DMI Klimaatlas v2024b - Fremskrivninger af det danske klima (Projections of climate indicators in Denmark)

Methods used in Klimaatlas, the Danish Climate Atlas (v2024b) DMI Report 24-12 National Centre for Climate Research (NCKF) at DMI 13 November 2024 National Centre for Climate Research (NCKF) at DMI www.dmi.dk Page 2 af 49 Colophon Serial title DMI Report Title Methods used in Klimaatlas, the Danish Climate Atlas (v2024b) Report Number DMI Report 24-12 Author(s) National Centre for Climate Research (NCKF) at DMI Editor Peter Thejil Language English Keywords Climate change, Klimaatlas URL https://www.dmi.dk/klimaatlas/ Digital ISBN 978-87-7478-755-6 Version v2024b Version date 13 November 2024 Copyright Danish Meterological Insitute Citation This report should be cited as: DMI (2024).Methods used in Klimaatlas, the Danish Climate Atlas (v2024b). DMI Report 24-12. https://doi.org/10.5281/zenodo.13753022 Klimaatlas data should be cited as: DMI. (2024). DMI Klimaatlas v2024b - Fremskrivninger af det danske klima (Projections of climate indicators in Denmark) [Data set]. Zenodo. https://doi.org/10.5281/zenodo.13753022 www.dmi.dk Page 3 af 49 Table of Contents Colophon ....................................................................................................................................... 2 Table of Contents .......................................................................................................................... 3 Changes in this version ................................................................................................................ 5 Sea Level Rise and Storm Surge Statistics ..................................................................... 5 Other Changes .............................................................................................................. 7 1. Introduction .......................................................................................................................... 8 2. Input data ............................................................................................................................. 9 2.1.Definitions .............................................................................................................. 9 2.2.EURO-CORDEX model data ..................................................................................... 9 2.3.Observational data .................................................................................................10 3. Model calibration techniques ............................................................................................ 13 3.1.Quantile-Quantile Matching .....................................................................................14 3.1.1. Nomenclature ............................................................................................14 3.1.2. Methods ....................................................................................................14 3.1.3. Summary ..................................................................................................16 3.1.4. Implementation details ...............................................................................16 3.1.5. Joint calibration of temperature maxima and minima ...................................17 3.2.Quantile-quantile for precipitation ...........................................................................18 3.3.Extreme values ......................................................................................................18 3.3.1. Extreme value analysis ..............................................................................18 3.3.2. Analytical quantile matching ......................................................................19 3.3.3. Implementation details ...............................................................................19 4. Sea level and storm surge indicators ............................................................................... 21 4.1. Data ..................................................................................................................21 4.2.Sea level change ....................................................................................................22 4.3.Return levels of extreme sea level events ................................................................23 4.4.Frequency of extreme sea level events ....................................................................24 5. Indicators ........................................................................................................................... 29 5.1.Overview ...............................................................................................................29 5.2.Notes on individual indicators .................................................................................31 5.2.1. 107 Cloudbursts ........................................................................................31 5.2.2. Wind speed indicators (301 and 302) ..........................................................32 5.3.Production of climate indicators from climate variables .............................................32 5.3.1. Relationship between tasmin, tasmax and tas .............................................32 5.3.2. Index calculation .......................................................................................32 5.3.3. Regrid indices to the KGDK 1x1 km grid. ....................................................32 5.3.4. Ensemble averaging ..................................................................................32 5.3.5. Area-aggregation ......................................................................................33 5.4.Emissions scenarios ...............................................................................................33 5.5.RCP4.5 error bars ..................................................................................................33 5.6.Land areas - municipalities and main catchment areas .............................................33 5.7.Shapefiles ..............................................................................................................34 www.dmi.dk Page 4 af 49 5.8.Grid transformations ...............................................................................................34 5.9.Smoothing .............................................................................................................34 6. Software ............................................................................................................................. 35 7. Acknowledgements ........................................................................................................... 36 8. References ......................................................................................................................... 37 9. Appendix A Previous versions ......................................................................................... 