EQC Quality Assessment: "CORDEX temperature biases over the Alpine region — assessment using E-OBS and CERRA"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q06  |  Category: Climate_Projections
Section: CORDEX temperature biases over the Alpine region — assessment using E-OBS and CERRA > Analysis and results > 3. Plot and describe results > 3.4. Elevation profiles of the impact of lapse-rate correction
---
This section highlights the change introduced by the lapse-rate correction. The temperature at each grid point of every model has been previously adjusted using a uniform lapse rate of −0.0065 °C m⁻¹ to align all datasets to the same target elevation, defined by the regridded CERRA orography (0.11° resolution). For example, if a grid point in a model is 200 m lower than the corresponding point in the target CERRA, the temperature at that point is corrected by 200 m × −0.0065 °C m⁻¹ = −1.3 °C. The plot below shows the vertical profiles of these differences, illustrating how the lapse-rate correction affects temperatures across elevation bands. In other words, it shows the difference between assuming that all models and reference datasets share the same elevation after regridding (as sometimes assumed in the literature) and applying a correction to account for residual elevation differences.

Fig 5.
        Elevation profiles of the impact of lapse-rate correction. The plot shows differences between lapse-rate corrected and uncorrected temperature profiles for E-OBS and EURO-CORDEX models. The correction adjusts temperatures to a common target elevation (that of regridded CERRA at 0.11°) using a uniform lapse rate (−0.0065 °C m⁻¹), ensuring consistent comparison across datasets. Negative values indicate that regridded model or E-OBS elevations are lower than CERRA. E-OBS is shown as a solid blue line, the ensemble median as a solid black line, individual models as grey dashed lines and the inter-model spread (standard deviation) as a grey shaded area. CERRA is not displayed since it defines the elevation target.

(climate_projections-cordex-domains-single-levels_validation_q06:section-3.5)=


EQC Quality Assessment: "CORDEX temperature biases over the Alpine region — assessment using E-OBS and CERRA"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q06  |  Category: Climate_Projections
Section: CORDEX temperature biases over the Alpine region — assessment using E-OBS and CERRA > Analysis and results > 3. Plot and describe results > 3.5. Results summary
---
- Regional Climate Models (RCMs) show biases relative to both reference datasets (E-OBS and CERRA).

- Systematic cold biases are observed in RCMs above 1000–1500 m during winter across the 5th, 50th, and 95th percentiles when evaluated against E-OBS, consistent with findings from [[3]](https://doi.org/10.1007/s00382-024-07376-y).

- CORDEX biases relative to CERRA are smaller in magnitude and do not increase systematically with altitude, unlike the case with E-OBS.

- Biases relative to E-OBS generally increase with elevation (becoming more negative), particularly for the 5th percentile in winter, where the ensemble median reaches its largest negative value.

- Even in summer, models exhibit negative biases at higher elevations relative to E-OBS, notably for the 50th and 95th percentiles.

- The greatest inter-model spread occurs for the 5th percentile in winter.

- CERRA shows large cold differences relative to E-OBS; for the 50th and 95th percentiles in winter, it is colder than the CORDEX ensemble median above 2000–2500 m.

- Applying a lapse-rate correction to ensure all datasets are compared at the same elevation does not substantially alter the shape of the vertical bias profiles.

- The lapse-rate correction introduces small (generally <1 °C) negative differences that increase with elevation, reflecting that regridded model and E-OBS elevations are typically lower than those of regridded CERRA.

(climate_projections-cordex-domains-single-levels_validation_q06:section-3.6)=


EQC Quality Assessment: "CORDEX temperature biases over the Alpine region — assessment using E-OBS and CERRA"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q06  |  Category: Climate_Projections
Section: CORDEX temperature biases over the Alpine region — assessment using E-OBS and CERRA > Analysis and results > 3. Plot and describe results > 3.6. Implications for the users
---
- Elevation-dependent biases in RCM outputs are systematic and significant above 1000–1500 m, particularly in winter, when evaluated against E-OBS, and affect all percentiles. Users working with climate data in mountainous regions should be aware that cold biases tend to intensify with elevation, especially for cold extremes (5th percentile), potentially influencing impact assessments and adaptation planning.

- Bias magnitude and inter-model spread vary by season and percentile, with the greatest variability observed in winter cold tails (5th percentile). This highlights substantial uncertainty for extreme cold conditions at high elevations, which should be explicitly considered in risk and vulnerability evaluations.

-  CERRA exhibits strong cold differences when compared to E-OBS. This has two key implications: (1) caution is needed when using CERRA as a reference or input dataset for mountain climate analyses, and (2) despite its high resolution, the underlying model may not adequately represent complex high-altitude dynamics and processes.

-  A critical caveat lies in the inherent uncertainty and sparsity of observational data at high elevations, particularly in E-OBS. These limitations—stemming from sparse station coverage, complex topography, and measurement challenges—can cause some of the apparent model biases to actually reflect deficiencies in the reference data.

- Interpolation accuracy generally declines with reduced station density, performs worse for spatially variable parameters (e.g. precipitation), and deteriorates further in areas of complex terrain such as mountainous regions [[8]](https://doi.org/10.1029/2009JD011799). Moreover, in some cases, E-OBS tends to report warmer values than national station datasets across the 5th, 50th, and 95th percentiles [[3]](https://doi.org/10.1007/s00382-024-07376-y), and has been shown to overestimate temperatures in the distribution tails, even over moderately complex orography [[9]](https://doi.org/10.1029/2010JD014123).

- Lapse-rate correction may slightly reduce biases by adjusting for elevation differences between datasets but does not fundamentally change the shape of vertical bias profiles. While useful for harmonising datasets, it is not a solution to the underlying model or observational issues driving the biases.

- Where feasible, users may benefit from complementing gridded analyses with station-based evaluations corrected for elevation. While the CDS does not currently provide access to raw station-level data, external sources may be used.

- Altogether, the combination of systematic model biases, observational uncertainties, and limited high-elevation data availability underscores the need for caution when interpreting temperature extremes and climate signals in mountainous regions.

- Bias-adjustment methods do not ensure that corrected future projections will more accurately reflect reality, as the underlying biases may change under evolving climate conditions [[10]](https://doi.org/10.5194/hess-25-273-2021).


EQC Quality Assessment: "CORDEX temperature biases over the Alpine region — assessment using E-OBS and CERRA"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q06  |  Category: Climate_Projections
Section: CORDEX temperature biases over the Alpine region — assessment using E-OBS and CERRA > ℹ If you want to know more > Key resources
---
Some key resources and further reading were linked throughout this assessment.

* Regional climate models - CORDEX: https://cds.climate.copernicus.eu/datasets/projections-cordex-domains-single-levels?tab=overview
* Gridded observation dataset for Europe, E-OBS: https://cds.climate.copernicus.eu/datasets/insitu-gridded-observations-europe?tab=overview
* CERRA sub-daily regional reanalysis data for Europe on single levels from 1984 to present: https://cds.climate.copernicus.eu/datasets/reanalysis-cerra-single-levels?tab=overview
* High-resolution global climate models: https://highresmip.org/
* Mountain tourism meteorological and snow indicators for Europe from 1950 to 2100 derived from reanalysis and climate projections: https://cds.climate.copernicus.eu/datasets/sis-tourism-snow-indicators?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/)


EQC Quality Assessment: "CORDEX temperature biases over the Alpine region — assessment using E-OBS and CERRA"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q06  |  Category: Climate_Projections
Section: CORDEX temperature biases over the Alpine region — assessment using E-OBS and CERRA > ℹ If you want to know more > References
---
[[1]](https://doi.org/10.1038/s41586-019-1822-y) Immerzeel, W.W., Lutz, A.F., Andrade, M. et al., 2020. Importance and vulnerability of the world’s water towers. Nature 577, 364–369. https://doi.org/10.1038/s41586-019-1822-y

[[2]](https://doi.org/10.1175/BAMS-D-23-0082.1) Rudisill, W., Rhoades, A., Xu, Z., and Feldman, D. R.,2024. Are Atmospheric Models Too Cold in the Mountains? The State of Science and Insights from the SAIL Field Campaign. Bull. Amer. Meteor. Soc., 105, E1237–E1264, https://doi.org/10.1175/BAMS-D-23-0082.1

[[3]](https://doi.org/10.1007/s00382-024-07376-y) Matiu, M., Napoli, A., Kotlarski, S. et al., 2024. Elevation-dependent biases of raw and bias-adjusted EURO-CORDEX regional climate models in the European Alps. Clim Dyn 62, 9013–9030. https://doi.org/10.1007/s00382-024-07376-y

[[4]](https://doi.org/10.3390/cli11070154) Shrestha, S., Zaramella, M., Callegari, M., Greifeneder, F., Borga, M., 2023. Scale Dependence of Errors in Snow Water Equivalent Simulations Using ERA5 Reanalysis over Alpine Basins. Climate, 11, 154. https://doi.org/10.3390/cli11070154

[[5]](https://doi.org/10.1007/s00704-018-2506-5) Haslinger, K., Holawe, F., and  Blöschl, G., 2019. Spatial characteristics of precipitation shortfalls in the Greater Alpine Region—a data-based analysis from observations. Theor Appl Climatol 136, 717–731. https://doi.org/10.1007/s00704-018-2506-5

