Prof. Dr. Markus Meier
\n",
" Leibniz Institute for Baltic Sea Research Warnemünde (IOW)
\n",
" E-Mail: markus.meier@io-warnemuende.de
Figure 1: The Max-Planck-Institute Earth System Model MPI-ESM1.2 is a combination of different sub-models, such as the GCMS ECHAM6.3 for the atmosphere and MPIOM1.6 for ocean dynamics.
\n", "```\n", "\n", "## Running a GCM\n", "\n", "- Model describing the General Circulation of the **atmosphere** and **ocean**. In a GCM latitude-longitude grid boxes cover the whole Earth over vertical levels in ocean and atmosphere.\n", "\n", "#### Spatial and temporal resolution\n", "- Typical resolutions are 100-400km horizontally with 20-40 vertical levels and time steps of around 30min.\n", "\n", "```{figure} figures/L7/L7_02_box.PNG\n", "---\n", "width: 30%\n", "---\n", "Figure 2: Cutout of a GCM grid.
\n", "```\n", "\n", "- Physical processes take place on different temporal and spatial scales. Difficulty lies in resolving them. If the model resolution is coarser than temporal or spatial scale of a process, this process cannot be resolved by the model!\n", "- Processes on all scales interact with each other\n", "\n", "```{figure} figures/L7/L7_03_oceanscale.png\n", "---\n", "width: 40%\n", "---\n", "Figure 3: Temporal and spatial scales of physical processes in the world ocean.
\n", "```\n", "\n", "```{figure} figures/L7/L7_04_atmoscale.PNG\n", "---\n", "width: 40%\n", "---\n", "Figure 4: Temporal and spatial scales of physical processes in the atmosphere.
\n", "```\n", "\n", "- Of course we want to make the grid cells as small as possible, but there is always the trade-off between resolution and computational effort. As a result ocean and atmosphere models have less degrees of freedom than the real ocean/atmosphere, because it is impossible to include processes of all length scales so the focus is put on the longest scales (which carry most energy annd momentum).\n", "\n", "```{figure} figures/L7/L7_05_resolution.png\n", "---\n", "width: 40%\n", "---\n", "Figure 5: Depiction of the European relief with two different resolution, illustrating the significance of high resolution.
\n", "```\n", "\n", "#### General procedure\n", "- Now we have chosen appropriate grid spacing and time evolution discretization. So let's go, we can run the model as follows:\n", " 1. Start from a given state of the climate system: Initialize each box for each state variable (temperature, pressure and many more)\n", " 2. Calculate time tendencies of the state variables based on their current configuration (simply put: the temperature of this box will increase because all of the surrounding boxes are much warmer -> heat flux through the boundaries of the box)\n", " 3. Add the calculated tendencies to the state of the system (these are the new temperature, pressure, etc. of this box)\n", " 4. Derive new tendencies, add to the state etc.\n", "- So far so easy. But their are two important remaining questions to be answered:\n", " - Which initial state should be chosen? The initial state has a crucial impact for the entire integration. Remember deterministic chaos.\n", " - How do we actually compute the tendencies in 2.? This is where the physics happens.\n", "\n", "#### Ensemble runs\n", "- A common method to acheive results that are least influenced by the inner variability of the system are ensemble runs. If a model is run from slightly differing initial states the outcome can be totally different due to the internal variability of the system. This variability is an important feature of the climate system, not only in models but in the real world. In order to obtain the tendencies of the model an ensemble of runs with slightly different initial conditions are performed and averaged. \n", "\n", "```{figure} figures/L7/L7_06_ensemble.png\n", "---\n", "width: 40%\n", "---\n", "Figure 6: Principle of initial condition ensemble simulations. By choosing slightly different sets of initial conditions, equally likely realizations of a climate variable (such as temprature) are created.