43 9.1.Version v2024a, June 2024 .....................................................................................43 9.2.Version v2022a, February 2023. ..............................................................................43 9.3.Version v2021a, December 2021. ............................................................................44 9.4.Version v2020b, December 2020 .............................................................................45 9.5.Version v2020a, June 2020 .....................................................................................45 9.6.Version 2019a, October 2019 ..................................................................................45 10. Appendix B Bootstrapping uncertainties ......................................................................... 47 www.dmi.dk Page 5 af 49 Changes in this version Klimaatlas v2024b represents a significant update of indicators associated with sea level rise and storm surges in Denmark. The release updates existing storm surge indicators based on upon new data (Højvandsstatistikker) from Kystdirektoratet released in July 2024 and updated again in November 2024. In addition, a rewrite of the sea-level and storm-surge processing code has aligned this part of the pipeline with the rest of the Klimaatlas processing chain. The resulting changes in indicators are generally minor, and within the uncertainty associated with estimates: notable changes may occur in some instances and are highlighted below. In addition, the number of emissions scenarios available for sea-level rise and storm-surge indicators has been increased. This reflects the increasing focus on scenarios beyond the core set previously used in Klimaatlas, and particularly on SSP3-7.0. Sea Level Rise and Storm Surge Statistics Input data  Update of Højvandsstatistikker from 2017 to 2024 version. There is generally good agreement between the resulting storm-surge indicators, with revisions generally being minor. Impacted indicators: 202-204, 206, 208, and 210.  Use of land-rise rates as reported in Højvandsstatistikker, rather than from the source report from DTU as done previously. This change ensures coherency between Højvandsstatistikker and Klimaatlas. Impacted indicators: all sea-level and storm surge indicators (201-204, 206, 208, 210, 213).  Improved utilization of sea-level rise projections from IPCC AR6. Previous versions of Klimaatlas built upon a simplified version of the available sea-level rise projections as inputs that required the uncertainties of interest (10th and 90th percentiles) to be inferred from the data available (83rd and 95th percentiles). v2024b uses the full set of sea-level rise projection data, allowing the relevant uncertainties to be extracted directly. Impacted indicators: all sea-level and storm surge indicators (201-204, 206, 208, 210, 213). Methods  The reference year for sea-level rise calculations has been moved to 1995, whereas it was previously 1990. This change resolves a minor inconsistency between the choice of reference year and the average sea level rise over the historical period. The resulting net change in sea level indicators is less than 2cm averaged across all stations. Impacted indicators: all sea-level and storm surge indicators (201-204, 206, 208, 210, 213).  Removal of DKSS storm-surge model based variance contributions. The calculation of future stormsurge indicators in Klimaatlas previously used a limited set of simulations using the DKSS storm surge model under two RCPs to estimate uncertainties in future storm surges associated with changes in wind patterns. However, while v2024b now presents five SSP-based emissions scenarios for sea-level rise and storm-surges, there are no corresponding SSP-based simulations available using the DKSS model system. The use of DKSS simulations in estimating the variance of future storm surge statistics has therefore been discontinued. The impact on the indicators is minor. www.dmi.dk Page 6 af 49 Impacted indicators: all storm surge indicators (202-204, 206, 208, 210, 213).  Rewrite of the calculation of sea-level rise and storm-surge indicators using Python. Agreement between indicators calculated with the old and new code with the same input data was generally excellent. Impacted indicators: all sea-level and storm surge indicators (201-204, 206, 208, 210, 213). Indicators  Addition of a new indicator (213), frequency with which the current 100 year storm surge level will be exceeded in the future.  Removal of indicator 205 (height of 10 000 year storm surge). Recent work in relation to the protection of Copenhagen against storm surges concluded that the use of statistical extrapolation to such long return periods was not supported by the (comparatively short-duration) time series available (Su et al 2024). This indicator has therefore been removed. The last published version of this indicator can be found in the Klimaatlas archive in version v2024a: https://zenodo.org/doi/10.5281/zenodo.11402835  Suspension of indicator 211 (Frequency of storm surge events exceeding current local warning level). Indicator 211 was previously calculated on the basis of DKSS simulations and cannot therefore be calculated as previously. A new calculation method, similar to that used for 210 and 213 is being developed, and indicator 211 has therefore been suspended for the meantime. A new version of the indicator will be released in a future update. The last published version of this indicator can be found in the Klimaatlas archive in version v2024a: https://zenodo.org/doi/10.5281/zenodo.11402835  Removal of indicator 212 (Accumulated duration of sea level exceeding current local warning level). Together with indicator 211, this indicator was previously calculated based on a limited set of DKSS model runs. It was not possible to find a new method to calculate this indicator with the new set of scenarios and it has therefore been removed. The last published version of this indicator can be found in the Klimaatlas archive in version v2024a: https://zenodo.org/doi/10.5281/zenodo.11402835  Indicator 210 shows the greatest change as a result of the above changes to methods and input data. Indicator 210 describes the frequency with which the level of a 20-year storm-surge in the current climate will be exceeded in the future and therefore integrates both changes in storm-surge statistics and sea level rise. The agreement between v2024b and v2024a is however good (R2 between v2024a and v2024b = 0.79, mean difference between v2024a and v2024b = 0.4 events per 20 years). Webpage and Documentation  Addition of extra SSP scenarios and time periods to the map viewer for sea level rise and storm surge statistics. Previously only three SSP scenarios were presented in the core Klimaatlas products (SSP1-2.6, SSP2-4.5 and SSP5-8.5), covering the last two periods (2041-2070 and 2071-2100). In line with the increased focus that SSP3-7.0 is receiving in an adaptation context, the set of scenarios has now been extended to include all five major SSP scenarios (i.e. addition of SSP3-7.0 and SSP1-1.9). Furthermore, the removal of DKSS data from the processing pipeline now makes it possible to generate Kommune reports and excel spreadsheets have