Ocean geochemical tracers such as radiocarbon, protactinium and thorium isotopes, and noble gases are widely used to constrain a range of physical and biogeochemical processes in the ocean. However, ...their routine simulation in global ocean circulation and climate models is hindered by the computational expense of integrating them to a steady state. Here, a new approach to this long‐standing “spin‐up” problem is introduced to efficiently compute equilibrium distributions of such tracers in seasonally‐forced models. Based on “Anderson Acceleration,” a sequence acceleration technique developed in the 1960s to solve nonlinear integral equations, the new method is entirely “black box” and offers significant speed‐up over conventional direct time integration. Moreover, it requires no preconditioning, ensures tracer conservation and is fully consistent with the numerical time‐stepping scheme of the underlying model. It thus circumvents some of the drawbacks of other schemes such as matrix‐free Newton Krylov that have been proposed to address this problem. An implementation specifically tailored for the batch HPC systems on which ocean and climate models are typically run is described, and the method illustrated by applying it to a variety of geochemical tracer problems. The new method, which provides speed‐ups by over an order of magnitude, should make simulations of such tracers more feasible and enable their inclusion in climate change assessments such as IPCC.
Plain Language Summary
Radiocarbon and other geochemical tracers have provided great insight into the workings of the ocean but are prohibitively expensive to simulate in climate models. This study introduces a new computational method that can be applied to any model to greatly speed‐up simulations of such tracers, enabling their routine inclusion in climate models and thus more effective use of those tracers.
Key Points
Geochemical tracers have provided great insight into oceanic processes but are prohibitively expensive to simulate in climate models
A new “sequence acceleration” method is introduced offering speed‐ups of 10–25 times for a range of typical geochemical tracer problems
The new method is completely “black box” and can be applied to any model
A novel computational framework is introduced for the efficient simulation of chemical and biological tracers in ocean models. The framework is based on the “transport matrix” formulation, a scheme ...for capturing the complex three‐dimensional transport of tracers in a general circulation model (GCM) as a sparse matrix, thus reducing the task of simulating tracers to a sequence of simple matrix‐vector products. The principal advantages of this formulation are efficiency and convenience. It is many orders of magnitude more efficient than GCMs, allowing us to address problems that are currently either difficult or unaffordable with GCMs. The scheme also allows us to quickly “prototype” new biogeochemical parameterizations or “plug in” existing ones. This paper describes the key features and advantages of the transport matrix method, and illustrates its application to a series of realistic problems in chemical and biological oceanography. The examples range from simulation of a transient tracer (SF6) to adjoint sensitivity of a complex coupled biogeochemical model. Finally, the paper describes an efficient, portable, and freely available implementation of this computational scheme that provides the necessary framework for simulating any biogeochemical tracer.
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 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 with 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 2,000 m and 0.028 ± 0.026 W/m² below 2,000 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 onehalf of the Atlantic Ocean warming and thermosteric sea-level rise at low latitudes to midlatitudes emerged due to heat convergence from changes in ocean transport.
Abstract 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.
Previous studies found large biases between individual observational and model estimates of historical ocean anthropogenic carbon uptake. We show that the largest bias between the Coupled Model ...Intercomparison Project phase 5 (CMIP5) ensemble mean and between two observational estimates of ocean anthropogenic carbon is due to a difference in start date. After adjusting the CMIP5 and observational estimates to the 1791–1995 period, all three carbon uptake estimates agree to within 3 Pg of C, about 4% of the total. The CMIP5 ensemble mean spatial bias compared to the observations is generally smaller than the observational error, apart from a negative bias in the Southern Ocean and a positive bias in the Southern Indian and Pacific Oceans compensating each other in the global mean. This dipole pattern is likely due to an equatorward and weak bias in the position of Southern Hemisphere westerlies and lack of mode and intermediate water ventilation.
Key Points
Observations and model simulations of ocean anthropogenic carbon assume different start dates
Once referenced to the same period, 1971–1995, models and observations of ocean anthropogenic carbon agree to within 4%
A model bias in the mean position of Southern Hemisphere westerlies results in a bias in the pattern of Southern Hemisphere carbon uptake
Dissolved organic carbon (DOC) data are presented from three meridional transects conducted in the North Atlantic as part of the US Climate Variability (CLIVAR) Repeat Hydrography program in 2003. ...The hydrographic sections covered a latitudinal range of 6°S to 63°N along longitudes 20°W (CLIVAR line A16), 52°W (A20) and 66°W (A22). Over 3700 individual measurements reveal unprecedented detail in the DOC distribution and systematic variations in the mesopelagic and bathypelagic zones of the North Atlantic basin. Latitudinal gradients in DOC concentrations combined with published estimates of ventilation rates for the main thermocline and North Atlantic Deep Water (NADW) indicate a net DOC export rate of 0.081
Pg
C
yr
−1 from the epipelagic zone into the mesopelagic and bathypelagic zones. Model II regression and multiple linear regression models applied to pairwise measures of DOC and chlorofluorocarbon (CFC-12) ventilation age, retrieved from major water masses within the main thermocline and NADW, indicate decay rates for exported DOC ranging from 0.13 to 0.94
μmol
kg
−1
yr
−1, with higher DOC concentrations driving higher rates. The contribution of DOC oxidation to oxygen consumption ranged from 5 to 29% while mineralization of sinking biogenic particles drove the balance of the apparent oxygen utilization.
The isotopic composition of the rare earth element neodymium (Nd) has the potential to serve as water-mass tracer, because it is naturally tagged by continental sources with distinct ages and ...lithologies. However, in order to understand the limitations of this approach we need to know more about the physical and biogeochemical processes controlling the distribution of Nd in the modern ocean. For example, Nd isotope ratios behave quasi-conservatively, while concentrations in the water column generally increase with depth, showing a broadly nutrient-like behaviour. We define this decoupling of Nd concentrations and isotopic compositions as the “Nd paradox”. For the first time we model Nd concentrations and isotopic compositions simultaneously and address the hypothesis that the Nd paradox can be explained by a combination of lateral advection and reversible scavenging. We impose a reversible-scavenging model of Nd removal from the ocean on the ocean circulation fields from the MIT general circulation model using the transport matrix method. We conclude that reversible scavenging is an active and important component in the cycling of Nd in the ocean. In the absence of an adequate alternative explanation, reversible scavenging should be considered a necessary component in explaining the Nd paradox.
PDF