\n", "```\n", "\n", "- The problem of the initialization of the model is solved. Now let's dive into the time propagation.\n", "\n", "\n", "#### Time propagation\n", "- Large-scale circulation models for ocean and atmosphere solve the dicretized ($\\frac{dT}{dt} \\rightarrow \\frac{\\Delta T}{\\Delta t}$) *primitive equations* for each time step: a system of non-linear partial differential equations for salinity, potential temperature and velocity plus an equation of state. They are derived from conservation principles for mass, salinty and momentum and the first and second law of thermodynamics.\n", "- For example a box has a given temperature. Now the temperature tendency for the box $\\Delta T$ (along with the tendencies of all other state variables for all boxes) is computed by solving the discretized primitive equations for a given time step. Adding the temperature tendency onto the previous temperature of the box yields the new temperature after the time step. This is done again and again until the time is propagated as wanted.\n", "\n", "\n", "Add explanation for following images 7-9:\n", "```{figure} figures/L7/L7_07_flame.png\n", "---\n", "width: 30%\n", "---\n", "Figure 7: FLAME-model: velocity at 100m depth.
\n", "```\n", "```{figure} figures/L7/L7_08_tracer.png\n", "---\n", "width: 30%\n", "---\n", "Figure 8: Tracer injected at 100m depth at the southern boundary.
\n", "```\n", "```{figure} figures/L7/L7_09_ACC.png\n", "---\n", "width: 40%\n", "---\n", "Figure 9: Typical snapshots of the surface velocities of the Antarctic Circumpolar Current. Left: Observation from space (Aviso, Math 3th 1995). Right: Simulated by the ocean model MOMSO, May 3th of nominal yer 2020.
\n", "```\n", "\n", "## General problems of climate models\n", "#### 1. Useful models must be simpler than the real atmosphere/ocean. \n", "- Time propagation is based on the primitive equations. These are derived from the Navier-Stokes equations using approximations which are carried into the model. That way the problem is simplified while retaining key physical phenomena:\n", " - Hydrostatic approximation: \n", " Eliminates vertical acceleration terms by assuming $\\frac{dp}{dz}=-\\rho g$\n", " - Traditional approximation: \n", " Neglecting coriolis terms in the horizontal momentum equations involving the vertical velocity and smaller metric terms.\n", " - Shallow-water approximation: \n", " Assuming that the depth of the ocean is small compared to the scale of characteristic processes.\n", " - Boussinesq approximation for the ocean: \n", " Eliminates sound waves while still accounting for buoyancy. It assumes that the ocean density is constant except in the buoyancy term, where small density differences play a significant role.\n", "- Another commonly applied method is the Reynolds averaging of the primitive equations:\n", " - Reynolds averaging: \n", " Separating the flow variables (i.e. $u,p,\\rho$) into mean values (i.e. $\\bar{u},\\bar{p},\\bar{\\rho}$ representing the large-scale flow and fluctuating values (i.e. $u',p',\\rho'$) representing the turbulence, and then time-averaging on a time scale large enough to filter out the turbulence but small enough to preserve the large-scale flow field.\n", "\n", "\n", "#### 2. Discrete equations are not the same as continous equations (calculation error). \n", "- The only way to solve the primitive equations (set of non-linear differential equations) is to discretize them and solve them numerically. The discretization happens on temporal and spatial scale: vertical columns of latitude-longitude boxes for which all variable values get updated each time step $\\Delta t$. The discretizations are derived from the Taylor-series expansions. Let's look at the pressure as a fuction of time $p(t)$ as an example. Taylor expansion around $p(t)$. A forward time step is given as:\n", "```{math}\n", ":label: efwd\n", "p(t+\\Delta t) &= p(t) + \\Delta t \\frac{\\partial p(t)}{\\partial t} + \\frac{1}{2} \\Delta t^2 \\frac{\\partial^2 p(t)}{\\partial t^2} + ...\\\\\n", "```\n", "- and a backward time can be described by:\n", "```{math}\n", ":label: ebwd\n", "p(t-\\Delta t) &= p(t) - \\Delta t \\frac{\\partial p(t)}{\\partial t} + \\frac{1}{2} \\Delta t^2 \\frac{\\partial^2 p(t)}{\\partial t^2} - ...