also been updated accordingly. www.dmi.dk Page 7 af 49 Other Changes Input data  Two additional atmospheric models that were previously excluded from calculations involving Tmax and Tmin have been incorporated into Klimaatlas, increasing the ensemble size for indicators derived from these two variables. While there are subsequent revisions to estimates of both the median and the uncertainties, the changes are generally minor. Impacted indicators: 002-005,007-010 www.dmi.dk Page 8 af 49 1. Introduction Klimaatlas, the Danish National Climate Atlas, provides Danish society with relevant and easy to-use information on expected future changes in climate, including changes in atmospheric temperatures, precipitation and derived indices, as well as from the sea surrounding Denmark (sea-level and storm surges). Klimaatlas is based primarily on regional climate models derived from the EURO-CORDEX archives [Jacob et al., 2014], (https://euro-cordex. net/). However, such model data must be adjusted or calibrated so that they represent the current climate correctly. Observational data therefore also plays a key role in the production of Klimaatlas outputs – a significant amount of the work performed in the development of Klimaatlas is focused on ensuring harmony between these two data sources. Klimaatlas products are provided in several data-formats – .xlsx spreadsheets, .netcdf files and as ’GIS layers’. This data is intended for users requiring download of material for further processing, but Klimaatlas also provides an online display of the information, with documentation and user guides. Furthermore, reports are generated for each of the 98 kommuner (municipalities) in Denmark, summarizing the key findings from Klimaatlas, together with a report covering the entire country. Each indicator describes absolute values as well as changes in the index, expressed in percent or physical units as appropriate. Information, except the ocean indices, is available on a 1x1 km grid as well as on an aggregated basis for municipalities and main catchment areas. The ocean indices are available on 34 coastal stretches. Information is made available for the four seasons (and an annual value) for multiple emission scenarios. Four time periods are used - a present-day reference period (1981-2010) and three future periods (near future 2011-2040, mid-century 2041-2070, and end of century 2071-2100). Klimaatlas is available online at http://www.dmi.dk/klimaatlas and is accompanied by detailed help and userinformation. Klimaatlas was launched on 6th October 2019 and has been updated frequently since. An overview of the different versions can be found in “Appendix A Previous versions”. This Technical Report describes the data processing leading to the results displayed. Where appropriate, justification for the choices made is provided and elaborated as necessary. The report is made up of several sections, and reading each in isolation should be possible. www.dmi.dk Page 9 af 49 2. Input data 2.1. Definitions As a first step, we define two types of data that we deal with in Klimaatlas.  Climate variable We refer to gridded climate data in its native time resolution as a "climate variable". This can include the output produced directly by a climate model (either global or regional) or observations. It can also include derived variables, that are produced as a combination of other variables from the same data source, or in interaction with other data sources (e.g. as in bias correction). Examples include temperature, maximum temperature, and precipitation.  Climate indicator Climate variables can then be translated into climate indicators via a processing scheme involving the generation of some form of summary statistic (e.g. a mean) over time. Examples include annual mean temperature, frequency of extreme rain events, and drought indices. The key distinction between a variable and an indicator is the act of time-averaging. Climate variables have a higher time resolution (e.g. months, days or hours) than the corresponding indicators (e.g. annual averages, 30 year averages). The information delivered by a climate service, including Klimaatlas, and that commonly serves as the basis for further decision making, is most commonly in the form of "indicators". Climate variables, however, are the precursor for indicators and often an intermediate step in the processing chain. 2.2. EURO-CORDEX model data The models we use from the CORDEX archive is a subset of what is available. In particular, we note the following changes:  CNRM version 1 models used the incorrect boundary forcing and were excluded.  Despite using a differently rotated grid, the Aladin regional climate model has been re-gridded to the EUR-11 standard grid, and is used. The final list of models used in Klimaatlas is given in Table 1. # GCM RCM member tas tasmax tasmin pr pr1h sfcWind sfcWindmax rsds hurs 1 CANESM CCLM r1i1p1 h8 h8 h8 h8 h8 h8 h8 h8 2 CANESM REMO15 r1i1p1 h8 h8 h8 h8 h8 h8 h8 h8 3 CNRM crCLIM r1i1p1 h8 h8 h8 h8 h8 h8 h8 h8 h8 4 CNRM ALADIN r1i1p1 h48 h48 h48 h48 h48 h48 h48 h48 5 CNRM HIRHAM r1i1p1 h8 h8 h8 h8 h8 h8 h8 h8 h8 6 CNRM REMO15 r1i1p1 h28 h28 h28 h28 h28 h28 h28 h28 h28 7 CNRM REGCM r1i1p1 h8 h8 h8 h8 h8 h8 h8 h8 h8 8 CNRM WRF381 r1i1p1 h8 h8 h8 h8 h8 h8 h8 9 CNRM RACMO r1i1p1 h248 h248 h248 h248 h248 h248 h248 h248 10 CNRM HADREM r1i1p1 h8 h8 h8 h8 h8 h8 h8 h8 h8 11 ECEARTH crCLIM r1i1p1 h8 h8 h8 h8 h8 h8 h8 h8 h8 12 ECEARTH HIRHAM r1i1p1 h8 h8 h8 h8 h8 h8 h8 h8 h8 13 ECEARTH RACMO r1i1p1 h48 h48 h48 h48 h48 h48 h48 h48 h48 14 ECEARTH RCA r1i1p1 h8 h8 h8 h8 h8 h8 h8 h8 h8 15 ECEARTH WRF361 r1i1p1 h8 h8 h8 16 ECEARTH crCLIM r3i1p1 h8 h8 h8 h8 h8 h8 h8 h8 h8 17 ECEARTH HIRHAM r3i1p1 h248 h248 h248 h248 h248 h248 h248 h248 h248 18 ECEARTH RACMO r3i1p1 h8 h8 h8 h8 h8 h8 h8 h8 19 ECEARTH RCA r3i1p1 h8 h8 h8 h8 h8 h8 h8 h8 h8 20 ECEARTH CCLM r12i1p1 h248 h248 h248 h248 h248 h248 h248 21 ECEARTH crCLIM r12i1p1 h8 h8 h8 h8 h8 h8 h8 h8 h8 22 ECEARTH HIRHAM r12i1p1 h8 h8 h8 h8 h8 h8 h8 h8 h8 23 ECEARTH REMO15 r12i1p1 h248 h248 h248 h248 h48 h248 h248 h248 www.dmi.dk Page 16 af 49 3.1.3. Summary Details of cross-validation experiments examining the performance of bias-correction techniques can be found in previous versions of this report (e.g. DMI Report 24-11). In general, the following conclusions are drawn:  In general, bias correction seems to be the best method.  Bias correction should be performed on daily data even if only monthly means are wanted. There are some other considerations:  Results are sensitive to length of calibration period, but in Klimaatlas the impact is minor since 30year periods of calibration data are available.  Bias correction gives temporal correlations as in model, not as in observations.  For δ-change, the length of the calibrated series is limited by the length of the observations.  We emphasize that these conclusions hold only for the average over many realizations and the situation may be different for a particular ‘truth’/model combination. The conclusions are probably somewhat on the optimistic side as they are based on model/model comparison and not on real observations. 