EQC Quality Assessment: "Testing the capability of CMIP6 GCMs to represent precipitation intra-seasonal variability"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q11  |  Category: Climate_Projections
Section: Testing the capability of CMIP6 GCMs to represent precipitation intra-seasonal variability > Analysis and results > 3. Plot and describe results
---
This section will display the following results:

- Maps showing the spatial distribution of the **variance of filtered daily precipitation anomalies**, calculated for the historical period 1940–2014. The results compare ERA5 and the ensemble median, defined as the median of the variance values for the selected subset of models, calculated for each grid cell. The layout includes ERA5, the ensemble median, the ensemble median bias, and the ensemble spread (derived as the standard deviation of the variance for the selected subset of models). The same layout is displayed for the coefficient of variation.

- Maps showing the spatial distribution of the **variance of filtered daily precipitation anomalies**, calculated for the historical period 1940–2014 for each model. The same layout is displayed for the coefficient of variation.

- **Bias maps of the variance of filtered daily precipitation anomalies**, calculated for the historical period 1940–2014 for each model. The same layout is displayed for the coefficient of variation.

- **Time series** showing the evolution of the 30-year variance and coefficient of variation (standard deviation divided by the mean) of filtered daily precipitation anomalies over the historical period, including trends and inter-model spread.

**Note**: A Lanczos band-pass filter is applied to isolate the 10–20-day (HFISOs) and 30–60-day (LFISOs) components of daily precipitation anomalies. The seasonal period is JJAS.

(climate_projections-cmip6_validation_q11:section-3.1)=


EQC Quality Assessment: "Testing the capability of CMIP6 GCMs to represent precipitation intra-seasonal variability"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q11  |  Category: Climate_Projections
Section: Testing the capability of CMIP6 GCMs to represent precipitation intra-seasonal variability > Analysis and results > 3. Plot and describe results > 3.1. Define plotting functions
---
The functions presented here are used to plot layouts of the variance and coefficient of variation of filtered daily precipitation anomalies over the whole historical period.

Three layout types can be displayed, depending on the chosen function:

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

Define function to plot the caption of the figures (for the ensemble case)
Add each line to the figure
end captioning
Define function to plot the caption of the figures (for the individual models case)
Add caption to the figure
Add each line to the figure
Default behaviour
Create figure and axes
--- ERA5 plot ---
--- Ensemble Median ---
--- Ensemble Bias (Median - ERA5) ---
--- Ensemble Standard Deviation ---

(climate_projections-cmip6_validation_q11:section-3.2)=


EQC Quality Assessment: "Testing the capability of CMIP6 GCMs to represent precipitation intra-seasonal variability"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q11  |  Category: Climate_Projections
Section: Testing the capability of CMIP6 GCMs to represent precipitation intra-seasonal variability > 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 variance values of filtered daily precipitation anomalies over the period 1940–2014 for the following: (a) the reference ERA5 product, (b) the ensemble median (defined as the median of the variance values for the selected subset of models, calculated for each grid cell), (c) the bias of the ensemble median, and (d) the ensemble spread (calculated as the standard deviation of the variance for the selected subset of models). The same layout of maps is displayed for the coefficient of variation. As mentioned throughout this notebook, before calculating the variance and coefficient of variation, a Lanczos band-pass filter has been applied to the daily precipitation anomalies to isolate the 10–20-day high-frequency intraseasonal oscillations (HFISOs) and the 30–60-day low-frequency intraseasonal oscillations (LFISOs).

Change default colorbars
Colourbar limits
Fig number counter
Common title
Colourbar kwargs for coefficient of variation
Select colourbar kwargs based on variable type

(climate_projections-cmip6_validation_q11:section-3.3)=


EQC Quality Assessment: "Testing the capability of CMIP6 GCMs to represent precipitation intra-seasonal variability"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q11  |  Category: Climate_Projections
Section: Testing the capability of CMIP6 GCMs to represent precipitation intra-seasonal variability > Analysis and results > 3. Plot and describe results > 3.3. Plot model maps
---
In this section, we invoke the `plot_models()` function to visualise the variance and the coefficient of variation of filtered daily precipitation anomalies over the period 1940–201, for every model individually. As mentioned throughout this notebook, before calculating the variance and coefficient of variation, a Lanczos band-pass filter has been applied to the daily precipitation anomalies to isolate the 10–20-day high-frequency intraseasonal oscillations (HFISOs) and the 30–60-day low-frequency intraseasonal oscillations (LFISOs). Note that the model data used in this section maintains its original grid.

(climate_projections-cmip6_validation_q11:section-3.4)=


EQC Quality Assessment: "Testing the capability of CMIP6 GCMs to represent precipitation intra-seasonal variability"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q11  |  Category: Climate_Projections
Section: Testing the capability of CMIP6 GCMs to represent precipitation intra-seasonal variability > Analysis and results > 3. Plot and describe results > 3.4. Plot bias maps
---
In this section, we invoke the `plot_models()` function to visualise the bias of the variance and the coefficient of variation for filtered daily precipitation anomalies over the period 1940–2014, for every model individually. As mentioned throughout this notebook, before calculating the variance and coefficient of variation, a Lanczos band-pass filter has been applied to the daily precipitation anomalies to isolate the 10–20-day high-frequency intraseasonal oscillations (HFISOs) and the 30–60-day low-frequency intraseasonal oscillations (LFISOs). Note that the model data used in this section has previously been interpolated to the ERA5 grid.

(climate_projections-cmip6_validation_q11:section-3.5)=


EQC Quality Assessment: "Testing the capability of CMIP6 GCMs to represent precipitation intra-seasonal variability"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q11  |  Category: Climate_Projections
Section: Testing the capability of CMIP6 GCMs to represent precipitation intra-seasonal variability > Analysis and results > 3. Plot and describe results > 3.5. Timeseries of the coefficient of variation
---
This section examines the time series of spatially averaged variance and coefficient of variation, calculated from filtered daily precipitation anomalies over the historical period using a 30-year window. The analysis compares the CMIP6 ensemble median, ERA5, and individual models, highlighting trends for both the CMIP6 ensemble median and ERA5. It also displays the ensemble spread, along with the slope values of the trends for ERA5 and the CMIP6 ensemble median.

As mentioned throughout this notebook, before calculating the variance and coefficient of variation, a Lanczos band-pass filter has been applied to the daily precipitation anomalies to isolate the 10–20-day high-frequency intraseasonal oscillations (HFISOs) and the 30–60-day low-frequency intraseasonal oscillations (LFISOs).

Define the colors
Cutout region
Get the spatial mean for ERA5
Get the spatial mean for CMIP6, preserving each model
Calculate the median, ensemble mean, and standard deviation
Initialize list to store trend information
Plot individual model series for each variance

Fig 13. Time series of the spatially averaged values for the chosen variability formulations: (a) variance and (b) coefficient of variation, for filtered daily precipitation anomalies over the period 1940–2014. The variance and coefficient of variation have been calculated using a 30-year window. Each time series displays the CMIP6 ensemble median (green), ERA5 (black), and individual models (grey), with dashed lines indicating the trend for the CMIP6 ensemble median and ERA5. The shaded area represents the ensemble spread. A grey box at the bottom displays the trend slope. Before calculating the variance and coefficient of variation, a Lanczos band-pass filter has been applied to the daily precipitation anomalies to isolate the 10–20-day high-frequency intraseasonal oscillations (HFISOs) and the 30–60-day low-frequency intraseasonal oscillations (LFISOs).