\\\\\n", "```\n", "\n", "\n", "- The two expansions [](#efwd) and [](#ebwd) can be processed differently to different gain schemes approximating $\\frac{\\partial p(t)}{\\partial t}$. Rewriting the expansion [](#efwd) up to the first-order term $+\\Delta t \\frac{\\partial p(t)}{\\partial t}$ yields:\n", "```{math}\n", "\\frac{\\partial p}{\\partial t} = \\frac{p(t+\\Delta t) - p(t)}{\\Delta t}+\\mathcal{O}(\\Delta t^2)~~(\\mathrm{forward~difference~scheme})\n", "```\n", "- Rewriting the expansion [](#ebwd) up to the first-order term $-\\Delta t \\frac{\\partial p(t)}{\\partial t}$ yields:\n", "```{math}\n", "\\frac{\\partial p}{\\partial t} = \\frac{p(t) - p(t-\\Delta t)}{\\Delta t}+\\mathcal{O}(\\Delta t^2)~~(\\mathrm{backward~difference~scheme})\n", "```\n", "- Substracting the two expansions results in:\n", "```{math}\n", "\\frac{\\partial p}{\\partial t} = \\frac{p(t+\\Delta t) - p(t-\\Delta t)}{2\\Delta t}+\\mathcal{O}(\\Delta t^2)~~(\\mathrm{central~difference~scheme})\n", "```\n", "- There are other methods to describe the first derivative with higher-order accuracy.\n", "- Derivatives with repsect to other variables are discretized in the same way. For higher-order derivatives schemes with different accuracies (leading order error term) can be deployed. The simplest example can be be deduced adding our two Taylor-expansions [](#efwd) and [](#ebwd). The result is called the three-point-stencil, because the value of the second derivative is given by the values of three points:\n", "```{math}\n", "\\frac{\\partial^2 p(t)}{\\partial t^2} = \\frac{p(t+\\Delta t)-2p(t) + p(t-\\Delta t)}{\\Delta t^2}\n", "```\n", "\n", "- There are many more funky tools to navigate the numerical solution of differential equations. The lecture [Computational Quantum and Many-Particle Physics](https://pruefung.uni-rostock.de/qisserver/rds?state=verpublish&publishContainer=modulDetail&_form=publish&modulversion.versionsid=7225&menuid=&topitem=locallinks&subitem=) facilitates a deeper dive into the topic.\n", "\n", "- Inevitably the discretization introduces several errors to the numerical output of the model:\n", " - Truncation error: The Taylor-expansions which build the foundation of the schemes have to be truncated at some point. Above we did it after the first-order and neglected all higher-order terms. This truncation inevitable leads to an error in the model computations.\n", " - Stability: Some numerical methods can cause instability when solving certain types of differential equations. This instability can cause solutions to diverge or to behave erraticly which leads to inaccurate results.\n", " - Numerical diffusion: Espacially for systems with sharp gradients some numerical methods can cause artificial diffusion, affecting the dynamics of the system and thus leading to inaccuracies.\n", " - Numerical dispersion: Solving wave propagation problems, discretization can introduce additional errors related to the dispersion characteristics of the numerical method. This can lead to deformations of the waveforms.\n", "\n", "\n", "- As an example we will look at three different advection schemes modeling the following problem:\n", "```{math}\n", "\\frac{\\partial T}{\\partial t} + u \\frac{\\partial T}{\\partial x} + v\\frac{\\partial T}{\\partial y}= 0\n", "```\n", "$T$: Tracer, $x,y$: Spatial variables, $t$: Time, $u,v$: Horizontal velocities.\n", "\n", "```{figure} figures/L7/L7_10_initial.png\n", "---\n", "width: 45%\n", "---\n", "Figure 10: Left: The initial state of the tracer is a cylinder streched in z-direction. Right: The tracer experiences a fixed rotation along the xy-plane.
\n", "```\n", "- The initial state of the problem is shown in Fig. 10: a cylindrical tracer distribution in a cylindrical velocity field. Now we propagate time until the fixed rotation has absolved one full rotation. Fig. 11 shows the resulting tracer states using different numerical propagation methods. Note how much the results differ only based on the applied scheme.\n", "```{figure} figures/L7/L7_11_rotation.png\n", "---\n", "width: 60%\n", "---\n", "Figure 11: States of the traces after one rotation for different numerical propagation schemes.
