Synchronization is a ubiquitous phenomenon occurring in social, biological, and technological systems when the internal rythms of their constituents are adapted to be in unison as a result of their coupling. This natural tendency towards dynamical consensus has spurred a large body of theoretical and experimental research in recent decades. The Kuramoto model constitutes the most studied and paradigmatic framework in which to study synchronization. In particular, it shows how synchronization appears as a phase transition from a dynamically disordered state at some critical value for the coupling strength between the interacting units. The critical properties of the synchronization transition of this model have been widely studied and many variants of its formulations have been considered to address different physical realizations. However, the Kuramoto model has been studied only within the domain of classical dynamics, thus neglecting its applications for the study of quantum synchronization phenomena. Based on a system-bath approach and within the Feynman path-integral formalism, we derive equations for the Kuramoto model by taking into account the first quantum fluctuations. We also analyze its critical properties, the main result being the derivation of the value for the synchronization onset. This critical coupling increases its value as quantumness increases, as a consequence of the possibility of tunneling that quantum fluctuations provide.
Abstract. Earth system models (ESMs) use bottom boundaries for their land surface model (LSM) components which are shallower than the depth reached by surface temperature changes in the centennial timescale associated with recent climate change. Shallow bottom boundaries reflect energy to the surface, which along with the lack of geothermal heat flux in current land surface models, alter the surface energy balance and therefore affect some feedback processes between the ground surface and the atmosphere, such as permafrost and soil carbon stability. To evaluate these impacts, we modified the subsurface model in the Community Land Model version 4.5 (CLM4.5) by setting a non-zero crustal heat flux bottom boundary condition uniformly across the model and by increasing the depth of the lower boundary from 42.1 to 342.1 m. The modified and original land models were run during the period 1901–2005 under the historical forcing and between 2005 and 2300 under forcings for two future scenarios of moderate (Representative Concentration Pathway 4.5; RCP4.5) and high (RCP8.5) emissions. Increasing the thickness of the subsurface by 300 m increases the heat stored in the subsurface by 72 ZJ (1 ZJ = 1021 J) by the year 2300 for the RCP4.5 scenario and 201 ZJ for the RCP8.5 scenario (respective increases of 260 % and 217 % relative to the shallow model), reduces the loss of near-surface permafrost area in the Northern Hemisphere between 1901 and 2300 by 1.6 %–1.9 %, reduces the loss of intermediate-depth permafrost area (above 42.1 m depth) by a factor of 3–5.5 and reduces the loss of soil carbon by 1.6 %–3.6 %. Each increase of 20 mW m−2 of the crustal heat flux increases the temperature at 3.8 m (the soil–bedrock interface) by 0.04±0.01 K. This decreases near-surface permafrost area slightly (0.3 %–0.8 %) and produces local differences in initial stable size of the soil carbon pool across the permafrost region, which reduces the loss of soil carbon across the region by as much as 1.1 %–5.6 % for the two scenarios. Reducing subsurface thickness from 42.1 to 3.8 m, used by many LSMs, produces a larger effect than increasing it to 342.1 m, because 3.8 m is not enough to damp the annual signal and the subsurface closely follows the air temperature. We determine the optimal subsurface thickness to be 100 m for a 100-year simulation and 200 m for a simulation of 400 years. We recommend short-term simulations to use a subsurface of at least 40 m, to avoid the perturbation of seasonal temperature propagation.