3.1.4. Implementation details The following generic procedure describes the implementation of quantile-quantile matching in Klimaatlas to produce calibrated climate variables.  Regridding of observational data to the CORDEX grid For all model grid points with at least 50% land coverage the nearest KGDK grid-point is found, and this ’nearest neighbour’ time series is used as the assigned observational data point for that model grid point. We use nearest neighbour method, rather than interpolation, to avoid any smoothing of data implicit in most interpolation methods. Distance is calculated in the straight line - no great-circle calculation is performed. We determine whether the model grid cell has at least 50% land by inspecting the same grid-cell in the model landsea mask. To ensure that small islands are included, for which the land-sea mask may indicate less than 50%, we specifically assign ls-mask values above 50% so that the data at the island have appropriate weight. This was done for Anholt and Læsø.  Bias Adjustment. For each model, and for each of the 4+1 seasons, the 99 separate percentiles are determined for the observed data and for the model by interpolation in the assembled values. A robust linear regression is then performed using the 99 data-pairs, and the slope of the regression line is noted. The slope is used to linearly extend the 99-point sequence beyond its range - to higher and lower values. See Figure 3 for an illustration of the procedure. The linear extensions are made starting in the last and first points of the sequence with the previously noted slope. On scenario data a quantile-quantile transformation is now performed using this constructed relationship. It is based on linear interpolation between points on the 99-pair percentile sequence if the interpoland (that is, the scenario value) is between the max and min of the sequence ordinate. If the interpoland falls either above or below the max and min of the ordinate range the linear extensions are used. The MATLAB robust regression routine is robustfit. When the 4 seasons have been completed, the results are combined to provide the annual time series. www.dmi.dk Page 17 af 49 3.1.5. Joint calibration of temperature maxima and minima Daily maximum and minimum temperatures represent a special case, where there is a need to maintain the relative relationship between the two variables at once. For example, at no point in the time series should the daily minimum exceed the daily maximum. While multi-dimensional bias-correction methods could be considered, in Klimaatlas we have used a simpler approach by calibrating the daily temperature-range using the steps below.  The modelled daily temperature range (DTR = Tmax − Tmin) was QQ-scaled against gridded observations for the period 2011-2019, resulting in DTRBA. All instances where DTRBA < 0 were set to 0.  The skewness Z = Tmean − (Tmax + Tmin)/2 was calculated for model data and then QQ-scaled against gridded observations, resulting in ZBA.  Then bias adjusted Tmin and Tmax were calculated using the equations Tmin,BA =Tmean,BA − ZBA − DTRBA/2 and Tmax,BA = Tmean,BA − ZBA + DTRBA/2. The KGDK data for daily maximum and minmum temperatures used here is limited to the period 2011-2019. In 2011, a change in observing praxis occurs: before end of 2010 data were recorded from 6AM to next 6AM, but after start of 2011 it was recorded midnight to midnight. While Tmax is very likely always recorded at a cadence of one day, we suspect that Tmin may be recorded with occasionally unpredictable offsets of one day in the older system of recording because the coldest time of day is usually in the morning hours - sometimes before 6 AM, sometimes after - thus producing the larger variation in Z before end of 2010. This problem effectively limits us to use data after the start of 2011 for indexes involving bias-adjusted temperature maxima and minima (Figure 4). Figure 4 The skewness (Z = Tmean − (Tmax + Tmin)/2) of 20x20 km gridded KGDK maximum and minimum temperature data changes at 2010/2011. www.dmi.dk Page 18 af 49 3.2. Quantile-quantile for precipitation For the precipitation a particular problem arises regarding the treatment of wet days and dry days. After some testing we have chosen the following simple and robust method. We adjust model precipitation series to replicate the fraction of wet days in the calibration period. In the case where the model has more wet days than observation, the days with the lowest model precipitation will be converted to dry days. In the inverse case, we promote modelled dry days to wet days by promoting days with the highest sub-threshold precipitation to the threshold precipitation amount; if necessary, random dry days will be similarly promoted. Two further modifications of the generic approach are also applied:  Before application of the BA algorithm all zero values are set to a small random number between 0 and 10−12 in model and observations; after BA all adjusted model numbers smaller than 0.1 are set to zero.  Extrapolation of the quantile-quantile plot in the negative direction is done with a line passing through (0,0) which helps avoid negative values where none ought to be possible. 3.3. Extreme values Extreme events occur rarely and therefore the empirical quantile-quantile calibration technique described in Section 3 cannot be used, since the tail of the empirical cumulative distribution function (CDF) is poorly defined. Therefore, for extreme events, extreme value analysis is applied, where the empirical CDF is replaced by an analytically formulated cumulative distribution function, as described below. A brief summary of work examining the performance of bias-correction techniques for extreme precipitation follows. Full details of this work can be found in the corresponding publication [Schmith et al., 2023]. 3.3.1. Extreme value analysis In extreme value analysis (EVA) one considers a time series of e.g. hourly values, and the aim is to estimate the frequency of occurrence of rare events, often expressed as the T -year return level, which is the level that on average is exceeded once every T years. We use the peak-over-threshold (POT) method, where all peak values above a specified threshold x0 and separated by a minimum time span are considered. It is assumed that peak occurrences are independent and Poisson-distributed with parameter λ, which is the average number of exceedances (events) per year. Alternatively, λ can be specified, in which case x0 is a stochastic variable. It can be shown that under very general conditions the distribution of the peak exceedances x−x0 > 0 are distributed as a Generalised Pareto distribution (GPD) with cumulative distribution function given by: 𝐹  ( 𝑥 − 𝑥  ) = 1 − 󰇡 1 − 𝜉 𝑥 − 𝑥  𝜎 󰇢   ⁄ , 𝑥 > 𝑥  3. 1 The T -year return level is determined as the level exceeded on average once every T years, and therefore the following holds: www.dmi.dk Page 19 af 49 𝜆𝑇 [ 1 − 𝐹  ( 𝑋  − 𝑋  ) ] = 1 3. 2 from which we get 𝑥  = 𝐹     1 − 1 𝜆𝑇  + 𝑥  3. 