The Langhian (15.98 to 13.82 Ma, here referred to as mid-Miocene) is a critical age of the Miocene marked by the warm event known as the mid-Miocene Climatic Optimum (MMCO), when global mean surface temperatures (GMST) were around 7.6 °C warmer than today . During this time, tropical gateways connected the Pacific, Atlantic and Indian oceans, while polar gateways connecting the Arctic with the Atlantic were more restricted than today and the Arctic-Pacific connection was closed off. Flora has substantially changed throughout the Miocene, which also saw the emergence of modern biomes .

Warm paleoclimates are often investigated as potential analogs for near-future climates . While the analog nature of past climate are never perfect, and there are many differences in how warming manifests itself in past and future climate states  , the past climates offer a comparison of modelling outcomes with proxy data, which in turn can provide insights into climate processes that also act in the future. An example is constraining the important climate change metric of equilibrium climate sensitivity (ECS), the long-term global mean surface temperature change in response to a doubling of CO₂ from its pre-industrial (PI) level, as it was previously done with the Pliocene .

In this context, the mid-Miocene has recently emerged as a particularly exciting testbed for understanding warm climates. In contrast to the more recent interglacials or the older Eocene epoch, mid-Miocene atmospheric CO₂ concentrations are thought to be close to modern values and near-future estimates (400 to 800 ppm), and potentially peaking at much higher values during the MMCO . As a result, this interval has been the focus of several recent modelling and proxy-synthesis studies . A formal two-phase Miocene Model Intercomparison Project (MioMIP) is now under development, with Phase 1 using older boundary conditions and Phase 2 using updated ones. This contracts with MioMIP1, which was as an opportunistic comparison .

Climate models have underestimated proxy-reconstructed temperatures of the mid-Miocene at equivalent CO₂ concentrations , in particular at high latitudes e.g.. This is not a specific issue of the Miocene, as polar amplified warmth is also weak in other warm paleoclimates, such as the Pliocene  and the Eocene . This suggests a misrepresentation of high latitude climate feedbacks in models, substantial uncertainties in climate forcings, and/or persistent biases in high-latitude proxies; most likely, it reflects a combination of both model and proxy biases, as suggested for the Pliocene by . These points are critical to address, as they can allow to improve simulations of the Miocene, as well as model processes and the accuracy of future model predictions.

The aim of this study is to explore the mid-Miocene climate and investigate its sensitivity around various uncertain boundary conditions and model parametrizations. We perform simulations with a previously unpublished paleogeography of the mid-Miocene, and compare the simulation to one in the same model using the published paleogeography of . We also perform simple computations of Miocene ECS as to evaluate its potential as a new line of evidence for constraining modern-day ECS, in the light of the upcoming MioMIP. We further explore the sensitivity to the Antarctic ice-sheet existence, CO₂ concentrations, solar constant and soil properties. These forcings are actively discussed for MioMIP1 models  as well as for the development of MioMIP2, and could be large contributors to the Miocene climate, besides geography. Finally, while not a forcing, we also test the sensitivity of the mid-Miocene climate to a different atmospheric model, as it is common to have changes of model components between different phases of a model intercomparison project (MIP).

We use the Community Earth System Model version 1.2 (CESM1.2) to simulate mid-Miocene climate states. CESM1.2 is a coupled model using the ocean model POP2, with a 1° horizontal grid and 60 vertical levels and the CAM4 model for the atmosphere , applying a horizontal grid of 1.9×2.5° with 26 vertical layers, as well as a sea-ice model (CICE4), a river runoff model (RTM) and a land model which includes the carbon-nitrogen cycle and dynamical vegetation (CLM4). CESM1.2 has been used in numerous studies simulating different paleoclimates, such as the Last Glacial Maximum (LGM) , the Pliocene , the Eocene  as well as older paleoclimates .

We perform a “best-to-knowledge” control simulation of the mid-Miocene (Mio_Ctrl), which includes an Antarctic ice sheet reconstruction, an updated CO₂ estimate, mid-Miocene solar constant, and is based on a topography and bathymetry reconstruction of the mid-Miocene, provided by Getech Plc. This reconstruction is based on geological data which include tectonics, sediment deposit and morphology, and which is fed into a tectonic model to generate paleogeographies at 0.1°×0.1° resolution, similarly as . The original geography as well as the plate model cannot be shared; however, the 1°×1° resolution used by CESM1.2 is shown in Fig.  and compared to an identical simulation using the paleogeography of MioMIP2 Phase 1 .