[[6]](https://doi.org/10.1002/joc.1377) Auer, I., Böhm, R., Jurkovic, A., Lipa, W., Orlik, A., Potzmann, R., Schöner, W., Ungersböck, M., Matulla, C., Briffa, K., Jones, P., Efthymiadis, D., Brunetti, M., Nanni, T., Maugeri, M., Mercalli, L., Mestre, O., Moisselin, J.-M., Begert, M., Müller-Westermeier, G., Kveton, V., Bochnicek, O., Stastny, P., Lapin, M., Szalai, S., Szentimrey, T., Cegnar, T., Dolinar, M., Gajic-Capka, M., Zaninovic, K., Majstorovic, Z. and Nieplova, E., 2007. HISTALP—historical instrumental climatological surface time series of the Greater Alpine Region. Int. J. Climatol., 27: 17-46. https://doi.org/10.1002/joc.1377

[[7]](https://doi.org/10.1002/joc.5249) Kotlarski, S., Szabó, P., Herrera S., et al., 2019. Observational uncertainty and regional climate model evaluation: A pan-European perspective. Int J Climatol. 39: 3730–3749. https://doi.org/10.1002/joc.5249

[[8]](https://doi.org/10.1029/2009JD011799) Hofstra, N., Haylock, M., New, M., and Jones, P. D., 2009. Testing E-OBS European high-resolution gridded data set of daily precipitation and surface temperature, J. Geophys. Res., 114, D21101. https://doi.org/10.1029/2009JD011799


EQC Quality Assessment: "CORDEX temperature biases over the Alpine region — assessment using E-OBS and CERRA"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q06  |  Category: Climate_Projections
Section: CORDEX temperature biases over the Alpine region — assessment using E-OBS and CERRA > ℹ If you want to know more > References
---
E-OBS European high-resolution gridded data set of daily precipitation and surface temperature, J. Geophys. Res., 114, D21101. https://doi.org/10.1029/2009JD011799

[[9]](https://doi.org/10.1029/2010JD014123) Kyselý, J., and Plavcová, E., 2010. A critical remark on the applicability of E-OBS European gridded temperature data set for validating control climate simulations, J. Geophys. Res., 115, D23118. https://doi.org/10.1029/2010JD014123

[[10]](https://doi.org/10.5194/hess-25-273-2021) Schmith, T., Thejll, P., Berg, P., Boberg, F., Christensen, O. B., Christiansen, B., Christensen, J. H., Madsen, M. S., and Steger, C., 2021. Identifying robust bias adjustment methods for European extreme precipitation in a multi-model pseudo-reality setting, Hydrol. Earth Syst. Sci., 25, 273–290, https://doi.org/10.5194/hess-25-273-2021


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region
---
Production date: 17-03-2026

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


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > Quality assessment question
---
* **How well do CORDEX models simulate drought compared to signals derived from ERA5?**

The Standardized Precipitation-Evapotranspiration Index (SPEI) [[1]](https://doi.org/10.1175/2009JCLI2909.1) is a widely used drought indicator that integrates precipitation and potential evapotranspiration, providing a more complete measure of water deficits than precipitation alone. Its multiscalar formulation allows the evaluation of different types of drought [[2]](https://digitalcommons.unl.edu/droughtfacpub/69/), from short-term agricultural or soil moisture deficits to long-term hydrological or ecological events. Being standardised, SPEI is dimensionless, facilitating comparisons across regions and climates. By capturing variations in frequency, duration, and severity, it effectively reflects the complex nature of drought, making it a robust and physically meaningful proxy for drought assessment in the context of climate change [[3]](https://doi.org/10.1175/2012EI000434.1).

Understanding SPEI is particularly relevant for the water management sector. By capturing multiple types of drought SPEI serves as a versatile indicator for various users. Climate projections using SPEI enable planners to anticipate future water deficits, guide allocation, and design effective strategies for reservoir management, irrigation, and drought preparedness, helping to reduce socio-economic and ecological impacts [[4]](https://doi.org/10.3390/eesp2025035029)[[5]](https://doi.org/10.1002/joc.7302).

This assessment evaluates SPEI6 (six-month accumulation) across a subset of [CORDEX](https://cds.climate.copernicus.eu/datasets/projections-cordex-domains-single-levels?tab=overview) models available through the Copernicus Climate Data Store (CDS). Model outputs are compared against SPEI6 derived from [ERA5](https://cds.climate.copernicus.eu/datasets/reanalysis-era5-complete?tab=doc) reanalysis, which serves as the reference product. We specifically evaluate whether changes in the 1991–2010 period relative to the 1971–1990 baseline are accurately represented by CORDEX models and the trend across the whole 1971-2010 period for the Mediterranean domain.

This notebook is the counterpart to the assessment performed for CMIP6 ([CMIP6 biases in the SPEI6 drought index over the Mediterranean region](https://ecmwf-projects.github.io/c3s2-eqc-quality-assessment/Climate_Projections/CMIP6/climate_projections-cmip6_validation_q13.html))


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > Quality assessment statement
---
These are the key outcomes of this assessment

* The CORDEX ensemble median for the subset of models considered in this assessment does not generally capture the general intensification of drought over the Mediterranean observed in ERA5, showing SPEI6 changes close to zero for most regions.

* Individual models exhibit highly diverse spatial patterns, with some closely resembling ERA5, underscoring the importance of taking into account the whole ensemble (and not only the ensemble mean) for planning purposes.

* Despite these biases, the selected subset of CORDEX models may still be useful for exploring SPEI-based future water deficits and guiding drought preparedness, as long as limitations are considered.

* Regions with high inter-model spread, such as North Africa, Turkey, and the eastern Mediterranean, may be associated with future higher uncertainty, suggesting that adaptation strategies in these areas should consider a wider range of possible futures.

```

attachment:591afcf9-a410-4d53-ac0f-713bd18acac5.png
---
width: 1500px
alt: Visual abstract
---
Spatial patterns of SPEI6 change over the Mediterranean region. Panels show (a) ERA5 reference, (b) CORDEX ensemble median (median of the selected subset of models at each grid cell), (c) ensemble median bias relative to ERA5, and (d) ensemble spread (standard deviation across the selected models). SPEI6 is standardised over the reference period 1971–2010. SPEI6 change is calculated at each grid point as the difference between the monthly climatologies of the target period (1991–2010) and the baseline period (1971–1990), and then averaged to obtain the ANNUAL mean.
```


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > Methodology
---
The Standardized Precipitation-Evapotranspiration Index accumulated to six months (SPEI6) has been calculated for this assessment — through the use of [xclim](https://xclim.readthedocs.io/en/stable/) — as a proxy to evaluate drought conditions for a subset of [CORDEX](https://cds.climate.copernicus.eu/datasets/projections-cordex-domains-single-levels?tab=overview) models, which are evaluated against SPEI6 derived from [ERA5](https://cds.climate.copernicus.eu/datasets/reanalysis-era5-complete?tab=doc) reanalysis. The study covers the Mediterranean domain, following IPCC-AR6 regional definitions [[6]](https://doi.org/10.5194/essd-12-2959-2020), and results include spatial maps of SPEI6 changes for ERA5, CORDEX, and the biases of these changes. Additionally, time series showing the temporal evolution of drought across the domain are calculated, comparing trends from the models with ERA5 over the historical period considered within this assessment (1971–2010).

Potential evapotranspiration (PET) is calculated with the Hargreaves method [[7]](https://doi.org/10.13031/2013.26773), which requires only maximum and minimum temperature (and optionally mean temperature), providing a computationally efficient yet robust estimate (e.g., [[8]](https://doi.org/10.1002/joc.3887)). The accumulated series of precipitation minus PET is then standardised for the reference period, defined by the [C3S Atlas](https://confluence.ecmwf.int/display/CKB/Gridded+data+underpinning+the+Copernicus+Interactive+Climate+Atlas%3A+Description+of+the+datasets+and+variables#GriddeddataunderpinningtheCopernicusInteractiveClimateAtlas:Descriptionofthedatasetsandvariables) (1971–2010).

Five key concepts are defined:

- **Reference period:** The period used to standardise SPEI values, here 1971–2010, following the [C3S Atlas](https://confluence.ecmwf.int/display/CKB/Gridded+data+underpinning+the+Copernicus+Interactive+Climate+Atlas%3A+Description+of+the+datasets+and+variables#GriddeddataunderpinningtheCopernicusInteractiveClimateAtlas:Descriptionofthedatasetsandvariables).
- **Baseline period:** The period against which changes are calculated, here 1971–1990.
- **Target period:** The period for which changes are evaluated, here 1991–2010.
- **Historical period:** The entire period considered in this assessment, here 1971–2010.
- **SPEI6 change:** Differences in SPEI6 between the target period and the baseline, representing anomalies in drought conditions.

