EQC Quality Assessment: "Bias in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q01  |  Category: Climate_Projections
Section: Bias in extreme temperature indices for the reinsurance sector > Methodology
---
This notebook provides an assessment of the systematic errors (trend and climate mean) in a subset of 9 models from [CORDEX](https://cds.climate.copernicus.eu/datasets/projections-cordex-domains-single-levels?tab=overview). It achieves this by comparing the model predictions with the ERA5 reanalysis for the maximum-temperature-based indices of 'SU' and 'TX90p', calculated over the temporal aggregation of JJA and for the historical period spanning from 1971 to 2000. In particular, spatial patterns of climate mean and trend, along with biases, are examined and displayed for each model and the ensemble median (calculated for each grid cell). Additionally, spatially-averaged trend values are analysed and presented using box plots to provide an overview of trend behavior across the distribution of the chosen subset of models when averaged across Europe.

The analysis and results follow the next outline:

**[](section-1)**
 * [](section-1.1)
 * [](section-1.2)
 * [](section-1.3)
 * [](section-1.4)
 * [](section-1.5)
 * [](section-1.6)

**[](section-2)**
 * [](section-2.1)
 * [](section-2.2)
 * [](section-2.3)

**[](section-3)**
 * [](section-3.1)
 * [](section-3.2)
 * [](section-3.3)
 * [](section-3.4)
 * [](section-3.5)
 * [](section-3.6)


EQC Quality Assessment: "Bias in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q01  |  Category: Climate_Projections
Section: Bias in extreme temperature indices for the reinsurance sector > Analysis and results > 1. Parameters, requests and functions definition > 1.2. Define Parameters
---
In the "Define Parameters" section, various customisable options for the notebook are specified:

- The initial and ending year used for the historical period can be specified by changing the parameters `year_start` and `year_stop` (1971-2000 is chosen for consistency between CORDEX and CMIP6).
- The `timeseries` set the temporal aggregation. For instance, selecting "JJA" implies considering only the JJA season.
- `collection_id` provides the choice between Global Climate Models CMIP6 or Regional Climate Models CORDEX. Although the code allows choosing between CMIP6 or CORDEX, the example provided in this notebook deals with CORDEX RCMs.
- `area` allows specifying the geographical domain of interest.
- The `interpolation_method` parameter allows selecting the interpolation method when regridding is performed over the indices.
- The `chunk` selection allows the user to define if dividing into chunks when downloading the data on their local machine. Although it does not significantly affect the analysis, it is recommended to keep the default value for optimal performance.

Choose annual or seasonal timeseries
Choose CORDEX or CMIP6
Interpolation method
Area to show
Chunks for download

(section-1.3)=


EQC Quality Assessment: "Bias in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q01  |  Category: Climate_Projections
Section: Bias in extreme temperature indices for the reinsurance sector > Analysis and results > 1. Parameters, requests and functions definition > 1.3. Define models
---
The following climate analyses are performed considering a subset of GCMs from CORDEX. Models names are listed in the parameters below. Some variable-dependent parameters are also selected, as the `index_names` parameter, which specifies the temperature-based indices ('SU' and 'TX90p' in our case) from the [icclim](https://icclim.readthedocs.io/en/stable/) Python package.

When choosing Cordex models, it is crucial to consider the availability of RCMs for the selected GCM and the specified region. The listed RCMs, for instance, are accessible for the GCM “mpi_m_mpi_esm_lr” in the “europe” cordex_domain. To confirm the available combinations, refer to the [CORDEX](https://cds.climate.copernicus.eu/datasets/projections-cordex-domains-single-levels?tab=overview) CDS catalogue entry.

Define dictionaries to use in titles and caption
Define dictionaries to use in titles and caption

(section-1.4)=


EQC Quality Assessment: "Bias in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q01  |  Category: Climate_Projections
Section: Bias in extreme temperature indices for the reinsurance sector > Analysis and results > 1. Parameters, requests and functions definition > 1.4. Define ERA5 request
---
Within this notebook, ERA5 serves as the reference product. In this section, we set the required parameters for the cds-api data-request of ERA5.

(section-1.5)=


EQC Quality Assessment: "Bias in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q01  |  Category: Climate_Projections
Section: Bias in extreme temperature indices for the reinsurance sector > Analysis and results > 1. Parameters, requests and functions definition > 1.5. Define model requests
---
In this section we set the required parameters for the cds-api data-request.

The `get_cordex_years` function is employed to choose suitable data chunks for CORDEX data requests.

When `Weights = True`, spatial weighting is applied for calculations requiring spatial data aggregation. This is particularly relevant for CMIP6 GCMs with regular lon-lat grids that do not consider varying surface extensions at different latitudes. In contrast, CORDEX RCMs, using rotated grids, inherently account for different cell surfaces based on latitude, eliminating the need for a latitude cosine multiplicative factor (`Weights = False`).

(section-1.6)=


EQC Quality Assessment: "Bias in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q01  |  Category: Climate_Projections
Section: Bias in extreme temperature indices for the reinsurance sector > Analysis and results > 1. Parameters, requests and functions definition > 1.6. Functions to cache
---
In this section, functions that will be executed in the caching phase are defined. Caching is the process of storing copies of files in a temporary storage location, so that they can be accessed more quickly. This process also checks if the user has already downloaded a file, avoiding redundant downloads.

Functions description:

- The `select_timeseries` function subsets the dataset based on the chosen `timeseries` parameter.

- The `compute_indices` function utilises the icclim package to calculate the selected maximum-temperature-based indices.

- The `compute_trends` function employs the Mann-Kendall test for trend calculation.

- Finally, the `compute_indices_and_trends` function selects the temporal aggregation using the `select_timeseries` function. It then computes daily maximum temperature (only if we are dealing with ERA5), calculates maximum-temperature-based indices via the `compute_indices` function, determines the indices mean over the historical period (1971-2000), obtain the trends using the `compute_trends` function, and offers an option for regridding to ERA5 if required.

Original bounds for conservative interpolation

(section-2)=


EQC Quality Assessment: "Bias in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q01  |  Category: Climate_Projections
Section: Bias in extreme temperature indices for the reinsurance sector > Analysis and results > 2. Downloading and processing > 2.1. Download and transform ERA5
---
In this section, the `download.download_and_transform` function from the 'c3s_eqc_automatic_quality_control' package is employed to download ERA5 reference data, select the temporal aggregation ("JJA" in our example), compute daily maximum temperature from hourly data, compute the maximum-temperature-based indices, calculate the mean and trend for the historical period (1971-2000) and cache the result (to avoid redundant downloads and processing).

(section-2.2)=


EQC Quality Assessment: "Bias in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q01  |  Category: Climate_Projections
Section: Bias in extreme temperature indices for the reinsurance sector > Analysis and results > 2. Downloading and processing > 2.2. Download and transform models
---
In this section, the `download.download_and_transform` function from the 'c3s_eqc_automatic_quality_control' package is employed to download daily data from the CORDEX models, compute the maximum-temperature-based indices for the selected temporal aggregation, calculate the mean and trend over the historical period (1971-2005), interpolate to ERA5's grid (only for the cases in which it is specified, in the other cases, the original model's grid is mantained), and cache the result (to avoid redundant downloads and processing).

Original model
Interpolated model

```text
model='clmcom_clm_cclm4_8_17'
model='clmcom_eth_cosmo_crclim'
model='cnrm_aladin63'
model='dmi_hirham5'
model='knmi_racmo22e'
model='mohc_hadrem3_ga7_05'
model='mpi_csc_remo2009'
model='smhi_rca4'
model='uhoh_wrf361h'
```

(section-2.3)=


EQC Quality Assessment: "Bias in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q01  |  Category: Climate_Projections
Section: Bias in extreme temperature indices for the reinsurance sector > Analysis and results > 2. Downloading and processing > 2.3. Apply land-sea mask, change attributes and cut the region to show
---
This section performs the following tasks:

1. Cut the region of interest.
2. Downloads the sea mask for ERA5.
3. Applies the sea mask to both ERA5 data and the model data, which were previously regridded to ERA5's grid (i.e., it applies the ERA5 sea mask to `ds_interpolated`).
4. Regrids the ERA5 land-sea mask to the model's grid and applies it to them.
5. Change some variable attributes for plotting purposes.

**Note:** `ds_interpolated` contains data from the models (mean and trend over the historical period, p-value of the trends...) regridded to ERA5. `model_datasets` contain the same data but in the original grid of each model.

Edit attributes

(section-3)=


EQC Quality Assessment: "Bias in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q01  |  Category: Climate_Projections
Section: Bias in extreme temperature indices for the reinsurance sector > Analysis and results > 3. Plot and describe results
---
This section will display the following results:

- Maps representing the spatial distribution of the **historical mean values** (1971-2000) of the 'SU' index for ERA5, each model individually, the ensemble median (understood as the median of the mean values of the chosen subset of models calculated for each grid cell), and the ensemble spread (derived as the standard deviation of the distribution of the chosen subset of models).
- Maps representing the spatial distribution of the **historical trends** (1971-2000) of the indices 'SU' and 'TX90p'. Similar to the first analysis, this includes ERA5, each model individually, the ensemble median (understood as the median of the trend values of the chosen subset of models calculated for each grid cell), and the ensemble spread (derived as the standard deviation of the distribution of the chosen subset of models).
- **Bias maps of the historical mean values**.
- **Trend bias maps**.
- **Boxplots** representing statistical distributions (PDF) built on the spatially-averaged historical trends from each considered model, displayed together with ERA5.

(section-3.1)=


EQC Quality Assessment: "Bias in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q01  |  Category: Climate_Projections
Section: Bias in extreme temperature indices for the reinsurance sector > Analysis and results > 3. Plot and describe results > 3.1. Define plotting functions
---
The functions presented here are used to plot the mean values and trends calculated over the historical period (1971-2000) for each of the indices ('SU' and 'TX90p').

