Efficient spin-up of Earth System Models using sequence acceleration

Marine and terrestrial biogeochemical models are key components of the Earth System Models (ESMs) used to project future environmental changes. However, their slow adjustment time also hinders effective use of ESMs because of the enormous computational resources required to integrate them to a preindustrial equilibrium. Here, a novel solution to this "spin-up" problem based on "sequence acceleration", is shown to accelerate equilibration of state-of-the-art marine biogeochemical models by over an order of magnitude. The technique can be applied in a "black box" fashion to existing models. Even under the challenging spin-up protocols used for Intergovernmental Panel on Climate Change (IPCC) simulations, the new algorithm is 5 times faster. Preliminary results suggest that terrestrial models can be similarly accelerated, enabling for the first time a quantification of major parametric uncertainties in ESMs, improved estimates of metrics such as climate sensitivity, and higher model resolution than currently feasible

Semi-implicit solver for the heat equation with Stefan–Boltzmann law boundary condition

The surface energy balance on an atmosphereless body consists of solar irradiance, subsurface heat conduction, and thermal radiation to space by the Stefan–Boltzmann law. Here we extend the semi-implicit Crank–Nicolson method to this specific nonlinear boundary condition and validate its accuracy. A rapid change in incoming solar flux can cause a numerical instability, and several approaches to dampen this instability are analyzed. A predictor based on the Volterra integral equation formulation for the heat equation is also derived and can be used to improve accuracy and stability. The publicly available implementation provides a fast and robust thermophysical model that has been applied to lunar, Martian, and asteroidal surfaces, on occasion to millions of surface facets or parameter combinations

Slope streaks on Mars: Correlations with surface properties and the potential role of water

The Mars Orbiter Camera on board the Mars Global Surveyor spacecraft has returned images of numerous dark streaks that are the result of down-slope mass movement occurring under present-day martian climatic conditions. We systematically analyze over 23,000 high-resolution images and demonstrate that slope streaks form exclusively in regions of low thermal inertia (confirming earlier results), steep slopes, and, remarkably, only where peak temperatures exceed 275 K. The northernmost streaks, which form in the coldest environment, form preferentially on warmer south-facing slopes. Repeat images of sites with slope streaks show changes only if the time interval between the two images includes the warm season. Surprisingly (in light of the theoretically short residence time of H_2O close to the surface), the data support the possibility that small amounts of water are transiently present in low-latitude near-surface regions of Mars and undergo phase transitions at times of high insolation, triggering the observed mass movements

Global reconstruction of historical ocean heat storage and transport

Most of the excess energy stored in the climate system due to anthropogenic greenhouse gas emissions has been taken up by the oceans, leading to thermal expansion and sea level rise. The oceans thus have an important role in the Earth’s energy imbalance. Observational constraints on future anthropogenic warming critically depend on accurate estimates of past ocean heat content (OHC) change. We present a novel reconstruction of OHC since 1871, with global coverage of the full ocean depth. Our estimates combine timeseries of observed sea surface temperatures, with much longer historical coverage than those in the ocean interior, together with a representation (a Green’s function) of time-independent ocean transport processes. For 1955-2017, our estimates are comparable to direct estimates made by infilling the available 3D time-dependent ocean temperature observations. We find that the global ocean absorbed heat during this period at a rate of 0.30 ± 0.06 W/m2 in the upper 2000 m and 0.028 ± 0.026 W/m2 below 2000 m, with large decadal fluctuations. The total OHC change since 1871 is estimated at 436 ±91 × 1021 J, with an increase during 1921-1946 (145 ± 62× 1021 J) that is as large as during 1990-2015. By comparing with direct estimates, we also infer that, during 1955-2017, up to half of the Atlantic Ocean warming and thermosteric sea level rise at low-to-mid latitudes emerged due to heat convergence from changes in ocean transport