The analysis and results follow the next outline:

**[](climate_projections-cordex_validation_q07:section-1)**
 * [](climate_projections-cordex_validation_q07:section-1.1)
 * [](climate_projections-cordex_validation_q07:section-1.2)
 * [](climate_projections-cordex_validation_q07:section-1.3)
 * [](climate_projections-cordex_validation_q07:section-1.4)
 * [](climate_projections-cordex_validation_q07:section-1.5)
 * [](climate_projections-cordex_validation_q07:section-1.6)

**[](climate_projections-cordex_validation_q07:section-2)**
 * [](climate_projections-cordex_validation_q07:section-2.1)
 * [](climate_projections-cordex_validation_q07:section-2.2)
 * [](climate_projections-cordex_validation_q07:section-2.3)

**[](climate_projections-cordex_validation_q07:section-3)**
 * [](climate_projections-cordex_validation_q07:section-3.1)
 * [](climate_projections-cordex_validation_q07:section-3.2)
 * [](climate_projections-cordex_validation_q07:section-3.3)
 * [](climate_projections-cordex_validation_q07:section-3.4)
 * [](climate_projections-cordex_validation_q07:section-3.5)
 * [](climate_projections-cordex_validation_q07:section-3.6)
 * [](climate_projections-cordex_validation_q07:section-3.7)
 * [](climate_projections-cordex_validation_q07:section-3.8)


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > Methodology
---
-cordex_validation_q07:section-3.6)
 * [](climate_projections-cordex_validation_q07:section-3.7)
 * [](climate_projections-cordex_validation_q07:section-3.8)

NOTE ON THE METHODOLOGY:

This notebook follows the same methodology as the assessment performed for CMIP6
(
CMIP6 biases in the SPEI6 drought index over the Mediterranean region).
The historical period considered here is slightly shorter (1971–2010) compared to 1961–2020 in the CMIP6 assessment. This choice helps to avoid memory overload, ensures efficient execution of the notebook, guarantees availability of CORDEX models for the historical period, and avoids including many years of scenario data (CORDEX historical runs only extend until 2005).


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > 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 historical period can be adjusted by modifying `historical_slice`; the default range is 1971-2010.
- The reference period can be adjusted by modifying `reference_slice`; the default range is 1971–2010, following the [C3S Atlas](https://confluence.ecmwf.int/display/CKB/Gridded+data+underpinning+the+Copernicus+Interactive+Climate+Atlas%3A+Description+of+the+datasets+and+variables#GriddeddataunderpinningtheCopernicusInteractiveClimateAtlas:Descriptionofthedatasetsandvariables).
- The baseline period can be adjusted by modifying `baseline_slice`; the default range is 1971-1990.
- The target period can be adjusted by modifying `target_slice`; the default range is 1991-2010.
- The `interpolation_method` parameter allows selecting the interpolation method when regridding is performed.
- `collection_id` is not customisable for this assessment and is set to 'CORDEX'.
- The `area` parameter specifies the geographical domain of interest. By default, the Mediterranean domain is used, following IPCC-AR6 regional definitions [[6]](https://doi.org/10.5194/essd-12-2959-2020)
- The `time_agg` allows selecting the time aggregation for the analysis. Options include: annual, DJF, MAM, JJA, SON, Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec.
- SPEI accumulation window (`window`): Defines the accumulation period in months for the SPEI calculation. Common options include 3, 6, or 12 months, depending on whether short-term or long-term droughts are of interest. In this assessment, a six-month accumulation is used.
- The `chunks` 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.

Periods definition
Interpolation method
Collection id
Define region for analysis
time aggregation
SPEI accumulation
Chunks for download

(climate_projections-cordex_validation_q07:section-1.3)=


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > Analysis and results > 1. Parameters, requests and functions definition > 1.3. Define models
---
The following climate analyses are performed using a subset of CORDEX models that provide both the historical and RCP8.5 experiments, as well as maximum, minimum and mean temperature and precipitation, within the Climate Data Store ([CDS](https://cds.climate.copernicus.eu/datasets/projections-cordex-domains-single-levels?tab=overview)). All Global Climate Models (GCMs) driving the selected CORDEX simulations were included, and the selection ensures a representative coverage of the available Regional Climate Models (RCMs). A total of 17 models were chosen to maintain consistency with the number used in the quality assessment [CMIP6 biases in the SPEI6 drought index over the Mediterranean region](https://ecmwf-projects.github.io/c3s2-eqc-quality-assessment/Climate_Projections/CMIP6/climate_projections-cmip6_validation_q13.html).

(climate_projections-cordex_validation_q07:section-1.4)=


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > 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.

(climate_projections-cordex_validation_q07:section-1.5)=


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > 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.

"experiment": "historical",
Historical (until 2005)
Only historical
Historical part (until 2005)
Future part (RCP8.5 from 2006 onwards)

(climate_projections-cordex_validation_q07:section-1.6)=


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > 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.

Description of the main functions:

- **`compute_spei_cordex`**: Uses the xclim package to calculate the Standardized Precipitation-Evapotranspiration Index (SPEI). The `reference_slice` argument specifies the reference period used for standardization, while the `window` argument defines the number of months over which precipitation and evapotranspiration are accumulated (6 months in this assessment).

- **`get_mask_below_03`**: Generates a mask identifying grid points where precipitation is below 0.3 mm/day, allowing filtering of extremely dry regions.

Original bounds for conservative interpolation
Rechunk spatial dimensions to a single chunk for xESMF / apply_ufunc
Ensure variables are numeric for xESMF
Apply correct daily reductions
Wrap into dataset
Apply correct daily reductions

(climate_projections-cordex_validation_q07:section-2)=


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > 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 used to retrieve ERA5 hourly reference data, resample it to daily frequency, compute daily potential evapotranspiration, calculate the daily water balance, and derive the SPEI (SPEI6 for this assessment). Results are cached to avoid redundant downloads and repeated processing.

(climate_projections-cordex_validation_q07:section-2.2)=


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > 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 used to download daily data from CORDEX models, compute daily potential evapotranspiration, calculate the daily water balance, and derive the SPEI (SPEI6 for this assessment). SPEI6 is computed on each model's native grid and also on the ERA5 grid to enable bias assessment. When regridding is required, it is performed for each essential climate variable before the index calculation to preserve standardisation. Results are cached to avoid redundant downloads and repeated processing.

Original model
Interpolated model

```text
model='cccma_canesm2_clmcom_clm_cclm4_8_17'
model='cccma_canesm2_gerics_remo2015'
model='cnrm_cerfacs_cm5_ipsl_wrf381p'
model='cnrm_cerfacs_cm5_smhi_rca4'
model='ichec_ec_earth_dmi_hirham5'
model='ichec_ec_earth_knmi_racmo22e'
model='ipsl_cm5a_mr_ipsl_wrf381p'
model='ipsl_cm5a_mr_knmi_racmo22e'
model='miroc_miroc5_clmcom_clm_cclm4_8_17'
model='miroc_miroc5_gerics_remo2015'
model='mohc_hadgem2_es_cnrm_aladin63'
model='mohc_hadgem2_es_mohc_hadrem3_ga7_05'
model='mpi_m_mpi_esm_lr_mpi_csc_remo2009'
model='mpi_m_mpi_esm_lr_cnrm_aladin63'
model='ncc_noresm1_m_dmi_hirham5'
model='ncc_noresm1_m_mohc_hadrem3_ga7_05'
model='ncc_noresm1_m_smhi_rca4'
```

(climate_projections-cordex_validation_q07:section-2.3)=


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > Analysis and results > 2. Downloading and processing > 2.3. Apply land-sea mask and change some attributes
---
This section changes some attributes and applies a land–sea mask to all models, as well as to ERA5. A bare-earth (barrean) mask is also applied to ensure meaningful results in arid regions, as in the [C3S atlas](https://atlas.climate.copernicus.eu/atlas). In particular, we follow the methodology available in their [Github repository](https://github.com/ecmwf-projects/c3s-atlas/blob/main/auxiliar/barrean_mask.ipynb). While their implementation of the mask also considers factors such as snow depth and vegetation cover, here we only apply the filter based on annual mean precipitation for 1971–2010 being less than 0.3 mm day⁻¹. This simplification is justified because, in the region under consideration, the bare-earth mask obtained with the full set of filters closely matches the one derived from the precipitation threshold alone.

**Note:** `ds_interpolated` contains data from the models regridded to the ERA5 grid. `model_datasets` contain the same data on the original grid of each model. Regridding is performed for every essential climate variable prior to the index calculation in order to avoid compromising standardisation.

Download and prepare lsm
Ensure CF-compliant attributes for model datasets
Apply land-sea mask to each model
Apply precipitation mask to ERA5 and interpolated
Apply PR mask to each model

```text
100%|██████████| 1/1 [00:00<00:00, 22.34it/s]
```

(climate_projections-cordex_validation_q07:section-3)=


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > Analysis and results > 3. Plot and describe results
---
This section will display the following results:

- SPEI6 change maps comparing ERA5 and the ensemble median (defined as the median of the change values for the selected subset of models at each grid cell). The layout includes ERA5, the ensemble median, the ensemble median bias, and the ensemble spread (calculated as the standard deviation of the change across the selected subset of models).
- SPEI6 change maps for each individual model.
- Bias maps of the SPEI6 change for each model.
- Time series of SPEI6 change (averaged over the Mediterranean region).

**Note:** SPEI6 change is calculated at each grid point as the arithmetic difference between climatologies in the target period (1991–2010) and the baseline period (1971–1990).

(climate_projections-cordex_validation_q07:section-3.1)=


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > Analysis and results > 3. Plot and describe results > 3.1. Define plotting functions
---
The functions presented here are used to calculate SPEI6 changes and generate corresponding layout plots. Three types of layout can be displayed, depending on the plotting function:

1. Reference and ensemble summary: Includes the ERA5 reference product, the ensemble median, the bias of the ensemble median, and the ensemble spread. This is generated using `plot_ensemble()`.

2. Individual models: Displays all models individually using `plot_models()`.

3. Model biases: Displays the bias of each model relative to the reference, also using `plot_models()`.

**Calculation of SPEI6 change:**

- `compute_spei_change()` calculates SPEI6 change at each grid point as the arithmetic difference between monthly climatologies of the target period (1991–2010) and the baseline period (1971–1990). It then aggregates the change according to the user-specified `time_agg` in Section 1.2.