(climate_projections-cmip6_validation_q11:section-3.6)=


EQC Quality Assessment: "Testing the capability of CMIP6 GCMs to represent precipitation intra-seasonal variability"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q11  |  Category: Climate_Projections
Section: Testing the capability of CMIP6 GCMs to represent precipitation intra-seasonal variability > Analysis and results > 3. Plot and describe results > 3.6. Results summary and discussion
---
* An assessment evaluating the [capability of CMIP6 GCMs to represent inter-annual precipitation variability](https://ecmwf-projects.github.io/c3s2-eqc-quality-assessment/Climate_Projections/CMIP6/climate_projections-cmip6_validation_q10.html#) complements the results presented in this notebook.

* Intra-seasonal variability during the Monsoon season (JJAS) shows substantial differences in spatial patterns depending on the formulation used—variance or the coefficient of variation (standard deviation divided by the mean). As detailed throughout, a Lanczos band-pass filter is applied to daily precipitation anomalies to isolate 10–20-day high-frequency (HFISOs) and 30–60-day low-frequency (LFISOs) oscillations. Anomalies are computed relative to the daily climatology to remove the seasonal cycle.

* Using variance to assess inter-annual variability reveals large differences in bias sign, magnitude, and spatial distribution. Despite model differences, biases are consistently influenced by orography and high-precipitation regions. These regions show high absolute biases due to high JJAS precipitation, though not necessarily large relative to the mean. The coefficient of variation (CV) normalises this effect, offering a potentially more meaningful measure of variability—though it can yield high values where climatological means are near zero.

* Differences between models are smaller when using CV compared to variance. Inland north-western regions (with near-zero or very low seasonal averages) show strong negative biases and high inter-model spread. One hypothesis to explain this may be that unusually wet spells are underestimated in comparison to ERA5.

* The spatial patterns of variance and CV for HFISOs and LFISOs are largely similar.

* Intra-seasonal variability patterns strongly resemble those seen in the inter-annual assessment, suggesting intra-seasonal timescales may influence inter-annual variability  [[10]](https://doi.org/10.1175/JCLI-D-18-0319.1).

* CMIP6 ensemble median does not accurately capture the temporal evolution of variance and coefficient of variation in filtered daily anomalies averaged over India (HFISOs and LFISOs). While ERA5 shows a decreasing trend in variance and increasing trend in coefficient of variation, CMIP6 models indicate opposite trends, highlighting discrepancies in temporal representation. The trends for the selection region are statistically significant with p-values below 0.05.

(climate_projections-cmip6_validation_q11:section-3.7)=


EQC Quality Assessment: "Testing the capability of CMIP6 GCMs to represent precipitation intra-seasonal variability"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q11  |  Category: Climate_Projections
Section: Testing the capability of CMIP6 GCMs to represent precipitation intra-seasonal variability > Analysis and results > 3. Plot and describe results > 3.7. Implications for the users
---
* **The selection of the variability formulation matters**. The Coefficient of Variation (CV) reduces orographic influence by normalising variability by the mean, and shows smaller inter-model differences than variance. However, it can produce artefactually high values in north-western inland regions where mean precipitation is very low.

* **ERA5 has biases** [[13]](https://doi.org/10.1002/qj.3616)[[14]](https://doi.org/10.3390/atmos12111462). While ERA5 is used for its temporal coverage, it has known biases. Users may consider alternative references like the [GPCP](https://cds.climate.copernicus.eu/datasets/satellite-precipitation?tab=overview) dataset, which may yield different results.

* Unlike the [inter-annual assessment](https://ecmwf-projects.github.io/c3s2-eqc-quality-assessment/Climate_Projections/CMIP6/climate_projections-cmip6_validation_q10.html#), CV and variance show opposite trends over time. ERA5 indicates a decline in variance and a rise in the coefficient of variation, while CMIP6 models show the reverse.

* It is **important to consider a larger ensemble and acknowledge that the time series in this assessment represent spatially averaged values**, which may lead to different results when focusing on specific sub-regions.

* **Frequency component consistency**: No significant differences are seen in the spatial or temporal patterns between the low-frequency (LFISOs) and high-frequency (HFISOs) components of intra-seasonal oscillations.

* Given the challenges in replicating the spatial patterns of variance and the coefficient of variation, as well as the difficulties in capturing their temporal evolution, **bias correction of CMIP6 projections may be essential for effectively using future projections of intra-seasonal precipitation variability. Such improvements could facilitate the adoption of CMIP6 future projections in the water management sector, aiding in the design of strategies to adapt to projected changes in precipitation.**

* **Intra-seasonal and inter-annual links.** The spatial patterns of intra-seasonal variability closely resemble those found in the inter-annual variability assessment. Intra-seasonal variability may influence inter-annual variability [[10]](https://doi.org/10.1175/JCLI-D-18-0319.1) and, therefore, it may be important to bias correct data at the daily timescale.

* **Assessments using regional climate models (RCMs) may produce different results** (not necessarily better) due to their higher spatial resolution, better representation of local processes, and more detailed treatment of orography and land-atmosphere interactions.

RESULTS NOTE:

It is important to note that the results presented are specific to the 16 models chosen, and users should aim to assess as wide a range of models as possible before making a sub-selection.


EQC Quality Assessment: "Testing the capability of CMIP6 GCMs to represent precipitation intra-seasonal variability"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q11  |  Category: Climate_Projections
Section: Testing the capability of CMIP6 GCMs to represent precipitation intra-seasonal variability > 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:
* CMIP6 climate projections (Daily - Precipitation): https://cds.climate.copernicus.eu/datasets/projections-cmip6?tab=overview
* ERA5 hourly data on single levels from 1940 to present (total precipitation): https://cds.climate.copernicus.eu/datasets/reanalysis-era5-single-levels?tab=overview

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


EQC Quality Assessment: "Testing the capability of CMIP6 GCMs to represent precipitation intra-seasonal variability"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q11  |  Category: Climate_Projections
Section: Testing the capability of CMIP6 GCMs to represent precipitation intra-seasonal variability > ℹ If you want to know more > References
---
[[1]](https://doi.org/10.1111/gcb.12581) Thornton, P. K., Ericksen, P. J., Herrero, M., and Challinor, A. J., 2014. Climate variability and vulnerability to climate change: A review. Global Change Biol. 20, https://doi.org/10.1111/gcb.12581

[[2]](https://doi.org/10.1016/j.wace.2020.100277) Masroor, M., Rehman, S., Avtar, R., Sahana, M., Ahmed, R., Sajjad, H., 2020. Exploring climate variability and its impact on drought occurrence: evidence from Godavari Middle sub-basin, India. Weather and Climate Extremes. 30, 100277. https://doi.org/10.1016/j.wace.2020.100277

[[3]](https://doi.org/10.1111/j.2153-3490.1980.tb01717.x) Krishnamurti, T. N. and Ardanuy, P., 1980. 10 to 20-day westward propagating mode and “breaks in the monsoons”. Tellus, 32, 15–26. https://doi.org/10.1111/j.2153-3490.1980.tb01717.x

[[4]](https://doi.org/10.1175/2007MWR1991.1) Wen, M. and Zhang, R., 2007. Role of the quasi-biweekly oscillation in the onset of convection over the Indochina Peninsula, Q. J. R. Meteor. Soc., 133, 433–444. https://doi.org/10.1002/qj.38