\n", "```\n", "- Take home message: Discretization schemes have to be used to solve (sets of) differential equations numerically. However different schemes can yield totally different results for the same problem. Consequently the choice of the most appropriate method is crucial.\n", "\n", "\n", "#### 3. Parametrisation of processes on a sub-grid scale is needed as the minimal space scale is finite.\n", "\n", "- Different ocean models work with different grids. Two examples are shown in Fig. 12. On the left you see can a tripolar grid, as used by all ORCA model configurations (Ocean model of the GEOMAR Helmholtz Centre for Oceanic Research in Kiel). North of the green line the model grid differs from a regular greographic grid with a single north pole (*Courtesy: GEOMAR Helmholtz Centre Kiel*). On the right the standard MPI-OM orthogonal curvilinear grid is shown.\n", "\n", "```{figure} figures/L7/L7_12_grids.png\n", "---\n", "width: 60%\n", "---\n", "Figure 12: Grids of the ORCA (left) and MPI-OM (right, every 5th line is shown).
\n", "```\n", "\n", "- Once again, the resolution determines the scale down to which the physical processes happening in the ocean can be included in the calculations.\n", "\n", "```{figure} figures/L7/L7_13_oceanscale.png\n", "---\n", "width: 40%\n", "---\n", "Figure 13: Temporal and spatial scales of physical processes in the world ocean.
\n", "```\n", "\n", "- The Rossby radius of deformation is a parameter used to describe the characteristic length scale over which the effects of rotation dominate the atmospheric motion, over other forces, such as pressure gradients. It is defined as:\n", "```{math}\n", "R_D = \\frac{\\sqrt{gh_e}}{f},\n", "```\n", "- $R_D$ explains which resolutions are able to resolve eddies. The Rossby radius has to be larger than lines of grid resolution; eddie resolution is important.\n", "- with $g$: gravitation, $h_e$: equivalent depth, $f$: Coriolis parameter\n", "\n", "```{figure} figures/L7/L7_14_rossbyradius.PNG\n", "---\n", "width: 30%\n", "---\n", "Figure 14: The zonally averaged first baroclinic Rossby radius in comparison with grid spacing of 0.1° and 0.28° respectively.
\n", "```\n", "\n", "- Let's take a look at how the Gulf Stream is resolved by a state of the art ocean model with different resolutions:\n", "\n", "1. Gulf Stream SST\n", "\n", "```{figure} figures/L7/L7_15_satellite.png\n", "---\n", "width: 30%\n", "---\n", "Figure 15: Sea surface temperature (SST) satellite observations of the Atlantic Ocean off the North American coast featuring the Gulf Stream.
\n", "```\n", "\n", "- We see that the Gulf Stream has a lot of turbulence and eddies of different sizes. The following three figures 16-18 show the SST of the same area computed by the OCCAM ocean model.\n", "```{figure} figures/L7/L7_16_res1.png\n", "---\n", "width: 30%\n", "---\n", "Figure 16: Gulf Stream SST computed by OCCAM with a resolution of 1°.
\n", "```\n", "```{figure} figures/L7/L7_17_res2.png\n", "---\n", "width: 30%\n", "---\n", "Figure 17: Gulf Stream SST computed by OCCAM with a resolution of 1/4°.
\n", "```\n", "```{figure} figures/L7/L7_18_res3.png\n", "---\n", "width: 30%\n", "---\n", "Figure 18: Gulf Stream SST computed by OCCAM with a resolution of 1/12°.
\n", "```\n", "\n", "- Another plot with all four graphics in one for a better comparison in Fig. 19. One can see the difference between the 1° and the higher resolutions, which are so called \"eddie-permitting\".\n", "```{figure} figures/L7/L7_19_SST.png\n", "---\n", "width: 60%\n", "---\n", "Figure 19: Gulf Stream SST computed by OCCAM with different resolutions compared to satellite observations.
