphere calculated from the PMOD is roughly 2% different compared to the SATIRE ozone in 1815. The solar effects on ozone for the past1000 experiment are scaled using the averaged solar UV irradiance (from 200 to 320 nm; Fig. 1d) because the 10.7 cm radio flux (F10.7) used for the CMIP6 historical simulation is not available for the past1000 time period.
The other two experiments are Volcano (volcanic aerosol + SATIRE) and Volcano&SolarStrong (volcanic aerosol + PMOD) 120 experiments, which include the same volcanic aerosols but different solar reconstructions to disentangle the interaction between the solar and volcanic cooling in the early 19 th century. Following the PMIP4 past1000 protocol, the time-varying aerosol optical depth (AOD) for volcanic forcing is calculated with the EVA (Easy Volcanic Aerosol) module (Toohey et al., 2016) using the eVolv2k dataset  as input. Two strong volcanic eruptions occur during the experiment period: the 1809 and the 1815 Tambora eruptions (Fig. 1c). With the combinations of with/without volcanic aerosol and 125 strong/weak solar irradiance we aim to better understand the possible contributions of different forcings to the early 19th cooling.
The anomalies in this study are calculated based on the ensemble mean of the seasonal cycle of the Basic experiments (anomalies = each ensemble member minus the ensemble mean climatology of Basic). This is because the Basic experiment has the smallest forcing of surface cooling (SATIRE-14C and no volcanic aerosol). 130 Several climate indices are used in this study. The Niño3.4 index is defined as the regional mean sea surface temperature (SST) anomalies over 5° S to 5° N and 170° W to 120° W. The relative Niño3.4 index, which represents the ENSO responses without impacts from global volcanic cooling, follows Khodri et al. (2017) by removing the tropical mean (20° S to 20° N) SST anomalies from the Niño3.4 index. The North Atlantic Oscillation (NAO) index (Wanner et al., 2001) is calculated by the difference of sea level pressure anomalies between the Azores (36° N to 40° N and 28° W to 20° W) and the Icelandic low 135 (63° N to 70° N and 25° W to 16° W). The Arctic Oscillation (AO; Thompson and Wallace 1998)  To investigate what process contributes the most to AA cooling, we use the rapid adjustment (Marshall et al. 2020) that disentangles the radiative contributions of each feedback in the Arctic and Tropics. The reason we used the rapid adjustment is that our forcing agents (solar and volcano) change over time and we consider a shorter period compared to general methods of radiative kernels (decades). The rapid adjustment is computed with two steps: 1) obtains the radiative kernel (Block and Mauritsen 2013) from the piControl run simulation of the same model (MPI-ESM1.2-LR), which is how much radiation will 150 change when the climate deviates (e.g., how much Planck feedback will change when surface air temperature change); 2) multiplies the kernel with the difference between the experiments and piControl run of corresponding variables for the feedback to estimate the radiative changes of each process (e.g., multiplies the kernel for Planck feedback with the surface air temperature difference between the experiments and piCotronl). As a result, the amount of heat change in the system can be obtained (e.g., surface cooling will cause the Planck feedback to release less heat to the system, meaning more heat in the 155 system).

The Surface Impacts from Solar and Volcano Forcing
Figures 2a and 2e show the global mean surface air temperature (SAT) and SST of the Basic and SolarStrong experiments. As a baseline for the other experiments, the Basic experiment (blue) has small temperature changes over this period, where the temperature bounces back to normal between 1795-1800 from the Icelandic Laki eruption in 1783, which is inherited from the 160 initial conditions (Fig. 1a). Also, the weaker (stronger) solar radiation before (after) 1815 causes a slightly lower (higher) temperature, meaning the SATIRE solar forcing during the Dalton minimum results in less than a monthly average of 0.03 K global SST cooling by comparing before and after 1815 (< 0.05 K for SAT) in the MPI-ESM1.2-LR. The spatial averages of different regions (Figs. 2b-d) also show similar temperature variations, but the tropical region (30° S to 30° N) exhibits a weaker temperature change compared to the southern extra-tropics (90° S to 30° S) and the northern extra-tropics (30° N to 165 90° N).
