A statistical model called the sea level simulator v1.0 is introduced. The model integrates mean sea level change and sea level extremes into a joint probabilistic framework that is useful for coastal spatial planning. Given a user-defined planning period, the model can estimate the flood risk as a function of height above the current mean sea level. These flood risk estimates are derived through Monte Carlo simulations of a very large number of planning periods. The derived flood risk is contingent on user-assigned probabilities for future greenhouse gas emission pathways, and the model is thus also useful for quantifying the dependence of flood risk on such pathways and their probabilities. Moreover, the simulator can quantify whether flood risk is dominated by sea level extremes or mean sea level rise and how this depends on the length of the planning period. The code, written in MATLAB, is parallelized and lightweight enough that it can be run on an ordinary PC. The code is easily adaptable to include new locations, new mean sea level projections and similar model developments. The flood risk estimates derived from the simulator are well suited to tackle adaptation and decision problems. Applications for construction of coastal protection and land development in coastal areas have been demonstrated in the past. The paper gives an in-depth technical description of the model. Example simulations from a Swedish nuclear site are also given, and the capabilities of the simulator are discussed. The main aim of the paper is to work as a technical reference for the first public release of the sea level simulator.

Mean sea level change alters the probability of coastal flooding in communities around the world. The globally averaged mean sea level rose by about 20 cm during the period 1901–2018. However, much larger changes are projected for the current century in all future emission scenarios investigated in the Intergovernmental Panel on Climate Change Sixth Assessment Report (IPCC, AR6)

The sea level simulator framework introduced by

The simulator uses two separate data sources in its calculations: mean sea level projections

The first study that utilized the simulator

implementation of parallel computing

implementation of new mean sea level scenarios

better uncertainty quantifications for sea level extremes

more realistic time dependence in the mean sea level projections.

The sea level simulator v1.0 is written in MATLAB. The program consists of one main script and some support scripts used to set up the model. It uses the statistics and parallel computing toolbox from MathWorks, as well as some routines from the free MATLAB toolbox Cupid (

The program simulates a large number of planning periods by randomly drawing time-dependent mean sea level changes and yearly sea level maxima. The standard setting is

Schematic view of the sea level simulator with insets showing some of the data the simulator depends on. Panel

A schematic of the simulator is shown in Fig.

The uncertainty in the GEV parameters is modeled in the same way as maximum-likelihood-based confidence intervals on return levels are estimated with MATLAB

Certain users might prefer to use peak over threshold rather than block maxima statistics and consequently to model extremes with a generalized Pareto (GP) instead of a GEV distribution. In v1.0 of the sea level simulator, there is no such option available. The main reason for this is that the GP approach requires more user-defined parameters, such as a threshold and a separation timescale between events that should be long enough that the events can be considered independent. Good guidance on how to choose these parameters is hard to give. The GEV approach has a similar parameter to the GP separation timescale, namely, the block length. However, using a block length of 1 year is more or less standard practice

A further issue worthy of note regarding the extreme sea level distributions used by the simulator are that these are unaffected by climate change and time. That is, the GEV distributions used are independent of both time and Shared Socioeconomic Pathway (SSP). This is simply because of lack of knowledge about how the GEV parameters might change through time under given SSPs. However, if such knowledge was available, it would be easy to include climate-change-induced trends in annual sea level maximum as a perturbation to the mean sea level projections. This can be done without any code changes to the simulator. How the mean sea level projections are made is discussed further down in this section.

In the next module a SSP is chosen randomly. Five different SSP–radiative-forcing combos are available from

This random number maps to a mean sea level projection through the user-defined probability range for the projections. Note that neither the sea level projections nor the SSPs have been attributed probabilities by their makers. However, for the SSPs, at least, some estimates of suitable probabilities have been derived using integrated assessment models (see, for example,

Probabilities given to the different mean sea level projections and the probability range in which the different projection are applied.