For a selected index, three layout types can be displayed, depending on the chosen function:

1. Layout including the reference ERA5 product, the ensemble median, the bias of the ensemble median, and the ensemble spread: `plot_ensemble()` is used.
2. Layout including every model (for the trend and mean values): `plot_models()` is employed.
3. Layout including the bias of every model (for the trend and mean values): `plot_models()` is used again.

`trend==True` argument allows displaying trend values over the historical period, while `trend==False` will show mean values. When the `trend` argument is set to `True`, regions with no significance are hatched. For individual models and ERA5, a grid point is considered to have a statistically significant trend when the p-value is lower than 0.05 (in such cases, no hatching is shown). However, for determining trend significance for the ensemble median (understood as the median of the trend values of the chosen subset of models calculated for each grid cell), reliance is placed on agreement categories, following the advanced approach proposed in AR6 [IPCC](https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_Atlas.pdf) on pages 1945-1950. The `hatch_p_value_ensemble()` function is used to distinguish, for each grid point, between three possible cases:

1. If more than 66% of the models are statistically significant (p-value < 0.05) and more than 80% of the models share the same sign, we consider the ensemble median trend to be statistically significant, and there is agreement on the sign. To represent this, no hatching is used.
2. If less than 66% of the models are statistically significant, regardless of agreement on the sign of the trend, hatching is applied (indicating that the ensemble median trend is not statistically significant).
3. If more than 66% of the models are statistically significant but less than 80% of the models share the same sign, we consider the ensemble median trend to be statistically significant, but there is no agreement on the sign of the trend. This is represented using crosses.

Define function to plot the caption of the figures (for the ensemble case)
Add caption to the figure
Add each line to the figure
end captioning
Define function to plot the caption of the figures (for the individual models case)
Add caption to the figure
Add each line to the figure

(section-3.2)=


EQC Quality Assessment: "Bias in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q01  |  Category: Climate_Projections
Section: Bias in extreme temperature indices for the reinsurance sector > Analysis and results > 3. Plot and describe results > 3.2. Plot ensemble maps
---
In this section, we invoke the `plot_ensemble()` function to visualise the mean values and trends calculated over the historical period (1971-2000) for the model ensemble and ERA5 reference product across Europe. Note that the model data used in this section has previously been interpolated to the ERA5 grid.

Specifically, for each of the indices ('SU' and 'TX90p'), this section presents two layouts:

1. Only for the 'SU' index: mean values of the historical period (1971-2000) for: (a) the reference ERA5 product, (b) the ensemble median (understood as the median of the mean values of the chosen subset of models calculated for each grid cell), (c) the bias of the ensemble median, and (d) the ensemble spread (derived as the standard deviation of the distribution of the chosen subset of models).

2. Trend values of the historical period (1971-2000) for: (a) the reference ERA5 product, (b) the ensemble median (understood as the median of the trend values of the chosen subset of models calculated for each grid cell), (c) the bias of the ensemble median, and (d) the ensemble spread (derived as the standard deviation of the distribution of the chosen subset of models).

Fig number counter
Common title

(section-3.3)=


EQC Quality Assessment: "Bias in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q01  |  Category: Climate_Projections
Section: Bias in extreme temperature indices for the reinsurance sector > Analysis and results > 3. Plot and describe results > 3.3. Plot model maps
---
In this section, we invoke the `plot_models()` function to visualise the mean values and trends calculated over the historical period (1971-2000) for every model individually across Europe. Note that the model data used in this section maintains its original grid.

Specifically, for each of the indices ('SU' and 'TX90p'), this section presents two layouts:

1. A layout including the historical mean (1971-2000) of every model (only for the 'SU' index).

2. A layout including the historical trend (1971-2000) of every model.

(section-3.4)=


EQC Quality Assessment: "Bias in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q01  |  Category: Climate_Projections
Section: Bias in extreme temperature indices for the reinsurance sector > Analysis and results > 3. Plot and describe results > 3.4. Plot bias maps
---
In this section, we invoke the `plot_models()` function to visualise the bias for the mean values and trends calculated over the historical period (1971-2000) for every model individually across Europe. Note that the model data used in this section has previously been interpolated to the ERA5 grid.

Specifically, for each of the indices ('SU' and 'TX90p'), this section presents two layouts:

1. A layout including the bias for the historical mean (1971-2000) of every model (only for the 'SU' index).

2. A layout including the bias for the historical trend (1971-2000) of every model.

(section-3.5)=


EQC Quality Assessment: "Bias in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q01  |  Category: Climate_Projections
Section: Bias in extreme temperature indices for the reinsurance sector > Analysis and results > 3. Plot and describe results > 3.5. Boxplots of the historical trend
---
In this last section, we compare the trends of the climate models with the reference trend from ERA5.

Dots represent the spatially-averaged historical trend over the selected region (change of the number of days per decade) for each model (grey), the ensemble mean (blue), and the reference product (orange). The ensemble median is shown as a green line. Note that the spatially averaged values are calculated for each model from its original grid (i.e., no interpolated data has been used here).

The boxplot visually illustrates the distribution of trends among the climate models, with the box covering the first quartile (Q1 = 25th percentile) to the third quartile (Q3 = 75th percentile), and a green line indicating the ensemble median (Q2 = 50th percentile). Whiskers extend from the edges of the box to show the full data range.

Ensemble mean

Fig 10. Boxplots illustrating the historical trends of the distribution of the chosen subset of models and ERA5 for: (a) the 'SU' index and (b) the 'TX90p' index. The distribution is created by considering spatially averaged trends across Europe. The ensemble mean and the ensemble median trends are both included. Outliers in the distribution are denoted by a grey circle with a black contour.

(section-3.6)=


EQC Quality Assessment: "Bias in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q01  |  Category: Climate_Projections
Section: Bias in extreme temperature indices for the reinsurance sector > Analysis and results > 3. Plot and describe results > 3.6. Results summary and discussion
---
- Across the examined region, the selected subset of Regional Climate Models (RCMs) consistently tend to underestimate historical trends compared to ERA5 for the JJA temporal aggregation. Specifically, for the 'SU' index, the CORDEX ensemble median, as derived from boxplots, displays a trend of approximately 0.5 days per decade, contrasting with ERA5's ~2 days per decade. Similarly, the 'TX90p' index reveals around 0.6 days per decade for the CORDEX ensemble median compared to the ~2 days per decade observed in ERA5. The interquartile range spans from approximately 0.25 to 0.75 for the 'SU' index and from 0.5 to 0.75 for the 'TX90p' index. These outcomes align with findings from the assessment done for CMIP6 Global Climate Models (GCMs) but the magnitudes of the trends are more underestimaded.

- While RCMs have demonstrated capability in enhancing GCMs' mean values for the considered indices, their efficacy in replicating historical trends appears limited. Analysing the spatial patterns of trend bias, the ensemble median of the CORDEX models results closely resemble those obtained in the CMIP6 exercise. Notably, the most significant underestimation of trends is evident in the Mediterranean basin.

- In contrast to climatological assessments, the consistency in trend bias patterns across diverse RCMs suggests a potential dependence on the driving GCM, shared among all RCMs. A more extensive GCM-RCM matrix is imperative to accurately quantify this dependency and delineate the partitioning of uncertainty between GCMs and RCMs.

- What do the results mean for users?  Are the biases relevant?

- For the JJA period and the subset of regional models considered, these outcomes aid in optimising reinsurance protections. However, they are accompanied by uncertainties that require careful consideration for informed decision-making. Users should be aware that biases impact the climatology and trend of the indices differently. In this case, the climatology of the indices appears to be better represented compared to another CMIP6 assessment that covers the same period and seasonal aggregation ("CMIP6 Climate Projections: evaluating bias in extreme temperature indices for the reinsurance sector"), but the trend is more underestimated than in that assessment. Therefore, users should carefully tailor their choice of bias correction method [[6]](https://doi.org/10.1002/asl.1072)[[7]](https://ibicus.readthedocs.io/en/latest/).

RESULTS NOTE:

It is important to note that the results presented are specific to the 9 models chosen, and users should aim to assess as wide a range of models as possible before making a sub-selection.


EQC Quality Assessment: "Bias in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q01  |  Category: Climate_Projections
Section: Bias in extreme temperature indices for the reinsurance sector > ℹ If you want to know more > Key resources
---
Some key resources and further reading were linked throughout this assessment.

The CDS catalogue entries for the data used were:
* CORDEX regional climate model data on single levels (Daily mean - Maximum 2m temperature in the last 24 hours): https://cds.climate.copernicus.eu/datasets/projections-cordex-domains-single-levels?tab=overview
* ERA5 hourly data on single levels from 1940 to present (2m temperature): https://cds.climate.copernicus.eu/datasets/reanalysis-era5-single-levels?tab=overview

Code libraries used:
* [C3S EQC custom functions](https://github.com/bopen/c3s-eqc-automatic-quality-control/tree/main/c3s_eqc_automatic_quality_control), `c3s_eqc_automatic_quality_control`,  prepared by [B-Open](https://www.bopen.eu/)
* [icclim](https://icclim.readthedocs.io/en/stable/) Python package


EQC Quality Assessment: "Bias in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q01  |  Category: Climate_Projections
Section: Bias in extreme temperature indices for the reinsurance sector > ℹ If you want to know more > References
---
[[1]](https://doi.org/10.3390/atmos11020146) Tesselaar, M., Botzen, W.J.W., Aerts, J.C.J.H. (2020). Impacts of Climate Change and Remote Natural Catastrophes on EU Flood Insurance Markets: An Analysis of Soft and Hard Reinsurance Markets for Flood Coverage. Atmosphere 2020, 11, 146. https://doi.org/10.3390/atmos11020146

[[2]](https://doi.org/10.5194/nhess-22-659-2022) Rädler, A. T. (2022). Invited perspectives: how does climate change affect the risk of natural hazards? Challenges and step changes from the reinsurance perspective. Nat. Hazards Earth Syst. Sci., 22, 659–664. https://doi.org/10.5194/nhess-22-659-2022

[[3]](https://www.ipcc.ch/site/assets/uploads/2018/03/wg2TARchap8.pdf) Vellinga, P., Mills, E., Bowers, L., Berz, G.A., Huq, S., Kozak, L.M., Paultikof, J., Schanzenbacker, B., Shida, S., Soler, G., Benson, C., Bidan, P., Bruce, J.W., Huyck, P.M., Lemcke, G., Peara, A., Radevsky, R., Schoubroeck, C.V., Dlugolecki, A.F. (2001). Insurance and other financial services. In J. J. McCarthy, O. F. Canziani, N. A. Leary, D. J. Dokken, & K. S. White (Eds.), Climate change 2001: impacts, adaptation, and vulnerability. Contribution of working group 2 to the third assessment report of the intergovernmental panel on climate change. (pp. 417-450). Cambridge University Press.