\n", "```\n", "\n", "2.Sea level variability\n", "- calculated as $\\sqrt{\\bar{h'^2}}$\n", "```{figure} figures/L7/L7_20_sealevel.png\n", "---\n", "width: 60%\n", "---\n", "Figure 20: Sea level variability of the North Atlantic calculated by the POP-model compared with satellite observations.
\n", "```\n", "\n", "3. Velocity at 100m depth\n", "- Fig. 21 shows the velocity at 100m depth in the ocean computed by the FLAME model with two different resolutions. Even though the resolution of 1/3° is already eddie-permitting there is a big difference to the resolution computed with a 1/12° resolution. It can be seen that the Atlantic Ocean actually consists of eddies and meanders.\n", "```{figure} figures/L7/L7_21_flame.png\n", "---\n", "width: 60%\n", "---\n", "Figure 21: North Atlantic velocity at 100m depth, via FLAME model.
\n", "```\n", "\n", "- For now we focused on the horizontal component of the coordinate system. But the vertical component is just as important! There are different solutions to the division of the vertical dimension, let's look at three of them shown in Fig. 22.\n", "```{figure} figures/L7/L7_22_verticalcoords.png\n", "---\n", "width: 40%\n", "---\n", "Figure 22: Schematic of three vertical coordinate systems.
\n", "```\n", "\n", "- Dense gravitational driven bottom flows pose a problem in the ocean modelling that the three prior coordinate systems solve differently well.\n", "```{figure} figures/L7/L7_23_bottomflows.png\n", "---\n", "width: 40%\n", "---\n", "Figure 23: Schematic of the treatment of bottom flows with level coordinates.
\n", "```\n", "\n", "## Evaluation of climate models\n", "\n", "- There is a permanent thrive to improve the accuracy of climate models. They started of incorporating the atmosphere, land surface, ocean and sea ice. Over time the description of these components has improved drastically. Furthermore different components of the climate system have been added to the computations. Fig. 24 shows which climate component the computations of the *IPCC* Assesment Reports employ.\n", "\n", "```{figure} figures/L7/L7_24_IPCC_models.png\n", "---\n", "width: 40%\n", "---\n", "Figure 24: The development of climate models used in IPCC Assessment Reports comprehending more and more components of the climate system.
\n", "```\n", "\n", "- Today's GCMs reproduce large parts of the observed climate, both in terms of long term averages, variability and extreme conditions. Anyhow they certainly are far from perfect. Some weaknesses are that:\n", " - GCMs only represent large scale (>100km) phenomena explicitly,\n", " - not all GCMs include all relevant processes (e.g. carbon cycle feedback),\n", " - we do not fully understand how relevant processes can be described in the models\n", "- Fig. 25 compares model results with measurements. It can be seen that the model resolves the general global patterns quite well. The problem lies in exact localisation of the patterns, a small shift in latitude between computations and measurements results in a high difference between them (see bottom plot).\n", "Better figure?\n", "\n", "```{figure} figures/L7/L7_25_comp.png\n", "---\n", "width: 30%\n", "---\n", "Figure 25: Comparison of modeled annual mean precipitation with actualy measurements.
\n", "```\n", "\n", "## Sources of uncertainy in climate change projections\n", "#### Overview\n", "1. Emission scenario uncertainty:\n", " - Future behaviour of mankind is unknown\n", "2. Modelling uncertainty:\n", " - Climate response to changes in atmospheric composition (GCM)\n", " - Modelling of ocean circulation, biogeochemistry, etc. (RCSM)\n", "3. Uncertainty due to natural climate variability:\n", " - Solar activity, volcanic eruptions (external forcing)\n", " - Internal (=unforced) variability generated by the non-linear dynamics of the climate system\n", "\n", "- The sources of uncertainty in model computations vary with time. Only for the first one or two decades of lead time the internal variability has a significant impact on the result. Model uncertainty (the difference between models) is largest at high latitudes and the emission scenario uncertainty grows with lead time particularly in lower latitudes. Hawkins and Sutton (2009) found that even at the end of the century the model uncertainty dominates at higher latitudes, while the emission scenario attributes for most of the explained variance at lower latitudes.\n", "```{figure} figures/L7/L7_26_uncertainty.png\n", "---\n", "width: 50%\n", "---\n", "Figure 26: Development of sources of uncertainty over model run time. The map plots show the total variance explained.