At the regional scale, the paleogeographies differ in both bathymetry and orography. The Getech paleogeography used in Mio_Ctrl features a notably shallower Arctic basin and generally higher elevations in mountainous and plateau regions compared to the Burls paleogeography. Due to lapse-rate effects, some of the surface temperature differences between the simulations likely arise directly from these topographic differences, particularly in regions such as the Rocky Mountains, the Andes, the Tibetan Plateau, and the Antarctic ice sheet. The Getech paleogeography also includes substantial changes in the representation of the South American Pebas mega-wetlands, which are absent in the Burls paleogeography. In addition, Greenland is represented as a slightly elevated plateau in Getech, rather than hosting an ice sheet. The Getech paleogeography differs from other recent mid-Miocene paleogeographies e.g. primarily in the depths of the Fram Strait, the eastern and western seaways of the Tethys and the depth of the Panama seaway, which reflect uncertainties on the timing of closing, deepening or shoaling of these gateways during the Miocene in general. For instance,  shows a much shallower eastern Tethys compared to Getech, and a western Paratethys connection, whereas  displays a close eastern Tethys at the mid-Miocene. Both  and  show a relatively shallow Panama seaway, which differ notably from . Overall the Fram strait and earlier connections to the Arctic are much shallower in the geography of Getech than these other paleogeographies we are comparing to. To our knowledge, none of these geographies explicitly include the Pebas wetlands in South America. This may partly reflect differences in how wetlands are represented in climate models; in our case, the Pebas wetlands were treated as the shallowest level of the ocean model. Finally, paleogeographic reconstructions also differ in soil properties and vegetation type. In our simulations, vegetation type is simulated using a dynamic scheme.

The extent of Arctic and Antarctic ice sheets between Mio_Ctrl and Mio_BurlsGeo is compared to PI in Fig. . The ice sheets are considered as topographic objects and therefore the topography is flattened in Antarctica in the experiments where the ice sheets are not included. We then compare several Miocene simulations that differ in their solar constant (Mio_noIS_solPI), the presence of Antarctic ice sheet (Mio_noIS), and the atmospheric model used (Mio_noIS_CAM5), as to identify the role of each onto the mid-Miocene climate state. A summary of each experiment is given in Table .

Unless specified for our sensitivity tests, our simulations use an atmospheric CO₂ concentration of 854.1 ppm, which is equivalent to three times PI CO₂ concentration of the model. This is planned as the standard concentration for the protocol of the MioMIP-phase 2 project. It is within the range of some reconstructions provided for the mid-Miocene , and it has also been used in other mid-Miocene simulations, which in general provides a closer match to proxy temperatures than simulations with lower CO₂ concentrations . The solar constant is calculated from a model of solar luminosity increase with time , which leads to a value of 1359.5 W m⁻² for the mid-Miocene, in comparison to 1360.9 W m⁻² at PI. Aerosols are kept as PI, but the sources are moved to match with the mid-Miocene paleogeography (for instance if an ocean turned to land). Non-CO₂ greenhouse gases and orbital forcing are kept as PI. Our simulations are compared to a proxy record presented in . It is an agglomeration of sea-surface and surface temperatures based on multi-proxy reconstructions, where the sites are then rotated onto the mid-Miocene geography using the tectonic model of Getech Plc.

For estimating Miocene ECS in our simulation, we base our approach on a variation of , which would require an equilibrium simulation of the mid-Miocene with PI CO₂ concentration, from where a new simulation is initialized with an abrupt and sustained quadrupling of the CO₂ concentration, for around 150 years, so that “fast” climate feedbacks (i.e. clouds, surface albedo, water vapor, lapse-rate and Planck feedbacks) have mostly responded to the initial forcing. In the case of our simulations, a mid-Miocene state with PI CO₂ is numerically unstable, therefore we initialize from Mio_Ctrl by instead abruptly doubling its CO₂ concentration (Mio_Ctrl_DblCO2), as to avoid reaching excessively high CO₂ concentrations under a quadrupling, which could introduce non-linear effects on climate feedbacks. The ECS is then extrapolated from the global mean annual surface temperature after 150 years of simulation minus the initial temperature of the simulation using ordinary least squares linear regression. As to roughly estimate the influence of the Miocene background temperature on ECS, we also apply the same method but from a simulation at lower CO₂ concentration, Mio_2x (Mio_2x_DblCO2), and we compare it to a PI simulation with an abrupt doubling of CO₂ (PI_DblCO2).