The SolarStrong experiment (orange) includes lower incoming solar radiation than the Basic experiment after 1795. Their TSI difference increases after 1795, peaks around 1815 and reduces afterward (Fig. 1b). Compared to Basic, the global mean SSTs weakening of the wind-driven circulation, which may be due to the weaker westerly winds (Kwon and Joyce, 2013) and the 190 reduced freshwater flux from Arctic sea ice changes (Zanchettin et al., 2012). The weaker westerlies are associated with a negative phase of the AO (Fig. 3h) in boreal winter, but not in summer (Fig. 3d), even though the SST cooling patterns show not much difference. The increase of the Arctic sea-ice extent is found in all seasons (Figs. 3c and g) with a smaller increase in the summer than in winter. We interpret this stronger seasonality of Arctic sea-ice extent under solar forcing to be related to the smaller SST seasonality, where less heat is stored in the summer ocean, leading to the stronger sea-ice formation in 195 winter (Carton et al., 2015). The reduction of the westerlies may also be caused by the weakening of the stratospheric polar vortex due to the reduction in the meridional temperature gradient in the lower stratosphere, which we will discuss in Section 4.2. In contrast, the Southern Ocean is characterized by a mix of warming and cooling signatures where the Antarctic sea-ice extent also decreases and increases, respectively. This entails why not much surface cooling is found in the region-averaged southern extra-tropics. 200 The Volcano experiment (green lines; Figs. 4a and 4e) shows clear surface temperature decreases immediately after the 1809 and 1815 eruptions with a maximum of ensemble mean SST cooling around -0.53 K and -0.94 K (-0.82 K and -1.36 K for SAT), respectively. As indicated in Figure 1c with the AOD changes, the effect of the prescribed volcanic radiative forcing is mostly removed after 3-4 years; however, the temperature in all regions is not only significantly different right after the eruptions compared to Basic after 1809, but the negative anomalies continue even when the direct volcanic effect is strongly 205 Directly responding to the aerosol forcing, the tropical cooling has a sharp increase followed by a decrease in the first few years after the eruptions, and the SST cooling maintains at ~0.2 K afterwards. This is because the cooling is stored in the upper 210 ocean and slowly diffuses and is transported to the entire ocean.
For the northern extra-tropics (Figs. 4c and g), SAT and SST show a distinct response. After the direct responses to volcanic eruptions, the SST cooling slowly reduces by ~0.1 K/year, while the SAT returns to around -0.5 K rapidly with the same pace as other regions along with the diminishing volcanic forcing (even clearer if considering land-only). We interpret this slower retrieval of SST to be related to interactions with the sea-ice extent as mentioned in solar-induced cooling (Carton et al. 2015), 215 where the SST cooling is stored in the mixed layer during summer to impede the summer sea ice loss and enhance the winter sea ice formation. In addition, a sea ice-ocean-atmosphere feedback, in which the sea ice (particularly in the Barents Sea) can be maintained by the change of ocean inflow and associated heat transport can contribute to the prolonged cooling (Lehner et al, 2013). The reduced SST seasonality with the colder summer and the steady retrieval of the cooling is found in the southern hemisphere only the first few years after eruptions, as the Antarctic sea ice shows both increases and decreases depending on 220 the region.
The cooling pattern of the Volcano experiment is similar to the SolarStrong experiment in general (Fig. 5), where the AA results in larger SAT cooling at high latitude in winter. The sea ice-related regions, such as the Gulf of Alaska and the Labrador Sea, exhibit the most apparent SST cooling. Differences can be found in the sea-ice extent and sea level pressure. The Volcano experiment shows more sea-ice extending to lower latitudes in both summer and winter due to the stronger cooling from 225 volcanic forcing. A positive AO (i.e., low pressure in the Arctic and high pressure in the midlatitude) is found in boreal winter in the Volcano experiment, while SolarStrong has a negative AO with high pressure in the Arctic (Fig.3). This different AO response is related to the distinct stratospheric responses from volcanic aerosol forcing and reduced solar irradiance, which will be further discussed in Section 4.2. That is, although differences are found between the Volcano and SolarStrong experiment, such as more southward extension of the sea-ice extent, opposite surface pressure patterns, and the cooling 230 magnitudes, the response patterns of surface temperature are similar. This similarity indicates that the top-down mechanism via the AO has limited impacts and the surface is more dominated by the bottom-up direct radiative cooling.