3 There are several procedures available for estimating the parameters from data, the most important being: maximum likelihood (ML), method of moments (MOM) and probability weighted moments (PWM). Hosking and Wallis [1987] and Hosking et al. [1985] demonstrate that PWM in general yields reliable results with low variance for the number of samples in this study, whereas in particular ML can be problematic. Therefore we use PWM in the following. For more details see Coles [2001]. 3.3.2. Analytical quantile matching In Section 4.2 the theoretical framework was presented for estimating extreme value distributions and associated return levels. This can be applied to obtain future projected values and climate factors, defined as the ratio between a future and a present value, which will be presented below. We make use of Equation 3 above, which is valid both for Mc and for O and for any return period T . If we apply this to O and Mc we obtain the expression (1 =)λMcT[1 − FGPD,Mc(Mc,T − Mc0)] = λOT[1 − FGPD,O(OT − O0)] 3. 4 relating Mc,T and OT , and after some manipulation, we arrive at 3. 5 Equation 3.5 defines a transformation from Mc,T to OT , which then in the calibration procedure is applied to Mf,T to obtain M˜f,T . 3.3.3. Implementation details The following procedure is used for rare precipitation events, except cloudbursts (see Generic Procedure 3 for that)  Re-creation of Spildevandskommiteens NRM model (see [Gregersen et al., 2014b]). This results in a 10x10 km grid (on ’det Danske Kvadratnet’) of the λ-parameter (number of exceedances of the threshold per year) and the scale-parameter for a generalized Pareto distribution. Both for 1-hour data and 24-hour data.  For the calibration-period and the reference as well as the three future periods, for land points only, for RCP4.5 and RCP8.5, we apply nearest-neighbour interpolation from the CORDEX model grid to the 10x10 km grid. The nearest-neighbour interpolation assigns the model series in the nearest CORDEX gridpoint to ’det Danske Kvadratnet’ point under consideration. www.dmi.dk Page 20 af 49  Perform extreme value analysis for all models and the calibration period and all scenarios, and 1 and 24-hour data. 24-hour analysis performed with sliding windows covering 24-hours but advancing one hour each step).  For lower and lower thresholds find model points exceeding the threshold until λ = 3 (events/year) is found (this will be a different threshold for each model, period and landpoint, but all with λ = 3. Ensure at least 24 hours between each selected event.  Fit a generalized Pareto distribution to the selected values, using the probability weighted method. Thereby find local scale and shape parameters.  Average the shape parameter to one national value.  Calculate return-levels from the GP parameters for the calibration-period.  use the parameterized q-q transformation (see section 4) to correct the return-levels of the calibration period.  In the reference-period and the three future periods correct the return-levels using the parameterized q-q transformation determined in the calibration period (with Equation 3.5).  Files with q-q corrected return-values are prepared for the reference-period and the three future periods, for the next processing steps. www.dmi.dk Page 21 af 49 4. Sea level and storm surge indicators In Klimaatlas we provide the projections of mean sea level change (index201), as well as for the changes in extreme sea levels until the end of the 21st century. They are calculated for the 36 coastal stretches defined by Kystdirektoratet (KDI), except Ringkøbing Fjord and Nissum Fjord, which are regulated by lock gates (Table 3, KDI code VK2 and VK3). Each coastal stretch is represented by one station (Table 5), chosen to have the most reliable present day high water statistics for the coastal stretch. The changes in extreme sea levels are represented by 1) changes in return levels (indices 202, 203, 204, 206, 208); and 2) changes in the frequencies of extreme sea level events (indices 210, 213). On our website we provide all projections for the start (20112040), mid- (2041-2070) and end-century (2071-2100) 30-year periods, for the very low (SSP1-1.9), low (SSP12.6), medium (SSP2-4.5), high (SSP3-7.0), and very high (SSP5-8.5) emission scenarios. Additionally, we provide a table with yearly projections for all scenarios. Sea level indicators are given as change compared to the 1995 baseline. 4.1. Data The sea level indicators in Klimaatlas are based on the sea level projections data set (Garner et al., 2021) associated with the Intergovernmental Panel for Climate Change Sixth Assessment Report (IPCC AR6; FoxKemper et al., 2021). This data set was created using the Framework for Assessment of Changes To Sea-level (FACTS; Kopp et al., 2023) and contains the projections of the total sea level change, as well as for each of the contributions separately. The contributions are Antarctic and Greenland ice sheet, glaciers, land water storage, ocean dynamics (including thermal expansion of the ocean), and vertical land motion. All projections are given every 10 years from 2020 until the end of the 21st century or longer, as sea level change relative to the 1995-2014 reference period. The projections are given for every grid point on a regular 1°×1° grid and for all stations in the Permanent Service for Mean Sea Level database (PSMSL, 2024; Holgate et al., 2013). There are two types of projections in the data set: 1) those based only on processes for whose projections we have medium or high confidence in, thus called medium confidence projections; and 2) those that additionally rely on processes for which we have only low confidence but if they happen could significantly increase sea level, such as the ice-shelf collapse and instability, which are therefore named low confidence projections. The medium confidence projections are given for five scenarios: SSP1-1.9, SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5, and low confidence for three: SSP1-2.6, SSP2-4.5, and SSP5-8.5. When available, we choose to present the low confidence projections in Klimaatlas because, as noted in IPCC AR6, stakeholders with a low risk tolerance such as those planning for coastal safety, may wish to consider the estimates above the likely range, but we also provide a table with projections for all scenarios, with both low and medium confidence. We also use the extreme sea level statistics provided by Kystdirektoratet (KDI). KDI provide a new set of return levels based on tide gauge records approximately every five years. The newest statistics were published in 2024 (Højvandsstatistikker, 2024) and contain return levels for 20, 50, 100, and 200-years return periods, including the uncertainties, determined from a generalized Pareto distribution based on 40 highest observed water levels at each station, from the beginning of the observations at that location until 01-012024. We also use an earlier version of their statistics (Højvandsstatistikker, 2012), which provides 1-year return levels obtained by directly counting the events in the tide gauge records. Despite the IPCC dataset containing the vertical land motion (VLM) contribution, which mainly consists of the land uplift due to glacial isostatic adjustment (GIA), we instead use the VLM model from DTU Space (2015), which is also used in the KDI statistics (2024), to be consistent. Since the vertical land motion is an important www.dmi.dk Page 22 af 49 contributor to sea level change in Denmark and it varies significantly across the country, this model, specifically made for Denmark, has a higher spatial resolution and thus covers local and regional differences better. 