EQC Quality Assessment: "Completeness of ocean colour observations for biogeochemical models"
Dataset: satellite-ocean-colour [CDS]
Aspect: completeness_q01  |  Category: Satellite_ECVs
Section: Completeness of ocean colour observations for biogeochemical models > Quality assessment statement
---
A.E., Jahn, O., Henson, S., Beaulieu, C., & Monier, E. (2019) Ocean colour signature of climate change. Nature Communications, 10, 578.

[[6]](https://doi.org/10.1029/2018JC014329) Pradhan, H.K., Völker, C., Losa, S. N., Bracher, A., & Nerger, L. (2019). Assimilation of global total chlorophyll OC-CCI data and its impact on individual phytoplankton fields. Journal of Geophysical Research: Oceans, 124, 470-490.

[[7]](https://doi.org/10.1016/0967-0637%2895%2900021-W) Orsi, A.H., Whitworth, T., & Nowlin, W.D. (1995). On the meridional extent and fronts of the Antarctic Circumpolar Current. Deep Sea Research Part I: Oceanographic Research Papers, 42(5), 641-673.

[[8]](https://doi.org/10.1029/2019GL083163) Del Castillo, C.E., Signorini, S.R., Karaköylü, E.M., & Rivero-Calle, S. (2019). Is the Southern Ocean Getting Greener? Geophysical Research Letters, 46, 6034-6040.

[[9]](https://doi.org/10.1029/95JC00458) Campbell, J.W. (1995). The lognormal distribution as a model for bio-optical variability in the sea. Journal of Geophysical Research, 100, 13237-13254.

[[10]](https://doi.org/10.3390/s19194285) Sathyendranath, S., et al. (2019). An Ocean-Colour time series for use in climate studies: the experience of the Ocean-Colour Climate Change Initiative (OC-CCI). Sensors, 19, 4285.

[[11]](https://doi.org/10.1029/2006jc004072) Sokolov, S., & Rintoul, S.R. (2007). On the relationship between fronts of the Antarctic Circumpolar Current and surface chlorophyll concentrations in the Southern Ocean, Journal of Geophysical Research, 112, C07030.

[[12]](https://doi.org/10.5670/oceanog.2018.408) Paparazzo, F.E., Crespi-Abril, A.C., Gonçalves,  R.J., Barbieri, E.S., Gracia Villalobos, L.L., Solís, M.E., & Soria, G. (2018). Patagonian dust as a source of macronutrients in the Southwest Atlantic Ocean. Oceanography, 31(4), 33-39.

[[13]](https://doi.org/10.3389/fmars.2024.1363088) Demasy, C., Boye, M., Lai, B., Burckel, P., Feng, Y., Losno, R., Borensztajn, S., & Besson, P. (2024). Iron dissolution from Patagonian dust in the Southern Ocean: under present and future conditions. Frontiers in Marine Science, 11, 1363088.

[[14]](https://doi.org/10.1016/j.rse.2007.03.008) Gregg, W.W., & Casey, N.W. (2007). Sampling biases in MODIS and SeaWiFS ocean chlorophyll data. Remote Sensing of Environment, 111(1), 25-35.

[[15]](https://doi.org/10.1038/s41467-020-19157-2) Arteaga, L.A., Boss, E., Behrenfeld, M.J., Westberry, T.K., & Sarmiento, J.L. (2020). Seasonal modulation of phytoplankton biomass in the Southern Ocean. Nature Communications, 11, 5364.

[[16]](https://doi.org/10.1016/j.marenvres.2024.106856) Venegas, R.M., Rivas, D., & Treml, E. (2025).  Global climate-driven sea surface temperature and chlorophyll dynamics. Marine Environmental Research, 204, 106856


EQC Quality Assessment: "Impact of using successive satellites on Ocean Colour time series"
Dataset: satellite-ocean-colour [CDS]
Aspect: consistency-assessment_q01  |  Category: Satellite_ECVs
Section: Impact of using successive satellites on Ocean Colour time series
---
Production Date: 16-03-2024
Produced by: Chiara Volta (ENEA, Italy) and Salvatore Marullo (CNR, Italy)