The Interplay at the Surface
The Volcano&SolarStrong experiment is conducted to analyze the combined response of the stronger solar forcing and the 235 volcanic aerosols. We find that the global average surface temperature response is, in general, additive when separately or after the eruptions. The SST changes match even 7 years after the 1815 Tambora eruption with the Volcano&SolarStrong 240 experiment. To further study whether the additivity also exists spatially on a regional scale, Figure 7 shows the zonal mean Hovmöller plot of the winter surface temperature difference of solar signals (Volcano&SolarStrong minus Volcano and SolarStrong minus Basic). The SAT responses are similar in the polar region (Figs. 7c and 7f). The AA dominates the cooling response when the reduced solar radiation is imposed on both cases with/without volcanic forcing, while the SST has a distinct response. The reduced solar radiation in the case without volcanic forcing causes the largest SST cooling steadily remaining 245 at around 50° N (Fig. 7i) and over time echos the large cooling at the Gulf of Alaska and the Labrador Sea in the SolarStrong experiment. On the other hand, when imposing the solar forcing in the case with volcanic forcing, a large cooling signature for the northern hemisphere is found mainly south of 50° N (Fig. 7l), with additional cooling related to the two eruptions.
Around 1815, additional cooling exists in the western tropical Pacific and Atlantic (Fig. 8d), and then propagates to the higher latitudes through the ocean circulation of the western boundary currents (Fig. 8d-f). Large cooling can also be found in the 250 Arctic (Norwegian Sea), related to the expansion of sea ice with reduced solar irradiance. These differences in spatial SST responses indicate that the regional response is different when solar forcing interacts with the volcanic forcing even though the large-scale average responses are additive.

The Interplay in the Atmosphere
Here, we further investigate the atmospheric responses to the volcanic and solar forcings by inspecting the zonal means of air 255 temperature and zonal wind anomalies (Fig. 9) for the volcano (1809-1820) and the post-volcanio (1821-1826) periods. In the SolarStrong experiment (Fig. 9a) over the volcano period, the reduced solar irradiance leads to an insignificant weaker polar vortex (shading) in the winter hemisphere due to the weaker meridional temperature gradient (contour). The easterly anomalies in the subpolar region can be found throughout the troposphere and stratosphere and reduce towards the surface to almost zero.
That is, the reduced solar radiation can warm the high-latitude atmosphere through the top-down mechanism (though not 260 significantly), but a limited response is found at the surface with no tendency for a negative AO index (Fig. 10d) even though a weak AO pattern can be observed in the sea level pressure (Fig. 3h). For the Volcano experiment, the direct responses from volcanic aerosols can be found in 1809-1820 (Fig. 9b). The warming in the tropical lower stratosphere from aerosol absorption enhances the meridional temperature gradient, leads to westerly anomalies around 25° N to 50° N, strengthens the polar vortex, and cools the polar stratosphere in the winter hemisphere. From the Volcano&SolarStrong experiment (Fig. 9c), we can see 265 that the impacts from volcanic aerosol forcing overwhelms the cooling induced by the reduced solar irradiance plus ozone in this period due to the relatively larger magnitude of the volcanic forcing.
To further investigate whether the responses are additive, Figure 9d shows the difference between the Volcano&SolarStrong and the addition of the SolarStrong and Volcano experiments. The additional westerly anomalies in the middle to upper stratosphere illustrate an even stronger polar vortex in the Volcano&SolarStrong experiment accompanied with a cooler polar 270 stratosphere. This entails that the reduced solar radiation may contribute to a stronger polar vortex in the middle stratosphere (although we can identify only a few significant grid points) or be overwhelmed by the volcanic eruptions when strong volcanic eruptions occur. Further detailed studies will need much larger ensemble members due to the strong internal variability in the Arctic climates (Liang et al. 2020). Volcano experiments (Figs. 9f). This may explain why no apparent response is found in the polar vortex and polar air temperature in the Volcano&SolarStrong experiment since the tropical stratospheric temperature changes from solar and volcanic forcing balance each other. In fact, if we inspect their difference (Fig. 9h), similar strengthening of the polar vortex 280 and colder air temperature in the middle stratosphere is observed (though not significant) as in the previous period (Fig. 9d).