- `compute_change_4timeseries()` computes SPEI6 anomalies relative to the baseline climatology for each month of the timeseries and aggregates them according to the `time_agg` parameter. This provides monthly, seasonal, or annual-level information depending on the user’s selection.

Mapping months to names
Mapping seasons to months
Select baseline and target periods
Monthly climatologies
Aggregate according to user choice
Mapping months to names
Mapping seasons to months
Select baseline period
Monthly climatology for the baseline
Compute monthly anomalies relative to baseline climatology
Preserve attributes
Aggregate anomalies
Group by year
Select months for the season, then group by year
Select the month, keep time as is
--- Determine colour parameters ---
--- Helper function to split GCM and RCM ---
--- Plot each model ---
--- Hide empty axes ---
--- Shared extent and colourbar ---
Default behaviour
Create figure and axes
--- ERA5 plot ---
--- Ensemble Median ---
--- Ensemble Bias (Median - ERA5) ---
--- Ensemble Standard Deviation ---

(climate_projections-cordex_validation_q07:section-3.2)=


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > 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 SPEI6 change for the following: (a) the reference ERA5 product, (b) the ensemble median (defined as the median of the change values for the selected subset of models at each grid cell), (c) the bias of the ensemble median, and (d) the ensemble spread (calculated as the standard deviation of the change across the selected subset of models).

**ANNUAL aggregation**

Change default colorbars
Shared colorbar for ERA5 and ensemble median
Get spei change

Fig 1.
        Spatial patterns of SPEI6 change over the Mediterranean region. Panels show (a) ERA5 reference, (b) CORDEX ensemble median (median of the selected subset of models at each grid cell), (c) ensemble median bias relative to ERA5, and (d) ensemble spread (standard deviation across the selected models). SPEI6 is standardised over the reference period 1971–2010. SPEI6 change is calculated at each grid point as the difference between the monthly climatologies of the target period (1991–2010) and the baseline period (1971–1990), and then averaged to obtain the ANNUAL mean.

NOTE:

The regridding artefacts visible in panel (d) result from the use of a conservative regridding method, which is commonly recommended when dealing with precipitation. They typically arise from large values in specific models and differences among the models’ native grids.

(climate_projections-cordex_validation_q07:section-3.3)=


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > Analysis and results > 3. Plot and describe results > 3.3. Plot ensemble maps - Seasonal aggregations
---
Same as 3.2 section but for: DJF, MAM, JJA and SON

**WINTER (DJF)**

Get spei change

Fig 2.
        Spatial patterns of SPEI6 change over the Mediterranean region. Panels show (a) ERA5 reference, (b) CORDEX ensemble median (median of the selected subset of models at each grid cell), (c) ensemble median bias relative to ERA5, and (d) ensemble spread (standard deviation across the selected models). SPEI6 is standardised over the reference period 1971–2010. SPEI6 change is calculated at each grid point as the difference between the monthly climatologies of the target period (1991–2010) and the baseline period (1971–1990), and then averaged across the winter to obtain the DJF mean.

**SPRING (MAM)**

Get spei change

Fig 3.
        Spatial patterns of SPEI6 change over the Mediterranean region. Panels show (a) ERA5 reference, (b) CORDEX ensemble median (median of the selected subset of models at each grid cell), (c) ensemble median bias relative to ERA5, and (d) ensemble spread (standard deviation across the selected models). SPEI6 is standardised over the reference period 1971–2010. SPEI6 change is calculated at each grid point as the difference between the monthly climatologies of the target period (1991–2010) and the baseline period (1971–1990), and then averaged across the spring to obtain the MAM mean.

**SUMMER (JJA)**

Get spei change

Fig 4.
        Spatial patterns of SPEI6 change over the Mediterranean region. Panels show (a) ERA5 reference, (b) CORDEX ensemble median (median of the selected subset of models at each grid cell), (c) ensemble median bias relative to ERA5, and (d) ensemble spread (standard deviation across the selected models). SPEI6 is standardised over the reference period 1971–2010. SPEI6 change is calculated at each grid point as the difference between the monthly climatologies of the target period (1991–2010) and the baseline period (1971–1990), and then averaged across the summer to obtain the JJA mean.

**AUTUMN (SON)**

Get spei change

Fig 5.
        Spatial patterns of SPEI6 change over the Mediterranean region. Panels show (a) ERA5 reference, (b) CORDEX ensemble median (median of the selected subset of models at each grid cell), (c) ensemble median bias relative to ERA5, and (d) ensemble spread (standard deviation across the selected models). SPEI6 is standardised over the reference period 1971–2010. SPEI6 change is calculated at each grid point as the difference between the monthly climatologies of the target period (1991–2010) and the baseline period (1971–1990), and then averaged across the autumn to obtain the SON mean.

(climate_projections-cordex_validation_q07:section-3.4)=


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > Analysis and results > 3. Plot and describe results > 3.4. Plot model maps
---
In this section, we invoke the `plot_models()` function to visualise the SPEI6 change of every model individually. Note that the model data used in this section maintains its original grid. Only the annual mean is shown here.

Reduce horizontal spacing between columns

Fig 6.
        Spatial patterns of SPEI6 change for each individual CORDEX model over the Mediterranean region. SPEI6 is standardised over the reference period 1971–2010. For each model, SPEI6 change is calculated at each grid point as the difference between the monthly climatologies of the target period (1991–2010) and the baseline period (1971–1990), and then averaged to obtain the annual mean.

(climate_projections-cordex_validation_q07:section-3.5)=


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > Analysis and results > 3. Plot and describe results > 3.5. Plot bias maps
---
In this section, we invoke the `plot_models()` function to visualise the bias of the SPEI6 change for every model individually. Note that the model data used in this section has previously been interpolated to the ERA5 grid. Regridding is performed for each essential climate variable before the index calculation to preserve standardisation. Only the annual mean is shown here.

Plot using the shared bias parameters

Fig 7.
        Bias of SPEI6 change for each individual CORDEX model relative to ERA5 over the Mediterranean region. SPEI6 is standardised over the reference period 1971–2010. For each model and ERA5, SPEI6 change is calculated at each grid point as the difference between the monthly climatologies of the target period (1991–2010) and the baseline period (1971–1990), and then averaged to obtain the annual mean.

(climate_projections-cordex_validation_q07:section-3.6)=


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > Analysis and results > 3. Plot and describe results > 3.6. Timeseries
---
This section shows the timeseries of SPEI6 anomalies relative to the baseline climatology. We first use `compute_change_4timeseries()`, which calculates SPEI6 anomalies for each month of the timeseries (relative to the baseline monthly climatologies) and aggregates them according to the `time_agg` parameter. Spatially averaged values are then obtained. Light blue shading highlights the baseline period, while light orange shading marks the target period. The analysis compares the CORDEX ensemble median, ERA5, and individual models, displaying trends for both ERA5 and the ensemble median. Additionally, it shows the ensemble spread and the slope values of the trends for ERA5 and the CORDEX ensemble median. Only the annual aggregation is shown here.

Define colors
Cutout region
Compute the change/anomaly for ERA5
Regionalise and compute spatially weighted mean
Compute change/anomaly for each model and spatially aggregate
Ensemble statistics
Initialize plot
Shade baseline period (light blue)
Shade target period (light orange)
--- Create custom legend entries with full opacity ---
Plot individual model time series
Add legend entry for individual models
Plot CORDEX median
Fill ±1 std (spread)
Compute trends
Labels and grid
Format x-axis as years
Annotate trends

Fig 8.
        Timeseries of SPEI6 anomalies over the Mediterranean region. Monthly anomalies are calculated relative to the monthly baseline climatologies, aggregated according to the specified timescale, and then spatially averaged over the region. Light blue shading indicates the baseline period, and light orange shading indicates the target period. The figure compares ERA5, the CORDEX ensemble median, and individual models, showing trends for ERA5 and the ensemble median, as well as the ensemble spread and slope values of the trends.

(climate_projections-cordex_validation_q07:section-3.7)=


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > Analysis and results > 3. Plot and describe results > 3.7. Results summary
---
- ERA5 indicates a general intensification of drought conditions over the Mediterranean region when comparing the baseline (1971–1990) and target (1991–2010) periods.

- The CORDEX ensemble median (obtained from the subset of models considered within this notebook) of the SPEI6 change is generally close to zero (Fig. 1). However, the inter-model spread is high, and is particularly pronounced over the Iberian Peninsula, southern France, North Africa, the Balkans region, and the easternmost Mediterranean areas (including Turkey, Lebanon, and Syria). In fact, the spatial pattern of the SPEI6 change is pretty different depending on the considered model (Fig. 6 and 7).

- Seasonal analysis (Figs. 2–5) indicates that, in ERA5, drought intensification is strongest in summer. Spring and autumn also show notable decreases in SPEI6, although localised increases partly offset the spatial mean, especially in spring. In winter, the sign of the SPEI6 change is region-dependent, with large decreases over the eastern Iberian Peninsula, the eastern Mediterranean, and North Africa, and increases over the western Iberian Peninsula, as well as parts of Italy and the Balkans. Considering the CORDEX ensemble median, SPEI6 changes remain close to zero for most seasons and regions, with no clear spatial patterns overall, or at least none consistent with those observed in ERA5.

- The timeseries of spatial means over the Mediterranean confirms an increase in drought conditions during the considered historical period in ERA5, with a trend of –0.24 (Fig. 8). For the ensemble median of CORDEX, the timeseries shows a trend close to zero, which is also not statistically significant. The timeseries plot also shows a high inter-model spread. Timeseries for seasonal aggregations are not shown here, but have been computed offline and exhibit behaviour similar to the annual case.

