## How are numerical models used to produce decadal climate predictions? From theory to a climate simulation

A numerical earth system model can be used to describe the coupled state of the atmosphere, ocean and land surface. In order to use this model to produce a climate simulation one additionally needs boundary and initial conditions of, if possible, all components of the climate system, as well as a high-performance computer, to calculate the compute-intensive ensemble of climate simulations.

An earth system model is a numerical model that describes the state of the atmosphere, the ocean and the land surface on the global scale. The model is divided into (thousands of) grid boxes, for each of which the state is calculated. With the help of mathematical equations and the knowledge of physical laws one can for instance calculate the time evolution of the surface temperature. To obtain a realistic time evolution of the surface temperature (whether in the past or for the future) the model needs to be initialised (started) and forced with real data.

The size of the gridboxes decides the so-called spatial resolution of the model. MiKlip uses the MPI-ESM earth system model, which, in the lowest spatial resolution used for the decadal prediction system, outputs results for the atmosphere on a 200 km x 200 km in the horizontal. In a second step, regional climate models, such as the COSMO-CCLM, can use the results of the global model to deliver similar results for a specific region, e.g., Europe, on a grid with a much higher spatial resolution (approximately 50km x 50km). Schematic of the grid of an Earth System Model

The model describes the state of the atmosphere, the ocean and the land surface. To calculate the state of the internal climate system the model continuously needs external information, such as solar radiation or the concentration of greenhouse gases or volcanic aerosols in the atmosphere. This information is called boundary conditions. The boundary conditions influence the development of the state of the climate system. A famous example is the influence of greenhouse gas concentrations on the evolution of the global surface temperature.

If one needs boundary conditions for simulations of the past (hindcasts), then these can be constructed from observational data. For simulations into the future, such as climate predictions or climate projections, projected boundary conditions are used: These so-called RCPs (Representative Concentration Pathways) describe possible scenarios for the future evolution, e.g., for the concentration of greenhouse gases, and are developed by expert groups, by using among other things projected economic and demographic developments. The different scenarios for the projected boundary conditions are in the first decade very close to each either, after that they quickly follow different trajectories. The difference between these boundary conditions thus play a minor role for decadal climate predictions, for long-term projections they are however decisive. The boundary conditions used for the MiKlip system follow the protocol of the international “Coupled model intercomparison project” (CMIP).

For the model to calculate the state of the earth system for future time periods in the most accurate way possible, the model must start from the most precise initial state possible. Ideally, this would mean that at the start of a simulation the model should have an observed value for all its gridboxes and all its variables. Unfortunately, observations do not exist for each point in time and all gridboxes, so that initial conditions usually consist of mixed forms of mean observational values and coupled model simulations (so-called reanalyses or state estimates).

Certain components or dynamical processes of the climate system change only slowly: when for instance a large change has developed in the ocean, then this change does not only have an influence on the atmosphere for a couple of days, but possibly over several years. Scientist have found out that one can use this multi-year “memory” of the climate system for better predictions, by at the start of the prediction simulation providing the model with the current state of certain variables of the earth system, like for instance the temperature and the salt content in the ocean, in the form of initial conditions. Correct initial conditions are essential for decadal climate predictions, for long-term projections, they only play a minor role.

It would be possible to use the earth system model to only calculate one simulation for the predictions. We do however know, that neither boundary or initial conditions nor the earth system model itself are free of error, and thus we need to consider several possible development trajectories for the future. To estimate the range of possible climatic evolutions, several (10-30) model simulations are conducted. These so-called ensemble simulations can be generated by several methods. To cover the uncertainty of the initial conditions (e.g., from measurement errors), the initial conditions are slightly varied for the decadal climate predictions, resulting in the slightly different ensemble simulations.

Systematic errors that arise from e.g., the incomplete knowledge of the theoretical background, the numerical approach used for the earth system model or minimal calculation error by the computer, can be discovered, discussed and improved by engaging in the scientific exchange with other institutions that develop climate predictions. There is also the approach to combine the results of different earth system or climate models into multi-model ensembles, to estimate the uncertainty that arises due to using different climate models. The circle in the upper right illustrates an ensemble of simulations. Each simulation, a so-called ensemble member, starts at the same time but with slightly different initial conditions. Each ensemble member then follows its own trajectory (brown). The ensemble mean (yellow) is calculated as the mean over all these ensemble members. The main plot is explained further down.

The climate predictions are calculated for 10 years into the future. To calculate a prediction from for 2017 to 2025, the first step is to obtain the initial conditions for this prediction. To produce a prediction for ten full calendar years, the simulations of the ensemble are started in November in the year before the first prediction year. The initial state needed is thus the last observed state of October in the year before the first predicted year. The ensemble that is used for the 2017-2026 prediction is thus calculated from 1 November 2016 til 31 December 2026. These predictions are at this stage only a production of model data and without further rigorous analysis these do not deliver reliable information.

Multi-year simulations with an earth system model need a lot of computing power and computing time and are thus calculated on a high-performance computer. The high-performance computer at the German Climate Computing Centre (DKRZ) has a computing power of approximately 100.000 normal laptops.

On a high-performance computer one can, depending on the resolution, calculate a 10-year global climate prediction with 10 ensemble members, i.e., 100 simulated years, in about 1-2 days. For the evaluation of the climate prediction one does however need many further simulations (hindcasts), so that for a complete climate prediction system one needs several thousand simulated years. For these simulations a high-performance computer needs some 100 days.

The topic of decadal climate predictions is currently a world-wide research topic. Apart from the German MiKlip project there are also several other projects that develop decadal climate prediction system along the same principles. The evaluation of these climate prediction systems need many simulations of the past (Hindcasts), so that the development of such systems can only be done where there are enough high-performance computing capacities.

There are also research projects, which compare the decadal climate predictions from different earth system models, such as the Decadal Prediction Exchange Project und  CMIP6.