Figure  shows global temperature averages for all the ensemble members listed in Table . As reported by in the case of the pre-PMIP3 LM experiments, there is a quasi-linear response of temperatures to changes in external forcing, with the major warmings occurring in periods with high solar activity and rise in GHGs and with coolings occurring in response to lower solar forcing and increased volcanic activity. For the 20th century, all the analyzed simulations consistently show a warming, but trends strongly differ among simulations due to the different climate sensitivities of each model and the considered forcings see discussion in. Simulations from IPSL, CCSM, and GISS show a very strong trend, while simulations from CESM show a significant but smaller 20th century temperature increase. The results for the GISS and CESM subensembles are shown in Fig. b by plotting the minimum–maximum spread of all subensemble members, while Fig. c shows, for the sake of clarity, the behavior of each subensemble member. These subensembles demonstrate that internal variability generates differences across simulations that are smaller than structural differences in model formulation across models. Figure c shows the range (dashed lines) of the residuals resulting from subtracting the ensemble mean from each ensemble member simulation. Since the average of all ensemble members cancels out uncorrelated contributions of internal variability, the resulting ensemble mean constitutes a smoothed estimation of the forced response, and the residuals of subtracting the ensemble mean from each ensemble member are an estimation of internal variability above 31-year timescales . Both the CESM and GISS ensembles in Fig. c show pre- and post-1850 low-frequency changes greater than the estimated changes of internal variability. Changes in the ensemble associated with external forcing are therefore in general more relevant than those of internal variability above 31-year timescales. A similar behavior is found when performing a PC analysis of the simulated temperatures, as shown in Fig. , with the first temperature EOF and PC estimates obtained from the simulations listed in Table . Agreement between the different simulations is very good, all of them showing the same long-term trends described for Fig. . Figure  also shows the correlation among the estimated PCs of different simulations. Note that most of the analyzed simulations show correlations higher than 0.5 and that for simulations of the same model the correlations reach values around 0.9 both when analyzing the whole period and when considering only the preindustrial era. This indicates that even if the EOF has been obtained with a combined analysis, it is also representative of the individual simulations. Additionally, the use of large sets of simulations for some of the models, and in particular the use of the 13 CESM-LME simulations, does not significantly bias the results because the correlation ranges for models with individual simulations are as large as for the others. The variance of temperature that the first PC accounts for in the ensemble is greater than 50 % across all of the models, significantly greater than the variance explained by the remaining modes (Fig. ). To evaluate whether this first mode is related to the forcing, the correlations of the PC of each simulation with the TEF (Fig. a) have been included in Table . All the correlations are significant and range between 0.61 and 0.79. The first PC of temperature is therefore mainly attributed to external forcing, and for this reason dynamics and hydroclimate variables are compared in the following sections against this mode to explore their forced responses.

Regarding the spatial pattern of the EOF, values are higher over continental regions and smaller over oceans. For high latitudes, higher values are obtained over ice-covered areas, which is consistent with the polar amplification response in climate change scenarios . For all regions, the first EOF shows positive loadings, meaning that situations of higher forcing correspond to higher temperatures for the whole planet and vice versa. This pattern has been discussed in and , and similarities can also be observed of the differences between the MCA and LIA (Fig. c). The transition from MCA to LIA in most regions leads to a decrease in simulated temperatures, which is consistent with the negative external forcing anomalies applied in the simulations. The MCA–LIA pattern does not emphasize the tropics as much as the EOF pattern, indicating that the low-frequency variability changes in that area are minor and that the higher tropical loadings in Fig. a stem from covariability at higher frequencies. Also note that area weighting has been applied to the EOF calculations, increasing the contribution of the tropical areas in these analyses.

At shorter timescales, the influence of external forcing is also evident. Figure d shows the average, maximum, and minimum temperatures for the composite with the 5 years before and 10 years after the 12 main volcanic eruptions of the LM. Note that global temperature significantly decreases after these events and that their influence lasts several years until it totally disappears. Important differences exist among models in the response to volcanic eruptions. Some simulations, such as those from GISS, MPI, CESM, and CCSM, show a drastic cooling after volcanic events that is mostly recovered after four years. However, simulations from HadCM and CSIRO show a moderate cooling that lasts for a longer period.