- The results obtained in this notebook differ from those reported in the quality assessment named [CMIP6 biases in the SPEI6 drought index over the Mediterranean region](https://ecmwf-projects.github.io/c3s2-eqc-quality-assessment/Climate_Projections/CMIP6/climate_projections-cmip6_validation_q13.html), where CMIP6 ensemble median captured the sign of the SPEI6 change for a similar historical period, although with an underestimation compared to ERA5.

- The limited change in SPEI6 simulated by some CORDEX models, compared to ERA5 and the previous CMIP6-based counterpart assessment, may partly reflect methodological and structural factors. In particular, the shorter analysis periods used here (20-year blocks instead of 30) may reduce the robustness of the signal. In addition, many CORDEX RCMs do not include time-evolving aerosols, which can lead to an underestimation of temperature trends in some regions and consequently affect drought-related indices such as SPEI6 [[9]](https://doi.org/10.1038/s43247-024-01332-8).

(climate_projections-cordex_validation_q07:section-3.8)=


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > Analysis and results > 3. Plot and describe results > 3.8. Implications for the users
---
- The pronounced inter-model spread over North Africa, Turkey, and the eastern Mediterranean implies that users in these regions may face higher future uncertainty. This highlights the need to stress-test adaptation strategies against a wide range of plausible futures rather than relying on a single scenario.

- Although the ensemble median does not capture the SPEI6 change signal for the historical period, this does not necessarily imply that the models are not suitable for investigating future changes, as the spatial pattern of change depends on the individual model considered and model biases are not necessarily stationary, but may evolve under changing climate conditions [[10]](https://doi.org/10.5194/hess-25-273-2021).

- The approach used in this notebook illustrates how a subset of GCM–RCM combinations can be selected while maintaining representation of all driving GCMs. This can be useful in situations where computational or practical constraints limit the use of the full ensemble. However, the results also reinforce that broader ensembles provide a more robust basis for assessing uncertainty.

- Finally, users should be aware that results may vary depending on the choice of historical periods and model configurations. In this context, complementary tools such as the [C3S Atlas](https://confluence.ecmwf.int/display/CKB/Gridded+data+underpinning+the+Copernicus+Interactive+Climate+Atlas%3A+Description+of+the+datasets+and+variables#GriddeddataunderpinningtheCopernicusInteractiveClimateAtlas:Descriptionofthedatasetsandvariables), which includes a larger ensemble and alternative period definitions, can provide additional context for interpreting these findings. In addition, this notebook helps users understand the basis of the SPEI index and its methodological assumptions, supporting its application in operational water management and drought preparedness.


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > 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 - Maximum 2m temperature in the last 24 hours, Minimum 2m temperature in the last 24 hours, 2m air temperature and 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 (2m temperature and total precipitation): https://cds.climate.copernicus.eu/datasets/reanalysis-era5-pressure-levels-monthly-means?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/)


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > ℹ If you want to know more > References
---
[[1]](https://doi.org/10.1175/2009JCLI2909.1) Vicente-Serrano, S. M., Beguerı́a, S., and López-Moreno, J. I., 2010.  A multiscalar drought index sensitive to global warming: The standardized precipitation evapotranspiration index, Journal of Climate, 23, 1696–1718. https://doi.org/10.1175/2009JCLI2909.1

[[2]](https://digitalcommons.unl.edu/droughtfacpub/69/) Wilhite, D. A., 2000. Droughts as a natural hazard: concepts and definitions. In: DROUGHT, A Global Assessment, vol. I and II, Routledge Hazards and Disasters Series, Routledge.

[[3]](https://doi.org/10.1175/2012EI000434.1) Vicente-Serrano, S. M., Beguerı́a, S., Lorenzo-Lacruz, J., Camarero, J. J., López-Moreno, J. I., Azorin-Molina, C., Revuelto, J., Morán-Tejeda, E., and Sanchez-Lorenzo, A., 2012. Performance of drought indices for ecological, agricultural, and hydrological applications, Earth Interactions, 16, https://doi.org/10.1175/2012EI000434.1

[[4]](https://doi.org/10.3390/eesp2025035029) Kalisoras, A., Georgoulias, A. K., Akritidis, D., and Zanis, P., 2025. Future Projections in Agricultural Drought Characteristics for Greece Under Different Climate Change Scenarios. Environmental and Earth Sciences Proceedings, 35(1), 29. https://doi.org/10.3390/eesp2025035029

[[5]](https://doi.org/10.1002/joc.7302) Spinoni, J., Barbosa, P., Bucchignani, E., Cassano, J., Cavazos, T., Cescatti, A., Christensen, J. H., Christensen, O. B., Coppola, E., Evans, J. P., Forzieri, G., Geyer, B., Giorgi, F., Jacob, D., Katzfey, J., Koenigk, T., Laprise, R., Lennard, C. J., Kurnaz, M. L., … Dosio, A., 2021. Global exposure of population and land-use to meteorological droughts under different warming levels and SSPs: A CORDEX-based study. International Journal of Climatology, 41(15), 6825–6853. https://doi.org/10.1002/joc.7302

[[6]](https://doi.org/10.5194/essd-12-2959-2020) Iturbide, M., Gutiérrez, J. M., Alves, L. M., Bedia, J., Cerezo-Mota, R., Cimadevilla, E., Cofiño, A. S., Di Luca, A., Faria, S. H., Gorodetskaya, I. V., Hauser, M., Herrera, S., Hennessy, K., Hewitt, H. T., Jones, R. G., Krakovska, S., Manzanas, R., Martínez-Castro, D., Narisma, G. T., Nurhati, I. S., Pinto, I., Seneviratne, S. I., van den Hurk, B., and Vera, C. S., 2020. An update of IPCC climate reference regions for subcontinental analysis of climate model data: definition and aggregated datasets, Earth Syst. Sci. Data, 12, 2959–2970, https://doi.org/10.5194/essd-12-2959-2020

[[7]](https://doi.org/10.13031/2013.26773) Hargreaves, G. H., and Samani, Z. A., 1985. Reference crop evapotranspiration from temperature, Applied engineering in agriculture, pp. 96–99.  https://doi.org/10.13031/2013.26773


EQC Quality Assessment: "CORDEX biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q07  |  Category: Climate_Projections
Section: CORDEX biases in the SPEI6 drought index over the Mediterranean region > ℹ If you want to know more > References
---
ani, Z. A., 1985. Reference crop evapotranspiration from temperature, Applied engineering in agriculture, pp. 96–99.  https://doi.org/10.13031/2013.26773

[[8]](https://doi.org/10.1002/joc.3887) Beguerı́a, S., Vicente-Serrano, S. M., Reig, F., and Latorre, B., 2014. Standardized precipitation evapotranspiration index (spei) revisited: Parameter fitting, evapotranspiration models, tools, datasets and drought monitoring, International Journal of Climatology, 34, 3001–3023. https://doi.org/10.1002/joc.3887

[[9]](https://doi.org/10.1038/s43247-024-01332-8) Schumacher, D.L., Singh, J., Hauser, M., et al., 2024. Exacerbated summer European warming not captured by climate models neglecting long-term aerosol changes. Commun Earth Environ 5, 182. https://doi.org/10.1038/s43247-024-01332-8

[[10]](https://doi.org/10.5194/hess-25-273-2021) Schmith, T., Thejll, P., Berg, P., Boberg, F., Christensen, O. B., Christiansen, B., Christensen, J. H., Madsen, M. S., and Steger, C., 2021. Identifying robust bias adjustment methods for European extreme precipitation in a multi-model pseudo-reality setting, Hydrol. Earth Syst. Sci., 25, 273–290, https://doi.org/10.5194/hess-25-273-2021


EQC Quality Assessment: "Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q08  |  Category: Climate_Projections
Section: Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region
---
Production date: 25-03-2026

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


EQC Quality Assessment: "Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q08  |  Category: Climate_Projections
Section: Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region > Quality assessment question
---
* **What are the projected future changes and associated uncertainties in droughts over the Mediterranean?**

The Standardized Precipitation-Evapotranspiration Index (SPEI) [[1]](https://doi.org/10.1175/2009JCLI2909.1) is a widely used drought indicator that integrates precipitation and potential evapotranspiration, providing a more complete measure of water deficits than precipitation alone. Its multiscalar formulation allows the evaluation of different types of drought [[2]](https://digitalcommons.unl.edu/droughtfacpub/69/), from short-term agricultural or soil moisture deficits to long-term hydrological or ecological events. Being standardised, SPEI is dimensionless, facilitating comparisons across regions and climates. By capturing variations in frequency, duration, and severity, it effectively reflects the complex nature of drought, making it a robust and physically meaningful proxy for drought assessment in the context of climate change [[3]](https://doi.org/10.1175/2012EI000434.1).

Understanding SPEI is particularly relevant for the water management sector. By capturing multiple types of drought SPEI serves as a versatile indicator for various users. Climate projections using SPEI enable planners to anticipate future water deficits, guide allocation, and design effective strategies for reservoir management, irrigation, and drought preparedness, helping to reduce socio-economic and ecological impacts [[4]](https://doi.org/10.3390/eesp2025035029)[[5]](https://doi.org/10.1002/joc.7302).