[[4]](https://doi.org/10.1002/wcc.71) Lemos, M.C. and Rood, R.B. (2010). Climate projections and their impact on policy and practice. WIREs Clim Chg, 1: 670-682. https://doi.org/10.1002/wcc.71

[[5]](https://doi.org/10.1002/wcc.579) Nissan H, Goddard L, de Perez EC, et al. (2019). On the use and misuse of climate change projections in international development. WIREs Clim Change, 10:e579. https://doi.org/10.1002/wcc.579

[[6]](https://doi.org/10.1002/asl.1072) Iturbide, M., Casanueva, A., Bedia, J., Herrera, S., Milovac, J., Gutiérrez, J.M. (2021). On the need of bias adjustment for more plausible climate change projections of extreme heat. Atmos. Sci. Lett., 23, e1072. https://doi.org/10.1002/asl.1072

[[7]](https://ibicus.readthedocs.io/en/latest/) https://ibicus.readthedocs.io/en/latest/

[[8]](https://doi.org/10.1002/wcc.8) Rummukainen, M. (2010). State-of-the-art with regional climate models. WIREs Clim Change, 1: 82-96. https://doi.org/10.1002/wcc.8

[[9]](https://doi.org/10.1088/1748-9326/aacc77) Silje Lund Sørland et al. (2018). Bias patterns and climate change signals in GCM-RCM model chains. Environ. Res. Lett. 13 074017. https://doi.org/10.1088/1748-9326/aacc77


EQC Quality Assessment: "Uncertainty in projected changes in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q02  |  Category: Climate_Projections
Section: Uncertainty in projected changes in extreme temperature indices for the reinsurance sector
---
Production date: 9-07-2024

Produced by: CMCC foundation - Euro-Mediterranean Center on Climate Change. Albert Martinez Boti.


EQC Quality Assessment: "Uncertainty in projected changes in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q02  |  Category: Climate_Projections
Section: Uncertainty in projected changes in extreme temperature indices for the reinsurance sector > Quality assessment question
---
* **What are the projected future changes and associated uncertainties in air temperature extremes in Europe?**
* **Do I get different results than if I use CMIP6 projections?**

Climate change has a major impact on the reinsurance market [[1]](https://doi.org/10.3390/atmos11020146)[[2]](https://doi.org/10.5194/nhess-22-659-2022). In the third assessment report of the IPCC, hot temperature extremes were already presented as relevant to insurance and related services [[3]](https://www.ipcc.ch/site/assets/uploads/2018/03/wg2TARchap8.pdf). Consequently, the need for reliable regional and global climate projections has become paramount, offering valuable insights for optimising reinsurance strategies in the face of a changing climate landscape. Nonetheless, despite their pivotal role, uncertainties inherent in these projections can potentially lead to misuse [[4]](https://doi.org/10.1002/wcc.71)[[5]](https://doi.org/10.1002/wcc.579). This underscores the importance of accurately calculating and accounting for uncertainties to ensure their appropriate consideration. This notebook utilises data from a subset of models from **[CORDEX](https://cds.climate.copernicus.eu/datasets/projections-cordex-domains-single-levels?tab=overview)** Regional Climate Models (RCMs) and explores the uncertainty in future projections of maximum temperature-based extreme indices by considering the ensemble inter-model spread of projected changes. Two maximum temperature-based indices from [ECA&D](https://www.ecad.eu/indicesextremes/) indices (one of physical nature and the other of statistical nature) are computed using the [icclim](https://icclim.readthedocs.io/en/stable/) Python package. The first index, identified by the ETCCDI short name 'SU', quantifies the occurrence of summer days (i.e., with daily maximum temperatures exceeding 25°C) within a year or a season (JJA in this notebook). The second index, labeled 'TX90p', describes the number of days with daily maximum temperatures exceeding the daily 90th percentile of maximum temperature for a 5-day moving window. For this notebook, the daily 90th percentile threshold is calculated for the historical period spanning from 1971 to 2000. The index calculations, though, are performed over the future period from 2015 to 2099, following the Representative Concentration Pathway RCP 8.5. It is important to note that the results presented here pertain to a specific subset of the CORDEX ensemble and may not be generalisable to the entire dataset. Also note that a separate assessment examines the representation of climatology and trends of these indices for the same models during the historical period (1971-2000).


EQC Quality Assessment: "Uncertainty in projected changes in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q02  |  Category: Climate_Projections
Section: Uncertainty in projected changes in extreme temperature indices for the reinsurance sector > Quality assessment statement
---
These are the key outcomes of this assessment

* All models within the considered subset agree on projecting positive future trends (2015-2099) for both indices across Europe during the temporal aggregation of JJA, with a particularly notable positive projected trend in the Mediterranean Basin for 'TX90p'. This finding is consistent with the results of Josep Cos et al. (2022) [[6]](https://doi.org/10.5194/esd-13-321-2022), who evaluated the Mediterranean climate change hotspot using CMIP6 projections. While certain regions exhibit near-zero trends for the 'SU' index, possibly due to threshold temperature constraints, others show higher values, highlighting the importance of considering both statistically and physically based extreme indices for comprehensive assessments. In fact this arise limitations of the 'SU' index, indicating the potential need to select a higher (or lower for northern areas) threshold to capture the changes in these regions. Such regions, where the changes may be just as impactful or even more so than areas with a significant increase in days above 25 degrees, require careful consideration.

* The magnitude of the trend is smaller and shows more spatial variability than in another CMIP6 future trend assessment ("Uncertainty in projected changes in extreme temperature indices for the reinsurance sector").

* The findings underscore the need for proactive measures to optimise reinsurance protections in the face of projected increases in air temperature extremes for the future period spanning from 2015 to 2099. While all considered models show a positive trend for these indices, the spatial variation in the magnitude of these trends and their uncertainty, quantified by the inter-model spread, underscores the need for careful consideration.

* A larger GCM-RCM matrix should be considered when addressing specific cases to enhance the robustness of the analysis and account for uncertainties [[7]](https://doi.org/10.1002/wcc.8)[[8]](https://doi.org/10.1088/1748-9326/aacc77)
```

attachment:6243ed90-3ae0-4340-bff3-5af1cead6e6b.png
---
alt: trend_future_TX90p_CORDEX
width: 900px
---
Number of days with daily maximum temperatures exceeding the daily 90th percentile of maximum temperature for a 5-day moving window ('TX90p') for the temporal aggregation of 'JJA'. Trend for the future period (2015-2099). For this index, the reference daily 90th percentile threshold is calculated based on the historical period (1971-2000). The layout includes data corresponding to: (a) the ensemble median (understood as the median of the trend values of the chosen subset of models calculated for each grid cell) and (b) the ensemble spread (derived as the standard deviation of the distribution of the chosen subset of models).
```


EQC Quality Assessment: "Uncertainty in projected changes in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q02  |  Category: Climate_Projections
Section: Uncertainty in projected changes in extreme temperature indices for the reinsurance sector > Methodology
---
This notebook offers an assessment of the projected changes and their associated uncertainties using a subset of 9 models from [CORDEX](https://cds.climate.copernicus.eu/datasets/projections-cordex-domains-single-levels?tab=overview). The uncertainty is examined by analysing the ensemble inter-model spread of projected changes for the maximum-temperature-based indices 'SU' and 'TX90p,' calculated over the temporal aggregation of JJA for the future period spanning from 2015 to 2099. In particular, spatial patterns of climate projected trends are examined and displayed for each model individually and for the ensemble median (calculated for each grid cell), alongside the ensemble inter-model spread to account for projected uncertainty. Additionally, spatially-averaged trend values are analysed and presented using box plots to provide an overview of trend behavior across the distribution of the chosen subset of models when averaged across Europe.

The analysis and results follow the next outline:

**[](section-1)**
 * [](section-1.1)
 * [](section-1.2)
 * [](section-1.3)
 * [](section-1.4)
 * [](section-1.5)
 * [](section-1.6)

**[](section-2)**
 * [](section-2.1)
 * [](section-2.2)
 * [](section-2.3)

**[](section-3)**
 * [](section-3.1)
 * [](section-3.2)
 * [](section-3.3)
 * [](section-3.4)
 * [](section-3.5)


EQC Quality Assessment: "Uncertainty in projected changes in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q02  |  Category: Climate_Projections
Section: Uncertainty in projected changes in extreme temperature indices for the reinsurance sector > Analysis and results > 1. Parameters, requests and functions definition > 1.2. Define Parameters
---
In the "Define Parameters" section, various customisable options for the notebook are specified. Most of the parameters chosen are the same as those used in other assessments ([](./climate_projections-cordex-domains-single-levels_climate-and-weather-extremes_q01.ipynb)), being them:
- The initial and ending year used for the future projections period can be specified by changing the parametes `future_slice` (2015-2099 is chosen for consistency between CORDEX and CMIP6).
- `historical_slice` determines the historical period used (1971 to 2000 is choosen to allow comparison to CORDEX models in other assessments).
- The `timeseries` set the temporal aggregation. For instance, selecting "DJF" implies considering only the winter season.
- `collection_id` provides the choice between Global Climate Models CMIP6 or Regional Climate Models CORDEX. Although the code allows choosing between CMIP6 or CORDEX, the example provided in this notebook deals with CORDEX RCMs.
- `area` allows specifying the geographical domain of interest.
- The `interpolation_method` parameter allows selecting the interpolation method when regridding is performed over the indices.
- The `chunk` selection allows the user to define if dividing into chunks when downloading the data on their local machine. Although it does not significantly affect the analysis, it is recommended to keep the default value for optimal performance.