[[5]](https://doi.org/10.1175/2011JCLI3916.1) Wen, M., Yang, S., Higgins, R. W., Zhang, R., 2011. Characteristics of the dominant modes of atmospheric quasi-biweekly oscillation over tropical-subtropical Americas, J. Climate, 24, 3956–3970. https://doi.org/10.1175/2011JCLI3916.1

[[6]](https://doi.org/10.1175/1520-0469%281971%29028%3C0702:DOADOI%3E2.0.CO;2) Madden, R. A. and Julian P. R., 1971. Detection of a 40–50 day oscillation in the zonal wind in the tropical Pacific, J. Atmos. Sci., 28, 702–708. https://doi.org/10.1175/1520-0469%281971%29028%3C0702:DOADOI%3E2.0.CO;2

[[7]](https://doi.org/10.1175/1520-0469%281972%29029<1109:DOGSCC>2.0.CO;2) Madden, R. A. and Julian P. R., 1972. Description of global scale circulation cells in the tropics with 40–50 day period, J. Atmos. Sci., 29, 1109–1123. https://doi.org/10.1175/1520-0469%281972%29029<1109:DOGSCC>2.0.CO;2

[[8]](https://doi.org/10.1038/s41612-022-00253-7) Liu, F., Wang, B., Ouyang, Y., Wang, H., Qiao,S., Chen, G., Dong, W., 2022. Intraseasonal variability of global land monsoon precipitation and its recent trend. npj Clim Atmos Sci 5, 30. https://doi.org/10.1038/s41612-022-00253-7

[[9]](https://doi.org/10.1002/jgrd.50422), Jia, X. and Yang, S., 2013. Impact of the quasi-biweekly oscillation over the western North Pacific on East Asian subtropical monsoon during early summer, J. Geophys. Res. Atmos., 118, 4421–4434, https://doi.org/10.1002/jgrd.50422


EQC Quality Assessment: "Testing the capability of CMIP6 GCMs to represent precipitation intra-seasonal variability"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q11  |  Category: Climate_Projections
Section: Testing the capability of CMIP6 GCMs to represent precipitation intra-seasonal variability > ℹ If you want to know more > References
---
North Pacific on East Asian subtropical monsoon during early summer, J. Geophys. Res. Atmos., 118, 4421–4434, https://doi.org/10.1002/jgrd.50422

[[10]](https://doi.org/10.1175/JCLI-D-18-0319.1) Jiang, X. and Ting, M., 2019. Intraseasonal Variability of Rainfall and Its Effect on Interannual Variability across the Indian Subcontinent and the Tibetan Plateau. J. Climate, 32, 2227–2245, https://doi.org/10.1175/JCLI-D-18-0319.1

[[11]](https://doi.org/10.1175/JCLI-D-16-0360.1) Hatsuzuka, D., and Fujinami, H., 2017. Effects of the South Asian Monsoon Intraseasonal Modes on Genesis of Low Pressure Systems over Bangladesh. J. Climate, 30, 2481–2499, https://doi.org/10.1175/JCLI-D-16-0360.1

[[12]](https://doi.org/10.1007/s00382-019-04946-3) Yan, X., Yang, S., Wang, T., Maloney, E.D., Dong, S., Wei, W., He, S., 2019. Quasi-biweekly oscillation of the Asian monsoon rainfall in late summer and autumn: different types of structure and propagation. Clim Dyn 53, 6611–6628. https://doi.org/10.1007/s00382-019-04946-3

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

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


EQC Quality Assessment: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands
---
Production date: 27-06-2025

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


EQC Quality Assessment: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands > Quality assessment question
---
* **How is warming propagating across pressure levels and different latitudinal bands?**
* **Is there signal consistence between CMIP6 ensemble results and ERA5, and among CMIP6 ensemble GCMs?**

The vertical profile of temperature trends is widely recognised as an important fingerprint of climate change (e.g., [[1]](https://doi.org/10.1002/joc.1756),[[2]](https://doi.org/10.1126/science.274.5290.1170)),[[3]](https://doi.org/10.1073/pnas.1305332110). One of the most studied features of this vertical structure is the amplified warming in the tropical upper troposphere compared to the surface, commonly referred to as tropical tropospheric amplification [[4]](https://doi.org/10.1126/science.1114867). This behaviour is consistent with the basic theory of moist adiabatic processes, which predicts stronger warming in the tropical free troposphere than near the surface due to latent heat release during deep convection [[5]](https://doi.org/10.1175/1520-0469%281979%29036<0415:ALRRAT>2.0.CO;2).

While tropical amplification has been widely studied, other regions and their representation in CMIP6 models remain less explored. To develop a more comprehensive evaluation framework, it is essential to assess how warming propagates vertically across pressure levels and latitudinal bands. Understanding the vertical structure of temperature trends across these bands provides critical insights into model performance and the physical processes driving climate change. This vertical perspective is key for model developers to identify and diagnose persistent biases, such as errors in atmospheric circulation, lapse rates, and vertical energy transport, and thereby improve model simulations. Since vertical temperature profiles are considered important fingerprints of climate change, improving their representation also strengthens confidence in these signals, benefiting researchers, impact assessors, and decision-makers.

This assessment evaluates temperature mean and trend biases across multiple pressure levels using the full ensemble of [CMIP6](https://cds.climate.copernicus.eu/datasets/projections-cmip6?tab=overview) models available through the Copernicus Climate Data Store (CDS). Model outputs are compared against the [ERA5](https://cds.climate.copernicus.eu/datasets/reanalysis-era5-complete?tab=doc) reanalysis, which is used as the reference product. The analysis is performed over latitudinal bands—including Global, Northern and Southern hemispheres, Tropics, Extratropics, and Polar regions—to characterise spatial variability in biases and explore their dependence on latitude and atmospheric dynamics.


EQC Quality Assessment: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands > Quality assessment statement
---
These are the key outcomes of this assessment

* Model spread in mean temperature climatology increases with altitude, especially above the tropopause, highlighting substantial uncertainty in simulating its height and structure—critical for model evaluation and development.

* The median of CMIP6 climatological temperatures shows predominantly cold biases across all latitudinal bands, largest near 250–200 hPa. Near-surface and lower-stratosphere biases are smaller (though the spread is high), except in polar regions, where both the bias and the spread increase.

* Temperature trends show robust tropospheric warming and stratospheric cooling across all latitudinal bands in both ERA5 and CMIP6. CMIP6 generally exhibits stronger warming trends than ERA5.

* Tropical amplification of trends is evident, with CMIP6 exhibiting both stronger surface and upper-troposphere warming than ERA5, resulting also in a more pronounced amplification. Amplification is also high when considering the southern-hemisphere for both ERA5 and CMIP6.