This assessment uses 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) to explore the signal and the uncertainty in future projections of the SPEI6 index. The analysis focuses on the Mediterranean region, evaluating changes in SPEI6 for the near-future period (2026–2055; under the RCP8.5 scenario) relative to the 1971–2000 baseline, which serves as the reference period for standardisation. The projected uncertainty is assessed by considering the ensemble inter-model spread of projected changes.

This notebook complements the evaluation of the biases of the same subset of CORDEX models performed through the assessment named *"CORDEX biases in the SPEI6 drought index over the Mediterranean region"*


EQC Quality Assessment: "Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q08  |  Category: Climate_Projections
Section: Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region > Quality assessment statement
---
These are the key outcomes of this assessment

* The CORDEX ensemble median for the subset of models considered in this assessment indicates an overall increase in projected drought conditions for the near-term future (2026–2055) under the RCP8.5 scenario.

* There is substantial inter-model spread, with differences in both the magnitude and, in some cases, the sign of projected SPEI6 changes, particularly at regional and seasonal scales, indicating that projections are highly model-dependent and should be interpreted in an ensemble-based framework.

* Despite this spread, SPEI6 anomalies remain predominantly negative at the Mediterranean scale, indicating a consistent basin-wide tendency towards drier conditions.

* The projected intensification of drought may be conservative, as indicated by a complementary historical assessment showing that the analysed CORDEX models tend to underestimate drought conditions relative to ERA5.
```

attachment:88b80b6a-fa7c-45f6-bdb0-51e2689e6529.png
---
width: 1500px
alt: Visual abstract
---
Spatial patterns of SPEI6 change over the Mediterranean region. Panels show (a) CORDEX ensemble median (median of the selected subset of models at each grid cell) and (b) ensemble spread (standard deviation across the selected models). SPEI6 is standardised over the reference period 1971–2000. SPEI6 change is calculated at each grid point as the difference between the monthly climatologies of the target period (2026–2055) and the baseline period (1971–2000), and then averaged to obtain the ANNUAL mean. Future projections used for the target period follow the RCP8.5 scenario.
```


EQC Quality Assessment: "Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q08  |  Category: Climate_Projections
Section: Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region > Methodology
---
The Standardized Precipitation-Evapotranspiration Index accumulated to six months (SPEI6) has been calculated for this assessment — through the use of [xclim](https://xclim.readthedocs.io/en/stable/) — as a proxy to evaluate projected drought conditions for a subset of [CORDEX](https://cds.climate.copernicus.eu/datasets/projections-cordex-domains-single-levels?tab=overview) models. The study covers the Mediterranean domain, following IPCC-AR6 regional definitions [[6]](https://doi.org/10.5194/essd-12-2959-2020). Results include spatial maps of SPEI6 changes for the near-future period (2026–2055) relative to the 1971–2000 baseline, which serves as the reference period for standardisation. Additionally, time series are computed to show the temporal evolution of future SPEI6 changes. Uncertainty is assessed through the inter-model ensemble spread, defined as the standard deviation across the selected subset of models, of projected SPEI6 changes.

Potential evapotranspiration (PET) is calculated with the Hargreaves method [[7]](https://doi.org/10.13031/2013.26773), which requires only maximum and minimum temperature (and optionally mean temperature), providing a computationally efficient yet robust estimate (e.g., [[8]](https://doi.org/10.1002/joc.3887)). The accumulated series of precipitation minus PET is then standardised over the 1971–2000 reference period.

Five key concepts are defined:

- **Reference period:** The period used to standardise SPEI values, here 1971–2000.
- **Baseline period:** The period against which changes are calculated. In this notebook the baseline period is selected to be the same as the reference period.
- **Target period:** The future period for which changes are evaluated, here 2026–2055. The Representative Concentration Pathway is set to the RCP8.5 scenario for this assessment.
- **SPEI6 change:** Differences in SPEI6 between the target period and the baseline, representing anomalies in drought conditions. Since, in this notebook, the baseline and the reference period are the same, these changes directly represent anomalies relative to the standardisation climatology used to compute SPEI6.

The analysis and results follow the next outline:

**[](climate_projections-cordex_validation_q08:section-1)**
 * [](climate_projections-cordex_validation_q08:section-1.1)
 * [](climate_projections-cordex_validation_q08:section-1.2)
 * [](climate_projections-cordex_validation_q08:section-1.3)
 * [](climate_projections-cordex_validation_q08:section-1.4)
 * [](climate_projections-cordex_validation_q08:section-1.5)
 * [](climate_projections-cordex_validation_q08:section-1.6)

**[](climate_projections-cordex_validation_q08:section-2)**
 * [](climate_projections-cordex_validation_q08:section-2.1)
 * [](climate_projections-cordex_validation_q08:section-2.2)
 * [](climate_projections-cordex_validation_q08:section-2.3)

**[](climate_projections-cordex_validation_q08:section-3)**
 * [](climate_projections-cordex_validation_q08:section-3.1)
 * [](climate_projections-cordex_validation_q08:section-3.2)
 * [](climate_projections-cordex_validation_q08:section-3.3)
 * [](climate_projections-cordex_validation_q08:section-3.4)
 * [](climate_projections-cordex_validation_q08:section-3.5)
 * [](climate_projections-cordex_validation_q08:section-3.6)
 * [](climate_projections-cordex_validation_q08:section-3.7)

NOTE ON REFERENCE PERIOD SELECTION:

This notebook follows the same methodology as the assessment ‘CORDEX biases in the SPEI6 drought index over the Mediterranean region’. However, the reference period (1971–2000) is shorter than the 1971–2010 period used in the historical assessment. This choice avoids including scenario data in the standardisation (as CORDEX historical simulations extend only until 2005), ensures computational efficiency due to the shorter period, and maintains consistency with the 30-year length of the future target period.


EQC Quality Assessment: "Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q08  |  Category: Climate_Projections
Section: Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region > 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 reference and baseline periods are set to be the same in this notebook and can be adjusted by modifying `reference_slice`; the default range is 1971-2000.
- The target period can be adjusted by modifying `target_slice`; the default range is 2026-2055.
- A check is performed on the `target_slice` and `reference_slice` to ensure consistency with CDS CORDEX requests and to verify that the reference period falls within the historical experiment, i.e. the last year of `reference_slice` does not exceed 2005.
- `collection_id` is not customisable for this assessment and is set to 'CORDEX'.
- The `area` parameter specifies the geographical domain of interest. By default, the Mediterranean domain is used, following IPCC-AR6 regional definitions [[6]](https://doi.org/10.5194/essd-12-2959-2020)
- The `time_agg` allows selecting the time aggregation for the analysis. Options include: annual, DJF, MAM, JJA, SON, Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec.
- SPEI accumulation window (`window`): Defines the accumulation period in months for the SPEI calculation. Common options include 3, 6, or 12 months, depending on whether short-term or long-term droughts are of interest. In this assessment, a six-month accumulation is used.
- `rcm_model_regrid` and `gcm_driven_model_regrid` specify the EURO-CORDEX regional climate model and the driving global climate model, respectively, whose grid will be used as the target for remapping. Note that both models must be included in the matrix of RCM-GCM combinations defined by the `models_cordex` dictionary in Section 1.3.
- The `chunks` 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.

Periods definition
Collection id
Define region for analysis
time aggregation
SPEI accumulation
Chunks for download

Rule: start ends in 1 or 6, end ends in 0 or 5
Historical constraint for baseline

(climate_projections-cordex_validation_q08:section-1.3)=


EQC Quality Assessment: "Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q08  |  Category: Climate_Projections
Section: Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region > Analysis and results > 1. Parameters, requests and functions definition > 1.3. Define models
---
The following climate analyses are performed using a subset of CORDEX models that provide both the historical and RCP8.5 experiments, as well as maximum, minimum and mean temperature and precipitation, within the Climate Data Store ([CDS](https://cds.climate.copernicus.eu/datasets/projections-cordex-domains-single-levels?tab=overview)). All Global Climate Models (GCMs) driving the selected CORDEX simulations were included, and the selection ensures a representative coverage of the available Regional Climate Models (RCMs). The selected models are the same as those used for the historical evaluation in the assessment titled *“CORDEX biases in the SPEI6 drought index over the Mediterranean region"*.

(climate_projections-cordex_validation_q08:section-1.4)=


EQC Quality Assessment: "Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q08  |  Category: Climate_Projections
Section: Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region > Analysis and results > 1. Parameters, requests and functions definition > 1.4. Define land-sea mask and ERA5 precipitation requests
---
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. A request for monthly ERA5 precipitation data is also defined to compute a bare-earth (barrean) mask, which needs to be applied to ensure meaningful results in arid regions.

(climate_projections-cordex_validation_q08:section-1.5)=


EQC Quality Assessment: "Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q08  |  Category: Climate_Projections
Section: Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region > 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.

Historical part (until 2005)
Future part (RCP8.5 from 2006 onwards)

(climate_projections-cordex_validation_q08:section-1.6)=


EQC Quality Assessment: "Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q08  |  Category: Climate_Projections
Section: Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region > 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.

Description of the main functions:

- **`compute_spei_cordex_fut`**: Uses the xclim package to calculate the Standardized Precipitation-Evapotranspiration Index (SPEI). The `reference_slice` argument specifies the reference period used for standardization, while the `window` argument defines the number of months over which precipitation and evapotranspiration are accumulated (6 months in this assessment).

- **`get_mask_pr`**: Generates a mask identifying grid points where precipitation is below 0.3 mm/day, allowing filtering of extremely dry regions.