To evaluate the possible influence of external forcing on global atmospheric dynamics, the same analyses performed for temperatures have been applied to SLP. Figure  shows results for the different timescales. The long-term behavior of the first PC of pressure is comparable to that of the first PC of temperature. For the case of pressure, the average PC (black line in Fig. b) tends to show higher values during the MCA, lower during the LIA, and a significant increase during the last century. The similarity of the first PC of SLP with that of temperature can be quantified through the correlation coefficient values (Table ), which are significant for 73 % of the simulations in the ensemble and above 0.5 for 23 % of them. The average PC correlates with a value of 0.59 (Table ) with the corresponding PC of temperature (black line in Fig. b). This suggests some response to external forcing in the SLP field. The first mode accounts for only 15 % of the variance in the pressure, showing an eigenvalue spectra flatter than the one of temperatures (Fig. ). This indicates that even if there is a response to external forcing, internal variability is more relevant than in the case of temperature. Additionally, the correlations among PCs of different simulations are in general not significant over the preindustrial period (Fig. b). When the whole period is considered, more significant correlations are obtained.

The EOF indicates that the first mode is mainly extratropical (Fig. a). In the SH, there is an increase in pressure (positive loadings) around 40∘ S and a decrease (negative loadings) around 80∘ S during the MCA (higher PC values) and conversely during the LIA. This spatial pattern, with positive loadings over the maxima of climatological SLP (black contours of Fig. a) and negative loadings over the minima (green contours of Fig. a), contributes to the positive phase of the mode to intensify gradients between subtropical and subpolar regions. This reinforces zonal circulation and contributes to more positive phases of the SAM , as shown in Fig. . Regarding the NH, the pattern of pressure associated with the first mode is not as zonal as in the SH mostly because of the interaction with the continents. Overall, higher positive (negative) loadings are distributed over subtropical (polar) regions contributing to an increase (decrease) in the zonal flow during the MCA and industrial period due to the slightly higher values of the PC, which are also consistent with NAM enhancement.

As in the leading EOF, the spatial pattern of the MCA–LIA differences (Fig. c) also emphasizes the latitudinal gradients. Even if the exact boundaries between areas with positive and negative MCA–LIA differences do not fully match the zonal features of the first EOF loadings, the ensemble average shows the largest differences over the subpolar and subtropical regions, which contribute to the enhancement of the zonal flow in the MCA and to the weakening of it during the LIA. This pattern is associated with an intensification (MCA) and weakening (LIA) of the SAM, NAM, and NAO, as shown in Fig. . The figure shows the percentage of years with positive NAO, NAM, and SAM indices for successive intervals of 50 years. Consistent with the spatial patterns and temporal evolutions shown in the PC analysis, a tendency toward more positive phases of the NAO, NAM, and SAM is observed during the MCA and industrial periods.

Due to the large range of internal variability, the short-term response to volcanic forcing is not so evident in the PC of SLP as it is in the case of temperature. However, a low-frequency signal is observed in the mean PC series (Fig. b) for which high frequencies are canceled out. If the largest volcanic events are considered, a clearer response emerges. Figure d shows the global average of SLP for the composites for the 5 years before and 10 years after the main volcanic eruptions of the LM. Note that the global average of SLP shows significant changes triggered by volcanic activity. The sign and magnitude of the global net changes strongly depend on the model, but there is good agreement among simulations of the same model. For instance, simulations from GISS show an increase in pressure after volcanic events, while simulations from CESM-LME consistently show a decrease. This difference in the global average of pressure is not related to an opposite response in different models but to the distribution of areas with positive and negative loadings in the mode of variability associated with the forcing. As shown in Fig. , simulations from CESM show a greater number of areas with negative anomalies during periods with volcanic events, while simulations from GISS tend to show more areas with positive anomalies. In spite of the differences in the global balance of regional positive and negative anomalies between GISS and CESM-LME simulations, both produce a global weakening in zonal circulation during volcanic eruptions.