* Trend magnitudes and structures vary with dataset processing, leading to moderate to low confidence in tropospheric warming rates (IPCC AR5 [[6]](https://www.ipcc.ch/site/assets/uploads/2017/09/WG1AR5_Chapter02_FINAL.pdf)).

```

attachment:b8bbb2de-eba2-453c-83d4-2d349379cdda.png
---
width: 900px
alt: Visual abstract
---
Vertical profiles of the annual mean temperature trend (1979-2014). Each subplot corresponds to a latitudinal band (Global, Northern Hemisphere, Southern Hemisphere, Tropics, Extratropics, and Polar). ERA5 is shown as a green line, the CMIP6 ensemble median as a solid black line, individual CMIP6 models as grey dashed lines, and the ensemble spread as a grey shaded area. ERA5 points with non-significant trends (p-value > 0.05) are marked with green crosses. For the CMIP6 ensemble median, trend significance is assessed using agreement categories based on the approach described in the [IPCC AR6 Atlas](https://www.ipcc.ch/report/ar6/wg1/downloads/report/IPCC_AR6_WGI_Atlas.pdf) (pp. 1945–1950). Black crosses indicate pressure levels where fewer than 66% of models show statistically significant trends (p-value < 0.05). If over 66% of the models are significant but fewer than 80% agree on the sign of the trend, a black dot is placed on the CMIP6 ensemble median to indicate low directional agreement.
```


EQC Quality Assessment: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands > Methodology
---
A subset of 33 models from [CMIP6](https://cds.climate.copernicus.eu/datasets/projections-cmip6?tab=overview) are used to assess temperature trends and climatology at different pressure levels, comparing them with those derived from
the [ERA5](https://cds.climate.copernicus.eu/datasets/reanalysis-era5-complete?tab=doc) reference product. While alternative radiosonde datasets, such as [RHARM](https://cds.climate.copernicus.eu/datasets/insitu-observations-igra-baseline-network?tab=overview) available through the CDS, exist, they are not used here because, despite extensive harmonisation efforts [[7]](https://doi.org/10.1029/2021JD035220), residual inconsistencies—such as limited station coverage, short time series, and sensitivity to data selection—could compromise global-scale analyses of vertical temperature profiles.

The analysis is performed across the following latitudinal bands:

- Global (90°S to 90°N)

- Northern-hemisphere (0°S to 90°N)

- Southern-hemisphere (90°S to 0°N)

- Tropics (23.5°S to 23.5°N)

- Extratropics (23.5° to 66.5° in both hemispheres)

- Polar (66.5° to 90° in both hemispheres)

For each latitudinal band, temperature climatology and trends are calculated at the following pressure levels: 925, 850, 700, 600, 500, 400, 300, 250, 200, 150, 100, 70, and 50 hPa. Results are presented using subplots—one per band—showing the vertical profiles of climatology and trends for each CMIP6 model alongside ERA5, following an approach similar to [[8]](https://doi.org/10.1175/JCLI-D-19-0998.1), who analysed ground- and satellite-based temperature trends over 1979–2018. Biases in both climatology and trends are also shown. The analysis period is 1979–2014.

The analysis and results follow the next outline:

**[](climate_projections-cmip6_validation_q12:section-1)**
 * [](climate_projections-cmip6_validation_q12:section-1.1)
 * [](climate_projections-cmip6_validation_q12:section-1.2)
 * [](climate_projections-cmip6_validation_q12:section-1.3)
 * [](climate_projections-cmip6_validation_q12:section-1.4)
 * [](climate_projections-cmip6_validation_q12:section-1.5)
 * [](climate_projections-cmip6_validation_q12:section-1.6)

**[](climate_projections-cmip6_validation_q12:section-2)**
 * [](climate_projections-cmip6_validation_q12:section-2.1)
 * [](climate_projections-cmip6_validation_q12:section-2.2)

**[](climate_projections-cmip6_validation_q12:section-3)**
 * [](climate_projections-cmip6_validation_q12:section-3.1)
 * [](climate_projections-cmip6_validation_q12:section-3.2)
 * [](climate_projections-cmip6_validation_q12:section-3.3)
 * [](climate_projections-cmip6_validation_q12:section-3.4)
 * [](climate_projections-cmip6_validation_q12:section-3.5)
 * [](climate_projections-cmip6_validation_q12:section-3.6)
 * [](climate_projections-cmip6_validation_q12:section-3.7)


EQC Quality Assessment: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands > Analysis and results > 1. Parameters, requests and functions definition > 1.1. Import packages
---
Set the custom temporary directory
Set the default temporary directory to the custom directory

(climate_projections-cmip6_validation_q12:section-1.2)=


EQC Quality Assessment: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands > 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 start and end years of the historical period can be adjusted using the parameters `year_start` and `year_stop`. The default period (1979–2014) is selected to ensure consistency with the satellite era in ERA5, which began assimilating satellite observations in 1979.
- The `chunk` selection allows the user to define if dividing into chunks when downloading the data on their local machine. Although it does not significantly affect the analysis, it is recommended to keep the default value for optimal performance.
- `variable` and `collection_id` are not customisable for this assessment and are set to 'temperature' and 'CMIP6'. Expert users can use this notebook as a guide to create similar analyses for other variables or model sets (such as CORDEX).

Interpolation method
Chunks for download
Collection id

(climate_projections-cmip6_validation_q12:section-1.3)=


EQC Quality Assessment: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands > Analysis and results > 1. Parameters, requests and functions definition > 1.3. Define models
---
The following climate analyses are performed considering the CMIP6 models that have available both the historical and SSP5-8.5 experiments within the Climate Data Store ([CDS](https://cds.climate.copernicus.eu/datasets/projections-cmip6?tab=overview)).

(climate_projections-cmip6_validation_q12:section-1.4)=


EQC Quality Assessment: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands > 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.

`request_era_ps_mask` is used to retrieve surface pressure data used to identify and mask out pressure levels below the surface.

(climate_projections-cmip6_validation_q12:section-1.5)=


EQC Quality Assessment: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands > 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.

"format": "zip",

(climate_projections-cmip6_validation_q12:section-1.6)=


EQC Quality Assessment: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands > 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_band_trends_clim`**: Computes vertical profiles of temperature climatology and trends. It first calculates annual means, then calls `get_latband_mean`, which averages over longitudes for each latitude within the band, and subsequently across those latitudes. The resulting time series is passed to `compute_trends_clim` to estimate the climatology and linear trend.

- **`compute_trends_clim`**: Computes the climatology and linear trend of a time series using ordinary least squares regression.

Ensure correct slicing order for descending or ascending latitude
harmonize pressure coordinate name
Concatenate along pressure_level
Compute means for each band
Add a new coordinate for each band and concatenate

(climate_projections-cmip6_validation_q12:section-2)=


EQC Quality Assessment: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands > 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 monthly reference data, compute annual means, calculate latitudinal band averages, and derive the climatology and linear trend at each pressure level for each latitudinal band. Results are cached to avoid redundant downloads and repeated processing.

(climate_projections-cmip6_validation_q12:section-2.2)=


EQC Quality Assessment: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands > Analysis and results > 2. Downloading and processing > 2.2. Download and transform models
---
In this section, the `download.download_and_transform` function from the 'c3s_eqc_automatic_quality_control' package is employed to download monthly data from the CMIP6 models, compute annual means, calculate latitudinal band averages, and derive the climatology and linear trend at each pressure level for each latitudinal band. Results are cached to avoid redundant downloads and repeated processing.

1000hPa are excluded (too close to surface)

```text
model='access_cm2'
model='awi_cm_1_1_mr'
model='canesm5'
model='canesm5_canoe'
model='ciesm'
model='cmcc_cm2_sr5'
model='cesm2'
model='cmcc_esm2'
model='cnrm_cm6_1'
model='cnrm_cm6_1_hr'
model='cnrm_esm2_1'
model='ec_earth3_cc'
model='ec_earth3_veg_lr'
model='fgoals_g3'
model='fgoals_f3_l'
model='fio_esm_2_0'
model='gfdl_esm4'
model='hadgem3_gc31_ll'
model='hadgem3_gc31_mm'
model='iitm_esm'
model='inm_cm4_8'
model='inm_cm5_0'
model='ipsl_cm6a_lr'
model='kiost_esm'
model='miroc6'
model='miroc_es2l'
model='mcm_ua_1_0'
model='mpi_esm1_2_lr'
model='mri_esm2_0'
model='nesm3'
model='noresm2_mm'
model='taiesm1'
model='ukesm1_0_ll'
```

(climate_projections-cmip6_validation_q12:section-3)=


EQC Quality Assessment: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands > Analysis and results > 3. Plot and describe results
---
This section will display the following results:

- **Vertical profiles of the climatology** for each latitudinal band, including ERA5, the median of the CMIP6 models, and the model spread.