Ensure CF-compliant attributes for model datasets
Original bounds for conservative interpolation
Wrap into dataset

(climate_projections-cordex_validation_q08:section-2)=


EQC Quality Assessment: "Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q08  |  Category: Climate_Projections
Section: Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region > 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 EURO-CORDEX regridding model, select the subregion of interest, compute daily potential evapotranspiration, calculate the daily water balance, and derive the SPEI (SPEI6 for this assessment). Results are cached to avoid redundant downloads and repeated processing.

The regridding model here refers to the model whose grid is used as the target grid for remapping the other models. This ensures all datasets share a common grid, facilitating direct comparison at each grid cell. Within this notebook, the regridding model is set to `"ichec_ec_earth_dmi_hirham5"` but it can be changed by modifying the `gcm_driven_model_regrid` and `rcm_model_regrid` parameters in Section 1.2. Note that both models must be included in the matrix of RCM-GCM combinations defined by the `models_cordex` dictionary in Section 1.3. It is important to highlight that the choice of the target grid can impact the analysis depending on the specific application.

(climate_projections-cordex_validation_q08:section-2.2)=


EQC Quality Assessment: "Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q08  |  Category: Climate_Projections
Section: Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region > 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 used to download daily data from CORDEX models, compute daily potential evapotranspiration, calculate the daily water balance, and derive the SPEI (SPEI6 for this assessment). SPEI6 is computed on each model's native grid and also on the `"ichec_ec_earth_dmi_hirham5"` grid to enable bias assessment. When regridding is required, it is performed for each essential climate variable before the index calculation to preserve standardisation. Results are cached to avoid redundant downloads and repeated processing.

Original model
Interpolated model

```text
model='cccma_canesm2_clmcom_clm_cclm4_8_17'
model='cccma_canesm2_gerics_remo2015'
model='cnrm_cerfacs_cm5_ipsl_wrf381p'
model='cnrm_cerfacs_cm5_smhi_rca4'
model='ichec_ec_earth_dmi_hirham5'
model='ichec_ec_earth_knmi_racmo22e'
model='ipsl_cm5a_mr_ipsl_wrf381p'
model='ipsl_cm5a_mr_knmi_racmo22e'
model='miroc_miroc5_clmcom_clm_cclm4_8_17'
model='miroc_miroc5_gerics_remo2015'
model='mohc_hadgem2_es_cnrm_aladin63'
model='mohc_hadgem2_es_mohc_hadrem3_ga7_05'
model='mpi_m_mpi_esm_lr_mpi_csc_remo2009'
model='mpi_m_mpi_esm_lr_cnrm_aladin63'
model='ncc_noresm1_m_dmi_hirham5'
model='ncc_noresm1_m_mohc_hadrem3_ga7_05'
model='ncc_noresm1_m_smhi_rca4'
```

(climate_projections-cordex_validation_q08:section-2.3)=


EQC Quality Assessment: "Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q08  |  Category: Climate_Projections
Section: Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region > Analysis and results > 2. Downloading and processing > 2.3. Apply land-sea mask and change some attributes
---
This section changes some attributes and applies a land–sea mask to all models. A bare-earth (barrean) mask is also applied to ensure meaningful results in arid regions, as in the [C3S atlas](https://atlas.climate.copernicus.eu/atlas). In particular, we follow the methodology available in their [Github repository](https://github.com/ecmwf-projects/c3s-atlas/blob/main/auxiliar/barrean_mask.ipynb). While their implementation of the mask also considers factors such as snow depth and vegetation cover, here we only apply the filter based on annual mean precipitation for 1971–2000 being less than 0.3 mm day⁻¹. This simplification is justified because, in the region under consideration, the bare-earth mask obtained with the full set of filters closely matches the one derived from the precipitation threshold alone.

**Note:** `ds_interpolated` contains data from the models regridded to the `"ichec_ec_earth_dmi_hirham5"` grid. `model_datasets` contain the same data on the original grid of each model. Regridding is performed for every essential climate variable prior to the index calculation in order to avoid compromising standardisation.

Download and prepare lsm
Apply land-sea mask to interpolate dataset
Apply land sea mask to each model dataset
Apply PR mask to interpolated dataset
Apply PR mask to each model

```text
100%|██████████| 1/1 [00:00<00:00, 25.66it/s]
```

(climate_projections-cordex_validation_q08:section-3)=


EQC Quality Assessment: "Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q08  |  Category: Climate_Projections
Section: Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region > Analysis and results > 3. Plot and describe results
---
This section will display the following results:

- SPEI6 change maps. The layout includes the ensemble median (defined as the median of the change values across the selected subset of models at each grid cell) and the ensemble spread (calculated as the standard deviation of the change across the selected subset of models).
- SPEI6 change maps for each individual model.
- Time series of SPEI6 change (averaged over the Mediterranean region).

**Note:** The projected SPEI6 change is calculated at each grid point as the arithmetic difference between climatologies in the target period (2026–2055) and the baseline period (1971–2000).

(climate_projections-cordex_validation_q08:section-3.1)=


EQC Quality Assessment: "Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q08  |  Category: Climate_Projections
Section: Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region > Analysis and results > 3. Plot and describe results > 3.1. Define plotting functions
---
The functions presented here are used to calculate SPEI6 changes and generate corresponding layout plots. Three types of layout can be displayed, depending on the plotting function:

1. Reference and ensemble summary: Includes the ensemble median and the ensemble spread. This is generated using `plot_ensemble()`.

2. Individual models: Displays all models individually using `plot_models()`.

**Calculation of SPEI6 change:**

- `compute_spei_change()` calculates SPEI6 change at each grid point as the arithmetic difference between monthly climatologies of the target period (2026–2055) and the baseline period (1971–2000). It then aggregates the change according to the user-specified `time_agg` in Section 1.2.

- `compute_change_4timeseries()` computes SPEI6 anomalies relative to the baseline climatology for each month of the timeseries and aggregates them according to the `time_agg` parameter. This provides monthly, seasonal, or annual-level information depending on the user’s selection.

Mapping months to names
Mapping seasons to months
Select baseline and target periods
Monthly climatologies
Aggregate according to user choice
Mapping months to names
Mapping seasons to months
Select baseline period
Monthly climatology for the baseline
Compute monthly anomalies relative to baseline climatology
Preserve attributes
Aggregate anomalies
Group by year
Select months for the season, then group by year
Select the month, keep time as is
--- Determine colour parameters ---
--- Helper function to split GCM and RCM ---
--- Plot each model ---
--- Hide empty axes ---
--- Shared extent and colourbar ---
Default behaviour
Create figure and axes
--- ERA5 plot ---
--- Ensemble Median ---
--- Ensemble Bias (Median - ERA5) ---
--- Ensemble Standard Deviation ---

(climate_projections-cordex_validation_q08:section-3.2)=


EQC Quality Assessment: "Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q08  |  Category: Climate_Projections
Section: Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region > 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 SPEI6 change for (a) the ensemble median (defined as the median of the change values for the selected subset of models at each grid cell) and (b) the ensemble spread (calculated as the standard deviation of the change across the selected subset of models).

**ANNUAL aggregation**

Change default colorbars
Shared colorbar for ERA5 and ensemble median
Get spei change

Fig 1.
        Spatial patterns of SPEI6 change over the Mediterranean region. Panels show (a) CORDEX ensemble median (median of the selected subset of models at each grid cell) and (b) ensemble spread (standard deviation across the selected models). SPEI6 is standardised over the reference period 1971–2000. SPEI6 change is calculated at each grid point as the difference between the monthly climatologies of the target period (2026–2055) and the baseline period (1971–2000), and then averaged to obtain the ANNUAL mean. Future projections used for the target period follow the RCP8.5 scenario.

(climate_projections-cordex_validation_q08:section-3.3)=


EQC Quality Assessment: "Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q08  |  Category: Climate_Projections
Section: Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region > Analysis and results > 3. Plot and describe results > 3.3. Plot ensemble maps - Seasonal aggregations
---
Same as 3.2 section but for: DJF, MAM, JJA and SON

**WINTER (DJF)**

Get spei change

Fig 2.
        Spatial patterns of SPEI6 change over the Mediterranean region. Panels show (a) CORDEX ensemble median (median of the selected subset of models at each grid cell) and (b) ensemble spread (standard deviation across the selected models). SPEI6 is standardised over the reference period 1971–2000. SPEI6 change is calculated at each grid point as the difference between the monthly climatologies of the target period (2026–2055) and the baseline period (1971–2000), and then averaged across the winter to obtain the DJF mean. Future projections used for the target period follow the RCP8.5 scenario.

**SPRING (MAM)**

Get spei change

Fig 3.
        Spatial patterns of SPEI6 change over the Mediterranean region. Panels show (a) CORDEX ensemble median (median of the selected subset of models at each grid cell) and (b) ensemble spread (standard deviation across the selected models). SPEI6 is standardised over the reference period 1971–2000. SPEI6 change is calculated at each grid point as the difference between the monthly climatologies of the target period (2026–2055) and the baseline period (1971–2000), and then averaged across the spring to obtain the MAM mean. Future projections used for the target period follow the RCP8.5 scenario.

**SUMMER (JJA)**

Get spei change

Fig 4.
        Spatial patterns of SPEI6 change over the Mediterranean region. Panels show (a) CORDEX ensemble median (median of the selected subset of models at each grid cell) and (b) ensemble spread (standard deviation across the selected models). SPEI6 is standardised over the reference period 1971–2000. SPEI6 change is calculated at each grid point as the difference between the monthly climatologies of the target period (2026–2055) and the baseline period (1971–2000), and then averaged across the summer to obtain the JJA mean. Future projections used for the target period follow the RCP8.5 scenario.