Choose annual or seasonal timeseries
Choose CORDEX or CMIP6
Interpolation method
Area to show
Chunks for download

(section-1.3)=


EQC Quality Assessment: "Uncertainty in projected changes in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q02  |  Category: Climate_Projections
Section: Uncertainty in projected changes in extreme temperature indices for the reinsurance sector > Analysis and results > 1. Parameters, requests and functions definition > 1.3. Define models
---
The following climate analyses are performed considering a subset of GCMs from CMIP6. Models names are listed in the parameters below. Some variable-dependent parameters are also selected, as the `index_names` parameter, which specifies the maximum-temperature-based indices ('SU' and 'TX90p' in our case) from the [icclim](https://icclim.readthedocs.io/en/stable/) Python package.

When choosing Cordex models, it is crucial to consider the availability of RCMs for the selected GCM and the specified region. The listed RCMs, for instance, are accessible for the GCM “mpi_m_mpi_esm_lr” in the “europe” cordex_domain, and they are the same as those used in other assessments ("CORDEX Climate Projections: evaluating bias in extreme temperature indices for the reinsurance sector"). To confirm the available combinations, refer to the [CORDEX](https://cds.climate.copernicus.eu/datasets/projections-cordex-domains-single-levels?tab=overview) CDS catalogue entry.

Define dictionaries to use in titles and caption
Define dictionaries to use in titles and caption

(section-1.4)=


EQC Quality Assessment: "Uncertainty in projected changes in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q02  |  Category: Climate_Projections
Section: Uncertainty in projected changes in extreme temperature indices for the reinsurance sector > Analysis and results > 1. Parameters, requests and functions definition > 1.4. Define land-sea mask request
---
Within this notebook, ERA5 will be used to download the land-sea mask when plotting. In this section, we set the required parameters for the cds-api data-request of ERA5 land-sea mask.

(section-1.5)=


EQC Quality Assessment: "Uncertainty in projected changes in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q02  |  Category: Climate_Projections
Section: Uncertainty in projected changes in extreme temperature indices for the reinsurance sector > Analysis and results > 1. Parameters, requests and functions definition > 1.5. Define model requests
---
In this section we set the required parameters for the cds-api data-request.

The `get_cordex_years` function is employed to choose suitable data chunks for CORDEX data requests.

When `Weights = True`, spatial weighting is applied for calculations requiring spatial data aggregation. This is particularly relevant for CMIP6 GCMs with regular lon-lat grids that do not consider varying surface extensions at different latitudes. In contrast, CORDEX RCMs, using rotated grids, inherently account for different cell surfaces based on latitude, eliminating the need for a latitude cosine multiplicative factor (`Weights = False`).

(section-1.6)=


EQC Quality Assessment: "Uncertainty in projected changes in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q02  |  Category: Climate_Projections
Section: Uncertainty in projected changes in extreme temperature indices for the reinsurance sector > Analysis and results > 1. Parameters, requests and functions definition > 1.6. Functions to cache
---
In this section, functions that will be executed in the caching phase are defined. Caching is the process of storing copies of files in a temporary storage location, so that they can be accessed more quickly. This process also checks if the user has already downloaded a file, avoiding redundant downloads.

Functions description:

- The `select_timeseries` function subsets the dataset based on the chosen `timeseries` parameter.

- The `compute_indices` function utilises the icclim package to calculate the maximum-temperature-based indices.

- The `compute_trends` function employs the Mann-Kendall test for trend calculation.

- Finally, the `compute_indices_and_trends` function calculates the maximum-temperature-based indices for the corresponding temporal aggregation using the `compute_indices` function, determines the indices mean for the future period (2015-2099), obtain the trends using the `compute_trends` function, and offers an option for regridding to `model_regrid`.

Original bounds for conservative interpolation

(section-2)=


EQC Quality Assessment: "Uncertainty in projected changes in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q02  |  Category: Climate_Projections
Section: Uncertainty in projected changes in extreme temperature indices for the reinsurance sector > Analysis and results > 2. Downloading and processing > 2.1. Download and transform the regridding model
---
In this section, the `download.download_and_transform` function from the 'c3s_eqc_automatic_quality_control' package is employed to download daily data from the selected CORDEX regridding model, compute the maximum-temperature-based indices for the selected temporal aggregation, calculate the mean and trend over the future projections period (2015-2099), and cache the result (to avoid redundant downloads and processing).

The regridding model is intended here as the model whose grid will be used to interpolate the others. This ensures all models share a common grid, facilitating the calculation of median values for each cell point. The regridding model within this notebook is "clmcom_eth_cosmo_crclim" but a different one can be selected by just modifying the `model_regrid` parameter at [](section-1.3). It is key to highlight the importance of the chosen target grid depending on the specific application.

(section-2.2)=


EQC Quality Assessment: "Uncertainty in projected changes in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q02  |  Category: Climate_Projections
Section: Uncertainty in projected changes in extreme temperature indices for the reinsurance sector > Analysis and results > 2. Downloading and processing > 2.2. Download and transform models
---
In this section, the `download.download_and_transform` function from the 'c3s_eqc_automatic_quality_control' package is employed to download daily data from the CORDDEX models, compute the maximum-temperature-based indices for the selected temporal aggregation, calculate the mean and trend over the future period (2015-2099), interpolate to the regridding model's grid (only for the cases in which it is specified, in the other cases, the original model's grid is mantained), and cache the result (to avoid redundant downloads and processing).

Original model
Interpolated model

```text
model='clmcom_clm_cclm4_8_17'
model='clmcom_eth_cosmo_crclim'
model='cnrm_aladin63'
model='dmi_hirham5'
model='knmi_racmo22e'
model='mohc_hadrem3_ga7_05'
model='mpi_csc_remo2009'
model='smhi_rca4'
model='uhoh_wrf361h'
```

(section-2.3)=


EQC Quality Assessment: "Uncertainty in projected changes in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q02  |  Category: Climate_Projections
Section: Uncertainty in projected changes in extreme temperature indices for the reinsurance sector > Analysis and results > 2. Downloading and processing > 2.3. Apply land-sea mask, change attributes and cut the region to show
---
This section performs the following tasks:

1. Cut the region of interest.
2. Downloads the sea mask for ERA5.
3. Regrids ERA5's mask to the `model_regrid` grid and applies it to the regridded data
4. Regrids the ERA5 land-sea mask to the model's original grid and applies it to them.
5. Change some variable attributes for plotting purposes.

**Note:** `ds_interpolated` contains data from the models regridded to the regridding model's grid. `model_datasets` contain the same data but in the original grid of each model.

Edit attributes

(section-3)=


EQC Quality Assessment: "Uncertainty in projected changes in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q02  |  Category: Climate_Projections
Section: Uncertainty in projected changes in extreme temperature indices for the reinsurance sector > Analysis and results > 3. Plot and describe results
---
This section will display the following results:

- Maps representing the spatial distribution of the **future trends** (2015-2099) of the indices 'SU' and 'TX90p' for each model individually, the ensemble median (understood as the median of the trend values of the chosen subset of models calculated for each grid cell), and the ensemble spread (derived as the standard deviation of the distribution of the chosen subset of models).
- **Boxplots** which represent statistical distributions (PDF) built on the spatially-averaged future trend from each considered model.

(section-3.1)=


EQC Quality Assessment: "Uncertainty in projected changes in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q02  |  Category: Climate_Projections
Section: Uncertainty in projected changes in extreme temperature indices for the reinsurance sector > Analysis and results > 3. Plot and describe results > 3.1. Define plotting functions
---
The functions presented here are used to plot the trends calculated over the future period (2015-2099) for each of the indices ('SU' and 'TX90p').

For a selected index, two layout types will be displayed, depending on the chosen function:

1. Layout including the ensemble median and the ensemble spread for the trend: `plot_ensemble()` is used.
2. Layout including every model trend: `plot_models()` is employed.

`trend==True` allows displaying trend values over the future period, while `trend==False` show mean values. In this notebook, which focuses on the future period, only trend values will be shown, and, consequently, `trend==True`. When the `trend` argument is set to True, regions with no significance are hatched. For individual models, a grid point is considered to have a statistically significant trend when the p-value is lower than 0.05 (in such cases, no hatching is shown). However, for determining trend significance for the ensemble median (understood as the median of the trend values of the chosen subset of models calculated for each grid cell), reliance is placed on agreement categories, following the advanced approach proposed in AR6 [IPCC](https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_Atlas.pdf) on pages 1945-1950. The `hatch_p_value_ensemble()` function is used to distinguish, for each grid point, between three possible cases:

1. If more than 66% of the models are statistically significant (p-value < 0.05) and more than 80% of the models share the same sign, we consider the ensemble median trend to be statistically significant, and there is agreement on the sign. To represent this, no hatching is used.
2. If less than 66% of the models are statistically significant, regardless of agreement on the sign of the trend, hatching is applied (indicating that the ensemble median trend is not statistically significant).
3. If more than 66% of the models are statistically significant but less than 80% of the models share the same sign, we consider the ensemble median trend to be statistically significant, but there is no agreement on the sign of the trend. This is represented using crosses.