4.2. Sea level change We extract the projections for individual sea level change contributions from the Greenland and Antarctic ice sheets, glaciers, land water storage, and ocean dynamics (incl. thermal expansion) for the 34 locations in Klimaatlas from the IPCC dataset. The IPCC dataset contains projections for both a regular 1° longitudelatitude grid, as well as for the locations of all stations in the Permanent Service for Mean Sea Level (PSMSL) database. We therefore apply two methods of extraction: 1) for locations that are in the PSMSL database and for locations that are very close to a grid point (less than 5 km), we use nearest neighbor interpolation and directly take the IPCC projection belonging to that location; 2) for the remaining locations we use bilinear interpolation from the four closest grid points. We extract values for the 10th, 50th (median), and 90th percentile for years from 2020 to 2100. The ocean dynamics contribution for the SSP2-4.5 (medium emission) climate scenario has extremely high values at a few grid points within Denmark, significantly higher than in the SSP5-8.5 (high emission) scenario, which is not realistic. Since the ocean dynamics contribution should not vary significantly across Denmark, to mitigate that we instead use the median of all grid points between 7°E and 16°E and 54°N and 58°N for every location for all scenarios. We calculate the VLM contribution to sea level change from the same VLM model rates that were used to create the Højvandsstatistikker (2024), relative to the same reference period the IPCC dataset uses (19952014). We then combine all sea level change contributions, both from the IPCC dataset and the separate VLM model. To get the total sea level change, we need to combine the contributions for both the median and the uncertainties: 𝑆𝐿𝑅   =  𝑆𝐿𝑅   4. 1 𝛥 𝑆𝐿𝑅  =   ( 𝛥 𝑆𝐿𝑅  )   4. 2 where 𝑆𝐿𝑅  is the median of the total sea level change, 𝑆𝐿𝑅 median of each contribution i, 𝛥𝑆𝐿𝑅 the uncertainty of the total and 𝛥𝑆𝐿𝑅 individual contribution uncertainties. The lower and upper uncertainties of some contributions, and therefore of the total sea level change, can be vastly different, so they are calculated separately as: 𝑆𝐿𝑅   =  𝑆𝐿𝑅   4. 3 𝛥 𝑆𝐿𝑅   ⁄ =  𝑆𝐿𝑅  − 𝑆𝐿𝑅   ⁄  4. 4 www.dmi.dk Page 23 af 49 where 𝑆𝐿𝑅  ⁄ are the 10th and the 90th percentiles of sea level change and 𝛥𝑆𝐿𝑅  ⁄ are the lower and the upper uncertainty. With that, the equations used to calculate the 10th and the 90th percentile are: 𝑆𝐿𝑅   = 𝑆𝐿𝑅   −    𝑆𝐿𝑅  − 𝑆𝐿𝑅     4. 5 𝑆𝐿𝑅   = 𝑆𝐿𝑅   +    𝑆𝐿𝑅  − 𝑆𝐿𝑅     4. 6 Since the VLM model does not include uncertainties, we assume they are zero and use the same values as both median and 10th and 90th percentile. The IPCC dataset provides projections with a 10 year temporal resolution starting from year 2020, as change relative to the 1995-2014 reference period. Since we need values from 2011 to be able to provide the average projection for the 2011-2040 period, we interpolate the sea level change between the reference period centered around year 2005, where the change is zero by definition, and the start of the projections. We also interpolate to yearly values for the whole time span for which we provide the projections. To provide projections relative to year 1995 (center of the 1981-2010 period), as in the previous versions of Klimaatlas, we shift all time series by assuming the change before the IPCC reference period is linear. 4.3. Return levels of extreme sea level events We extract the 20, 50, and 100-year return levels from the most recent KDI statistics (2024), and the 1-year return level from the earlier KDI statistics (2012) for each of the 34 stations in Klimaatlas. Return levels from both datasets are adjusted to our 1995 reference using the rates given for each station in the KDI 2024 data set. We then interpolate between them in the log-period space to obtain the 5-year return level at each location. The observations at the station Fåborg, representative for the Sydfynske Øhav coastal stretch, only started in 2000, so the observed time series was too short to be included into the KDI 2012 statistics. For the longer series, the 40 highest observed sea levels used to find the return level distribution are usually well above the 1or even 5-year return periods, making it unsuitable to determine the 1-year return levels from it. However, since the Fåborg time series is so short, it has many data points with short return periods, so the fitted curve is reliable at low return periods. Therefore, for Fåborg we take the 1and 5-year return levels from the KDI 2024 distribution. To calculate future projections of extreme sea levels we combine the historical storm surge statistics with the sea level rise using again the same principles as in equations (1) and (4), which for return levels are: 𝑅𝐿   = 𝑅𝐿    + 𝑆𝐿𝑅   4. 7 𝑅𝐿   = 𝑅𝐿   −   𝑅𝐿    − 𝑅𝐿      +  𝑆𝐿𝑅   − 𝑆𝐿𝑅     4. 8 www.dmi.dk Page 24 af 49 𝑅𝐿   = 𝑅𝐿   +   𝑅𝐿    − 𝑅𝐿      +  𝑆𝐿𝑅   − 𝑆𝐿𝑅     4. 9 where 𝑅𝐿  , 𝑅𝐿  , and 𝑅𝐿  are the 10th, 50th, and 90th percentile of the projected future return levels, 𝑅𝐿  , 𝑅𝐿  , and 𝑅𝐿  represent the historical storm surge statistics, and 𝑆𝐿𝑅 , 𝑆𝐿𝑅 , and 𝑆𝐿𝑅  are the median and uncertainties of the total sea level change calculated above. We do this calculation for all the years between 2011 and 2100 and all scenarios provided in the IPCC database. 4.4. Frequency of extreme sea level events We then calculate what will in the future be the frequency of the 20and 100-year events in the present climate. We first convert the return periods to logarithmic scale, then for each of the levels, we interpolate the projected return level curve to obtain the future return period. If the future frequency of extreme event is less than 1 event per year (lowest value in the return level curve), we linearly extrapolate the curve using the 1and 5-year return levels. The same process is applied to the median and the 10th percentile. However, this process can result in extremely large values for the 90th percentile and in some cases for the median. We therefore set a limit to 3 extreme events per year. We then convert the future return period to frequency of events in 20 years for the 20-year event, and 100 years for the 100-year event. Finally, we calculate the averages for the start- (2011-2040), mid- (2041-2070), and end-century (2071-2100) period for all indicators and for all emission scenarios. www.dmi.dk Page 25 af 49 Figure 5 Sea level change contributions (a-f) and total sea level change (g) relative to the 1995-2014 reference period for the Vadehavskyst nordlig coastal stretch (represented by the station Esbjerg) in SSP5-8.5 scenario. www.dmi.dk Page 32 af 49 The change in 3-year return-level in hourly precipitation can be obtained from the parameters of POT fits to present-day and future extreme precipitation. From the present-day parameters, the three-year return level can be obtained for each point. This value is now entered into the corresponding CDF for the future period, and the return frequency of this value can be calculated. The uncertainty is calculated as the pointwise spread among models. 