**AUTUMN (SON)**

Get spei change

Fig 5.
        Spatial patterns of SPEI6 change over the Mediterranean region. Panels show (a) CORDEX ensemble median (median of the selected subset of models at each grid cell) and (b) ensemble spread (standard deviation across the selected models). SPEI6 is standardised over the reference period 1971–2000. SPEI6 change is calculated at each grid point as the difference between the monthly climatologies of the target period (2026–2055) and the baseline period (1971–2000), and then averaged across the autumn to obtain the SON mean. Future projections used for the target period follow the RCP8.5 scenario.

(climate_projections-cordex_validation_q08:section-3.4)=


EQC Quality Assessment: "Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q08  |  Category: Climate_Projections
Section: Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region > Analysis and results > 3. Plot and describe results > 3.4. Plot model maps
---
In this section, we invoke the `plot_models()` function to visualise the SPEI6 change of every model individually. Note that the model data used in this section maintains its original grid. Only the annual mean is shown here.

Reduce horizontal spacing between columns

Fig 6.
        Spatial patterns of SPEI6 change for each individual CORDEX model over the Mediterranean region. SPEI6 is standardised over the reference period 1971–2000. For each model, SPEI6 change is calculated at each grid point as the difference between the monthly climatologies of the target period (2026–2055) and the baseline period (1971–2000), and then averaged to obtain the annual mean. Future projections used for the target period follow the RCP8.5 scenario.

(climate_projections-cordex_validation_q08:section-3.5)=


EQC Quality Assessment: "Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q08  |  Category: Climate_Projections
Section: Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region > Analysis and results > 3. Plot and describe results > 3.5. Timeseries
---
This section shows the timeseries of SPEI6 anomalies relative to the reference period climatology (same period as the baseline for this notebook). We first use `compute_change_4timeseries()`, which calculates SPEI6 anomalies for each month of the target period (relative to the baseline monthly climatologies) and aggregates them according to the `time_agg` parameter. Spatially averaged values are then obtained. The analysis compares the CORDEX ensemble median and individual models and shows the ensemble spread and the slope value of the trend for the CORDEX ensemble median. Only the annual aggregation is shown here.

Define colors
Cutout region
Compute change/anomaly for each model and spatially aggregate
Ensemble statistics
--- Select ONLY target period ---
Initialize plot
Plot individual model time series
Add legend entry for individual models
Plot CORDEX median
Fill ±1 std (spread)
Compute trend ONLY for CORDEX (already filtered to target period)
Labels and title
Format x-axis as years
Annotate trends

Fig 7.
       Timeseries of SPEI6 anomalies over the Mediterranean region. Monthly anomalies are calculated relative to the monthly baseline climatologies, aggregated according to the specified timescale, and then spatially averaged over the region. The figure compares the CORDEX ensemble median and individual models, showing the trend for the ensemble median, as well as the ensemble spread and the corresponding trend slope. Future projections used for the target period follow the RCP8.5 scenario.

(climate_projections-cordex_validation_q08:section-3.6)=


EQC Quality Assessment: "Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q08  |  Category: Climate_Projections
Section: Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region > Analysis and results > 3. Plot and describe results > 3.6. Results summary
---
- The projected SPEI6 change for the near-term future (2026–2055) indicates an overall decrease in the index (Fig. 1), suggesting a general intensification of drought conditions. However, a large inter-model spread is evident, with substantial disparities not only in the magnitude of change but also in its sign (see Fig. 6). Some models project wetter conditions than the baseline, particularly over regions such as the Balkans, southern France, the Adriatic coast of Italy, and parts of Turkey.

- The inter-model spread spatial patterns are sensitive to the seasonal aggregation considered (Figs. 2–5), with the largest inter-model discrepancies occurring in spring.

- The timeseries of spatial means over the Mediterranean shows an increase in projected drought conditions for the near-term future period (Fig. 7). For the CORDEX ensemble median, the timeseries shows a slight (but statistically significant) negative trend over this period. Although the trend is weak and the inter-model spread is substantial, most individual models—and the ensemble median—remain consistently below zero. This indicates that drier conditions are projected for the annual aggregation over the region, as anomalies are defined relative to the historical baseline period.

- This assessment is broadly consistent with results from the [interactive C3S Atlas](https://atlas.climate.copernicus.eu/atlas). The Atlas indicates slightly stronger decreases in SPEI6, which may be partly explained by differences in the standardisation periods used and the larger ensemble of models considered.

(climate_projections-cordex_validation_q08:section-3.7)=


EQC Quality Assessment: "Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q08  |  Category: Climate_Projections
Section: Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region > Analysis and results > 3. Plot and describe results > 3.7. Implications for the users
---
- The substantial uncertainty in projected drought conditions, particularly at regional and seasonal scales, supports the use of risk-based approaches in water management and drought preparedness, where strategies should be tested against a range of plausible futures rather than relying on a single model or ensemble summary.

- The historical bias assessment (***CORDEX biases in the SPEI6 drought index over the Mediterranean region***) shows that the analysed CORDEX models tend to underestimate drought conditions relative to ERA5. Based on this, the projected intensification of drought in this notebook may be conservative and should be interpreted with this limitation in mind.

- Complementary tools such as the [interactive C3S Atlas](https://atlas.climate.copernicus.eu/atlas), which include a larger ensemble and additional dimensions such as months, global warming levels, and multiple time horizons, can provide further context for interpreting these results.

- Beyond the direct interpretation of results, this notebook emphasises the basis and methodological construction of the SPEI index, supporting its use in operational contexts.


EQC Quality Assessment: "Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q08  |  Category: Climate_Projections
Section: Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region > 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 - Maximum 2m temperature in the last 24 hours, Minimum 2m temperature in the last 24 hours, 2m air temperature and Mean precipitation flux): https://cds.climate.copernicus.eu/datasets/projections-cordex-domains-single-levels?tab=overview
* ERA5 monthly averaged data on single levels from 1940 to present (total precipitation): https://cds.climate.copernicus.eu/datasets/reanalysis-era5-single-levels-monthly-means?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/)


EQC Quality Assessment: "Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: validation_q08  |  Category: Climate_Projections
Section: Near-future CORDEX projections of the SPEI6 drought index over the Mediterranean region > ℹ If you want to know more > References
---
[[1]](https://doi.org/10.1175/2009JCLI2909.1) Vicente-Serrano, S. M., Beguerı́a, S., and López-Moreno, J. I., 2010.  A multiscalar drought index sensitive to global warming: The standardized precipitation evapotranspiration index, Journal of Climate, 23, 1696–1718. https://doi.org/10.1175/2009JCLI2909.1

[[2]](https://digitalcommons.unl.edu/droughtfacpub/69/) Wilhite, D. A., 2000. Droughts as a natural hazard: concepts and definitions. In: DROUGHT, A Global Assessment, vol. I and II, Routledge Hazards and Disasters Series, Routledge.

[[3]](https://doi.org/10.1175/2012EI000434.1) Vicente-Serrano, S. M., Beguerı́a, S., Lorenzo-Lacruz, J., Camarero, J. J., López-Moreno, J. I., Azorin-Molina, C., Revuelto, J., Morán-Tejeda, E., and Sanchez-Lorenzo, A., 2012. Performance of drought indices for ecological, agricultural, and hydrological applications, Earth Interactions, 16, https://doi.org/10.1175/2012EI000434.1

[[4]](https://doi.org/10.3390/eesp2025035029) Kalisoras, A., Georgoulias, A. K., Akritidis, D., and Zanis, P., 2025. Future Projections in Agricultural Drought Characteristics for Greece Under Different Climate Change Scenarios. Environmental and Earth Sciences Proceedings, 35(1), 29. https://doi.org/10.3390/eesp2025035029

[[5]](https://doi.org/10.1002/joc.7302) Spinoni, J., Barbosa, P., Bucchignani, E., Cassano, J., Cavazos, T., Cescatti, A., Christensen, J. H., Christensen, O. B., Coppola, E., Evans, J. P., Forzieri, G., Geyer, B., Giorgi, F., Jacob, D., Katzfey, J., Koenigk, T., Laprise, R., Lennard, C. J., Kurnaz, M. L., … Dosio, A., 2021. Global exposure of population and land-use to meteorological droughts under different warming levels and SSPs: A CORDEX-based study. International Journal of Climatology, 41(15), 6825–6853. https://doi.org/10.1002/joc.7302

[[6]](https://doi.org/10.5194/essd-12-2959-2020) Iturbide, M., Gutiérrez, J. M., Alves, L. M., Bedia, J., Cerezo-Mota, R., Cimadevilla, E., Cofiño, A. S., Di Luca, A., Faria, S. H., Gorodetskaya, I. V., Hauser, M., Herrera, S., Hennessy, K., Hewitt, H. T., Jones, R. G., Krakovska, S., Manzanas, R., Martínez-Castro, D., Narisma, G. T., Nurhati, I. S., Pinto, I., Seneviratne, S. I., van den Hurk, B., and Vera, C. S., 2020. An update of IPCC climate reference regions for subcontinental analysis of climate model data: definition and aggregated datasets, Earth Syst. Sci. Data, 12, 2959–2970, https://doi.org/10.5194/essd-12-2959-2020

[[7]](https://doi.org/10.13031/2013.26773) Hargreaves, G. H., and Samani, Z. A., 1985. Reference crop evapotranspiration from temperature, Applied engineering in agriculture, pp. 96–99.  https://doi.org/10.13031/2013.26773