The model is initialized from a warm ocean state, where the average deep-ocean temperature is around 6.6 °C. This value comes from an earlier, unpublished mid-Miocene simulation performed with CESM1.2, and is used to accelerate our deep-ocean equilibrium. The salinity is initialized globally at 35 PSU. In South America, in the so-called Lake Pebas, salinity becomes negative due to excessive precipitation and river runoff in these warm conditions. Therefore, we apply a marginal sea balancing scheme which redistributes the gain of freshwater onto the world oceans to avoid the spread of nonphysical, negative salinity into the oceans. This scheme has previously been used with CESM1.2 in warm paleoclimates e.g.. The sea-ice model is initialized ice-free and the dynamic vegetation is initialized as bare soil. All runs have been integrated for at least 3100 years and up to 5000 years when using CAM5 (experiment Mio_noIS_CAM5), starting from default initial conditions, and the last 100 years are averaged and used for the results.

Several aspects of the ocean model are modified to handle the large changes in land-sea mask and bathymetry at the mid-Miocene. Overflows and tidal mixing are turned off, as they are hard-coded on a pre-industrial ocean grid. We follow the recommendations for deep-time paleoclimates of the National Center for Atmospheric Research (NCAR) to increase ocean background vertical diffusivity, to compensate for the lack of tidal mixing (found at https://www2.cesm.ucar.edu/models/paleo/faq/, last access: 11 April 2025). The same approach was taken by  using CESM1.0.5 to simulate the Eocene. The background vertical diffusivity kw is horizontally homogenous but depends on model depth, and corresponds to kw=vdc1+vdc2tan-1((|z|-depth)linv), where vdc1 =0.524 cm² s⁻¹, vdc2 =0.313 cm² s⁻¹, depth =1000 m, and linv =4.5×10−3 m⁻¹. This equation of background vertical diffusivity follows a  tangential profile, where the upper ocean diffusivity is 0.1 cm² s⁻¹ and the deep ocean diffusivity is a constant 1 cm² s⁻¹ below 1000 m. As a comparison, the PI state overall has a lower background diffusivity in the deep ocean, but the bottom-intensified tidal mixing can be up to two orders of magnitude larger than the background mixing. The timestep of the ocean model is reduced from calculating its step every 63 min model-time, to 41 min model-time. Modifying the timestep of models which use numerical integrations is known to affect their results, as was shown for CAM3 , yet it remains generally poorly documented. It is not uncommon for paleoclimate simulations to use shorter computational time steps, as the ocean model in particular can generate numerous numerical instabilities which can lead to an early crash of the model. Our mid-Miocene results are compared to the “best-to-knowledge” PI simulation using modern parameterizations, as this should more accurately resemble the PI climate state. we explore the impact of these choice of ocean parametrizations in Appendix , as further work on the ocean component of our mid-Miocene simulations is kept for a future study.

There have been different plausible estimates of atmospheric CO₂ concentrations for the mid-Miocene due to differences in methodology and calibrations . The concentration is usually thought to lie between two and three times PI concentrations, three being the concentration discussed for the upcoming MioMIP experimental design, in line with recent high estimates during the MMCO (around 700–1100 ppm, ). Here, we compare Mio_Ctrl, which has a CO₂ concentration of three times PI, to two simulations using mid-Miocene boundary conditions and two times (Mio_2x) and four times (Mio_4x) PI in Fig. , relative to the proxy record. Although CO₂ concentrations as high as four times PI during the mid-Miocene are at the high threshold of the estimates, such levels are useful for estimating ECS and feedbacks , which are both important elements for quantifying global and regional responses to CO₂.

In Mio_2x, the GMST is 18.0 °C, which is 3.6 °C warmer than PI (Table ), and even lower than proxy estimates of the colder Late Miocene . In Mio_4x, the GMST is 21.2 °C, and its anomaly relative to PI is 6.8 °C (Table ). This is in agreement with proxy estimates for the GMST of the mid-Miocene. Similarly,  showed that CO₂ concentrations between three and four times PI concentrations provide the most reduced bias in total precipitation at a global scale, but some regions critically lack proxy sites, and there are few simulations at such high CO₂ concentrations for comparison .