EQC Quality Assessment: "Impact of using successive satellites on Ocean Colour time series"
Dataset: satellite-ocean-colour [CDS]
Aspect: consistency-assessment_q01  |  Category: Satellite_ECVs
Section: Impact of using successive satellites on Ocean Colour time series > Quality assessment question
---
**Does the consistency of chlorophyll-a and remote sensing reflectance get affected by the succession of satellite sensors over time?**

The Ocean Colour dataset version 6.0, as produced for the Copernicus Climate Change Service (C3S), includes the variables, mass concentration of chlorophyll-a and remote sensing reflectance (Rrs) for six wavelengths from October 1997 to present [[1]](https://dast.copernicus-climate.eu/documents/satellite-ocean-colour/v6.0/WP2-FDDP-2022-04_C3S2-Lot3_PUGS-of-v6.0-OceanColour-product_v1.1_FINAL.pdf).
Chlorophyll-a concentration is typically used as proxy for algal biomass and fisheries production [[2]](https://doi.org/10.4319/lo.1997.42.7.1479) [[3]](https://doi.org/10.1371/journal.pone.0028945) and is derived through specific algorithms  which rely on remote sensing reflectance (Rrs) [[4]](https://dast.copernicus-climate.eu/documents/satellite-ocean-colour/v6.0/WP2-FDDP-2022-04_C3S2-Lot3_ATBD-of-v6.0-OceanColour-product_v1.1_FINAL.pdf).
The dataset combines measurements carried out by six satellite sensors [[1]](https://dast.copernicus-climate.eu/documents/satellite-ocean-colour/v6.0/WP2-FDDP-2022-04_C3S2-Lot3_PUGS-of-v6.0-OceanColour-product_v1.1_FINAL.pdf): SeaWiFS, MERIS, MODIS-Aqua, VIIRS, OLCI-3A and OLCI-3B. No sensor was operational over the whole temporal coverage of the datasets and only OLCI-3A and OLCI-3B are still operational.
Here, the goal is to assess if the stability of Ocean Colour time series is affected by the transition of different satellite sensors over time.


EQC Quality Assessment: "Impact of using successive satellites on Ocean Colour time series"
Dataset: satellite-ocean-colour [CDS]
Aspect: consistency-assessment_q01  |  Category: Satellite_ECVs
Section: Impact of using successive satellites on Ocean Colour time series > Quality assessment statement
---
These are the key outcomes of this assessment

The Ocean Colour dataset version 6.0:
* provides a time consistent record of remote sensing reflectance at 443 and 560 nm, and derived chlorophyll-a concentrations, which is not affected by the succession of different satellite sensors. However, data prior to March 2002 should be carefully evaluated.
* would overestimate chlorophyll-a concentrations before March 2002, especially when high-latitude, more productive oceanic regions are included in the analysis.
* indicates decreasing chlorophyll-a trends in the more productive regions analysed, while the most oligotrophic area exhibits an increasing trend.

![Graphical_abstract.png](attachment:4244bac9-1f7d-45b9-a358-ee1e46162ae8.png)
Fig.1 The top panel shows the 48-month rolling mean of chlorophyll-a concentrations calculated in the four regions selected for the analysis, as well as the name and duration of each satellite mission used to produce the dataset. Mean chlorophyll-a concentrations are also provided in the legend. The lower panel shows a global map of the 25-year average chlorophyll-a concentration. Dashed, dotted and yellow boxes on the map indicate the oceanic region between latitudes 50°S-50°N, the NASTG's region and the STG's region, respectively.

## 📋 Methodology

This notebook provides an assessment of the ability of Ocean Colour dataset version 6.0 to describe the temporal variability of chlorophyll-a concentrations and Rrs at 443 and 560 nm over different oceanic regions.

The analysis and results are detailed in the sections below:

[](section-1)
   * Import required packages
   * Define parameters to be analysed (time period, variables, regions) and data request

[](section-2)
   * Area average function
   * Retrieve daily averages for the selected variables, time period and regions

[](section-3)
   * Compute statistics and define plot function
   * Define satellite missions

[](section-4)
   * Display results
   * Discussion

## 📈 Analysis and results
(section-1)=
### 1. Choose the data to use and set up the code
#### Import required packages
Besides the standard libraries used to manage and analyse multidimensional arrays, the [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`is imported to download data and calculate statistics.