Define function to plot the caption of the figures (for the ensemble case)
Add caption to the figure
Add each line to the figure
end captioning
Define function to plot the caption of the figures (for the individual models case)
Add caption to the figure
Add each line to the figure

(section-3.2)=


EQC Quality Assessment: "Uncertainty in projected changes in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q02  |  Category: Climate_Projections
Section: Uncertainty in projected changes in extreme temperature indices for the reinsurance sector > Analysis and results > 3. Plot and describe results > 3.2. Plot ensemble maps
---
In this section, we invoke the `plot_ensemble()` function to visualise the trend calculated over the future period (2015-2099) for the model ensemble across Europe. Note that the model data used in this section has previously been interpolated to the "regridding model" grid (`"clmcom_eth_cosmo_crclim"` for this notebook).

Specifically, for each of the indices ('SU' and 'TX90p'), this section presents a single layout including trend values of the future period (2015-2099) for: (a) the ensemble median (understood as the median of the trend values of the chosen subset of models calculated for each grid cell) and (b) the ensemble spread (derived as the standard deviation of the distribution of the chosen subset of models).

Fig number counter
Common title

(section-3.3)=


EQC Quality Assessment: "Uncertainty in projected changes in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q02  |  Category: Climate_Projections
Section: Uncertainty in projected changes in extreme temperature indices for the reinsurance sector > Analysis and results > 3. Plot and describe results > 3.3. Plot model maps
---
In this section, we invoke the `plot_models()` function to visualise the trend over the future period (2015-2099) for every model individually. Note that the model data used in this section maintains its original grid.

Specifically, for each of the indices ('SU' and 'TX90p'), this section presents a single layout including the trend for the future period (2015-2099) of every model.

(section-3.4)=


EQC Quality Assessment: "Uncertainty in projected changes in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q02  |  Category: Climate_Projections
Section: Uncertainty in projected changes in extreme temperature indices for the reinsurance sector > Analysis and results > 3. Plot and describe results > 3.4. Boxplots of the future trend
---
Finally, we present boxplots representing the ensemble distribution of each climate model trend calculated over the future period (2015-2099) across Europe.

Dots represent the spatially-averaged future trend over the selected region (change of the number of days per decade) for each model (grey) and the ensemble mean (blue). The ensemble median is shown as a green line. Note that the spatially averaged values are calculated for each model from its original grid (i.e., no interpolated data has been used here).

The boxplot visually illustrates the distribution of trends among the climate models, with the box covering the first quartile (Q1 = 25th percentile) to the third quartile (Q3 = 75th percentile), and a green line indicating the ensemble median (Q2 = 50th percentile). Whiskers extend from the edges of the box to show the full data range.

Ensemble mean

Fig 5. Boxplots illustrating the future trends of the ensemble distribution for: (a) the 'SU' index and (b) the 'TX90p' index. The distribution is created by considering spatially averaged trends across Europe. The ensemble mean and the ensemble median trends are both included. Outliers in the distribution are denoted by a grey circle with a black contour.

(section-3.5)=


EQC Quality Assessment: "Uncertainty in projected changes in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q02  |  Category: Climate_Projections
Section: Uncertainty in projected changes in extreme temperature indices for the reinsurance sector > Analysis and results > 3. Plot and describe results > 3.5. Results summary and discussion
---
- For the temporal aggregation of JJA, future trends (2015-2099) exhibit positive values over Europe for both considered indices. For the number of summer days index (SU), the southern part of the Mediterranean Basin and the northernmost regions of Europe have trends near 0. This may be due to the fact that, for the future period, the number of summer days remains constant near 0 for the northern parts of Europe (where the threshold temperature of 25°C may be too high to be reached). Meanwhile, for the southern part of the Mediterranean Basin, this phenomenon may be attributed to the fact that the threshold is already surpassed for the entire JJA season. This emphasises the necessity to consider both statistically and physically based extreme indices for a proper assessment.

- Regional differences can also be observed for the 'TX90p' index. Notably, values are higher for the Mediterranean Basin, consistent with the findings of [[6]](https://doi.org/10.5194/esd-13-321-2022), who assessed the Mediterranean climate change hotspot using CMIP6 projections. These regional differences appear to be greater than those observed for the CMIP6 future trend analysis of the same index ("CMIP6 Climate Projections: evaluating uncertainty in projected changes in extreme temperature indices for the reinsurance sector").

- The boxplots show spatially averaged positive trends over Europe. For the 'SU' index, the ensemble median trends reach a value of 1.4 days per decade. For the 'TX90p' index, the ensemble median is nearly 5 days per decade. The interquantile range of the ensemble spans from 1.3 to 1.7 days per decade for the 'SU' index and from 4.5 to more than 5.2 days per decade for the 'TX90p' index. As for the historical analyses, the spatially-averaged trend values are lower than those obtained for the CMIP6 exercise.

- What do the results mean for users?  Are the biases relevant?

- The findings underscore the need for proactive measures to optimise reinsurance protections in the face of projected increases in air temperature extremes for the future period spanning from 2015 to 2099. While all considered models show a positive trend for these indices, the spatial variation in the magnitude of these trends and their uncertainty, quantified by the inter-model spread, underscores the need for careful consideration.

- It is also important to point out that the magnitude of the trend is lower than that obtained in another CMIP6 assessment that covers the same period and seasonal aggregation ("CMIP6 Climate Projections: evaluating uncertainty in projected changes in extreme temperature indices for the reinsurance sector").

- Finally, it should also be taken into account the biases of the trend obtained for a CORDEX assessment ("CORDEX Climate Projections: evaluating bias in extreme temperature indices for the reinsurance sector"), which showed an important underestimation for the trend during the historical period (1971-2000).

RESULTS NOTE:

It is important to note that the results presented are specific to the 9 models chosen, and users should aim to assess as wide a range of models as possible before making a sub-selection.


EQC Quality Assessment: "Uncertainty in projected changes in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q02  |  Category: Climate_Projections
Section: Uncertainty in projected changes in extreme temperature indices for the reinsurance sector > ℹ If you want to know more > Key resources
---
Some key resources and further reading were linked throughout this assessment.

The CDS catalogue entries for the data used were:
* CORDEX regional climate model data on single levels (Daily mean - Maximum 2m temperature in the last 24 hours): https://cds.climate.copernicus.eu/datasets/projections-cordex-domains-single-levels?tab=overview

Code libraries used:
* [C3S EQC custom functions](https://github.com/bopen/c3s-eqc-automatic-quality-control/tree/main/c3s_eqc_automatic_quality_control), `c3s_eqc_automatic_quality_control`,  prepared by [B-Open](https://www.bopen.eu/)
* [icclim](https://icclim.readthedocs.io/en/stable/) Python package


EQC Quality Assessment: "Uncertainty in projected changes in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q02  |  Category: Climate_Projections
Section: Uncertainty in projected changes in extreme temperature indices for the reinsurance sector > ℹ If you want to know more > References
---
[[1]](https://doi.org/10.3390/atmos11020146) Tesselaar, M., Botzen, W.J.W., Aerts, J.C.J.H. (2020). Impacts of Climate Change and Remote Natural Catastrophes on EU Flood Insurance Markets: An Analysis of Soft and Hard Reinsurance Markets for Flood Coverage. Atmosphere 2020, 11, 146. https://doi.org/10.3390/atmos11020146

[[2]](https://doi.org/10.5194/nhess-22-659-2022) Rädler, A. T. (2022). Invited perspectives: how does climate change affect the risk of natural hazards? Challenges and step changes from the reinsurance perspective. Nat. Hazards Earth Syst. Sci., 22, 659–664. https://doi.org/10.5194/nhess-22-659-2022

[[3]](https://www.ipcc.ch/site/assets/uploads/2018/03/wg2TARchap8.pdf) Vellinga, P., Mills, E., Bowers, L., Berz, G.A., Huq, S., Kozak, L.M., Paultikof, J., Schanzenbacker, B., Shida, S., Soler, G., Benson, C., Bidan, P., Bruce, J.W., Huyck, P.M., Lemcke, G., Peara, A., Radevsky, R., Schoubroeck, C.V., Dlugolecki, A.F. (2001). Insurance and other financial services. In J. J. McCarthy, O. F. Canziani, N. A. Leary, D. J. Dokken, & K. S. White (Eds.), Climate change 2001: impacts, adaptation, and vulnerability. Contribution of working group 2 to the third assessment report of the intergovernmental panel on climate change. (pp. 417-450). Cambridge University Press.

[[4]](https://doi.org/10.1002/wcc.71) Lemos, M.C. and Rood, R.B. (2010). Climate projections and their impact on policy and practice. WIREs Clim Chg, 1: 670-682. https://doi.org/10.1002/wcc.71

[[5]](https://doi.org/10.1002/wcc.579) Nissan H, Goddard L, de Perez EC, et al. (2019). On the use and misuse of climate change projections in international development. WIREs Clim Change, 10:e579. https://doi.org/10.1002/wcc.579

[[6]](https://doi.org/10.5194/esd-13-321-2022) Cos, J., Doblas-Reyes, F., Jury, M., Marcos, R., Bretonnière, P.-A., and Samsó, M. (2022). The Mediterranean climate change hotspot in the CMIP5 and CMIP6 projections, Earth Syst. Dynam., 13, 321–340. https://doi.org/10.5194/esd-13-321-2022

[[7]](https://doi.org/10.1002/wcc.8) Rummukainen, M. (2010). State-of-the-art with regional climate models. WIREs Clim Change, 1: 82-96. https://doi.org/10.1002/wcc.8

[[8]](https://doi.org/10.1088/1748-9326/aacc77) Silje Lund Sørland et al. (2018). Bias patterns and climate change signals in GCM-RCM model chains. Environ. Res. Lett. 13 074017. https://doi.org/10.1088/1748-9326/aacc77


EQC Quality Assessment: "Bias in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q03  |  Category: Climate_Projections
Section: Bias in precipitation-based indices for impact models
---
Production date: 29-05-2024

Produced by: CMCC foundation - Euro-Mediterranean Center on Climate Change. Albert Martinez Boti.