Earth System Models (ESMs) use bottom boundaries for their land surface model components which are shallower than the depth reached by surface temperature changes in the centennial time scale associated with recent climate change. Shallow bottom boundaries reflect energy to the surface, which along with the lack of geothermal heat flux in current land surface models, alter the surface energy balance and therefore affect some feedback processes between the ground surface and the 5 atmosphere, such as permafrost and soil carbon stability. To evaluate these impacts, we modified the subsurface model in the Community Land Model version 4.5 (CLM4.5) by setting a non-zero crustal heat flux bottom boundary condition and by increasing the depth of the lower boundary by 300 m. The modified and original land models were run during the period 1901-2005 under the historical forcing and between 2005-2300 under two future scenarios of moderate (RCP 4.5) and high (RCP 8.5) emissions. Increasing the thickness of the subsurface by 300 m increases the heat stored in the subsurface by 72 ZJ 10(1 ZJ = 10 21 J) by year 2300 for the RCP 4.5 scenario and 201 ZJ for the RCP 8.5 scenario (respective increases of 260% and 217% relative to the shallow model), reduces the loss of near-surface permafrost between 1901 and 2300 by 1.6%-1.9%, and reduces the loss of soil carbon by 1.6%-3.6%. Each increase of 0.02 W m −2 of the crustal heat flux increases the temperature at the soil-bedrock frontier by 0.4 ± 0.01 K, which decreases near-surface permafrost area slightly (0.3-0.8%), but reduces the loss of soil carbon by as much as 1.1%-5.6% for the two scenarios. 15Geosci. Model Dev. Discuss., https://doi.and snow cover (Hansen and Nazarenko, 2004). In these Land Surface Models (LSMs) the bedrock layer present below soil is impermeable, and when explicitly modeled, the only process taking place in bedrock is thermal diffusion.Thermal diffusion in the subsurface allows the land system to act like a heat reservoir, contributing to the thermal inertia of Earth's climate. However, this contribution is relatively small as the capacity of the oceans to absorb energy is orders of magnitude above that of the continents (Stocker et al., 2013). Estimates of the energy accumulation during the second half of 5 the 20th century in the land system show that the heat stored in continents (9 ± 1 ZJ, where 1 ZJ = 10 21 J) is less than the uncertainty on the heat stored in oceans during the same period (240±19 ZJ) (Beltrami et al., 2002;Levitus et al., 2012;Rhein et al., 2013). This justifies many ESMs to only consider the land subsurface to the shallow depth (3 − 4 m) needed for soil modeling (Schmidt et al., 2014;Wu et al., 2014) and neglect the bedrock entirely. Still, the thermal regime of the subsurface affects the energy balance at the surface, which in turn influences the surface and soil processes with a feedback on the climate 10 system. Energy variations at the land surface propagate underground, and the use of a too shallow subsurface in land models impl...
Abstract. The representation of snow processes in forest growth models is necessary to accurately predict the hydrological cycle in boreal ecosystems and the isotopic signature of soil water extracted by trees, photosynthates and tree-ring cellulose. Yet, most process-based models do not include a snow module; consequently, their simulations may be biased in cold environments. Here, we modified the MAIDENiso model to incorporate a new snow module that simulates snow accumulation, melting and sublimation, as well as thermal exchanges driving freezing and thawing of the snow and the soil. We tested these implementations in two sites in eastern and western Canada for black spruce (Picea mariana (Mill.) B.S.P.) and white spruce (Picea glauca (Moench) Voss) forests, respectively. The new snow module improves the skills of the model to predict components of the hydrological cycle. The MAIDENiso model is now able to reproduce the spring discharge peak and to simulate stable oxygen isotopes in tree-ring cellulose more realistically than in the original snow-free version of the model. The new implementation also results in simulations with a higher contribution from the source water on the oxygen isotopic composition of the simulated cellulose, leading to more accurate estimates of cellulose isotopic composition. Future work may include the development of inverse modelling with this new version of MAIDENiso to produce robust reconstructions of the hydrological cycle and isotope processes in cold environments.
We thank the reviewer for his comments, which show that several points both in the description of the model and in the objectives and limitations of our study needed to be clarified. We have made some corrections and added several paragraphs to address the reviewer's questions. In addition, we have made many editorial corrections throughout the manuscript to improve the readability and flow of the text. We have also changed the Figure 18 (P21) to show the differences to the original model and changed its color code to make it colorblind-friendly. In response to a suggestion made by reviewer 2, we have also moved several figures to supplementary materials. We C1 GMDD Interactive commentPrinter-friendly version Discussion paper
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