#### Define parameters to be analysed (time period, variables, regions) and data request
The analysis performed in this notebook focuses on the time series of chlorophyll-a concentration and Rrs at 443 and 560 nm, the most commonly used bands to derive chlorophyll-a data, over a 25-year period (January 1998 - December 2022), in four regions: the global ocean, the oceanic region between 50°S and 50°N, the region where the North Atlantic SubTropical Gyre (NASTG) is located [[5]](https://doi.org/10.1029/2021GL096965) and a 10°x10° area, within the South Pacific Gyre (SPG), over which the inter-sensor bias-correction process was validated [[6]](https://dast.copernicus-climate.eu/documents/satellite-ocean-colour/v6.0/WP2-FDDP-2022-04_C3S2-Lot3_PQAR-of-v6.0-OceanColour-product_v1.1_FINAL.pdf).

Enforce sorting as original data
Define data request

(section-2)=
### 2. Area average function and data retrieval
#### Area average function
The `regionalised_spatial_weighted_mean` function, which accounts for the varying surface area at different latitudes, is defined to calculate the area averages over the selected regions. Area averages for chlorophyll-a concentration are computed using log-transformed daily data, and then unlogged [[7]](https://doi.org/10.1029/95JC00458).

#### Data retrieval
The `regionalised_spatial_weighted_mean` is applied to the selected variables and regions, and the time series are downloaded as a single array. Chlorophyll-a concentrations outside the range 0.01-100 mg m-3 are excluded from the download and the analysis [[8]](https://doi.org/10.3390/s19194285).


EQC Quality Assessment: "Impact of using successive satellites on Ocean Colour time series"
Dataset: satellite-ocean-colour [CDS]
Aspect: consistency-assessment_q01  |  Category: Satellite_ECVs
Section: Impact of using successive satellites on Ocean Colour time series > Quality assessment statement
---
ophyll-a concentrations outside the range 0.01-100 mg m<sup>-3</sup> are excluded from the download and the analysis [[8]](https://doi.org/10.3390/s19194285).

(section-3)=
### 3. Plot and statistics functions
#### Compute statistics and define plot function
Functions to calculate 48-month rolling mean and linear trend for the selected variables and regions are embedded in the plot function. Linear trend equations and their statistical significance (p) are specified in the legend of each figure. Time-averaged values are also computed for the selected variables and regions.

Compute running mean
Compute linear trend
Final settings

#### Define satellite missions
The name and data acquiring period are specified for each satellite sensor used to produce the dataset [[1]](https://dast.copernicus-climate.eu/documents/satellite-ocean-colour/v6.0/WP2-FDDP-2022-04_C3S2-Lot3_PUGS-of-v6.0-OceanColour-product_v1.1_FINAL.pdf). This information is displayed in the time series figures (see below).

(section-4)=
### 4. Display and discuss results
#### Display results
Time series of chlorophyll-a concentrations and Rrs at 443 and 560 nm are displayed for each region analysed, together with the duration of every satellite mission used to retrieve data. Linear trend equations and their statistical significance are indicated in the legends. Data are plotted on the same zoomed-in scale to focus on long-term chlorophyll-a and Rrs trends in the four regions analysed and facilitate their comparison.

#### Discussion
Results show that the Ocean Colour dataset version 6.0 captures both the seasonal and interannual variability of the variables analysed in the four selected regions.

**Chlorophyll-a:**
Chlorophyll-a timeseries in the global ocean and the region between 50°S and 50°N show similar seasonal and interannual variabilities, and trends. Long-term trends obtained through a 48-month rolling mean show a maxima around 2002 in both the global ocean and the oceanic region between latitudes 50°S and 50°N, followed by a sharp decrease until 2004. Afterwards, a progressive decrease until around 2015 and a slight increase until 2022 are observed.
The largest chlorophyll-a seasonal variability is observed in the NASTG's region, due to the strong seasonal expansion/contraction cycle of the gyre [[5]](https://doi.org/10.1029/2021GL096965), together with a rather constant long-term decreasing trend.
The lowest chlorophyll-a concentrations and seasonal variability are observed in the SPG's region and indicate a high stability in the area [[6]](https://dast.copernicus-climate.eu/documents/satellite-ocean-colour/v6.0/WP2-FDDP-2022-04_C3S2-Lot3_PQAR-of-v6.0-OceanColour-product_v1.1_FINAL.pdf). Linear trends are statistically significant (p<0.05) in all regions analyzed here, indicating that chlorophyll-a is decreasing everywhere except in the SPG. These results align with the recent paper [[9]](https://doi.org/10.1038/s41586-023-06321-z), where decreasing (increasing) chlorophyll-a is associated with increasing (decreasing) sea surface temperature trends.