EQC Quality Assessment: "Bias in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q03  |  Category: Climate_Projections
Section: Bias in precipitation-based indices for impact models > Quality assessment question
---
* **How well do CORDEX projections represent climatology and trends of precipitation-based indices in Europe?**

Soil erosion stands as one of the primary environmental concerns in Europe [[1]](https://doi.org/10.1016/j.envsci.2015.08.012). Its accelerated occurrence can precipitate a decline in ecosystem stability, land productivity, and overall land degradation, resulting in diminished income for farmers [[2]](https://doi.org/10.1016/j.landusepol.2012.11.007). This notebook is designed to evaluate the effectiveness of a specific set of models from **[CORDEX](https://cds.climate.copernicus.eu/datasets/projections-cordex-domains-single-levels?tab=overview)** Regional Climate Models (RCMs) in accurately replicating historical precipitation extreme indices. These selected rainfall indicators are recognised as valuable proxies for rainfall erosivity, a factor directly linked to empirical calculations of soil loss, as outlined in an application available through the old CDS platform ([dataset documentation](https://dast.copernicus-climate.eu/documents/sis-soil-erosion/C3S_D429d.2.3.2_Product_User_Guide_v1.2.pdf)). The five precipitation-based indices used here are calculated using the **[icclim](https://icclim.readthedocs.io/en/stable/)** package, them being:
- Spell length of days with precipitation greater than 1 mm (also known as "Maximum consecutive wet days" - "CWD")
- Number of heavy precipitation days (Precip >= 20mm - "R20mm")
- Number of wet days (Precip >= 1mm - "RR1")
- Maximum 1-day total precipitation ("RX1day")
- Maximum 5-day total precipitation ("RX5day").

Within this notebook, these calculations are performed over the temporal aggregation of DJF and for the historical period spanning from 1971 to 2000. It is important to note that the results presented here pertain to a specific subset of the CORDEX ensemble and may not be generalisable to the entire dataset. Also note that a separate assessment examines the representation of trends of these indices for the same models during a fixed future period (2015-2099).


EQC Quality Assessment: "Bias in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q03  |  Category: Climate_Projections
Section: Bias in precipitation-based indices for impact models > Quality assessment statement
---
These are the key outcomes of this assessment

* The assessment of CORDEX projections regarding the climatology and trend of precipitation-based indices across Europe requires a comprehensive evaluation of the historical period.

* The subset of Regional Climate Models (RCMs) considered in this notebook for the seasonal aggregation of DJF generally struggle to replicate both the observed climatology and historical trends of the selected precipitation-based indices, with particular difficulty in capturing the trends. However, the models manage to accurately capture the climatology and trend directions for certain regions and indices. For instance, the models reflect an increasing trend for the CWD index in the western part of the Iberian Peninsula and an upward trend for RR1 in central Europe. Users should take into account these regional variations, the specific indices they intend to use, the differing bias behaviours between climatology and trends, and the necessity of bias-correcting data before using it for hydrological applications [[3]](https://doi.org/10.1016/j.jhydrol.2012.05.052).

* Precipitation trends in observational and reanalysis datasets are generally less robust and more challenging to detect compared to temperature trends. This limitation is also evident in model simulations.

* While ERA5 serves as a reference dataset in this notebook, it is important to recognise its inherent uncertainties. Although uncertainties exist for all variables, these biases are especially relevant for variables like surface wind or precipitation, as shown in [[4]](https://doi.org/10.1002/qj.3616) and [[5]](https://doi.org/10.3390/atmos12111462). This highlights the need for cautious interpretation, particularly in the context of precipitation extremes.

* A larger GCM-RCM matrix should be considered when addressing specific cases to enhance the robustness of the analysis and account for uncertainties [[6]](https://doi.org/10.1002/wcc.8)[[7]](https://doi.org/10.1088/1748-9326/aacc77).
```

attachment:4890e24e-847d-40bd-91e3-ea3202916a49.png
---
alt: mean_bias_RR1
width: 900px
---
Number of wet days (Precip >= 1mm) ('RRI') for the temporal aggreggtion of 'DJF'. Mean bias for the historical period (1971 - 2000) of each individual CORDEX model.
```

NOTE on the DJF selection:

It is important to note that using seasonal temporal aggregations offers only partial insights into the dynamics. For more comprehensive results, it is advisable to also consider other seasons and annual aggregations. However, for the sake of efficiency and to avoid making the notebook too heavy, we have opted to prioritise seasonal aggregations.


EQC Quality Assessment: "Bias in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q03  |  Category: Climate_Projections
Section: Bias in precipitation-based indices for impact models > Methodology
---
This notebook provides an assessment of the systematic errors (trend and climatology) in a subset of 9 models from [CORDEX](https://cds.climate.copernicus.eu/datasets/projections-cordex-domains-single-levels?tab=overview). The analysis involves comparing model predictions with ERA5 reanalysis data using several precipitation-based indices. These indices, calculated over the DJF period for the historical period spanning from 1971 to 2000, include:

- Spell length of days with precipitation greater than 1 mm (also known as "Maximum consecutive wet days" - "CWD")
- Number of heavy precipitation days (Precip >= 20mm - "R20mm")
- Number of wet days (Precip >= 1mm - "RR1")
- Maximum 1-day total precipitation ("RX1day")
- Maximum 5-day total precipitation ("RX5day").

In particular, spatial patterns of climate mean and trend, along with biases, are examined and displayed for each model and the ensemble median (calculated for each grid cell). Additionally, spatially-averaged trend values are analysed and presented using box plots to provide an overview of trend behavior across the distribution of the chosen subset of models when averaged across Europe.

The analysis and results follow the next outline:

**[](section-1)**
 * [](section-1.1)
 * [](section-1.2)
 * [](section-1.3)
 * [](section-1.4)
 * [](section-1.5)
 * [](section-1.6)

**[](section-2)**
 * [](section-2.1)
 * [](section-2.2)
 * [](section-2.3)

**[](section-3)**
 * [](section-3.1)
 * [](section-3.2)
 * [](section-3.3)
 * [](section-3.4)
 * [](section-3.5)
 * [](section-3.6)


EQC Quality Assessment: "Bias in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q03  |  Category: Climate_Projections
Section: Bias in precipitation-based indices for impact models > Analysis and results > 1. Parameters, requests and functions definition > 1.2. Define Parameters
---
In the "Define Parameters" section, various customisable options for the notebook are specified:

- The initial and ending year used for the historical period can be specified by changing the parameters `year_start` and `year_stop` (1971-2000 is chosen for consistency between CORDEX and CMIP6).
- The `timeseries` set the temporal aggregation. For instance, selecting "DJF" implies considering only the winter season.
- `collection_id` provides the choice between Global Climate Models CMIP6 or Regional Climate Models CORDEX. Although the code allows choosing between CMIP6 or CORDEX, the example provided in this notebook deals with CORDEX RCMs.
- `area` allows specifying the geographical domain of interest.
- The `interpolation_method` parameter allows selecting the interpolation method when regridding is performed over the indices.
- The `chunk` selection allows the user to define if dividing into chunks when downloading the data on their local machine. Although it does not significantly affect the analysis, it is recommended to keep the default value for optimal performance.

Choose annual or seasonal timeseries
Choose CORDEX or CMIP6
Interpolation method
Area to show
Chunks for download

(section-1.3)=


EQC Quality Assessment: "Bias in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q03  |  Category: Climate_Projections
Section: Bias in precipitation-based indices for impact models > Analysis and results > 1. Parameters, requests and functions definition > 1.3. Define models
---
The following climate analyses are performed considering a subset of GCMs from CMIP6. Models names are listed in the parameters below. Some variable-dependent parameters are also selected, as the `index_names` parameter, which specifies the precipitation-based indices ('CWD', 'R20mm', 'RR1', 'RX1day' and 'RX5day' in our case) from the [icclim](https://icclim.readthedocs.io/en/stable/) Python package.

When choosing Cordex models, it is crucial to consider the availability of RCMs for the selected GCM and the specified region. The listed RCMs, for instance, are accessible for the GCM “mpi_m_mpi_esm_lr” in the “europe” cordex_domain. To confirm the available combinations, refer to the [CORDEX](https://cds.climate.copernicus.eu/datasets/projections-cordex-domains-single-levels?tab=overview) CDS catalogue entry.

Define dictionaries to use in titles and caption
Define dictionaries to use in titles and caption

(section-1.4)=


EQC Quality Assessment: "Bias in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q03  |  Category: Climate_Projections
Section: Bias in precipitation-based indices for impact models > Analysis and results > 1. Parameters, requests and functions definition > 1.4. Define ERA5 request
---
Within this notebook, ERA5 serves as the reference product. In this section, we set the required parameters for the cds-api data-request of ERA5.

(section-1.5)=


EQC Quality Assessment: "Bias in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q03  |  Category: Climate_Projections
Section: Bias in precipitation-based indices for impact models > Analysis and results > 1. Parameters, requests and functions definition > 1.5. Define model requests
---
In this section we set the required parameters for the cds-api data-request.

The `get_cordex_years` function is employed to choose suitable data chunks for CORDEX data requests.

When `Weights = True`, spatial weighting is applied for calculations requiring spatial data aggregation. This is particularly relevant for CMIP6 GCMs with regular lon-lat grids that do not consider varying surface extensions at different latitudes. In contrast, CORDEX RCMs, using rotated grids, inherently account for different cell surfaces based on latitude, eliminating the need for a latitude cosine multiplicative factor (`Weights = False`).

(section-1.6)=


EQC Quality Assessment: "Bias in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q03  |  Category: Climate_Projections
Section: Bias in precipitation-based indices for impact models > Analysis and results > 1. Parameters, requests and functions definition > 1.6. Functions to cache
---
In this section, functions that will be executed in the caching phase are defined. Caching is the process of storing copies of files in a temporary storage location, so that they can be accessed more quickly. This process also checks if the user has already downloaded a file, avoiding redundant downloads.