- **Vertical profiles of the mean bias** for each latitudinal band, showing the median of the CMIP6 model biases and their spread.

- **Vertical profiles of the trend** for each latitudinal band, including ERA5, the median of the CMIP6 models, and the spread.

- **Vertical profiles of the trend bias** for each latitudinal band, showing the median of the CMIP6 model biases and their spread.

(climate_projections-cmip6_validation_q12:section-3.1)=


EQC Quality Assessment: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands > Analysis and results > 3. Plot and describe results > 3.1. Define plotting functions
---
The function **`plot_profile`** is used to display vertical profiles of the climatology and trend for each latitudinal band. When the `bias` option is set to False, ERA5 is shown as a green line, the CMIP6 ensemble median as a solid black line, individual CMIP6 models as grey dashed lines, and the model spread as a grey shaded area. When `bias=True`, the function instead plots the corresponding biases: the median CMIP6 bias is shown in blue, individual model biases in grey dashed lines, and their spread as a blue shaded area.

Convert pressure to hPa if needed
Sort pressure descending
Setup according to plot type
Extract data
Compute model biases
Zero line always for bias
Plot individual model biases
Plot bias median and spread
Zero line for trends only
Plot individual CMIP6 models
CMIP6 median + spread
=== Significance markers only here ===
For pressures where at least 66% of models are significant:
Count models with positive and negative trend signs (ALL models, regardless of significance)
Calculate sign ratio as max count divided by total number of models
Find pressures where sign agreement < 0.80
X-axis limits and labels
Y-axis label only for first column
Collect handles for shared legend

(climate_projections-cmip6_validation_q12:section-3.2)=


EQC Quality Assessment: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands > Analysis and results > 3. Plot and describe results > 3.2. Plot climatology maps
---
In this section, we invoke the `plot_profile()` function to display the vertical profiles of the climatology for each latitudinal band, including ERA5, the median of the CMIP6 models, and the model spread.

Fig 1.
        Vertical profiles of the annual mean temperature climatology (1979-2014). Each subplot shows a latitudinal band (Global, Northern and Southern hemispheres, Tropics, Extratropics, and Polar). ERA5 is shown as a green line, the CMIP6 median as a solid black line, individual CMIP6 models as grey dashed lines, and the spread of models as a grey shaded area.

(climate_projections-cmip6_validation_q12:section-3.3)=


EQC Quality Assessment: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands > Analysis and results > 3. Plot and describe results > 3.3. Plot mean bias maps
---
In this section, we invoke the `plot_profile()` function to display the vertical profiles of the mean bias for each latitudinal band, showing the median of the CMIP6 model biases and their spread.

Fig 2.
        Vertical profiles of the mean bias of the annual mean temperature (1979-2014). Each subplot shows a latitudinal band (Global, Northern and Southern hemispheres, Tropics, Extratropics, and Polar). The CMIP6 median is shown as a solid blue line, individual CMIP6 models as grey dashed lines, and the spread of models as a blue shaded area.

(climate_projections-cmip6_validation_q12:section-3.4)=


EQC Quality Assessment: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands > Analysis and results > 3. Plot and describe results > 3.4. Plot trend maps
---
In this section, we invoke the `plot_profile()` function to display the vertical profiles of the trend for each latitudinal band, including ERA5, the median of the CMIP6 models, and the spread

Fig 3.
      Vertical profiles of the annual mean temperature trend (1979-2014). Each subplot corresponds to a latitudinal band (Global, Northern Hemisphere, Southern Hemisphere, Tropics, Extratropics, and Polar). ERA5 is shown as a green line, the CMIP6 ensemble median as a solid black line, individual CMIP6 models as grey dashed lines, and the ensemble spread as a grey shaded area. ERA5 points with non-significant trends (p-value > 0.05) are marked with green crosses. For the CMIP6 ensemble median, trend significance is assessed using agreement categories based on the approach described in the IPCC AR6 Atlas (pp. 1945–1950). Black crosses indicate pressure levels where fewer than 66% of models show statistically significant trends (p-value < 0.05). If over 66% of the models are significant but fewer than 80% agree on the sign of the trend, a black dot is placed on the CMIP6 ensemble median to indicate low directional agreement.

(climate_projections-cmip6_validation_q12:section-3.5)=


EQC Quality Assessment: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands > Analysis and results > 3. Plot and describe results > 3.5. Plot trend bias maps
---
In this section, we invoke the `plot_profile()` function to display the vertical profiles of the trend bias for each latitudinal band, showing the median of the CMIP6 model biases and their spread.

Fig 4.
        Vertical profiles of the trend bias of the annual mean temperature (1979-2014). Each subplot shows a latitudinal band (Global, Northern and Southern hemispheres, Tropics, Extratropics, and Polar). The CMIP6 median is shown as a solid blue line, individual CMIP6 models as grey dashed lines, and the spread of models as a blue shaded area.

(climate_projections-cmip6_validation_q12:section-3.6)=


EQC Quality Assessment: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands > Analysis and results > 3. Plot and describe results > 3.6. Results summary and discussion - Climatologies
---
- Vertical temperature profiles are broadly consistent across latitudinal bands, with the tropopause—defined as the level where the temperature inversion begins—occurring at lower pressures in the tropics and higher pressures in colder regions (e.g. polar and extratropical).

- Biases are predominantly cold, with the median of the model biases showing the largest discrepancies around 250–200 hPa, where CMIP6 models exhibit a sharper temperature transition than ERA5. Near-surface and stratospheric median biases are generally smaller, except in polar regions.

- Model spread increases with altitude, particularly in the stratosphere, highlighting reduced inter-model agreement at higher levels.

- The large spread near the tropopause underscores the substantial uncertainty in simulating its height and structure, which may have important implications for model evaluation and development.

(climate_projections-cmip6_validation_q12:section-3.7)=


EQC Quality Assessment: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands > Analysis and results > 3. Plot and describe results > 3.7. Results summary and discussion - Trends
---
* Tropospheric warming and stratospheric cooling are robust fingerprints of greenhouse-gas-induced climate change [[3]](https://doi.org/10.1073/pnas.1305332110). ERA5 and CMIP6 both reproduce this vertical structure across all latitudinal bands, although the magnitude and detailed profile are sensitive to dataset processing and homogenisation, leading to medium to low confidence in long-term trend estimates [[6]](https://www.ipcc.ch/site/assets/uploads/2017/09/WG1AR5_Chapter02_FINAL.pdf).

* Since vertical temperature trend profiles are important fingerprints of climate change, it is important to improve their representation, as this would enhance confidence in these signals and benefit researchers, impact assessors, and decision-makers.

* Tropical amplification—enhanced warming in the upper tropical troposphere relative to the surface—is evident in both ERA5 and CMIP6, although CMIP6 tends to show a stronger signal.

* Amplification varies across latitudinal bands. CMIP6 models display amplification in all regions except the polar zones, whereas ERA5 shows amplification everywhere except in the polar and Northern Hemisphere bands, where warming is stronger near the surface. However, in the global and extratropical bands, both CMIP6 and ERA5 exhibit minimal amplification.