Some studies have shown that elevated forcings during the 20th century may be linked to a displacement of the ITCZ and an expansion of Hadley cells . This can be described in terms of wind velocity, in which the ITCZ is defined by the location of the trade winds and the extension of Hadley cells is marked by the position of the westerlies . Thus, the previous analysis is also performed for the zonal wind (Fig. ). In this case, the first mode accounts for 10 % of the total variance, a smaller percentage than for the case of temperature and SLP. The average PC of zonal wind shows a correlation of 0.51 with the average PC of temperature and 0.96 with that of SLP, indicating a response to the external forcing consistent with the one observed in temperature and SLP. However, the correlation with the PC of temperature for the individual simulations is in general small, indicating a greater impact of internal variability. As shown in Table , only five simulations show significant correlations, and only two of them are higher than 0.5. The agreement among different simulations can also be assessed through the correlations among their respective PCs, which are in general not significant when the preindustrial period is considered and are only significant for certain simulations when they are based on the whole period (Fig. b). The correlation between the corresponding PC time series of zonal wind and that of SLP for each simulation is always above 0.7.

Thus, the distribution of zonal wind in the first EOF is consistent with the distribution of pressures previously shown. In the positive phase of the mode, negative (positive) loadings tend to distribute over the easterlies (westerlies) and over their high-latitude side, thus increasing latitudinal gradients and contributing to a polar displacement of the wind system; trade winds are enhanced towards higher latitudes in the Atlantic and eastern Pacific. This is consistent with an expansion of the Hadley cell and the higher intertropical loadings and MCA–LIA anomalies in Fig. . The same behavior can be observed in the composites for the MCA and LIA, in which a poleward displacement of the westerlies is present during the simulated MCA relative to the LIA. However, the spatial pattern of the difference between the MCA and LIA differs for some regions relative to the one obtained from the EOF. For example, the differences between MCA and LIA indicate a reduction of zonal wind in the Mediterranean basin and an increase over Japan in the transition from MCA to LIA (Fig. c), while the loading in the EOF for these particular areas (Fig. a) is negative and positive, respectively.

In the short term, the behavior of zonal wind resembles that of SLP. In most simulations, the short-term noise associated with internal variability dominates over the peaks associated with volcanic eruptions, as can be observed in Fig. b. When composites of the main volcanic eruptions are defined (Fig. d), a clear influence of volcanic activity emerges. As for the case of pressures, the sign of the impact depends on the model mostly because of the different spatial distribution of areas with positive and negative anomalies. This can also be observed when comparing maps of zonal wind during volcanic events obtained with the CESM and GISS subensembles (Fig. ). In spite of the differences in some areas like the northern and tropical Atlantic and Pacific basins, both subensembles tend to weaken the global zonal circulation. However, the simulations from CESM (GISS) show more areas with positive (negative) zonal winds, which translate into a larger (smaller) increase in the global average. These zonal changes are also evident in the behavior of the meridional wind component. Figure  shows the differences between MCA and LIA in terms of meridional wind, as well as the zonal mean of these differences for zonal and meridional components for both global and regional Pacific (180–120∘ W) and Atlantic (50–0∘ W) basins (Fig. b). During the simulated MCA, changes in zonal and meridional winds took place with antiphase relationships that strengthened the zonal circulation at middle and high latitudes (Fig. b) with increases in the NAO, NAM, and SAM (Fig. ), while within the intertropical regions the trade winds and convergence were intensified (Figs. c and ). The opposite holds for the LIA.

For the case of precipitation, Figs.  and.  show the EOF and PC series for the leading two modes. Both modes show cross-basin influences in the tropical regions that connect the Indian, Pacific, and Atlantic oceans. Precipitation loadings are suggestive of ENSO, Pacific Decadal Oscillation (PDO), and monsoon influences , thus showing large-scale coordinated responses that can connect in-phase or out-of-phase intra- and intercontinental responses. Although the first PC shows large negative values during the volcanically active 13th century and some slight increase during the 20th century, it is the second PC that resembles the external forcing response. Furthermore, its EOF emphasizes the distribution of monsoon precipitation over the global monsoon domain within the intertropical region. In the extratropics, the EOF pattern (Fig. a) shows distributions of loadings that are consistent with changes in NH NAM and SH SAM circulation. The PC series (Fig. b) clearly shows the long-term trends associated with the external forcing with higher values during the MCA and 20th century and lower values during the LIA, as well as the short-term response to volcanic events, which is in agreement with the analysis of pressures (Fig. ) and winds (Fig. ).