5.2.2. Wind speed indicators (301 and 302) Due to of large gradients in wind speed inland from the coasts, the smoothing is reduced compared to other indices: a 25 x 25 km filter is applied instead of the general 75 x 75 km filter. 5.3. Production of climate indicators from climate variables Here we detail the generic additional processing steps employed to come from bias-corrected variables to indicators. 5.3.1. Relationship between tasmin, tasmax and tas Initial explorations in the development of Klimaatlas revealed that the model-fields for temperatures, their maxima and their minima – which are delivered from CORDEX as separate files generated by the individual contributors – did not all fulfill such basic requirements as Tmin < Tmean < Tmax. So before starting the bias adjustment procedure for modelled daily minimum and maximum temperature, we made corrections for each model, each day and each grid cell so that Tmin is given the lowest value of Tmin, Tmean, Tmax, and Tmax is given the highest value of the three variables and Tmean is given the middle value of the three. 5.3.2. Index calculation For each year, and each of the 4+1 seasons, and for each CORDEX model grid-point, in each model we calculate the index in question using the bias-adjusted data. Split the results into the 30-year long reference and future scenario periods (some models only have 29 years of data in the last of the future periods, and some end in November of the last year). Take means over the 30 values in each period, at each grid-point, and for each season etc. Calculate changes in indices (differences or ratios, in %, as appropriate, and noted for each index below) between the future periods in question and the reference period. 5.3.3. Regrid indices to the KGDK 1x1 km grid. Use the MATLAB routine scatteredInterpolant with option ’natural’. This ’smooths the result’ into neighbouring cells to a small degree. The 1x1 km land-sea mask is applied to remove apparent values over sea points. Smooth the observed results with MATLAB routine smooth2a using square 25x25 km windows - the window moves in 1-km steps; smooth projections for the future with 75x75 km windows. 5.3.4. Ensemble averaging For each 1x1 km grid-point collect the 68 model-index values relevant for the season and extract the 10, 50 and 90 percentiles, using the MATLAB routine named prctile (used with the implicit argument “exact”), which interpolates in the values presented to it. This grid is one end-product for the homepage. www.dmi.dk Page 33 af 49 5.3.5. Area-aggregation For each municipality or main catchment area, identify the 1x1 km grid-points inside the boundary polygon - i.e. find all grid-points with centre-coordinate inside the given polygon. Calculate the mean of the 10, 50 and 90 percentile data generated above. This product is another product for the homepage. 5.4. Emissions scenarios The following emissions scenarios are currently presented in Klimaatlas. The scenario naming follows that of the IPCC and attempts to form a linkage between the relative concentration pathways (RCPs) of IPCC AR5 and CMIP5, and the shared socioeconomic pathways (SSPs) of IPCC AR6 and CMIP6. Scenario description Atmospheric indexes Oceanic indexes Very high RCP 8.5 SSP 5 - 8.5 High - SSP 3 - 7.0 Medium RCP 4.5 SSP 2 - 4.5 Low RCP 2.6 SSP 1 - 2.6 Very Low - SSP 1 - 1.9 Table 5. Emission scenarios used in Klimaatlas. 5.5. RCP4.5 error bars The number of RCP4.5 models is about a factor of 2.5 less than for RCP8.5 and this leads to unfortunate effects due to small sample size and model inter-correlations (the few models present are somewhat dependent). The error bars for RCP4.5 results therefore show a tendency to vary a lot between future time periods, as well as, now and then, having unrealistically small widths. This prompts us to apply an adjustment scheme so that we can present estimated error bars for RCP4.5 results that are realistic. We ensure that  The RCP4.5 error bars in near future and mid-century are adjusted so that the smaller one is scaled to the width of the larger one, and  the end of century error bar is scaled so that it is never the smallest of the three error bars. The scaling algorithm applies a factor on the error bars, when scaling is called for, which retains the ratio of the upper (50 to 90 percentile interval) error bar to that of the lower (10 to 50 percentile) error bar, while keeping the median value fixed. A larger ensemble of models would remedy this problem from the root, but the EUROCORDEX ensemble of models is limited in scope for the RCP4.5 scenario. 5.6. Land areas - municipalities and main catchment areas The detailed implementation of the calculation of each index is given in the following. For each index calculations proceed as follows: Annual and seasonal mean (or also max/min, depending on the nature of the index) values are calculated at each EUR-11 gridpoint from daily-mean model values. This gives 30 annual values for each of the chosen reference (historical and scenario) periods we have chosen. The mean of the 30 values is then taken. Then differences between historical and future periods are calculated for indices requiring relative changes. Then re-gridding and smoothing is applied to relative www.dmi.dk Page 34 af 49 changes and absolute values to attain a smooth 1x1 km grid. 10, 50 and 90 percentile values are determined from these values. 5.7. Shapefiles The following shapefiles were used as the basis for spatial averaging  The boundaries for municipalities (kommuner) are defined by Styrelsen for Dataforsyning og Effektivisering (SDFE) and as this product can be updated we state here that the information was downloaded in May of 2018. Future updates by SDFE are bound to be have very minor impacts and are typically incremental when, typically, water-bodies (streams) and beach-lines change. See SDFE [2019]. The shapefile can be downloaded from: https://www.dmi.dk/fileadmin/klimaatlas/municipalities.json  The boundaries for main catchment areas (vandopland) are given by Miljøstyrelsen [MST, 2019] and can be downloaded from https://www.dmi.dk/fileadmin/klimaatlas/DK_hovedvandoplande_klimaatlas_UTM32N.json  Coastal stretches (kystrækninger) can be downloaded from: https://www.dmi.dk/fileadmin/klimaatlas/DK_kystinddeling_klimaatlas_UTM32N.json 5.8. Grid transformations Interpolation is performed linearly to render the index values onto a 1x1 km grid (’det Danske Kvadratnet’) from the EUR-11 grid of the models. The interpolation uses Matlab routine scatteredInterpolant which uses a Voronoi triangulation of the scattered sample points to perform interpolation. Natural neighbour interpolation is used via the natural option [Sibson,1981]. Further implementation details for the scatteredInterpolant routine is given at Mathworks [2019]. 