* Differences between CMIP6 and ERA5 can be linked to biases in surface warming [[9]](https://doi.org/10.1002/grl.50465). Studies using models with prescribed SSTs (e.g. [[10]](https://doi.org/10.1088/1748-9326/ab9af7)) report reduced biases. In addition, upper-troposphere trend estimates can vary depending on the analysis period, due to factors such as ozone changes.

* Given the uncertainties associated with individual datasets, using multiple reference products—including those external to the CDS—would be advisable for this type of assessment. For example, [[8]](https://doi.org/10.1175/JCLI-D-19-0998.1) compared tropospheric and stratospheric trends using both ground- and satellite-based observations.


EQC Quality Assessment: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands > 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:
* CMIP6 climate projections (Monthly - Air temperature): https://cds.climate.copernicus.eu/datasets/projections-cmip6?tab=overview
* ERA5 monthly averaged data on pressure levels from 1940 to present (Temperature): https://cds.climate.copernicus.eu/datasets/reanalysis-era5-pressure-levels-monthly-means?tab=overview
* ERA5 monthly averaged data on single levels from 1940 to present (Surface pressure): 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: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands > ℹ If you want to know more > References
---
[[1]](https://doi.org/10.1002/joc.1756) Santer, B.D., Thorne, P.W., Haimberger, L., Taylor, K.E., Wigley, T.M.L., Lanzante, J.R., Solomon, S., Free, M., Gleckler, P.J., Jones, P.D., Karl, T.R., Klein, S.A., Mears, C., Nychka, D., Schmidt, G.A., Sherwood, S.C. and Wentz, F.J., 2008. Consistency of modelled and observed temperature trends in the tropical troposphere. Int. J. Climatol., 28: 1703-1722. https://doi.org/10.1002/joc.1756

[[2]](https://doi.org/10.1126/science.274.5290.1170) Simon F. B. Tett et al., 1996. Human Influence on the Atmospheric Vertical Temperature Structure: Detection and Observations.Science274,1170-1173. https://doi.org/10.1126/science.274.5290.1170

[[3]](https://doi.org/10.1073/pnas.1305332110) Santer, B.D., Painter, J.F., Bonfils, C., Mears, C.A., Solomon, S., Wigley, T.M.L., Gleckler,P.J., Schmidt, G.A., Doutriaux,C., Gillett, N.P., Taylor,K.E., Thorne, P.W., and Wentz, F.J., 2013. Human and natural influences on the changing thermal structure of the atmosphere, Proc. Natl. Acad. Sci. U.S.A. 110 (43) 17235-17240. https://doi.org/10.1073/pnas.1305332110

[[4]](https://doi.org/10.1126/science.1114867) B. D. Santer et al., 2005. Amplification of Surface Temperature Trends and Variability in the Tropical Atmosphere.Science309,1551-1556. https://doi.org/10.1126/science.1114867

[[5]](https://doi.org/10.1175/1520-0469%281979%29036<0415:ALRRAT>2.0.CO;2) Stone, P. H., and Carlson, J. H., 1979. Atmospheric lapse rate regimes and their parameterization. J. Atmos. Sci., 36, 415–423. https://doi.org/10.1175/1520-0469%281979%29036<0415:ALRRAT>2.0.CO;2 .

[[6]](https://www.ipcc.ch/site/assets/uploads/2017/09/WG1AR5_Chapter02_FINAL.pdf) Hartmann, D. L., et al., 2013. Observations: Atmosphere and surface. Climate Change 2013: The Physical Science Basis, T. F. Stocker et al., Eds., Cambridge University Press, 159–254.

[[7]](https://doi.org/10.1029/2021JD035220) Madonna, F., Tramutola, E., SY, S., Serva, F., Proto, M., Rosoldi, M., et al., 2022. The new Radiosounding HARMonization (RHARM) data set of homogenized radiosounding temperature, humidity, and wind profiles with uncertainties. Journal of Geophysical Research: Atmospheres, 127, e2021JD035220. https://doi.org/10.1029/2021JD035220

[[8]](https://doi.org/10.1175/JCLI-D-19-0998.1) Steiner, A. K. et al., 2020. Observed Temperature Changes in the Troposphere and Stratosphere from 1979 to 2018. J. Climate, 33, 8165–8194, https://doi.org/10.1175/JCLI-D-19-0998.1

[[9]](https://doi.org/10.1002/grl.50465) Mitchell, D. M., Thorne, P. W., Stott, P. A., and Gray, L. J., 2013. Revisiting the controversial issue of tropical tropospheric temperature trends, Geophys. Res. Lett., 40, 2801–2806, https://doi.org/10.1002/grl.50465


EQC Quality Assessment: "Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q12  |  Category: Climate_Projections
Section: Biases in temperature trends at different pressure levels using CMIP6 across latitudinal bands > ℹ If you want to know more > References
---
2013. Revisiting the controversial issue of tropical tropospheric temperature trends, Geophys. Res. Lett., 40, 2801–2806, https://doi.org/10.1002/grl.50465

[[10]](https://doi.org/10.1088/1748-9326/ab9af7) Dann M. Mitchell et al., 2020. The vertical profile of recent tropical temperature trends: Persistent model biases in the context of internal variability. Environ. Res. Lett. 15 1040b4. https://doi.org/10.1088/1748-9326/ab9af7


EQC Quality Assessment: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 biases in the SPEI6 drought index over the Mediterranean region
---
Production date: 20-09-2025

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


EQC Quality Assessment: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 biases in the SPEI6 drought index over the Mediterranean region > Quality assessment question
---
* **How well do CMIP6 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 standardized, 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/10.1016/j.scitotenv.2019.135245)[[5]](https://doi.org/10.3390/w17101507).

This assessment evaluates SPEI6 (six-month accumulation) across the full ensemble of [CMIP6](https://cds.climate.copernicus.eu/datasets/projections-cmip6?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. The standard reference period is 1971–2010. We specifically evaluate whether changes in the 1991–2020 period relative to the 1961–1990 baseline are accurately represented by CMIP6 models and the trend acroos the whole 1961-2020 period for the Mediterranean domain.


EQC Quality Assessment: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 biases in the SPEI6 drought index over the Mediterranean region > Quality assessment statement
---
These are the key outcomes of this assessment

* CMIP6 ensemble median captures the general intensification of drought over the Mediterranean seen in ERA5, though the magnitude of the change is underestimated, particularly over eastern Spain, southern France, and much of Turkey.

* Individual models do not reproduce the same spatial pattern, highlighting the importance of using large ensembles rather than relying on a single model for planning purposes.

* Despite inherent biases, the considered subset of CMIP6 models provides a foundation for understanding the evolution of past drought conditions. These results support the use of SPEI to anticipate water deficits and guide drought preparedness, increasing confidence (though not ensuring accuracy) when assessing future trends.