\n", "```\n", "\n", "#### Emission scenario uncertainty\n", "- Emission of greenhouse gases is the key component in human made climate change. In order to quantify the future emissions the *IPCC* has developed Representative Concentration Pathways (RCPs) representing different future emission scenarios and the caused increase in radiative forcing (the number of the RCP scenario describes the increase in radiative forcing in W/m$^2$). Fig. 27 shows atmospheric CO$_2$, surface temperature change and global mean sea level rise related to different RCPs by the *IPCC*.\n", "\n", "```{figure} figures/L7/L7_27_rcp.png\n", "---\n", "width: 30%\n", "---\n", "Figure 27: Future climate projections simulated by the ESMs of the IPCC based on atmospheric carbon dioxide scenarios (a). Surface temperature change (b) and global mean sea level rise (c) were computed following the four RCPs up to 2300 pursued by constant forcing. The bars in (c) repesent the outcome range of the few available model runs, not uncertainty ranges. The impact of Antarctic ice sheet melting is likely underestimated. Courtesy: IPCC AR5, Fig 2.8
\n", "```\n", "\n", "\n", "#### Modelling uncertainty\n", "- Different models will compute significantly different results under the same initial conditions or ensemble runs. Fig. 28 shows different GCM projections for change trends in precipitation and temperature for Northern Sweden.\n", "```{figure} figures/L7/L7_28_model_uncertainty.PNG\n", "---\n", "width: 50%\n", "---\n", "Figure 28: Modelled temperature and precipitation changes in Northern Sweden under the same initial conditions.
\n", "```\n", "\n", "\n", "#### Uncertainty due to natural climate variability\n", "Example I\n", "- Natural variability has a different impact on the model outpt for different variables. Fig. 29 how it affects the mean sea level spatial patterns stronger than it does for the 2m temperature.\n", "```{figure} figures/L7/L7_29_natvar.png\n", "---\n", "width: 40%\n", "---\n", "Figure 29: Runs of the ECHAM5 with different initial conditions computing the 2m temperature (top row) and mean sea level pressure (bottom row) trend (difference between 2011-2040 and 1961-1990 mean values).
\n", "```\n", "\n", "Example II\n", "- The impact of natural climate variability on model results can also be seen comparing diifferent model results. Let's look at one example. Different models computed the average winter 2m temperature over land and 10m wind over water for the Southern Baltic Sea region, shown in Fig. 30. Fig. 31-33 display the results using 30 year moving averages.\n", "```{figure} figures/L7/L7_30_map.png\n", "---\n", "width: 40%\n", "---\n", "Figure 30: Map of Northern Europe. The areas used for the 2m temperature (left) and 10m wind (right) model runs are marked red.
\n", "```\n", "\n", "- All models project a gradual long term winter temperature increase, see Fig. 31. Different interpretations of the initial state cause the scalar offset between different models. This effect can be filtered out by computing the anomalies with respect to the 1961-1990 mean temperature, shown in Fig. 32. All models show a similar tendency to higher temperature with a difference among the runs of about 2K while the decadal and multi-decadal variability is fairly small.\n", "```{figure} figures/L7/L7_31_2mt.png\n", "---\n", "width: 40%\n", "---\n", "Figure 31: Winter 2m temperature trends of the land around the Southern Baltic Sea (see Fig. 30, left) calculated by several climate models (30y moving average is shown).
\n", "```\n", "```{figure} figures/L7/L7_32_2mt_anomaly.png\n", "---\n", "width: 40%\n", "---\n", "Figure 32: Winter 2m temperature trend anomalies with respect to the 1961-1990 mean of the land around the Southern Baltic Sea (see Fig. 30, left) calculated by several climate models (30y moving average is shown).