This additional strengthening of the polar vortex when combining solar and volcanic forcing needs to be further examined. In addition, significant results are found in the polar troposphere between the difference in the later period (Fig. 9h), which is related to a corresponding response in the same region in the Volcano experiment (Fig. 9f). This indicates that the volcanic response may be impacted by easterly responses from the solar forcing, even though we cannot assign statistical significance 285 to that. To be noticed, the MPI-ESM1.2-LR used in this study has a prescribed ozone (not interacting with volcanic aerosol changes) and no QBO is simulated, which may impact our results, especially in the stratosphere . In our simulations, there is on average 2% difference in the stratospheric ozone between the calculations from SATIRE and PMOD reconstructions, which is within the observed variability (Fioletov et al., 2002) and should not have statistically detectable temperature changes. 290

The Interplay in the Ocean and in Climate Indices
The subsurface ocean responses are additive in global mean/large-scale (not shown) as they are related to the surface ocean changes, which are also additive when separately and/or together including solar and volcanic forcing. Despite the additivity in most regions, the El Niño-Southern Oscillation (ENSO) shows a distinct response when combining the solar-and volcanoinduced responses. The SolarStrong experiment has no apparent tendency of the Niño3.4 index, while the Volcano and 295 Volcano&SolarStrong experiments have negative values after volcanic eruptions (Fig. 10a). These negative values are, in fact, not a La Niña response but a global cooling signature from the eruptions. The actual ENSO activities can be estimated by the relative Niño3.4 index (Fig. 10b). By removing the tropical mean SST, an El Niño response after an eruption is often found in model simulations (Khodri et al., 2017). In the Volcano experiment, the 1809 eruption is followed by strong El Niño signatures for two consecutive years, while no apparent ENSO activity is found after the 1815 Tambora. This is because there is an El 300 Niño signature in 1814/15 that tends to trigger a La Niña in the 1815 winter and suppress the El Niño tendency after Tambora.
On the other hand, the Volcano&SolarStrong experiment has only weak and nonsignificant El Niño responses for two years (the two small spikes) after both the 1809 and 1815 eruptions, indicating that the lower solar irradiance may reduce the tendency toward El Nino after the 1809 eruption.
We further investigate the solar-and volcano-induced responses for other climate indices. The higher latitudes are 305 characterized by the NAO, AO, and SAM. Positive NAO (Fig. 10c) and AO (Fig. 10d) phases are simulated right after the volcanic eruption, signals which are often also observed in the first winter after eruptions (Christiansen, 2008). Limited significant signal, however, is simulated for the 1810 winter and the 1816 winter, and no significance is found afterward, showing that the large internal variability dominates in the northern extratropical region. These limited signatures explain the weak response of sea level pressure composited over a longer period (Figs 3h and 5h), and indicate the limited impact from 310 the top-down mechanism in the MPI-ESM-LR1.2. For the southern hemisphere, small positives (non-significant) of austral summer SAM are found right after the eruptions (Fig. 10e), which is consistent with the high pressure sitting in the Antarctic and no signature is found afterward.
Multi-decadal-scale responses can be observed for the PDO, AMV, and AMOC. The PDO does not respond significantly to the solar forcing, while volcanic forcing leads the PDO to a negative phase right after the eruptions (Fig. 10f). However, the 315 Volcano&SolarStrong experiment leads to a stronger and longer lasting negative phase after volcanic eruptions compared to the Volcano experiment, especially for the Tambora eruption. This indicates that the solar forcing can enhance the PDO response from volcanic forcing, echoing the additional SST cooling transport to the northern extra-tropics found in the Volcano&SolarStrong experiment (section 4.1; Fig. 7). The AMV has clear negative signatures from all forcings as expected ( Fig. 10g), but whether this cooling response is truly an AMV signal is still under debate since the negative AMV may include 320 the global volcanic cooling signature (Fang et al. 2021). No apparent signature is found in the AMOC (Fig. 10h) except a weak reduction tendency is found in the SolarStrong experiment.
In this section, we investigate the AA response to solar and volcanic forcing. Figure 11a shows the strength of AA cooling over 1809-1826 as approximated by the ratio between the polar surface temperature and the global surface temperature. The 325 SolarStrong experiment has a stronger ensemble mean AA cooling (3.2) compared to the Volcano (1.9) and Volcano&SolarStrong (2.1) experiments over 1809-1826. This difference is, however, not significant since a large spread is found in SolarStrong. This is because the global cooling is weak and unstable in individual ensemble members, which is also true in the Basic experiment. If we only consider the post-volcano period (1821-1826), the AA in the Volcano and Volcano&SolarStrong experiments increases and so does the intra-ensemble spread and shows similar values as in the 330 SolarStrong experiment. That is, the strength of AA caused by solar and volcano is comparable (despite differences in absolute global mean cooling) after the direct volcanic forcing diminishes, while only weak AA is found when strong tropical cooling exists in the first 3-5 years corresponding to the direct volcanic forcing.