Changes in oceanic radiocarbon and CFCs since the 1990s

Anthropogenic perturbations from fossil fuel burning, nuclear bomb testing, and chlorofluorocarbon (CFC) use have created useful transient tracers of ocean circulation. The atmospheric 14C/C ratio (∆14C) peaked in the early 1960s and has decreased now to pre-industrial levels, while atmospheric CFC-11 and CFC-12 concentrations peaked in the early 1990s and early 2000s, respectively, and have now decreased by 10%–20%. We present the first analysis of a decade of new observations (2007 to 2018–2019) and give a comprehensive overview of the changes in ocean ∆14C and CFC concentration since the WOCE surveys in the 1990s. Surface ocean ∆14C decreased at a nearly constant rate from the 1990–2010s (20‰/decade). In most of the surface ocean ∆14C is higher than in atmospheric CO2 while in the interior ocean, only a few places are found to have increases in ∆14C, indicating that globally, oceanic bomb 14C uptake has stopped and reversed. Decreases in surface ocean CFC-11 started between the 1990 and 2000s, and CFC-12 between the 2000–2010s. Strong coherence in model biases of decadal changes in all tracers in the Southern Ocean suggest ventilation of Antarctic Intermediate Water was enhanced from the 1990 to the 2000s, whereas ventilation of Subantarctic Mode Water was enhanced from the 2000 to the 2010s. The decrease in surface tracers globally between the 2000 and 2010s is consistently stronger in observations than in models, indicating a reduction in vertical transport and mixing due to stratification

A derivative-free optimisation method for global ocean biogeochemical models

The skill of global ocean biogeochemical models, and the earth system models in which they are embedded, can be improved by systematic calibration of the parameter values against observations. However, such tuning is seldom undertaken as these models are computationally very expensive. Here we investigate the performance of DFO-LS, a local, derivative-free optimisation algorithm which has been designed for computationally expensive models with irregular model–data misfit landscapes typical of biogeochemical models. We use DFO-LS to calibrate six parameters of a relatively complex global ocean biogeochemical model (MOPS) against synthetic dissolved oxygen, phosphate and nitrate “observations” from a reference run of the same model with a known parameter configuration. The performance of DFO-LS is compared with that of CMA-ES, another derivative-free algorithm that was applied in a previous study to the same model in one of the first successful attempts at calibrating a global model of this complexity. We find that DFO-LS successfully recovers five of the six parameters in approximately 40 evaluations of the misfit function (each one requiring a 3000-year run of MOPS to equilibrium), while CMA-ES needs over 1200 evaluations. Moreover, DFO-LS reached a “baseline” misfit, defined by observational noise, in just 11–14 evaluations, whereas CMA-ES required approximately 340 evaluations. We also find that the performance of DFO-LS is not significantly affected by observational sparsity, however fewer parameters were successfully optimised in the presence of observational uncertainty. The results presented here suggest that DFO-LS is sufficiently inexpensive and robust to apply to the calibration of complex, global ocean biogeochemical models

Sensitivity analysis of simple global marine biogeochemical models

This study presents results from 46 sensitivity experiments carried out with three structurally simple (2, 3, and 6 biogeochemical state variables, respectively) models of production, export and remineralization of organic phosphorus, coupled to a global ocean circulation model and integrated for 3000 years each. The models' skill is assessed via different misfit functions with respect to the observed global distributions of phosphate and oxygen. Across the different models, the global root-mean square misfit with respect to observed phosphate and oxygen distributions is found to be particularly sensitive to changes in the remineralization length scale, and also to changes in simulated primary production. For this metric, changes in the production and decay of dissolved organic phosphorus as well as in zooplankton parameters are of lesser importance. For a misfit function accounting for the misfit of upper-ocean tracers, however, production parameters and organic phosphorus dynamics play a larger role. Regional misfit patterns are investigated as indicators of potential model deficiencies, such as missing iron limitation, or deficiencies in the sinking and remineralization length scales. In particular, the gradient between phosphate concentrations in the northern North Pacific and the northern North Atlantic is controlled predominantly by the biogeochemical model parameters related to particle flux. For the combined 46 sensitivity experiments performed here, the global misfit to observed oxygen and phosphate distributions shows no clear relation to either simulated global primary or export production for either misfit metric employed. However, a relatively tight relationship that is very similar for the different model of different structural complexity is found between the model-data misfit in oxygen and phosphate distributions to simulated meso- and bathypelagic particle flux. Best agreement with the observed tracer distributions is obtained for simulated particle fluxes that agree most closely with sediment trap data for a nominal depth of about 1000 m, or deeper