At all CO₂ levels, the mid-Miocene simulations are cold and underestimate surface temperatures reconstructed from proxy data in most mid to high latitudes locations (Fig. ). The cold pattern simulated in the north Atlantic contributes even more to the temperature bias relative to proxy data. This pattern is likely connected to an absent AMOC in our model at all three CO₂ levels. Problematically, a weak mid-Miocene AMOC is a persistent feature in climate models , with some rare exceptions , the associated colder North Atlantic surface temperature is not necessarily supported by proxies e.g.. Nevertheless, a recent study using coccolith clumped isotopes showed a modest northern Atlantic warming during the mid-Miocene compared to the high warming reported in earlier studies , which suggest that some model-proxy discrepancies may be due to limitations in proxy interpretation. Further discussion on the ocean circulation in our simulations is planned for a follow-up paper.

In Mio_2x, the temperatures are too cold even in tropical locations compared to proxy data (Fig. ). On the contrary, in Mio_4x, some of the mid and high latitudes negative biases are dampened, but tropical locations are too warm compared to proxy data. These issues affecting polar and tropical warmth are commonly found in other Miocene simulations with various models , and most mid-Pliocene simulations during PlioMIP1 , although there was no systematic bias in PlioMIP2 models . Climate models are not tuned for paleoclimates, which contributes to the challenges they face in representing polar amplified temperatures in warm paleoclimates . Moreover, climate models may show other biases in high latitudes, notably due to poor representation of vegetation from dynamic vegetation models, as shown in Sect. , or lack of interactive ice sheets. Additionally, it is likely that model-proxy biases are a combination of both model and proxy errors. Notably, pollen and marine organic proxies can have substantial seasonal biases, which can strongly affect their temperature signal when compared to annually-averaged modelled temperatures, as described by  for the Pliocene.

ECS is widely regarded as one of the most critical metrics for characterizing future climate change . However, due to the difficulty of constraining it, several independent methods have been used, notably including evidence from the paleoclimate record e.g.. Some of these methods involve directly calculating the radiative forcing and global temperature of a past climate from the proxy record e.g, or emergent-constraint approaches, which are statistical methods connecting proxy reconstruction with the outputs from several models, usually under the umbrella of a MIP, such as for the LGM under PMIP  or PlioMIP .

The ECS of a paleoclimate and how it relates to modern ECS is not necessarily obvious. The effects of “fast” climate feedbacks (i.e. clouds, surface albedo, water vapor, lapse-rate and Planck feedbacks) need to be disentangled from “slow” climate feedbacks (notably carbon cycle, ice sheets and aerosols feedbacks), where the latter affects temperature on geological time-scale and usually connect to a different concept, the Earth system sensitivity . Climate feedbacks also depend on the background climate and the forcing imposed, which can lead to high ECS in warm, high-CO₂ paleoclimates . Those aspects result in important challenges when using evidence from new paleo-MIP to deduce ECS .

A way to approach these issues is to estimate ECS directly from a paleoclimate simulation, and compare it to the ECS in a modern simulation in the same model e.g.. Here, we have performed two simulations: Mio_Ctrl_DblCO2, which corresponds to a doubling of CO₂ from Mio_Ctrl (1708.2 ppm), and Mio_2x_DblCO2, which is a doubling of CO₂ from Mio_2x (1138.8 ppm). Further details on the methodology are provided in Sect. .

In Mio_Ctrl_DblCO2 (1708.2 ppm), ECS is 2.9 °C (2.5–3.3 °C, 95 % predicted interval, Fig. B), in comparison to 2.8 °C from PI conditions with this model (2.2–3.4 °C, 95 % predicted interval, Fig. A). From a lower CO₂ concentration, Mio_2x_DblCO2 (1138.8 ppm), ECS is 2.6 °C, which, similarly as the estimate from PI climate, is also within the 95 % predicted interval for the ECS of Mio_Ctrl_DblCO2. Even when considering the higher background CO₂ concentration, and consequently higher background mean temperature of the mid-Miocene, these estimates tend to indicate that the PI-based ECS of CESM1.2 can characterize the Miocene climate, or that ECS estimates obtained from the Miocene climate using CESM1.2, for instance in an emergent constraint approach, could be representative of its modern-based ECS. Previous studies on the Miocene have also estimated its ECS to be close to 3 °C, and in general relatively close to the ECS estimated for modern climate from Miocene evidence , as well as the ECS reported from multiple lines of evidence in the latest assessment report of the International Panel on Climate Change (IPCC AR6: 3 °C, 2–5 °C, 90 % confidence interval, ), in comparison to some older warm paleoclimates (e.g. the Eocene) where ECS estimates easily exceed 6 °C .