To understand whether the AAs from solar and volcanic forcings are related to the same processes, we use the rapid adjustment (Marshall et al. 2020) of each process over the period. This method obtains the radiative changes (W/m 2 ) in the system caused 335 by each process (or feedback) by multiplying the radiative kernel with the difference to the reference model (see Method Section for details). For instance, the albedo feedback is positive feedback, meaning surface cooling results in more albedo, which increases the outgoing shortwave radiation at top of the atmosphere and thus reduces heat in the system (see SW_albedo). That is, with surface cooling, the rapid adjustment is negative meaning the heat in the system will further reduce.
On the other hand, the temperature feedback is negative feedback that increases the heat in the system (positive values; see 340 LW_ta and LW_temp2) by releasing less longwave radiation at top of the atmosphere. Figures 11c-f show the differences of rapid adjustments between the solar and/or volcano forcing experiment and the Basic experiment for the tropics and the Arctic averaged over two periods. The total increase of radiative difference in the Arctic over 1809-1826 is smaller than the respective change in the tropics for all experiments, indicating a weaker recovery from the cooling in the Arctic. For SolarStrong, the albedo feedback is the most crucial process that compensates for the temperature feedback in the Arctic (Fig. 11c), while the 345 compensation with longwave water vapor change is relatively small in the tropics (Fig. 11e). Sea-ice increase (and partly snow) contributes mainly to the AA in SolarStrong. For the Volcano experiment, besides the temperature feedback, the shortwave cloud radiative changes also contribute to warm the Arctic, which is suggested to be associated with the reduction of highlevel clouds (Marshall et al. 2020). Although half of the changes are compensated by the longwave cloud feedback, the total cloud feedback is an additional strong negative feedback that helps the system return to its climatology. If we only consider 350 the post-volcano period (1821-1826), we can see that the cloud feedback contributes little (Figs. 11d and f). Instead, the radiative changes from the albedo are maintained at ~70% of the period right after volcanic eruptions (Fig. 11d), which is the main feedback that keeps the Arctic colder than the tropics.
We conduct a set of early 19th century simulations with 20 ensemble members of MPI-ESM1.2 model from combinations of 355 forcing agents of one volcanic forcing and two solar reconstructions. The solar forcing from the SATIRE solar reconstruction (Basic experiment) contributes less than a monthly average of 0.05 K SAT cooling before and after 1815, while the forcing with the PMOD solar reconstruction (SolarStrong experiment) contributes an additional 0.1 K SAT cooling (1809-1826). The 1809 unknown and 1815 Tambora eruptions contribute 0.82 K and 1.36 K SAT cooling at their peak. The cooling then rapidly returns to ~0.35K around the year 1820 and the temperature slowly approaches the climatological value. The cooling signatures 360 are strongest in the northern extra-tropics due to Arctic Amplification, except during the first few years after eruptions when the prescribed volcanic forcing directly cools the tropics. In addition, the SST cooling in the northern extra-tropics is characterized by a larger slow recovery after the direct volcano-induced cooling compared to the SAT and other regions. This slow recovery from the SST cooling is interpreted as a connection with the slow reduction of the Arctic sea-ice extent and is accompanied by a smaller SST seasonality. 365 The additivity of the climate responses to the volcanic and solar forcing is studied by a set of simulations with combined and separated volcanic and solar forcing agents. We find that the global mean/large-scale surface climate responses are additive, but the responses on the regional scale can be non-additive. In the middle stratosphere, the reduced solar radiation and volcanic aerosol separately cause opposite sign changes in stratospheric temperatures and thus the NH polar vortex, but the response in combined simulations shows a strengthening of the polar vortex of a similar or somewhat stronger magnitude to that in a 370 volcanic simulation alone, although the significance of this finding is limited due to large internal variability. of a similar or somewhat stronger magnitude to that in a volcanic simulation alone. This suggests that the solar forcing may have little impact on, or even enhance, the volcano-induced strengthening of the polar vortex. Besides the strong internal variability of the polar vortex, it is noticed that ozone is not included interactively and no QBO is simulated in this version of MPI-ESM. As both ozone (Shindell et al., 1999;Oehrlein et al., 2020) and QBO (Holten and Tan 1980;Garfinkel et al. 2012;Labe et al. 2019) 375 can impact the polar vortex, these processes may lead to more complex interactions between solar and volcanic forcing, which is not considered in our study.
Model simulations generally show an El Niño signature right after tropical volcanic eruptions (Khodri et al. 2017); however, in our simulations the El Niño tendency is found to be weaker when including the solar forcing (though not significantly). This may be related to the La Niña tendency found during solar minimum (Lin et al. 2021) but no such tendency is found in our 380 solar forcing-only simulations. That is, the solar irradiance may contribute to the tendency of ENSO events after eruptions and give a hint on why no consistent ENSO responses from volcanoes have been found over the past centuries (Dee et al., 2020).