There is good agreement between different models and different simulations with correlations being higher than 0.5 for simulations of different models and reaching 0.9 for different simulations of the same model (Fig. b; ALL). The correlation between the second mode of precipitation and the first mode of temperature (Table ) is significant for all the analyzed simulations, ranging from 0.5 to 1 and being higher in the simulations from GISS, IPSL, and MPI and lower in the simulations from CESM and MRI. These values are higher than those obtained for pressure and winds. However, this mode accounts only for 5.8 % of the precipitation variance, a lower value than the one obtained for variables of dynamics. As seen in Fig. , the modes associated with internal variability acquire a greater relevance in the case of precipitation. This suggests that the potential detection of this signal in reconstructions would be difficult and, if possible, more likely at very local scales. The MCA–LIA differences (Fig. c) show some similarities with the EOF loadings in extratropical regions, indicating greater precipitation at northern latitudes in the MCA (Fig. c) or with increased forcing at all timescales above 31 years (Fig. a, b). Within the tropical regions, agreement is regionally complex, with MCA–LIA differences emphasizing low-frequency changes and EOF loadings including covariability at all timescales. Changes in dynamics described in Sect. 3.2 are consistent with the changes in precipitation. As for the case of dynamics, some zonal symmetry is observed in extratropical areas, suggesting that changes in the Northern and Southern Annular modes affect the distribution of precipitation in these regions. The highest variability occurs in intertropical areas over the regions with the greatest amount of annual rainfall, thus overlapping well with changes in the global monsoon domain and ITCZ convergence. MCA–LIA differences are regional in scope and show anomalies of different signs over the North and South American monsoon systems NAMS, SAMS;, therefore without a clear response of NAMS and SAMS. This agrees with uncertainty in climate change projections over the NAMS, with CMIP5 models producing changes in precipitation that distribute around zero . The same occurs over the Australian and Maritime Continent monsoon systems AUSMC;. Positive values are found over the East Asian and South Asian summer monsoon areas EAS, SAS;, which is in agreement with scenario simulations . Even if changes are not significant over many of these regions due to the high variability of precipitation, they show a pattern of response to forcing in LM PMIP3 simulations consistent with that of scenario simulations; the consistency also extends to convergence zones. In the Atlantic and eastern Pacific north of the Equator e.g.,, positive MCA–LIA differences suggest increases in mean precipitation during the MCA. Likewise, in the South Pacific Convergence Zone extending from the western Pacific southeastwards e.g.,, positive differences also emerge, indicating increased rainfall during the MCA. Over South America, negative anomalies are found in the northwest of the climatological maxima (black contours in Fig. b) and positive anomalies in the southeast, depicting rainfall shifts in the South Atlantic Convergence Zone .

To better analyze these changes, MCA–LIA precipitation differences are calculated for the monsoon domains in Fig. a. Changes in precipitation in the transition from the MCA to LIA (Fig. b) are small in NAMS and SAMS for all the analyzed simulations. Notice that over the NAMS and SAMS regions (Fig. a) both positive and negative MCA–LIA anomalies (Fig. c) are distributed, thus hampering a clear net response. The same happens over the northern African (NAF) and southern African (SAF) regions with an increase in model spread and SAF being biased towards increased precipitation during the MCA. Therefore, even if net regional responses are small due to the compensation of anomalies of different signs, subregional differences may be large. The greatest impact of the MCA-to-LIA transition in the monsoon systems appears over Asia, where EAS and SAS are significantly altered. Rainfall anomalies in EAS and SAS monsoon areas are larger during the MCA relative to the LIA. This pattern is consistently found in most of the simulations. For the AUSMC, some simulations show very positive differences while others are very negative, indicating that models all show important variations over this area but the magnitude and spatial distribution of these changes are strongly model-dependent. The global zonal mean of precipitation for the MCA–LIA (Fig. c) does not show important changes but only slightly larger values of precipitation anomalies during the MCA than during the LIA for most latitudes. However, if ranges of longitude over the Pacific and Atlantic basins are considered, relevant changes in the convergence areas are observed. The zonal mean for the range of 150∘ E–150∘ W shows higher precipitation rates during the MCA relative to the LIA in equatorial areas of the central and western Pacific. In the eastern Pacific (150–80∘ W), precipitation is decreased (increased) north (south) of the Equator during the MCA-to-LIA transition, suggesting a southward displacement of the convergence zone. Ranges of 60–30 and 30–0∘ W show that the convergence zone is also altered in the Atlantic basin with less intense precipitation around the Equator during the MCA than during the LIA.