**Rrs:**
Compared to chlorophyll-a, average Rrs at 443 nm shows reverse patterns and statistically significant (p<0.05) trends in all selected regions, which are consistent with results in [[9]](https://doi.org/10.1038/s41586-023-06321-z). It is worth noting that results for the SPG's region are consistent with the post-bias correction validation [[6]](https://dast.copernicus-climate.eu/documents/satellite-ocean-colour/v6.0/WP2-FDDP-2022-04_C3S2-Lot3_PQAR-of-v6.0-OceanColour-product_v1.1_FINAL.pdf) and show no suspicious artefacts along with the satellite succession.
Rrs at 560 nm trends are rather linear in all the regions analysed here, except the NASTG, where a progressive increase between 1998 and 2017, followed by a rapid decrease until 2022, is observed. Linear trends calculated here for Rrs at 560 nm are not statistically significant (p>0.05), although an increasing tendency is observed everywhere, except in the SPG where Rrs at 560 nm decreases over time.


EQC Quality Assessment: "Impact of using successive satellites on Ocean Colour time series"
Dataset: satellite-ocean-colour [CDS]
Aspect: consistency-assessment_q01  |  Category: Satellite_ECVs
Section: Impact of using successive satellites on Ocean Colour time series > Quality assessment statement
---
. Linear trends calculated here for Rrs at 560 nm are not statistically significant (p>0.05), although an increasing tendency is observed everywhere, except in the SPG where Rrs at 560 nm decreases over time.

Relatively high chlorophyll-a concentrations and low Rrs at 443 nm are observed when SeaWiFS was the only active satellite (i.e., from January 1998 to March 2002) in both the global ocean and the oceanic region between 50°S and 50°N, but not in the NASTG's and SPG's regions.
Overall, these results suggest that, prior to March 2002, Rrs at 443 would be underestimated, especially when the analysis is extended to include high-latitude, more productive oceanic zones, and trigger chlorophyll-a overestimates.
Despite the extensive time series analyzed here and the relatively short time series length required to detect climate-driven variations in low-latitude and/or oligotrophic regions, such as the NASTG and the SPG [[9]](https://doi.org/10.1038/s41586-023-06321-z) [[10]](https://doi.org/10.5194/bg-7-621-2010), it is not yet possible to unequivocally associate the trends calculated here with climate change.
An additional analysis, performed using the same notebook, but excluding SeaWiFS data prior to March 2002, indicates that they do not significantly modify the long-term trends computed for the variables analysed here nor their statistics in all selected regions.

## ℹ If you want to know more

### Key resources
* CDS catalogue entry used in this notebook is the [Ocean colour daily data from 1997 to present derived from satellite observations](https://cds.climate.copernicus.eu/datasets/satellite-ocean-colour?tab=overview)
* Data download is from [CDS](https://cds.climate.copernicus.eu/datasets/satellite-ocean-colour?tab=form)
* Product Documentation is available on the [CDS](https://cds.climate.copernicus.eu/datasets/satellite-ocean-colour?tab=doc) website

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/)