The distributions of mean sea level projections are available every 10 years

The IPCC mean sea level distributions are discreet. For use with the simulator, they are therefore approximated by continuous skew-normal distributions. The three parameters defining the skew-normal distributions are chosen so that the sum of the squared differences between the continuous skew-normal distribution and the discreet IPCC distribution is minimized at the 5th, 17th, 50th, 83rd and 95th percentiles. These differences are very small, typically within a centimeter, for all mean sea level distributions except those for SSP5-8.5

The sixth module in the diagram adds the mean sea level projection for the planning period to the annual sea level maxima modeled for the period. The resulting time series contains the planning periods annual maxima referenced to the current mean sea level. It is from this time series that the planning period sea level maximum and its mean sea level and extreme sea level components are extracted. These variables are saved in the form of discreet probability density functions (PDFs). The grid resolution of these PDFs is set by the parameter

As was mentioned in the Introduction, multiple planning periods are simulated in parallel. The scaling of runtime vs. number of cores, shown in Fig.

Runtime plotted against number of cores for the sea level simulator v1.0. In the experiment shown,

In the examples that follow, the sea level simulator has been set up to model annual maximum water levels at the Swedish Ringhals nuclear power station. Ringhals is situated in Varberg municipality on the Swedish west coast. The sea outside Ringhals is called the Kattegat. It is a shallow sea situated between the Baltic Sea and Skagerak to the south and north and Sweden and Denmark to the east and west. The Kattegat has weak tides and strong stratification. The strong stratification is a consequence of less saline Baltic Sea water meeting more saline North Sea water, yielding a hydrography well described by a two-layer system

Planing period probability of sea level maximum for three different lengths of the planning period. Panel

Figure

Same as Fig.

Figure

Same as Fig.

The influence of the GEV parameter uncertainty on the joint sea level maximum is sizeable in short planning periods but relatively insignificant in long ones. Figure

The average outcome of the stochastic processes depicted in Fig.

The simulator can also be used to infer how the outcome of the different stochastic processes depicted in Fig.

Same as Fig.

Figure

The sea level simulator can also output directly the respective contributions from sea level extremes and mean sea level rise to joint sea level events. Such a diagnostic is shown in Fig.

Mean sea level and extreme sea level contributions to joint sea level maximum. Upper panels

Same as Fig.

The modeling framework incorporated into the sea level simulator v1.0 has been presented in detail, and example simulations for a Swedish nuclear site have been discussed. Earlier versions of the sea level simulator have been used in scientific publications

The code is easily adaptable to new locations and uses widely available input data of the same kind that is used in more traditional methods of sea level planning. Essentially, what is needed to run simulations are a time series of yearly sea level maxima and at least one mean sea level projection. Apart from the obvious usage for creating decision support, the sea level simulator is also extremely well equipped for making uncertainty quantifications. A feature that has been further illustrated in a number of examples by

The list of possible new applications is extensive. An obvious but yet unexplored possibility would be to use the simulator to estimate future flood damage costs using information on the height above sea level and value of existing infrastructure. Moreover, the statistical framework could be used to model other hazards where short weather-related events are superimposed on long-term climate-related trends. Heat waves would be one such possibility.

In the current implementation, the vast majority of the runtime is spent making the mean sea level projections for the planning period. The most time-consuming part is to find the inverse of the cumulative distribution function of the mean sea level projections, which gives the mean sea level projections for the desired quantile. If this part could be sped up, it would lead to significant decreases in the overall runtime. Nevertheless, in its current form the simulator is still fast enough that it can be run on an ordinary PC, and speed is thus mostly an issue for users who wish to run very many simulations.

The GEV distributions used to model yearly sea level maxima are taken to be independent of time and SSP, which is an obvious caveat. In the Swedish context, this is likely a fair approximation given that

Lastly, it seems prudent to mention that both mean sea level projections

The current version of the model is available from the project website:

The author has declared that there are no competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This research has been supported by the project Nuclear pOwer And long tail flood risK (NOAK), which is financed by the Swedish radiation safety authority.

This paper was edited by Riccardo Farneti and reviewed by two anonymous referees.