Figure d shows the global average of precipitation anomalies in the 5 years before and 10 years after the 12 main volcanic eruptions of the LM. A consistent decrease in global precipitation can be observed in all of the simulations after these volcanic events, being significant for most of them. The responses described for different timescales in Fig.  are consistent with changes in scenario simulations described in : increases in external forcing strengthen the hydrological cycle, enhancing zonal circulation in extratropical regions and increasing the global monsoon activity and equatorial convergence. This is found in the global average of precipitation after volcanic events and in the alteration of monsoons and latitudinal distribution obtained in the EOF, indicating a relevant response to external forcing in precipitation.

Figure  explores the robustness of regional forcing influences on precipitation across models and simulations. It shows areas of high positive correlation (above 0.6, p<0.05; panel a) and regions of high negative correlation (below -0.6, p<0.05; panel b) between precipitation and the mode of precipitation associated with the forcing of the ensemble of model simulations. Most model simulations correlate with external forcing over the same large-scale regions: the high-latitude bands related to zonal NAM and SAM circulation changes (e.g., negative correlations in the south of Europe and positive in the north) and the intertropical regions related to monsoon domains and convergence. Some models show larger areas of sensitivity to forcing, while others present fewer regions where precipitation relates to the long-term changes in temperature produced by external forcing. For example, simulations from GISS show negative correlations in the north of Australia and the south of Africa that do not appear in simulations from CESM-LME. Despite most of the models showing positive correlations in the extratropical and tropical areas of the Pacific basin and negative correlations in tropical areas of the Atlantic basin and in southeastern Asia, the areas of high correlation are spatially constrained to regional and even local scales and may not overlap in different models or even in simulations of the same model. These regional differences are likely the sign of the important influence of internal variability. Correlations in high-latitude bands are all positive, while negative correlations arise mostly over the areas of monsoon activity in Africa, Asia, and America (Fig. b), as in the case of negative MCA–LIA anomalies discussed above. This view has implications for the detection of a potential response to global temperature and forcing changes in drought-sensitive proxy data e.g., as the spatial dimension of the response can be quite limited particularly over land. Figure  shows examples of simulated precipitation at the grid-point level in cases that tend to show some correlation with forcing like Spain, China, and Peru (see grid-point locations highlighted with points in Fig. ) and also at locations that tend to show limited connections to forcing within the ensemble: California, Quebec, and Brazil. At all these points, the different ranges of internal variability tend to be larger than the forcing signal. In some areas, the 20th century trends show precipitation increases, like in the selected Brazil and Peru sites, while in others there is no response (e.g., the California site) or precipitation tends to decrease (e.g., the selected sites in Spain and China). Inter-simulation correlations tend to increase during the 20th century for sites showing trends and remain insignificant for most inter-ensemble pairs in preindustrial times.

Similar results to those obtained for precipitation are obtained when analyzing other variables representative of the water content of the soil. P–E, scPDSI, and soil moisture in particular have been analyzed in this work. Even if these variables provide similar information, important differences exist between them. Because soil moisture takes into account the water balance in previous time steps, together with precipitation, evaporation, and temperature, its variations are typically smoother than those observed in atmospheric variables. Something similar happens with scPDSI, which similarly takes into account soil moisture conditions from the previous months. Due to the higher number of factors considered in the computation of soil moisture and the fact that this variable is fully integrated within the models, it is a preferred variable for assessing drought variability in the models. However, different GCMs and their respective soil models may provide different treatments of soil moisture, making it difficult to combine data from different models in a single analysis. For this reason, the use of indices, such as scPDSI, may provide more consistent comparisons across different models e.g.,.

