Basic Numerical Methods in Meteorology and Oceanography

The purpose of this book is to provide an introduction to numerical modelling of the ocean and the atmosphere. It originates from courses given at Stockholm University and is intended to serve as a textbook for students in meteorology and oceanography with a background in mathematics and physics. Focus is on numerical schemes for the most commonly used equations in oceanography and meteorology as well as on the stability, precision and other properties of these schemes. Simple equations capturing the properties of the primitive equations employed in models of the ocean and atmosphere will be used. These model equations are solved numerically on a grid by discretisation, the derivatives of the differential equations being replaced by finite-difference approximations. The focus will be on the basic numerical methods used for oceanographic and atmospheric modelling. These models are based on the Navier-Stokes equations (including the Coriolis effect) and a tracer equation for heat in both the atmosphere and ocean and tracer equations for humidity and salt in the atmosphere and ocean, respectively. A coupled atmospheric and oceanic general circulation model represents the core part of an Earth System climate model. The book starts by presenting the most common types of partial differential equations and finite difference schemes used in meteorology and oceanography. Subsequently the limitations of these numerical schemes as regards stability, accuracy, presence of computational modes and accuracy the computationally determined phase speed are discussed. The shallow-water equations are discretised for different spatial grids and friction and diffusion terms are introduced. Hereafter implicit and semi-implicit schemes are discussed as well as the semi-Lagrangian technique. Coordinates for atmospheric as well as oceanic models are presented as well as a highly simplified 3D model. A brief description is given of how some atmospheric general circulation models use spectral methods as ""horizontal coordinates"". Finally, some ""pen-and-paper"" theoretical exercises and a number of GFD computer exercises are given

Meridional ocean carbon transport

The ocean's ability to take up and store CO2 is a key factor for understanding past and future climate variability. However, qualitative and quantitative understanding of surface‐to‐interior pathways, and how the ocean circulation affects the CO2 uptake, is limited. Consequently, how changes in ocean circulation may influence carbon uptake and storage and therefore the future climate remains ambiguous. Here we quantify the roles played by ocean circulation and various water masses in the meridional redistribution of carbon. We do so by calculating streamfunctions defined in dissolved inorganic carbon (DIC) and latitude coordinates, using output from a coupled biogeochemical‐physical model. By further separating DIC into components originating from the solubility pump and a residual including the biological pump, air‐sea disequilibrium, and anthropogenic CO2, we are able to distinguish the dominant pathways of how carbon enters particular water masses. With this new tool, we show that the largest meridional carbon transport occurs in a pole‐to‐equator transport in the subtropical gyres in the upper ocean. We are able to show that this pole‐to‐equator DIC transport and the Atlantic meridional overturning circulation (AMOC)‐related DIC transport are mainly driven by the solubility pump. By contrast, the DIC transport associated with deep circulation, including that in Antarctic bottom water and Pacific deep water, is mostly driven by the biological pump. As these two pumps, as well as ocean circulation, are widely expected to be impacted by anthropogenic changes, these findings have implications for the future role of the ocean as a climate‐buffering carbon reservoir

Atmospheric and oceanic circulation from a thermodynamic perspective

The climate system is continuously transporting and exchanging heat, freshwater, carbon and other tracers in different spatio-temporal scales. Therefore, analysing the system from a thermodynamic or biogeochemical framework is highly convenient. In this thesis the interaction between the ocean and the atmospheric circulation is analysed using thermodynamical and biogeochemical coordinates. Due to the dimensionality of the climate system stream functions are used to reduce this complexity and facilitate the understanding of the different processes that take place. The first half of this thesis, focuses on the interaction between the atmospheric and the ocean circulation from a thermodynamic perspective. We introduce the hydrothermohaline stream function which combines the atmospheric circulation in humidity-potential temperature (hydrothermal) space and the ocean circulation in salinity-temperature coordinates (thermohaline). A scale factor of 7.1 is proposed to link humidity and salinity coordinates. Future scenarios are showing an increase of humidity in the atmosphere due to the increase of temperatures which results in a widening of the hydrothermal stream function along the humidity coordinate. In a similar way, the ocean circulation in the thermohaline space expands along the salinity coordinate. The link between salinity and humidity changes is strongest at net evaporation regions where the gain of water vapour in the atmosphere results in a salinification in the ocean. In addition, the ocean circulation in latitude-carbon space is investigated. By doing so, we are able to distinguish the roles of different water masses and circulation pathways for ocean carbon. We find that the surface waters in the subtropical gyres are the main drivers of the meridional carbon transport in the ocean. By separating the carbon in its different constituents we show that the carbon transported by the majority of the water masses is a result of the solubility pump. The contribution of the biological pump is predominant in the deep Pacific Ocean. The effects of the Mediterranean Overflow Waters on the North Atlantic are discussed in the final part of the thesis.At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: Manuscript. Paper 3: Manuscript. Paper 4: Manuscript.</p