\n", "```\n", "\n", "- The winter wind projections (see Fig. 33) look totally different than the temperature projections. The ensemble mean shows a strengthening of wind over time but is strongly influenced by one model result (the RCA3(BCM)). Altogether the wind trend is highly uncertain which is caused by and showcasing the strong influence of the internal variability of the system, or in other words the natural climate variability.\n", "```{figure} figures/L7/L7_33_10mwind_anomaly.png\n", "---\n", "width: 40%\n", "---\n", "Figure 33: Winter 10m wind trend anomalies with respect to the 1961-1990 mean over the Southern Baltic Sea (see Fig. 30, right) calculated by several climate models (30y moving average is shown).
\n", "```\n", "\n", "Example III\n", "- Another important, characteristic climate variable is given in precipitation. The certainty of precipitation projections varies globally. While most models agree on a positive precipitation trend close the the poles, temperature trends for lower latitudes remain fairly uncertain, as shown in Fig. 34. The precipitation trend for the Baltic Sea region is questionable for summer months (JJA), whereas most models agree on an increase in precipitation during winter months (DJF).\n", "```{figure} figures/L7/L7_34_prec.png\n", "---\n", "width: 50%\n", "---\n", "Figure 34: Relative changes in precipitation for the period 2090-2099, relative to 1980-1999. Values are multi-model averages based on the SRES A1B scenario for December to February (left) and June to August (right). White areas indicate that less than 66% of the models agree on the sign of the change and stippled areas mark where more than 90% of the models are in agreement on the sign of the change. Note the changes for the Baltic Sea region marked by the black box.
\n", "```" ] }, { "attachments": {}, "cell_type": "markdown", "id": "877dd63f-1889-48f7-a9a7-4423b87438da", "metadata": {}, "source": [ "## Table of Figures\n", "Figure 1: AIR Worldwide. https://www.air-worldwide.com/publications/air-currents/2020/anatomy-of-a-climate-model/, access on 28.03.2024 \n", "Figure 2: Nichols, C. & Raghukumar, K.. Marine Environmental Characterization. Synthesis Lectures on Ocean Systems Engineering. 1. 1-103. https://doi.org/10.2200/S01006ED1V01Y202004OSE002 \n", "Figure 3: Steve Easterbrook. https://www.pinterest.de/pin/spatial-and-temporal-scales--540713498981088529/, access on 28.03.2024 \n", "Figure 4: Fig. 12.3 in Sommer, J., Chassignet, E. & Wallcraft, A. (2018). Ocean circulation modeling for operational oceanography:current status and future challenges. \n", "Figure 5: Figure 1-14 in IPCC AR5, https://www.ipcc.ch/report/ar5/wg1/introduction/gmt-v4-3-1-document-from-psxyz/ \n", "Figure 6: AIR Worldwide. https://www.air-worldwide.com/publications/air-currents/2020/anatomy-of-a-climate-model/, access on 28.03.2024 \n", "Figure 7 and 8: Source: J. Dengg as of PP. Any more info? Could find't the figures on google \n", "Figure 9: Figure 5 in Dietze, H., Löptien, U. & Getzlaff, J.: MOMSO 1.0 – an eddying Southern Ocean model configuration with fairly equilibrated natural carbon, Geosci. Model Dev., 13, 71–97, https://doi.org/10.5194/gmd-13-71-2020, 2020. \n", "Figure 10 left: Figure 2.1 top left in Master thesis of Strömgren, T. Implementation of a Flux Corrected Transport scheme in the Rossby Centre Ocean model. Swedish Meteorological and Hydrological Institute (2005). \n", "Figure 10 right: Figure 2.1 top right in Master thesis of Strömgren, T. Implementation of a Flux Corrected Transport scheme in the Rossby Centre Ocean model. Swedish Meteorological and Hydrological