The influence of warming patterns on passive ocean heat uptake

The climate's response to forcing depends on how efficiently heat is absorbed by the ocean. Much, if not most, of this ocean heat uptake results from the passive transport of warm surface waters into the ocean's interior. Here we examine how geographic patterns of surface warming influence the efficiency of this passive heat uptake process. We show that the average pattern of surface warming in CMIP5 damps passive ocean heat uptake efficiency by nearly 25%, as compared to homogeneous surface warming. This “pattern effect” occurs because strong ventilation and weak surface warming are robustly colocated, particularly in the Southern Ocean. However, variations in warming patterns across CMIP5 do not drive significant ensemble spread in passive ocean heat uptake efficiency. This spread is likely linked to intermodel differences in ocean circulation, which our idealized results suggest may be dominated by differences in Southern Ocean and subtropical ventilation processes

Global ocean cooling of 2.3°C during the Last Glacial Maximum

Quantitative constraints on past mean ocean temperature (MOT) critically inform our historical understanding of Earth's energy balance. A recently developed MOT proxy based on paleoatmospheric Xe, Kr, and N2 ratios in ice core air bubbles is a promising tool rooted in the temperature dependences of gas solubilities. However, these inert gases are systematically undersaturated in the modern ocean interior, and it remains unclear how air-sea disequilibrium may have changed in the past. Here, we carry out 30 tracer-enabled model simulations under varying circulation, sea ice cover, and wind stress regimes to evaluate air-sea disequilibrium in the Last Glacial Maximum (LGM) ocean. We find that undersaturation of all three gases was likely reduced, primarily due to strengthened high-latitude winds, biasing reconstructed MOT by −0.38 ± 0.37°C (1σ). Accounting for air-sea disequilibrium, paleoatmospheric inert gases indicate that LGM MOT was 2.27 ± 0.46°C (1σ) colder than the pre-industrial era

Influence of GEOTRACES data distribution and misfit function choice on objective parameter retrieval in a marine zinc cycle model

Biogeochemical model behaviour for micronutrients is typically hard to constrain because of the sparsity of observational data, the difficulty of determining parameters in situ, and uncertainties in observations and models. Here, we assess the influence of data distribution, model uncertainty, and the misfit function on objective parameter optimisation in a model of the oceanic cycle of zinc (Zn), an essential micronutrient for marine phytoplankton with a long whole-ocean residence time. We aim to investigate whether observational constraints are sufficient for reconstruction of biogeochemical model behaviour, given that the Zn data coverage provided by the GEOTRACES Intermediate Data Product 2017 is sparse. Furthermore, we aim to assess how optimisation results are affected by the choice of the misfit function and by confounding factors such as analytical uncertainty in the data or biases in the model related to either seasonal variability or the larger-scale circulation. The model framework applied herein combines a marine Zn cycling model with a state-of-the-art estimation of distribution algorithm (Covariance Matrix Adaption Evolution Strategy, CMA-ES) to optimise the model towards synthetic data in an ensemble of 26 optimisations. Provided with a target field that can be perfectly reproduced by the model, optimisation retrieves parameter values perfectly regardless of data coverage. As differences between the model and the system underlying the target field increase, the choice of the misfit function can greatly impact optimisation results, while limitation of data coverage is in most cases of subordinate significance. In cases where optimisation to full or limited data coverage produces relatively distinct model behaviours, we find that applying a misfit metric that compensates for differences in data coverage between ocean basins considerably improves agreement between optimisation results obtained with the two data situations