Functions description:

- The `select_timeseries` function subsets the dataset based on the chosen `timeseries` parameter.

- The `compute_indices` function utilises the icclim package to calculate the precipitation-based indices.

- The `compute_trends` function employs the Mann-Kendall test for trend calculation.

- Finally, the `compute_indices_and_trends` accumulates the daily precipitation (only if we are dealing with ERA5), calculates the precipitation-based indices for the corresponding temporal aggregation using the `compute_indices` function, determines the indices mean over the historical period (1971-2000), obtain the trends using the `compute_trends` function, and offers an option for regridding to ERA5 if required.

Original bounds for conservative interpolation

(section-2)=


EQC Quality Assessment: "Bias in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q03  |  Category: Climate_Projections
Section: Bias in precipitation-based indices for impact models > Analysis and results > 2. Downloading and processing > 2.1. Download and transform ERA5
---
In this section, the `download.download_and_transform` function from the 'c3s_eqc_automatic_quality_control' package is employed to download ERA5 reference data, accumulate daily precipitation from hourly data, compute the precipitation-based indices for the selected temporal aggregation ("DJF" in this example), calculate the mean and trend over the historical period (1971-2000) and cache the result (to avoid redundant downloads and processing).

(section-2.2)=


EQC Quality Assessment: "Bias in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q03  |  Category: Climate_Projections
Section: Bias in precipitation-based indices for impact models > Analysis and results > 2. Downloading and processing > 2.2. Download and transform models
---
In this section, the `download.download_and_transform` function from the 'c3s_eqc_automatic_quality_control' package is employed to download daily data from the CORDEX models, compute the precipitation-based indices for the selected temporal aggregation, calculate the mean and trend over the historical period (1971-2005), interpolate to ERA5's grid (only for the cases in which it is specified, in the other cases, the original model's grid is mantained), and cache the result (to avoid redundant downloads and processing).

Original model
Interpolated model

```text
model='clmcom_clm_cclm4_8_17'
model='clmcom_eth_cosmo_crclim'
model='cnrm_aladin63'
model='dmi_hirham5'
model='knmi_racmo22e'
model='mohc_hadrem3_ga7_05'
model='mpi_csc_remo2009'
model='smhi_rca4'
model='uhoh_wrf361h'
```

(section-2.3)=


EQC Quality Assessment: "Bias in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q03  |  Category: Climate_Projections
Section: Bias in precipitation-based indices for impact models > Analysis and results > 2. Downloading and processing > 2.3. Apply land-sea mask, change attributes and cut the region to show
---
This section performs the following tasks:

1. Cut the region of interest.
2. Downloads the sea mask for ERA5.
3. Applies the sea mask to both ERA5 data and the model data, which were previously regridded to ERA5's grid (i.e., it applies the ERA5 sea mask to `ds_interpolated`).
4. Regrids the ERA5 land-sea mask to the model's grid and applies it to them.
5. Change some variable attributes for plotting purposes.

**Note:** `ds_interpolated` contains data from the models (mean and trend over the historical period, p-value of the trends...) regridded to ERA5. `model_datasets` contain the same data but in the original grid of each model.

Edit attributes

(section-3)=


EQC Quality Assessment: "Bias in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q03  |  Category: Climate_Projections
Section: Bias in precipitation-based indices for impact models > Analysis and results > 3. Plot and describe results
---
This section will display the following results:

- Maps representing the spatial distribution of the **historical mean values** (1971-2000) of the indices ('CWD', 'R20mm', 'RR1', 'RX1day' and 'RX5day') for ERA5, each model individually, the ensemble median (understood as the median of the mean values of the chosen subset of models calculated for each grid cell), and the ensemble spread (derived as the standard deviation of the distribution of the chosen subset of models).
- Maps representing the spatial distribution of the **historical trends** (1971-2000) of the considered indices. Similar to the first analysis, this includes ERA5, each model individually, the ensemble median (understood as the median of the trend values of the chosen subset of models calculated for each grid cell), and the ensemble spread (derived as the standard deviation of the distribution of the chosen subset of models).
- **Bias maps of the historical mean values**.
- **Trend bias maps**.
- **Boxplots** representing statistical distributions (PDF) built on the spatially-averaged historical trends from each considered model, displayed together with ERA5.

(section-3.1)=


EQC Quality Assessment: "Bias in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q03  |  Category: Climate_Projections
Section: Bias in precipitation-based indices for impact models > Analysis and results > 3. Plot and describe results > 3.1. Define plotting functions
---
The functions presented here are used to plot the mean values and trends calculated over the historical period (1971-2000) for each of the indices ('CWD', 'R20mm', 'RR1', 'RX1day' and 'RX5day').

For a selected index, three layout types can be displayed, depending on the chosen function:

1. Layout including the reference ERA5 product, the ensemble median, the bias of the ensemble median, and the ensemble spread: `plot_ensemble()` is used.
2. Layout including every model (for the trend and mean values): `plot_models()` is employed.
3. Layout including the bias of every model (for the trend and mean values): `plot_models()` is used again.

`trend==True` argument allows displaying trend values over the historical period, while `trend==False` will show mean values. When the `trend` argument is set to `True`, regions with no significance are hatched. For individual models and ERA5, a grid point is considered to have a statistically significant trend when the p-value is lower than 0.05 (in such cases, no hatching is shown). However, for determining trend significance for the ensemble median (understood as the median of the trend values of the chosen subset of models calculated for each grid cell), reliance is placed on agreement categories, following the advanced approach proposed in AR6 [IPCC](https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_Atlas.pdf) on pages 1945-1950. The `hatch_p_value_ensemble()` function is used to distinguish, for each grid point, between three possible cases:

1. If more than 66% of the models are statistically significant (p-value < 0.05) and more than 80% of the models share the same sign, we consider the ensemble median trend to be statistically significant, and there is agreement on the sign. To represent this, no hatching is used.
2. If less than 66% of the models are statistically significant, regardless of agreement on the sign of the trend, hatching is applied (indicating that the ensemble median trend is not statistically significant).
3. If more than 66% of the models are statistically significant but less than 80% of the models share the same sign, we consider the ensemble median trend to be statistically significant, but there is no agreement on the sign of the trend. This is represented using crosses.

Define function to plot the caption of the figures (for the ensemble case)
Add caption to the figure
Add each line to the figure
end captioning
Define function to plot the caption of the figures (for the individual models case)
Add caption to the figure
Add each line to the figure

(section-3.2)=


EQC Quality Assessment: "Bias in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q03  |  Category: Climate_Projections
Section: Bias in precipitation-based indices for impact models > Analysis and results > 3. Plot and describe results > 3.2. Plot ensemble maps
---
In this section, we invoke the `plot_ensemble()` function to visualise the mean values and trends calculated over the historical period (1971-2000) for the model ensemble and ERA5 reference product across Europe. Note that the model data used in this section has previously been interpolated to the ERA5 grid.

Specifically, for each of the indices ('CWD', 'R20mm', 'RR1', 'RX1day' and 'RX5day'), this section presents two layouts:

1. Mean values of the historical period (1971-2000) for: (a) the reference ERA5 product, (b) the ensemble median (understood as the median of the mean values of the chosen subset of models calculated for each grid cell), (c) the bias of the ensemble median, and (d) the ensemble spread (derived as the standard deviation of the distribution of the chosen subset of models).

2. Trend values of the historical period (1971-2000) for: (a) the reference ERA5 product, (b) the ensemble median (understood as the median of the trend values of the chosen subset of models calculated for each grid cell), (c) the bias of the ensemble median, and (d) the ensemble spread (derived as the standard deviation of the distribution of the chosen subset of models).

Fig number counter
Common title

(section-3.3)=


EQC Quality Assessment: "Bias in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q03  |  Category: Climate_Projections
Section: Bias in precipitation-based indices for impact models > Analysis and results > 3. Plot and describe results > 3.3. Plot model maps
---
In this section, we invoke the `plot_models()` function to visualise the mean values and trends calculated over the historical period (1971-2000) for every model individually across Europe. Note that the model data used in this section maintains its original grid.

Specifically, for each of the indices ('CWD', 'R20mm', 'RR1', 'RX1day' and 'RX5day'), this section presents two layouts:

1. A layout including the historical mean (1971-2000) of every model (only for the 'SU' index).

2. A layout including the historical trend (1971-2000) of every model.

(section-3.4)=


EQC Quality Assessment: "Bias in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q03  |  Category: Climate_Projections
Section: Bias in precipitation-based indices for impact models > Analysis and results > 3. Plot and describe results > 3.4. Plot bias maps
---
In this section, we invoke the `plot_models()` function to visualise the bias for the mean values and trends calculated over the historical period (1971-2000) for every model individually across Europe. Note that the model data used in this section has previously been interpolated to the ERA5 grid.

Specifically, for each of the indices ('CWD', 'R20mm', 'RR1', 'RX1day' and 'RX5day'), this section presents two layouts:

1. A layout including the bias for the historical mean (1971-2000) of every model (only for the 'SU' index).

2. A layout including the bias for the historical trend (1971-2000) of every model.

(section-3.5)=


EQC Quality Assessment: "Bias in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q03  |  Category: Climate_Projections
Section: Bias in precipitation-based indices for impact models > Analysis and results > 3. Plot and describe results > 3.5. Boxplots of the historical trend
---
In this last section, we compare the trends of the climate models with the reference trend from ERA5.

Dots represent the spatially-averaged historical trend over the selected region (change of the number of days per decade) for each model (grey), the ensemble mean (blue), and the reference product (orange). The ensemble median is shown as a green line. Note that the spatially averaged values are calculated for each model from its original grid (i.e., no interpolated data has been used here).