Institute (2005). \n", "Figure 11 left: Figure 2.1 bottom right in Master thesis of Strömgren, T. Implementation of a Flux Corrected Transport scheme in the Rossby Centre Ocean model. Swedish Meteorological and Hydrological Institute (2005). \n", "Figure 11 middle: Figure 2.1 bottom left in Master thesis of Strömgren, T. Implementation of a Flux Corrected Transport scheme in the Rossby Centre Ocean model. Swedish Meteorological and Hydrological Institute (2005). \n", "Figure 11 right: Figure 3.5 bottom right in Master thesis of Strömgren, T. Implementation of a Flux Corrected Transport scheme in the Rossby Centre Ocean model. Swedish Meteorological and Hydrological Institute (2005). \n", "Figure 12 left: GEOMAR Helmholtz Centre for Ocean Research Kiel, https://www.geomar.de/fb1-od/ozean-modelle-hpc, access on 02.04.2024 \n", "Figure 12 right: Fig. 1 in Jungclaus, J. & Bonzet, M & Haak, Helmuth & Keenlyside, Noel & Luo, Jing-Jia & Latif, M. & Marotzke, J. & Mikolajewicz, U. & Reockner, E. (2006). Ocean circulation and tropical variability in the coupled model ECHAM5/MPI-OM. J. Climate. https://doi.org/10.1175/JCLI3827.1. \n", "Figure 13: Steve Easterbrook. https://www.pinterest.de/pin/spatial-and-temporal-scales--540713498981088529/, access on 28.03.2024 \n", "Figure 14: Fig. 1 in Smith, R. D., M. E. Maltrud, F. O. Bryan, and M. W. Hecht, 2000: Numerical Simulation of the North Atlantic Ocean at 1/10°. J. Phys. Oceanogr., 30, 1532–1561, https://doi.org/10.1175/1520-0485(2000)030<1532:NSOTNA>2.0.CO;2. \n", "Figure 15-18: A. Coward as of PP. Any more info? Could find't the figures on google \n", "Figure 20: left: Fig. 17(B) in Smith, R. D., M. E. Maltrud, F. O. Bryan, and M. W. Hecht, 2000: Numerical Simulation of the North Atlantic Ocean at 1/10°. J. Phys. Oceanogr., 30, 1532–1561, https://doi.org/10.1175/1520-0485(2000)030<1532:NSOTNA>2.0.CO;2. \n", "Figure 20: right: Fig. 17(C) in Smith, R. D., M. E. Maltrud, F. O. Bryan, and M. W. Hecht, 2000: Numerical Simulation of the North Atlantic Ocean at 1/10°. J. Phys. Oceanogr., 30, 1532–1561, https://doi.org/10.1175/1520-0485(2000)030<1532:NSOTNA>2.0.CO;2. \n", "Figure 21: J. Dengg as of PP. Any more info? Could find't the figures on google \n", "Figure 22: http://www.ifm.uni-kiel.de/fb/fb1/tm/research/dynamo/dyn_m.html as of PP. Any more info? Link is no longer valid \n", "Figure 24: Figure 2 in Ambrizzi, Tércio & Reboita, Michelle & Rocha, Rosmeri & Llopart, Marta. (2018). The state-of-the-art and fundamental aspects of regional climate modeling in South America. Annals of the New York Academy of Sciences. 1436. https://doi.org/10.1111/nyas.13932. \n", "Figure 26: Figure 6 in Hawkins, E., and R. Sutton, 2009: The Potential to Narrow Uncertainty in Regional Climate Predictions. Bull. Amer. Meteor. Soc., 90, 1095–1108, https://doi.org/10.1175/2009BAMS2607.1. \n", "Figure 27: Figure 2.8 in IPCC, 2014: Climate Change 2014: Synthesis Report. Contribution of Working Groups I, II and III to the Fifth Assessment Report of the Intergovernmental Panel of Climate Change [Core Writing Team, R.K. Pachauri and L.A. Meyer (eds.)]. IPCC, Geneva, Switzerland, 151pp. in IPCC AR5 Synthesis Report \n", "Figure 30 - Figure 33: Courtesy of G. Nikolin, SMHI \n", "Figure 34: Figure 3.3 in IPCC, 2007: Climate Change 2007: Synthesis Report. Contribution of Working Groups I, II and III to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change [Core Writing Team, Pachauri, R.K and Reisinger, A. (eds.)]. IPCC, Geneva, Switzerland, 104 pp." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.6" } }, "nbformat": 4, "nbformat_minor": 5 }