Further readings:
* Ocean Colour Monitoring Portals: [CMEMS](https://marine.copernicus.eu/), [ESA-GlobColour Project](https://hermes.acri.fr/), [ESA-OC-CCI](https://climate.esa.int/en/projects/ocean-colour/), [ESA-Sentinel 3](https://sentiwiki.copernicus.eu/web/s3-mission), [IMOS](https://imos.org.au/facility/satellite-remote-sensing/ocean-colour), [NASA](https://oceancolor.gsfc.nasa.gov/#), [NOAA CoastWatch](https://coastwatch.noaa.gov/cwn/index.html)
* Use cases: [EUMETSAT](https://user.eumetsat.int/search-view?sort=startDate%20desc&facets=%7B%22theme%22:%5B%22Marine%7COcean%20biogeochemistry%22%5D,%22contentTypes%22:%5B%22Resources%7CCase%20studies%22%5D%7D), [C3S](https://climate.copernicus.eu/ocean)
* Groom, S., et al. (2019). [Satellite Ocean Colour: Current Status and Future Perspective](https://doi.org/10.3389/fmars.2019.00485). Frontiers in Marine Science, 6.
* [International Ocean Colour Coordinating Group (ICCG)](https://ioccg.org/)

### References

[[1]](https://dast.copernicus-climate.eu/documents/satellite-ocean-colour/v6.0/WP2-FDDP-2022-04_C3S2-Lot3_PUGS-of-v6.0-OceanColour-product_v1.1_FINAL.pdf) Jackson, T., et al. (2023). C3S Ocean Colour Version 6.0: Product User Guide and Specification. Issue 1.1. E.U. Copernicus Climate Change Service. Document ref. WP2-FDDP-2022-04_C3S2-Lot3_PUGS-of-v6.0-OceanColour-product.


EQC Quality Assessment: "Impact of using successive satellites on Ocean Colour time series"
Dataset: satellite-ocean-colour [CDS]
Aspect: consistency-assessment_q01  |  Category: Satellite_ECVs
Section: Impact of using successive satellites on Ocean Colour time series > Quality assessment statement
---
1.1. E.U. Copernicus Climate Change Service. Document ref. WP2-FDDP-2022-04_C3S2-Lot3_PUGS-of-v6.0-OceanColour-product.

[[2]](https://doi.org/10.4319/lo.1997.42.7.1479) Behrenfeld, M.J., & Falkowski, P.G. (1997). A consumer's guide to phytoplankton primary productivity models. Limnology and Oceanography, 42, 1479-1491. 9.

[[3]](https://doi.org/10.1371/journal.pone.0028945) Friedland, K.D., et al. (2012). Pathways between Primary Production and Fisheries Yields of Large Marine Ecosystems. PLoS ONE, 7(1), e28945.

[[4]](https://dast.copernicus-climate.eu/documents/satellite-ocean-colour/v6.0/WP2-FDDP-2022-04_C3S2-Lot3_ATBD-of-v6.0-OceanColour-product_v1.1_FINAL.pdf) Jackson, T., et al. (2022). C3S Ocean Colour Version 6.0: Algorithm Theoretical Basis Document. Issue 1.1. E.U. Copernicus Climate Change Service. Document ref. WP2-FDDP-2022-04_C3S2-Lot3_ATBD-of-v6.0-OceanColour-product.

[[5]](https://doi.org/10.1029/2021GL096965) Leonelli, F.E., et al. (2022). Ultra-oligotrophic waters expansion in the North Atlantic Subtropical Gyre revealed by 21 years of satellite observations. Geophysical Research Letters, 49, e2021GL096965.

[[6]](https://dast.copernicus-climate.eu/documents/satellite-ocean-colour/v6.0/WP2-FDDP-2022-04_C3S2-Lot3_PQAR-of-v6.0-OceanColour-product_v1.1_FINAL.pdf) Jackson, T., et al. (2023) C3S Ocean Colour Version 6.0: Product Quality Assessment Report. Issue 1.1. E.U. Copernicus Climate Change Service. Document ref. WP2-FDDP-2022-04_C3S2-Lot3_ PQAR-of-v6.0-OceanColour-product.

[[7]](https://doi.org/10.1029/95JC00458) Campbell, J.W. (1995). The lognormal distribution as a model for bio-optical variability in the sea. Journal of Geophysical Research, 100, 13237-13254.

[[8]](https://doi.org/10.3390/s19194285) Sathyendranath, S., et al. (2019). An Ocean-Colour time series for use in climate studies: the experience of the Ocean-Colour Climate Change Initiative (OC-CCI). Sensors, 19, 4285.