The non-additive responses, including the Arctic atmosphere and tropical surface ocean, cannot be distinguished statistically from the strong internal variability in those regions. This indicates a much larger ensemble size may need for studying the regional additivities. For example, the Arctic climate is suggested to be studied with more than 60 ensemble members (Liang 385 et al., 2020), and different ensemble sizes (can be larger than 50 members) are needed for each ENSO characteristic and model (Lee et al., 2021).
Furthermore, when imposing reduced solar radiation in the volcano experiment, an additional tropical cooling is simulated right after the eruptions and then further propagates to the northern extra-tropics through ocean circulation and reduces the near-surface air temperature along the propagation. This indicates that solar forcing may have an additional impact on regional 390 temperature change caused by volcanic eruptions, which further enhances the difficulty when combining or interpreting the proxy reconstruction originating from different regions. A large spread is found when comparing the model simulations to the proxy reconstructions and an experimental period of reanalysis (Fig. 12). Depending on the product, large differences are found across reconstructions and reanalysis and across their internal uncertainties. Consistent with Wagner and Zorita (2005), the early 19th cooling is mainly a result of volcanic eruptions in our simulations. The long-lasting cooling found in 395 reconstructions in the northern extra-tropics can be explained largely also by the post-volcano responses or partly by the solar forcing (Anet et al. 2014) when using the PMOD reconstruction. The large spread of the reconstructions and our ensemble simulations, however, cannot confirm the necessity to include solar forcing even when solar forcing (with PMOD reconstruction) can contribute to cooling in the post-volcano period.
Lastly, the Arctic Amplification response to volcano-and solar-forced global cooling is investigated in this study. A colder 400 Arctic compared to the globe is rarely discussed since the warming perspective is generally the focus, such as Arctic Amplification responses to global warming. We find that the albedo feedback is the main positive feedback (cooling causing further cooling) that slows the Arctic temperature from returning to climatology after volcanic eruptions. Since the sea-ice extent is not directly depending on the air temperature and is related to the interaction with SST (Carton et al., 2015) and the surface ocean circulation (Lehner et al. (2013), the sea-ice albedo feedback remains at roughly 70% in the post-volcano period, 405 indicating the importance of Arctic sea ice for the post-volcanic cooling.
This study shows that the comparably small solar forcing cannot be ignored for understanding the regional climate of the early 19th century, even though it has small global impacts compared to the two large volcanoes. This indicates that other small disturbances may also contribute to regional climate anomalies after strong tropical volcanic eruptions. For instance, small-tomoderate eruptions, which are not included in the EVA volcano forcing from the PMIP4 past1000 protocol, may also play a 410 role in regional changes.

Conclusion
This study investigates how much each of the volcanic and solar forcing can separately contribute to the well-known early 19th century cooling and examines the combined climate responses from the two forcing agents with 20-member ensemble simulations from the MPI-ESM1.2 model. To our knowledge, this is the first study comparing the two solar reconstructions 415 from the PMIP4 past1000 protocol as well as examining the interactions of solar and volcanic signals in the early 19th century with a large number (20) of ensemble members. The 1809 (unknown location) and the 1815 Tambora eruptions are found to be the main contributor to the early 19th century cooling. Depending on the reconstructions, the solar forcing contributes to slightly enhancing the cooling before 1815 (with SATIRE) or the long-lasting cooling after the 1815 Tambura eruption (with PMOD). We find that the solar-and volcano-induced cooling are additive in global mean/large-scale, even for the northern 420 extra-tropics, which have a longer-lasting cooling. Besides the additivity of the responses, regional impacts (such as polar vortex and surface temperature propagations) can be nonadditive when together or separately imposing the solar and volcanic forcing. However, these non-additive responses may not be separated with the internal variability with statistical significance.
Furthermore, an Arctic Amplification associated with global cooling, which is rarely discussed in literatures, is found in both solar and volcanic impacts, revealing the importance of the albedo feedback (or sea-ice change) in controlling the post-volcano 425 surface cooling in the early 19th century.

Code Availability
The Python code for generating the figures can be accessed at Zenodo with DOI: 10.5281/zenodo.6567188.         the Tropics (30° S to 30° N). The SW and LW mean shortwave and longwave radiation changes, respectively; and ta is air temperature difference; temp2 is surface air temperature; q is water vapour; albedo is albedo; c is cloud; total is the summation of the 7 radiation changes.