* 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:7b5c6a55-25e9-4938-99e9-a977bad344e6.png
---
width: 1500px
alt: Visual abstract
---
Spatial patterns of SPEI6 change over the Mediterranean region. Panels show (a) ERA5 reference, (b) CMIP6 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 (1991–2020) and the baseline period (1961–1990), and then averaged to obtain the annual mean.
```


EQC Quality Assessment: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 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 [CMIP6](https://cds.climate.copernicus.eu/datasets/projections-cmip6?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, CMIP6, 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 (1961–2020).

Potential evapotranspiration (PET) is calculated with the Hargreaves method [[7]](https://doi.org/10.13031/2013.26773), which requires only maximum and minimum temperatures (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 standardized 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 standardize 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 1961–1990.
- **Target period:** The period for which changes are evaluated, here 1991–2020.
- **Historical period:** The entire period considered in this assessment, here 1961–2020.
- **Change assessment:** 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-cmip6_validation_q13:section-1)**
 * [](climate_projections-cmip6_validation_q13:section-1.1)
 * [](climate_projections-cmip6_validation_q13:section-1.2)
 * [](climate_projections-cmip6_validation_q13:section-1.3)
 * [](climate_projections-cmip6_validation_q13:section-1.4)
 * [](climate_projections-cmip6_validation_q13:section-1.5)
 * [](climate_projections-cmip6_validation_q13:section-1.6)

**[](climate_projections-cmip6_validation_q13:section-2)**
 * [](climate_projections-cmip6_validation_q13:section-2.1)
 * [](climate_projections-cmip6_validation_q13:section-2.2)
 * [](climate_projections-cmip6_validation_q13:section-2.3)

**[](climate_projections-cmip6_validation_q13:section-3)**
 * [](climate_projections-cmip6_validation_q13:section-3.1)
 * [](climate_projections-cmip6_validation_q13:section-3.2)
 * [](climate_projections-cmip6_validation_q13:section-3.3)
 * [](climate_projections-cmip6_validation_q13:section-3.4)
 * [](climate_projections-cmip6_validation_q13:section-3.5)
 * [](climate_projections-cmip6_validation_q13:section-3.6)
 * [](climate_projections-cmip6_validation_q13:section-3.7)


EQC Quality Assessment: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 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 1961-2020.
- 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 1961-1990.
- The target period can be adjusted by modifying `target_slice`; the default range is 1991-2020.
- 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 'CMIP6'. Expert users can use this notebook as a guide to create similar analyses for other model sets (such as 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-cmip6_validation_q13:section-1.3)=


EQC Quality Assessment: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 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 CMIP6 models that provide both the historical and SSP5-8.5 experiments, as well as maximum, minimum and mean temperatures and precipitation, within the Climate Data Store ([CDS](https://cds.climate.copernicus.eu/datasets/projections-cmip6?tab=overview)).

(climate_projections-cmip6_validation_q13:section-1.4)=


EQC Quality Assessment: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 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-cmip6_validation_q13:section-1.5)=


EQC Quality Assessment: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 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.

Only historical data
Historical until 2014
Future from 2015 to historical_slice.stop

(climate_projections-cmip6_validation_q13:section-1.6)=


EQC Quality Assessment: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 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`**: 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.

Download the other vars if we are dealing with CMIP6
Original bounds for conservative interpolation
Apply correct daily reductions
Wrap into dataset
Select pr and
Apply correct daily reductions

(climate_projections-cmip6_validation_q13:section-2)=


EQC Quality Assessment: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 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-cmip6_validation_q13:section-2.2)=


EQC Quality Assessment: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 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 CMIP6 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='access_cm2'
model='canesm5'
model='cmcc_esm2'
model='cnrm_cm6_1'
model='cnrm_cm6_1_hr'
model='cnrm_esm2_1'
model='ec_earth3_cc'
model='gfdl_esm4'
model='inm_cm4_8'
model='inm_cm5_0'
model='kace_1_0_g'
model='miroc6'
model='miroc_es2l'
model='mpi_esm1_2_lr'
model='mri_esm2_0'
model='nesm3'
model='noresm2_mm'
```

(climate_projections-cmip6_validation_q13:section-2.3)=


EQC Quality Assessment: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 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 1991–2020 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
Regrid each model dataset
Apply precipitation mask to ERA5 and interpolated
Apply PR mask to each model

```text
100%|██████████| 1/1 [00:00<00:00, 27.58it/s]
```

(climate_projections-cmip6_validation_q13:section-3)=


EQC Quality Assessment: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 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 (1991–2020) and the baseline period (1961–1990).

(climate_projections-cmip6_validation_q13:section-3.1)=


EQC Quality Assessment: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 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 (1991–2020) and the baseline period (1961–1990). It then aggregates the change according to the user-specified `time_agg` (annual, seasonal, or monthly).

- `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 ---
Use user-defined cmap_params if provided; otherwise compute automatically
--- 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-cmip6_validation_q13:section-3.2)=


EQC Quality Assessment: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 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).

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

Fig 1.
        Spatial patterns of SPEI6 change over the Mediterranean region. Panels show (a) ERA5 reference, (b) CMIP6 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 (1991–2020) and the baseline period (1961–1990), 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-cmip6_validation_q13:section-3.3)=


EQC Quality Assessment: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 biases in the SPEI6 drought index over the Mediterranean region > Analysis and results > 3. Plot and describe results > 3.3. Plot model maps
---
In this section, we invoke the `plot_models()` function to visualise the SPEI6 change of every model individually. Note that the model data used in this section maintains its original grid.

Fig 2.
        Spatial patterns of SPEI6 change for each individual CMIP6 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 (1991–2020) and the baseline period (1961–1990), and then averaged to obtain the annual mean.

(climate_projections-cmip6_validation_q13:section-3.4)=


EQC Quality Assessment: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 biases in the SPEI6 drought index over the Mediterranean region > Analysis and results > 3. Plot and describe results > 3.4. Plot bias maps
---
In this section, we invoke the `plot_models()` function to visualise the bias of the vSPEI6 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.

Plot using the shared bias parameters

Fig 3.
        Bias of SPEI6 change for each individual CMIP6 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 (1991–2020) and the baseline period (1961–1990), and then averaged to obtain the annual mean.

(climate_projections-cmip6_validation_q13:section-3.5)=


EQC Quality Assessment: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 biases in the SPEI6 drought index over the Mediterranean region > Analysis and results > 3. Plot and describe results > 3.5. Timeseries
---
This section examines the time series 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 climatology of each month) 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 CMIP6 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 CMIP6 ensemble median.

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 CMIP6 median
Fill ±1 std (spread)
Compute trends
Labels and grid
Format x-axis as years
Annotate trends

Fig 4.
        Time series of SPEI6 anomalies over the Mediterranean region, calculated relative to the baseline climatology. Monthly anomalies are 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 CMIP6 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-cmip6_validation_q13:section-3.6)=


EQC Quality Assessment: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 biases in the SPEI6 drought index over the Mediterranean region > Analysis and results > 3. Plot and describe results > 3.6. Results summary
---
- ERA5 indicates a general intensification of drought conditions over the Mediterranean region when comparing the baseline (1961–1990) and target (1991–2020) periods.

- The CMIP6 ensemble median captures this SPEI6 change signal, but the magnitude of the increase in drought conditions is underestimated, particularly over eastern Spain, southern France, and much of Turkey.

- With respect to inter-model spread, models do not reproduce the same spatial pattern. The largest spread appears over North African countries bordering the Mediterranean, Turkey, Lebanon, and Syria, and to a lesser extent over the Balkans, Portugal, and central and western Spain.

- Time series of spatial means over the Mediterranean confirm this increase in drought conditions and the underestimation by CMIP6 models, with trends of –0.15 for ERA5 and –0.08 (about half) for the CMIP6 median.

- Although users can modify the time aggregation in this notebook to analyse other seasons or specific months, 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) also provides complementary information on CMIP6 and ERA5 SPEI changes by season.