[[9]](https://doi.org/10.1038/s41586-023-06321-z) Cael, B.B., et al. (2023). Global climate-change trends detected in indicators of ocean ecology. Nature, 619, 551-554.

[[10]](https://doi.org/10.5194/bg-7-621-2010) Henson, S.A., et al. (2010). Detection of anthropogenic climate change in satellite records of ocean chlorophyll and productivity. Biogeosciences, 7, 621-640.


EQC Quality Assessment: "Intercomparison of satellite multi-year sea ice extent estimates"
Dataset: satellite-sea-ice-edge-type [CDS]
Aspect: intercomparison_q01  |  Category: Satellite_ECVs
Section: Intercomparison of satellite multi-year sea ice extent estimates
---
Production date: 19-05-2025

Produced by: Timothy Williams (Nansen Environmental and Remote Sensing Center; NERSC) and Fabio Mangini (Nansen Environmental and Remote Sensing Center; NERSC)


EQC Quality Assessment: "Intercomparison of satellite multi-year sea ice extent estimates"
Dataset: satellite-sea-ice-edge-type [CDS]
Aspect: intercomparison_q01  |  Category: Satellite_ECVs
Section: Intercomparison of satellite multi-year sea ice extent estimates > Quality assessment question
---
* **How consistent is the evolution of multi-year sea-ice extent in the Arctic across different satellite sea-ice products?**

This study examines the geographical distribution of multi-year sea ice (MYI) in the Arctic, providing an analysis of its evolution since the early 1990s. The assessment focuses on multi-year sea ice, which is sea ice that has survived at least one melting season, because its extent in the Arctic has significantly declined over the last few decades (e.g., [[1]](https://doi.org/10.1029/2011GL047735)). Changes in MYI extent are of interest because of the repercussions they have on the Earth's climate which, in turn, can impact the Arctic ecosystem and affect human activities in the region (e.g., [[2]](https://www.cambridge.org/core/books/ocean-and-cryosphere-in-a-changing-climate/polar-regions/8D76B8865B796C16991F7A9FB6271C2D)).

The assessment uses two different sea-ice products. This choice helps determine the robustness of the results and highlight the properties of the two datasets. The first dataset, referred to as "CDS dataset", provides information on sea-ice types in the region, while the second, the "NERSC dataset", classifies sea ice into age categories.

Both datasets indicate a general decrease in Arctic multi-year sea ice extent over the last three decades, especially in the Beaufort Sea, the Chukchi Sea, and the Eurasian Basin. However, they show several differences on a regional scale. For example, compared to the CDS dataset, the NERSC dataset reports a consistent higher presence of multi-year sea ice in the Greenland Sea away from the coast.


EQC Quality Assessment: "Intercomparison of satellite multi-year sea ice extent estimates"
Dataset: satellite-sea-ice-edge-type [CDS]
Aspect: intercomparison_q01  |  Category: Satellite_ECVs
Section: Intercomparison of satellite multi-year sea ice extent estimates > Quality assessment statement
---
These are the key outcomes of this assessment

* Both the CDS and the NERSC datasets reveal an overall decrease in multi-year sea ice extent over the Arctic since 1991, with the most significant reductions occurring in the Beaufort Sea, the Chukchi Sea, and the Eurasian Basin.

* Despite their consistent conclusions, notable differences exist between the two datasets. Specifically, the CDS dataset tends to overestimate multi-year sea ice presence in the Beaufort Sea and underestimate it in the Greenland Sea when compared to the NERSC dataset. It is shown that these discrepancies tend to be minimum in October and to become more pronounced as each winter progresses.