Figures  to  show the modes of P–E, scPDSI, and soil moisture that bear a relationship with global temperature and thus external forcing responses. The associated mode is the second for P–E (Fig. ) and soil moisture (Fig. ) and the first for scPDSI (Fig. ). P–E and scPDSI present PCs that correlate significantly with the temperature response mode (Fig. ; Table ); the correlation of the average PC with that of temperature being 0.62 and 0.94 for P–E and scPDSI, respectively. Individual correlations are significant for most simulations and particularly high for those of GISS, IPSL, and CCSM. The highest correlations are attained for scPDSI, being significant and above 0.5 for all simulations, while for soil moisture correlations are lower and in general not significant. The correlations with precipitation (Table ) are significant for both P–E and scPDSI, being generally higher for P–E. The correlation of the average PC of P–E and scPDSI with that of precipitation reaches values of 0.93 and 0.91, respectively. For P–E and scPDSI there is a clear time response pattern that shows an evolution very similar to that of precipitation (Fig. ) and temperature (Fig. ), P–E being more related to precipitation and scPDSI to temperature, as shown in the correlations of Table . In the case of P–E, the EOF spatial pattern is similar to that of precipitation (Fig. a), showing large negative values over parts of the central American and north of the South American monsoon regions, as well as over the East Asian continent and over parts of the African monsoon regions, where the EOF of precipitation also includes negative loadings. Positive loadings are shown over extratropical continents – in northern Europe, southeastern North America, Alaska, and eastern Siberia – and thus over areas influenced by changes in zonal circulation, which is consistent with the results of the precipitation analyses. As in the case of precipitation, volcanic forcing produces global negative anomalies in the model ensemble that tend to last over 2–3 years.

The scPDSI shows a very similar EOF pattern to that of P–E but with greater emphasis on the negative loadings that dominate over larger scales, extending over Australia, the broader African continent, South America, and large areas of North America and Eurasia (Fig. a). Thus, contrary to the P–E and precipitation results, which show more areas with positive anomalies during the 20th century, scPDSI shows negative trends for most regions. Negative scores in the PC during the volcanic episodes, associated with global spread negative loadings, are indicative of wetter soils, and indeed Fig. d shows increments in the global average of scPDSI in the model ensemble over timescales of about 5 years. Correlations between various ensemble members are high for P–E (Fig. b) if the 20th century trends are considered and lower and often not significant for preindustrial times, indicating the influence of internal variability as in the case of precipitation (Fig. b). The scPDSI correlations are, however, significant and high during preindustrial times as well, which is likely a sign of the influence of temperature evolution in this variable. MCA–LIA changes for P–E (Fig. c) are very similar to the continental component of the corresponding precipitation pattern (Fig. c). As in the case of the EOF loadings, Fig. c shows MCA–LIA changes consistent with Fig. c though with widespread negative scPDSI values.

The analysis of soil moisture (Fig. ) does not show a clear relationship to external forcing, with some of the simulations in the ensemble showing poor correlations with temperature (Table ). Some sensitivity to volcanic events and 20th century warming is apparent in the behavior of the PC time series. The composite of volcanic eruptions shows some increase in variability in the ensemble but not a clear response to increasing or decreasing soil moisture during volcanic events, indicating that internal variability may dominate over a potential response to the forcing. The associated EOF and MCA–LIA map (Fig. a, c) shows similarities to those of Figs. a, c and a, c with negative values over northern South America and parts of central and southern Africa. Over northern Africa, soil moisture shows positive loadings in the EOF and wetter values in the MCA–LIA differences. Interestingly, all EOF (MCA–LIA) maps in Figs. , , and  show negative (positive) values over eastern Asia and positive (negative) values over eastern North America. Despite an absence of a universal response of soil moisture to external forcing, some of the simulations have clearer responses. This is the case of the CESM and GISS models. When an analysis is carried out independently for these subensembles, the resulting PC series (Fig. ) show a clear correspondence with the temperature PC. Their corresponding EOFs show, however, considerable spatial differences.

These results suggest that a more focused analysis would be required to address the behavior of drought-related variables and, specifically, soil moisture while also considering more ad hoc techniques and homogeneous definitions of the soil moisture content. Soil moisture, scPDSI, and P–E measure different parts of the hydrological cycle. Additionally, soil moisture behavior during the 20th century may be affected by CO2 fertilization effects which are not present in other variables such as scPDSI. For this reason, the analyses based on these variables should be considered complementary and not necessarily comparable.