Hydrothermohaline streamfunctions computed in EC-Earth

NetCDF files containing hydrothermohaline streamfunctions computed from the ESM EC-Earth. The streamfunctions have been computed for the last 10 years of a historical run (1996-2005) and the last 10 years of a RCP 8.5 scenario run (2090-2100)

Atmospheric water transport connectivity within and between ocean basins and land

The global atmospheric water transport from the net evaporation to the net precipitation regions has been traced using Lagrangian trajectories. A matrix has been constructed by selecting various group of trajectories based on their surface starting (net evaporation) and ending (net precipitation) positions to show the connectivity of the 3-D atmospheric water transport within and between the three major ocean basins and the global landmass. The analysis reveals that a major portion of the net evaporated water precipitates back into the same region, namely 67 % for the Indian Ocean, 64 % for the Atlantic Ocean, 85 % for the Pacific Ocean and 72 % for the global landmass. It has also been calculated that 58 % of the net terrestrial precipitation was sourced from land evaporation. The net evaporation from the subtropical regions of the Indian, Atlantic and Pacific oceans is found to be the primary source of atmospheric water for precipitation over the Intertropical Convergence Zone (ITCZ) in the corresponding basins. The net evaporated waters from the subtropical and western Indian Ocean were traced as the source for precipitation over the South Asian and eastern African landmass, while Atlantic Ocean waters are responsible for rainfall over North Asia and western Africa. Atlantic storm tracks were identified as the carrier of atmospheric water that precipitates over Europe, while the Pacific storm tracks were responsible for North American, eastern Asian and Australian precipitation. The bulk of South and Central American precipitation is found to have its source in the tropical Atlantic Ocean. The land-to-land atmospheric water transport is pronounced over the Amazon basin, western coast of South America, Congo basin, northeastern Asia, Canada and Greenland. The ocean-to-land and land-to-ocean water transport through the atmosphere was computed to be 2×10^9 and 1×10^9 kg s^−1, respectively. The difference between them (net ocean-to-land transport), i.e. 1×10^9 kg s^−1, is transported to land. This net transport is approximately the same as found in previous estimates which were calculated from the global surface water budget

TRACMASS - A mass conserving trajectory code for ocean and atmosphere general circulation models

We present the latest version of the TRACMASS trajectory code, version 7.0. The new version includes new features such as water tracing in the atmosphere, parameterisation scheme for sub-grid scale turbulence, generalisation of the tracer handling, etc. The code has also become more user friendly and easier to get started with. Previous versions of TRACMASS only allowed temperature, salinity and potential density to be calculated along the trajectories, but the new version allows any tracer to be followed e.g. biogeochemical tracers or chemical compounds in the atmosphere. The new parameterisation of sub-grid turbulence will enhance the kinetic energy and dispersion of trajectories in the ocean so that results from eddy-permitting ocean models (dx ∼25km) resemble those from “eddy-resolving” models (dx ∼8km). We will demonstrate some use cases of these new capabilities for atmosphere and ocean sciences. TRACMASS calculates Lagrangian trajectories offline for both the ocean and atmosphere by using already stored velocity fields, and optionally tracer fields. The velocity fields may be taken from ocean or atmosphere circulation models (e.g. NEMO, OpenIFS), reanalysis products (e.g. ERA-5) or observations (e.g. geostrophic currents from satellite altimetry). The fact that the numerical scheme in TRACMASS is mass conserving allows us to associate each trajectory with a mass transport and calculate the Lagrangian mass transport between different regions as well as construct Lagrangian stream functions. A live demonstration on how to set up, configure and run the TRACMASS code will be given

Meridional Ocean Carbon Transport

The ocean's ability to take up and store CO2 is a key factor for understanding past and future climate variability. However, qualitative and quantitative understanding of surface-to-interior pathways, and how the ocean circulation affects the CO2 uptake, is limited. Consequently, how changes in ocean circulation may influence carbon uptake and storage and therefore the future climate remains ambiguous. Here we quantify the roles played by ocean circulation and various water masses in the meridional redistribution of carbon. We do so by calculating streamfunctions defined in dissolved inorganic carbon (DIC) and latitude coordinates, using output from a coupled biogeochemical-physical model. By further separating DIC into components originating from the solubility pump and a residual including the biological pump, air-sea disequilibrium, and anthropogenic CO2, we are able to distinguish the dominant pathways of how carbon enters particular water masses. With this new tool, we show that the largest meridional carbon transport occurs in a pole-to-equator transport in the subtropical gyres in the upper ocean. We are able to show that this pole-to-equator DIC transport and the Atlantic meridional overturning circulation (AMOC)-related DIC transport are mainly driven by the solubility pump. By contrast, the DIC transport associated with deep circulation, including that in Antarctic bottom water and Pacific deep water, is mostly driven by the biological pump. As these two pumps, as well as ocean circulation, are widely expected to be impacted by anthropogenic changes, these findings have implications for the future role of the ocean as a climate-buffering carbon reservoir