The boxplot visually illustrates the distribution of trends among the climate models, with the box covering the first quartile (Q1 = 25th percentile) to the third quartile (Q3 = 75th percentile), and a green line indicating the ensemble median (Q2 = 50th percentile). Whiskers extend from the edges of the box to show the full data range.

Ensemble mean

Fig 31. Boxplots illustrating the historical trends of the ensemble distribution and ERA5 for the precipitation-based indices: (a)'CWD', (b)'R20mm', (c)'RR1', (d)'RX1day' and (e)'RX5day'. The distribution is created by considering spatially averaged trends across Europe. The ensemble mean and the ensemble median trends are both included. Outliers in the distribution are denoted by a grey circle with a black contour.

(section-3.6)=


EQC Quality Assessment: "Bias in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q03  |  Category: Climate_Projections
Section: Bias in precipitation-based indices for impact models > Analysis and results > 3. Plot and describe results > 3.6. Results summary and discussion
---
- The bias behaviour varies depending on the index and whether we are dealing with trends or climatologies. Generally speaking, the subset of models selected overestimates the magnitudes of climatologies for DJF, except in the northwest of Great Britain, the west coast of the Scandinavian Peninsula, parts of the Mediterranean Basin, and the east of Europe for the CWD index, where there is underestimation. For the RR1 index, the models also underestimate the magnitudes for the west coast of the Scandinavian Peninsula and parts of the Mediterranean Basin.

- For the historical period and the seasonal aggregation of DJF, ERA5 exhibits trends that are highly dependent on the region and index. Indices like CWD, R20mm, and RX1day show scattered spatial patterns that are generally not well-reproduced by the considered models, except in some specific areas. The spatial patterns for the trends of RR1 and RX5day are less scattered and are slightly better captured than those of the other indices.

- The boxplots displaying spatially-averaged values reveal diverse outcomes depending on the index under consideration. Notably, significant inter-model variability is evident for certain indices, whose interquantile range encompasses trends of varying directions, and in some cases, even exhibits a trend opposite to that shown by the ERA5 data. This discrepancy is particularly noticeable for the R20mm, RR1, and RX1day indices, where the interquantile range showcases a trend contrary to that portrayed by ERA5. Meanwhile, the RX5day index displays an interquantile range centered around zero, with the trend sign dependent on the model. In contrast, the CWD index demonstrates a trend direction consistent with ERA5.

- It is crucial to emphasise that the boxplots present spatially-averaged values, and their interpretation should be approached with caution, as the outcomes can vary significantly when considering different regions across Europe. For regional analyses, it is essential to focus solely on the region of interest, as the influence of other European regions may distort the results, leading to conclusions that do not accurately reflect the specific area under study.

- Although ERA5 is used as our reference dataset, it is important to be aware of its inherent uncertainties. While uncertainties affect all variables, biases are particularly pronounced for variables such as surface wind and precipitation, as demonstrated in [[4]](https://doi.org/10.1002/qj.3616) and [[5]](https://doi.org/10.3390/atmos12111462). This underscores the importance of careful interpretation, especially regarding precipitation extremes.

- A larger GCM-RCM matrix should be considered when addressing specific cases to enhance the robustness of the analysis and account for uncertainties [[6]](https://doi.org/10.1002/wcc.8)[[7]](https://doi.org/10.1088/1748-9326/aacc77).

- What do the results mean for users? Are the biases relevant?

- The subset of Regional Climate Models (RCMs) considered for this notebook and for this seasonal aggregation struggle to replicate both the observed climatology and the trends during the historical period, with particular difficulty in capturing the trends.

- However, for specific regions and indices, the models successfully capture the climatology and even the direction of the trend. Examples include the increasing trend for the CWD index in the western part of the Iberian Peninsula and the positive trend for RR1 in central Europe. Users should consider these regional variations, the indices they aim to use, the differences in bias behavior between climatology and trends, and the necessity of bias-correcting data before using it for hydrological applications [[3]](https://doi.org/10.1016/j.jhydrol.2012.05.052).

- Precipitation trends in observational and reanalysis datasets are generally less robust and more challenging to detect compared to temperature trends. This limitation is also evident in model simulations.

RESULTS NOTE:

It is important to note that the results presented are specific to the 9 models chosen, and users should aim to assess as wide a range of models as possible before making a sub-selection.


EQC Quality Assessment: "Bias in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q03  |  Category: Climate_Projections
Section: Bias in precipitation-based indices for impact models > ℹ If you want to know more > Key resources
---
Some key resources and further reading were linked throughout this assessment.

The CDS catalogue entries for the data used were:
* CORDEX regional climate model data on single levels (Daily mean - Mean precipitation flux): https://cds.climate.copernicus.eu/datasets/projections-cordex-domains-single-levels?tab=overview
* ERA5 hourly data on single levels from 1940 to present (Total precipitation): https://cds.climate.copernicus.eu/datasets/reanalysis-era5-single-levels?tab=overview

Code libraries used:
* [C3S EQC custom functions](https://github.com/bopen/c3s-eqc-automatic-quality-control/tree/main/c3s_eqc_automatic_quality_control), `c3s_eqc_automatic_quality_control`,  prepared by [B-Open](https://www.bopen.eu/)
* [icclim](https://icclim.readthedocs.io/en/stable/) Python package


EQC Quality Assessment: "Bias in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q03  |  Category: Climate_Projections
Section: Bias in precipitation-based indices for impact models > ℹ If you want to know more > References
---
[[1]](https://doi.org/10.1016/j.envsci.2015.08.012) Panagos, P., Borrelli, P., Poesen, J., Ballabio, C., Lugato, E., Meusburger, K., Montanarella, L., Alewell, C. (2015). The new assessment of soil loss by water erosion in Europe. Environ. Sci. Policy, 54, pp. 438-447. https://doi.org/10.1016/j.envsci.2015.08.012

[[2]](https://doi.org/10.1016/j.landusepol.2012.11.007) Salvati, L., Carlucci, M. (2013). The impact of mediterranean land degradation on agricultural income: a short-term scenario. Land Use Policy, 32, pp. 302-308. https://doi.org/10.1016/j.landusepol.2012.11.007

[[3]](https://doi.org/10.1016/j.jhydrol.2012.05.052) Teutschbein, C., Seibert, J. (2012). Bias correction of regional climate model simulations for hydrological climate-change impact studies: Review and evaluation of different methods. Journal of Hydrology,
Volumes 456–457, pp. 12-29. https://doi.org/10.1016/j.jhydrol.2012.05.052

[[4]](https://doi.org/10.1002/qj.3616) Ramon, J., Lledó L., Torralba, V., Soret, A., Doblas-Reyes, F.J. (2019). What global reanalysis best represents near-surface winds?. Q J R Meteorol Soc. 2019; 145: 3236–3251. https://doi.org/10.1002/qj.3616

[[5]](https://doi.org/10.3390/atmos12111462) Hassler, B. and Lauer, A. (2021). Comparison of Reanalysis and Observational Precipitation Datasets Including ERA5 and WFDE5. Atmosphere, 12, 1462. https://doi.org/10.3390/atmos12111462

[[6]](https://doi.org/10.1002/wcc.8) Rummukainen, M. (2010). State-of-the-art with regional climate models. WIREs Clim Change, 1: 82-96. https://doi.org/10.1002/wcc.8

[[7]](https://doi.org/10.1088/1748-9326/aacc77) Silje Lund Sørland et al. (2018). Bias patterns and climate change signals in GCM-RCM model chains. Environ. Res. Lett. 13 074017. https://doi.org/10.1088/1748-9326/aacc77


EQC Quality Assessment: "Projected changes in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q04  |  Category: Climate_Projections
Section: Projected changes in precipitation-based indices for impact models
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Production date: 29-05-2024

Produced by: CMCC foundation - Euro-Mediterranean Center on Climate Change. Albert Martinez Boti.


EQC Quality Assessment: "Projected changes in precipitation-based indices for impact models"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q04  |  Category: Climate_Projections
Section: Projected changes in precipitation-based indices for impact models > Quality assessment question
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* **What are the projected future changes and associated uncertainties of precipitation-based indices in Europe?**

Soil erosion stands as one of the primary environmental concerns in Europe [[1]](https://doi.org/10.1016/j.envsci.2015.08.012). Its accelerated occurrence can precipitate a decline in ecosystem stability, land productivity, and overall land degradation, resulting in diminished income for farmers [[2]](https://doi.org/10.1016/j.landusepol.2012.11.007). This notebook is designed to evaluate the uncertainty in future projections of a specific set of models from **[CORDEX](https://cds.climate.copernicus.eu/datasets/projections-cordex-domains-single-levels?tab=overview)** Regional Climate Models (RCMs) by considering the ensemble inter-model spread of projected changes. These selected rainfall indicators are recognised as valuable proxies for rainfall erosivity, a factor directly linked to empirical calculations of soil loss, as outlined in an application available through the old CDS platform ([dataset documentation](https://dast.copernicus-climate.eu/documents/sis-soil-erosion/C3S_D429d.2.3.2_Product_User_Guide_v1.2.pdf)) The five precipitation-based indices used here are calculated using the **[icclim](https://icclim.readthedocs.io/en/stable/)** package, them being:

- Spell length of days with precipitation greater than 1 mm (also known as "Maximum consecutive wet days" - "CWD")
- Number of heavy precipitation days (Precip >= 20mm - "R20mm")
- Number of wet days (Precip >= 1mm - "RR1")
- Maximum 1-day total precipitation ("RX1day")
- Maximum 5-day total precipitation ("RX5day").

Within this notebook, these calculations are performed over the temporal aggregation of DJF and for the future period spanning from 2015 to 2099, following the Representative Concentration Pathway RCP 8.5. It is important to note that the results presented here pertain to a specific subset of the CORDEX ensemble and may not be generalisable to the entire dataset. Also note that a separate assessment examines the representation of climatology and trends of these indices for the same models during the historical period (1971-2000).