- According to ERA5, SPEI6 decreased most strongly in autumn and summer, although increases in some localised regions during autumn moderate the Mediterranean’s spatial mean. Spring shows weaker but more spatially consistent decreases, producing mean values similar to autumn, while winter (DJF) exhibits the smallest reductions. CMIP6 broadly reproduces this seasonal pattern, with the strongest decreases in autumn and summer and weaker changes in winter and spring; in spring, some northern parts of the Euro-Mediterranean region even show increases, contrary to ERA5.

(climate_projections-cmip6_validation_q13:section-3.7)=


EQC Quality Assessment: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 biases in the SPEI6 drought index over the Mediterranean region > Analysis and results > 3. Plot and describe results > 3.7. Implications for the users
---
- Models do not reproduce the same exact spatial pattern, but the ensemble median captures the SPEI6 change. This underlines the importance of considering large ensembles rather than relying on a single or a few models.

- Although the CMIP6 ensemble median captures the intensification of drought conditions, caution is needed when looking into the future. Precipitation projections generally involve more uncertainty than temperature, and model biases may evolve under changing climate conditions [[9]](https://doi.org/10.5194/hess-25-273-2021).

- This assessment shows consistent results with those obtained in 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). In addition, it provides users with insight into the rationale behind SPEI and how models reproduce historical conditions over the Mediterranean, reinforcing its value as a tool for water management and drought preparedness.

- 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.


EQC Quality Assessment: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 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:
* CMIP6 climate projections (daily - daily maximum near-surface air temperature, daily minimum near-surface air temperature and precipitation): https://cds.climate.copernicus.eu/datasets/projections-cmip6?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: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 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/10.1016/j.scitotenv.2019.135245) Yao, N., Li, L., Feng, P., Feng, H., Liu, D. L., Liu, Y., Jiang, K., Hu, X., and Li, Y., 2020. Projections of drought characteristics in China based on a standardized precipitation and evapotranspiration index and multiple GCMs. Science of The Total Environment, 704, 135245. https://doi.org/10.1016/j.scitotenv.2019.135245

[[5]](https://doi.org/10.3390/w17101507) Tuong, V. Q., Kiet, B. A., and Pham, T. T., 2025. Assessment of Future Drought Characteristics Using Various Temporal Scales and Multiple Drought Indices over Mekong Basin Under Climate Changes. Water, 17(10), 1507. https://doi.org/10.3390/w17101507

[[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

[[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


EQC Quality Assessment: "CMIP6 biases in the SPEI6 drought index over the Mediterranean region"
Dataset: projections-cmip6 [CDS]
Aspect: validation_q13  |  Category: Climate_Projections
Section: CMIP6 biases in the SPEI6 drought index over the Mediterranean region > ℹ If you want to know more > References
---
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/10.5194/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: "Bias in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q01  |  Category: Climate_Projections
Section: Bias in extreme temperature indices for the reinsurance sector
---
Production date: 29-05-2024

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


EQC Quality Assessment: "Bias in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q01  |  Category: Climate_Projections
Section: Bias in extreme temperature indices for the reinsurance sector > Quality assessment question
---
* **How well do CORDEX projections represent climatology and trends of air temperature extremes in Europe?**
* **Do I get different results than if I use CMIP6 projections?**

Climate change has a major impact on the reinsurance market [[1]](https://doi.org/10.3390/atmos11020146)[[2]](https://doi.org/10.5194/nhess-22-659-2022). In the third assessment report of the IPCC, hot temperature extremes were already presented as relevant to insurance and related services [[3]](https://www.ipcc.ch/site/assets/uploads/2018/03/wg2TARchap8.pdf). Consequently, the need for reliable regional and global climate projections has become paramount, offering valuable insights for optimising reinsurance strategies in the face of a changing climate landscape. Nonetheless, despite their pivotal role, uncertainties inherent in these projections can potentially lead to misuse [[4]](https://doi.org/10.1002/wcc.71)[[5]](https://doi.org/10.1002/wcc.579). This underscores the importance of accurately calculating and accounting for uncertainties to ensure their appropriate consideration. This notebook utilises data from a subset of models from **[CORDEX](https://cds.climate.copernicus.eu/datasets/projections-cordex-domains-single-levels?tab=overview)** Regional Climate Models (RCMs) and compares them with [ERA5](https://cds.climate.copernicus.eu/datasets/reanalysis-era5-complete?tab=doc) reanalysis, serving as the reference product. Two maximum-temperature-based indices from [ECA&D](https://www.ecad.eu/indicesextremes/) indices (one of physical nature and the other of statistical nature) are computed using the [icclim](https://icclim.readthedocs.io/en/stable/) Python package. The first index, identified by the ETCCDI short name 'SU', quantifies the occurrence of summer days (i.e., with daily maximum temperatures exceeding 25°C) within a year or a season (JJA in this notebook). The second index, labeled 'TX90p', describes the number of days with daily maximum temperatures exceeding the daily 90th percentile of maximum temperature for a 5-day moving window. Within this notebook, these calculations are performed over the historical period spanning from 1971 to 2000. It is important to note that the results presented here pertain to a specific subset of the CORDEX ensemble and may not be generalisable to the entire dataset. Also note that a separate assessment examines the representation of trends of these indices for the same models during a fixed future period (2015-2099).


EQC Quality Assessment: "Bias in extreme temperature indices for the reinsurance sector"
Dataset: projections-cordex-domains-single-levels [CDS]
Aspect: climate-and-weather-extremes_q01  |  Category: Climate_Projections
Section: Bias in extreme temperature indices for the reinsurance sector > Quality assessment statement
---
These are the key outcomes of this assessment

* During the JJA period and for the subset of regional models considered, CORDEX projections offer valuable insights into reproducing the climatology and trend of air temperature extremes across Europe for the historical period spanning from 1971 to 2000. These insights aid in the optimisation of reinsurance protections. Nevertheless, they are accompanied by uncertainties that necessitate careful consideration for informed decision-making. Users need to understand that biases affect the climatology and trend of the indices differently and that the choice of bias correction method should be tailored accordingly [[6]](https://doi.org/10.1002/asl.1072)[[7]](https://ibicus.readthedocs.io/en/latest/).

* The subset of Regional Climate Models (RCMs) consistently show a tendency to underestimate trends for the 'SU' and 'TX90p' indices compared to ERA5 during the JJA period. This underestimation of the trend magnitude is even greater than observed for another CMIP6 assessment that is performed for the same period and seasonal aggregation  ("CMIP6 Climate Projections: evaluating bias in extreme temperature indices for the reinsurance sector."). While RCMs improve mean values compared to Global Climate Models (GCMs), they often struggle to replicate historical trends accurately, particularly underestimating in the Mediterranean basin. These findings underscore the importance of a comprehensive GCM-RCM matrix to address uncertainties effectively.

* In contrast to climatological assessments, the consistency in trend bias patterns across diverse RCMs suggests a potential dependence on the driving GCM, shared among all RCMs. A more extensive GCM-RCM matrix is imperative to accurately quantify this dependency and delineate the partitioning of uncertainty between GCMs and RCMs [[8]](https://doi.org/10.1002/wcc.8)[[9]](https://doi.org/10.1088/1748-9326/aacc77).

* The outcomes of this notebook also increase confidence (though they do not ensure accuracy) when analysing future trends using these models.
```

attachment:f986e53c-d903-459a-8a4a-02caea9644da.png
---
alt: Mean Bias SU CORDEX
width: 900px
---
Number of summer days ('SU') for the temporal aggregation of 'JJA'. Mean bias for the historical period (1971 - 2000) of each individual CORDEX model.
```