Here, we investigate the impact of the Antarctic ice sheet, atmospheric model, and solar constant on the mid-Miocene temperature and precipitation. The sensitivity runs for the atmospheric model and the solar constant were performed without the Antarctic ice sheet, as the ice sheet data was not available to us at the time of the simulations, and these simulations are computationally expensive to perform. Therefore, in this section we use Mio_noIS, a mid-Miocene simulation without Antarctic ice sheet as the control simulation around which the sensitivities are tested. Global temperature anomalies and percent change of total precipitation relative to PI are reported in Table .

In this study, we have developed a set of simulations using a new and previously unpublished geography for the mid-Miocene, using CESM1.2. Research centered on the mid-Miocene has shown a potential for it to be a partial analog of near-future climate e.g., yet uncertainties remain on atmospheric CO₂ concentration and non-CO₂ forcing, and consequently the scale of the warming and the strength of its potential analogy. In particular, model simulations do not match the high latitude warming inferred from some proxies, potentially due to changes in ocean circulation, poor understanding of polar amplification in models or poor representation of vegetation. Alternatively, proxy-reconstructed temperatures might also be uncertain, as recent studies suggest colder mid-Miocene northern Atlantic temperatures, more in-line with climate models' outputs . It is in fact likely that these discrepancies reflect issues from both models and proxies, and the mid-Miocene experiments performed in this study aimed to bring a new light onto those questions.

Variations in CO₂ concentrations for the mid-Miocene have a substantial influence on its estimated temperatures. Between the high end (four times PI concentration) and the low end (two times PI concentration) of tested concentrations, we find a difference of 3.2 °C on mid-Miocene global mean surface temperature, suggesting a substantial role of CO₂ forcing on the mid-Miocene climate, as also previously observed in the case of the Pliocene . The mid-Miocene is also sensitive to non-CO₂ forcing, such as the land-sea mask, ice sheet and solar forcing, but the variations tested for those components had a lower influence on the mid-Miocene temperature than CO₂. Finally, we identified that switching the atmospheric model from CAM4 to CAM5, which has a substantial influence on cloud feedbacks, leads to a warmer mid-Miocene by up to 3.2 °C, which highlights the critical need of improving model climate feedbacks, as much as it is to better constrain climate forcing in paleoclimates.

Similarly as for the LGM  and the Pliocene , the mid-Miocene can be used to quantify ECS, owing to its relative proximity to modern climate. In this study, we estimated that the ECS of CESM1.2 at the mid-Miocene is 2.9 °C (2.5–3.3 °C, 95 % prediction interval), which is close to the modern-based estimate of ECS of CESM1.2 (2.8 °C, 2.2–3.4 °C, 95 % prediction interval). From this short glance on ECS in CESM1.2, as well as previous work on Miocene ECS , we believe there is motivation in supporting ECS estimates using Miocene evidence, particularly as Miocene modelling is moving towards an official PMIP design. Despite uncertainties in the proxy record or model disagreements, the Pliocene, the warm epoch following the Miocene, has shown that recent warm paleoclimates can provide robust constraint on ECS . Additionally, emergent constraint framework can be used to identify disagreements between models, and between model and data . Thus, estimates from the Miocene could either support existing methods using paleoclimate evidence , or be used within a new emergent constraint framework as previously done with emergent constraint frameworks for the LGM  or the Pliocene .

Compared to the proxy record, mid-Miocene simulations are usually either too cold globally, too cold at high latitudes, or both . Over different sensitivity experiments, we find the same issues using CESM1.2, which arise from a weak polar amplification. Simulated high latitudes temperatures underestimate the proxy record by as much as 20 °C, and warm vegetation biomes are more contracted towards low latitudes. However, high CO₂ levels and better representation of high latitude cloud parametrizations produce a better match with high latitude proxy sites and also provided a better match with precipitation proxy reconstruction . Additionally, northern Atlantic sea-surface temperatures reconstructed from coccolith clumped isotopes suggest a more modest warming compared to PI . This would lead to a decrease in the proxy-model bias observed in this region, without overestimating low-latitude ocean temperatures, as inferred from high-CO₂ simulations.

A mid-Miocene state close to reality is likely to include a combination of different sensitivities tested in this paper. A continued focus on high-latitude climate feedbacks to enhance polar amplification in models remains important, as this has been a recurring challenge in paleoclimate simulations and could influence projections of future climates. Further research is also needed to assess potential biases and uneven coverage in the proxy record, which can still affect model-proxy comparisons and interpretations of global Miocene climate.