5.9. Smoothing Smoothing of the resulting 1x1 km grid is performed to avoid unrealistic details. We smooth all fields, after interpolation, by taking averages over moving box-windows of size 25×25 km. Since observed spatial structure is more credible than modelled future spatial structures in changes, we smooth the projections spatially with a bigger (75x75 km) filter, before calculating index changes (exception for winds, see Section 8.3). Details on det Danske KvadratNet are available at Danmarks Statistik [2019]. For each index relative as well as absolute values of the expected values of the period mean quantities are calculated. For relative changes we use the historical reference period 1981-2010, and the future periods 2011-2040, 2041-2070 and 2071-2100. These future periods are also used when giving the absolute values. The 10, 50 and 90 percentiles are calculated from the differences between the mean values over reference vs. scenario periods for each available model. The percentiles thus illustrate model-spread. www.dmi.dk Page 35 af 49 6. Software The atmospheric-data methods described above are shown in diagrammatic form in the flowchart in Figure 11. The data resulting from these procedures are stored. Figure 8. Flowchart showing the atmospheric-data processing steps. www.dmi.dk Page 36 af 49 7. Acknowledgements We acknowledge the World Climate Research Programme’s Working Group on Regional Climate, and the Working Group on Coupled Modelling, former coordinating body of CORDEX and responsible panel for CMIP5. We also thank the climate modelling groups (listed in Table 1) for producing and making available their model output. We also acknowledge the Earth System Grid Federation infrastructure an international effort led by the U.S. Department of Energy’s Program for Climate Model Diagnosis and Intercomparison, the European Network for Earth System Modelling and other partners in the Global Organisation for Earth System Science Portals (GO-ESSP).” We thank the projection authors for developing and making the sea-level rise projections available, multiple funding agencies for supporting the development of the projections, and the NASA Sea Level Change Team for developing and hosting the IPCC AR6 Sea Level Projection Tool. www.dmi.dk Page 37 af 49 8. References  Arns, T. 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ISSN 0831-8247.  Christopher S Watson, Neil J White, John A Church, Matt A King, Reed J Burgette, and Benoit  Legresy. Unabated global mean sea-level rise over the satellite altimeter era. Nature Climate Change, 5(6):565–568, 2015. URL https://www.nature.com/articles/nclimate2635. www.dmi.dk Page 48 af 49 So far, only 9 bootstraps have been performed, and only partially on factors S1 (observations) and S2 (models). However, these first results allow some general conclusions. We see some differences in the effects of bootstrapping S1 (observation years) and S2 (models), respectively: For index 001 and 106, the effects due to bootstrapping on S1 and S2 are about the same for the absolute values and the climate signals in these (i.e. their changes over time). For indices 101-105 the standard deviation in the climate change signal is much bigger for S2 bootstrapping than it is for S1 bootstrapping. For indices 107 and 151-162 we only have results for S2 bootstrapping. Here we note that the standard deviation on the climate signal for 151-162, due to S2 bootstrapping, is in the range 5-16%. 107 has very small response to bootstrapping, it appears. Only minor differences are seen throughout when comparing standard deviations induced by bootstrapping for any of the percentiles 10, 50 and 90 when just considering the 50th percentile. In summary:  choice of models has greater influence than the choice of calibration period, by factors of from 4 to 10 (indices 101-105)  uncertainties due to model choice can reach 16% in the change of indices related to extreme precipitation  robustness of the 10, 50 and 90th percentiles to S1 (observation years) and S2 (models) bootstrapping are similar. We should thus seek to extend the number of models used, and we should accommodate an analysis of the importance of calibration period position in time which could not be sampled by the present bootstrap analysis. More and longer observed data series should be obtained. Extending the number of factors considered in bootstrapping could provide us with an important tool for calculating ’total uncertainty’ on Klimaatlas information. www.dmi.dk Page 49 af 49 Indicator ID Name of index U nits S1 (obs) S2 (mod) 001 Mean temperature C C ± 0.18 : ± 0.13 ±0.18 : ±0.13 ± 0.16 : ± 0.17 ±0.12 : ±0.12 101 Mean precip. mm/day % ± 0.13 : ± 1.0 ±0.13 : ±0.9 ± 0.12 : ± 5 ±0.09 : ±4 102 Daily - max precip. mm % ± 1.7 : ± 0.6 ±1.7 : ±0.5 ± 1.6 : ± 6 ±1.0 : ±4 103 5 - day max precip. mm % ± 2.6 : ± 0.86 ±2.5 : ±0.74 ± 2.0 : ± 4 ±1.5 : ±3 104 14 - day max precip. mm % ± 3.9 : ± 0.9 ±3.8 : ±0.8 ± 4.5 : ± 5 ±2.4 : ±4 105 Days with over 10 mm Daily precip. days days ± 0.7 : ± 0.15 ± 0.55 : ± 0.57 ± 0.7 : ± 0.13 ± 0.43 : ± 0.48 106 Days with over 20 mm Daily precip. days days ± 0.35 : ± 0.12 ± 0.20 : ± 0.20 ± 0.35 : ± 0.10 ± 0.14 : ± 0.15 107 Number of cloud - bursts per year events events - ± 0.074 : ± 0.073 - ± 0.074 : ± 0.073 151 Hourly precip. in 2 - year events mm % - ± 0.90 : ± 7 - ± 0.69 : ± 6 153 Hourly precip. in 10 - year events mm % - ± 3.0 : ± 10 - ± 2.4 : ± 9 156 Hourly precip. in 100 - year events mm % - ± 8.6 : ± 16 - ± 5.9 : ± 13 157 Daily precip. in 2 - year events mm % - ± 2.2 : ± 5.3 - ± 1.7 : ± 4.3 159 Daily precip. in 10 - year events mm % - ± 4.9 : ± 7.8 - ± 3.0 : ± 5.4 162 Daily precip. in 100 - year events mm % - ± 11.7 : ± 11.4 - ± 5.8 : ± 6.1 Table 6 Standard deviations in climate indexes, based on bootstrapping of local anomaly data (i.e. excluding the enhanced variability otherwise due to inclusion of geographic variations). Observation year and models are bootstrapped – labelled S1 and S2. Two pieces of information is given for each index - one is the absolute value of an index in the far future period 2071-2100, and the other is the change in that index between the far future period and the historical reference period. These two quantities are shown in each column before and after the semi-colon. The changes are either absolute (indexes 001, 105, 106 and 107), or are given as percentages. Values shown are for the scenario RCP8.5 and the distributions generated by the bootstrap include the various values from each bootstrap across the whole 1x1 km land-only grid of Denmark. 9 bootstraps were performed. For each index two lines are shown - the first line gives the largest standard deviation found in any of the 10, 50 and 90%iles - the second line is restricted to just the 50%ile (i.e., the median). The seasonal and the annual values are all included, except for index 107, which is annual only.