* The inclusion of "ambiguous" data points in the CDS dataset has two main implications on the estimates of multi-year sea ice extent in the Arctic. At first, it affects the total amount of multi-year sea ice in the region, even though it only little alters its geographic distribution. Secondly, it increases its day-to-day variability.
```


EQC Quality Assessment: "Intercomparison of satellite multi-year sea ice extent estimates"
Dataset: satellite-sea-ice-edge-type [CDS]
Aspect: intercomparison_q01  |  Category: Satellite_ECVs
Section: Intercomparison of satellite multi-year sea ice extent estimates > Methodology
---
The evolution of multi-year sea ice extent in the Arctic is based on two different datasets. This choice helps show the properties of the two products as well as assessing the robustness of the results. The first dataset is freely available on the Copernicus Climate Data Store (CDS) website under the name ["Sea ice edge and type daily gridded data from 1978 to present derived from satellite observations"](https://cds.climate.copernicus.eu/datasets/satellite-sea-ice-edge-type?tab=overview). The data provides information on sea-ice types in the Arctic Ocean by classifying sea ice into four categories: "open water", "first-year ice", "multi-year ice", and "ambiguous". The classification primarily relies on brightness temperature observed by passive microwave radiometers. For the purposes of this Notebook, only the subset of the dataset labelled as Climate Data Records (CDRs) is considered, thereby excluding the Interim Climate Data Records (ICDRs). The ICDRs have been excluded from this work because their consistency has not been as thoroughly verified as that of the CDRs.

The second dataset is described by [[3]](https://tc.copernicus.org/articles/12/2073/2018/) and is provided by Dr. Anton Korosov (anton.korosov@nersc.no) on request. This dataset differs from the previous one as it uses an Eulerian advection scheme, together with passive-microwave-derived concentration and drift estimations, to classify sea ice into age categories, instead of ice types. Specifically, the dataset provides an estimate of sea-ice age over the Arctic, and an estimate of individual ice-age fractions at each grid point. For convenience, the former dataset will be referred to as "CDS dataset" whereas the latter as "NERSC dataset".

The assessment uses two distinct approaches to identify the grid points characterized by multi-year sea ice in the CDS and in the NERSC datasets. In the CDS dataset, the presence of multi-year sea ice is determined using two different criteria: first, by selecting the pixels classified as "multi-year ice", and second, by considering the pixels classified as both "multi-year ice" and "ambiguous". The results obtained with these two criteria are then compared to highlight the role of the pixels classified as ambiguous. Instead, in the NERSC dataset, multi-year sea ice is identified by selecting the pixels where the concentration of first-year sea ice (FYI) does not exceed that of sea ice that is older than one year, and where the sum of the two exceeds 30% (where there is some ice present). Note that this threshold, which is usually 15%, is chosen to be consistent with the CDS product.

The analysis is performed on the overlapping interval of the two datasets during the boreal winters between October 1991 and April 2020, where with boreal winter we refer to the period ranging from the 1st of October of one year to the 30th of April of the following year. The upper limit is set by the CDS dataset, which provides information on sea-ice types for the boreal winter months between October 1978 and December 2020, whereas the lower limit is set by the NERSC dataset, which covers the period from September 1991 to May 2023.

The "Analysis and results" section is structured as follows:

**[](section-1)**

**[](section-2)**

**[](section-3)**

     **[](section-3.1)**

     We present and compare the temporal evolution of the area covered by multi-year sea ice over the Arctic Basin as provided by the CDS and the NERSC datasets. This section also quantifies the mismatch between the two datasets by analysing the bias and the integrated ice type error (IITE) of the NERSC dataset relative to CDS dataset. The bias is the difference between the area where the CDS dataset reports multi-year sea ice while the NERSC dataset does not, and the area where the CDS dataset does not report multi-year sea ice while the NERSC dataset does. Instead, the integrated ice type error is the sum of these two areas.

     **[](section-3.2)**

     We investigate further the temporal evolution of multi-year sea ice in the Arctic with the help of maps. Specifically, we present and compare, for each dataset, month and pixel, the percentage of days associated with multi-year sea ice over three decades.


EQC Quality Assessment: "Intercomparison of satellite multi-year sea ice extent estimates"
Dataset: satellite-sea-ice-edge-type [CDS]
Aspect: intercomparison_q01  |  Category: Satellite_ECVs
Section: Intercomparison of satellite multi-year sea ice extent estimates > Analysis and results > 1. Parameters, requests and functions definition
---
- Define the parameters and formulate the requests for downloading with the EQC toolbox.
- Define the functions to process and reduce the size of the downloaded data.
- Define the functions to post-process and visualize the data.


EQC Quality Assessment: "Intercomparison of satellite multi-year sea ice extent estimates"
Dataset: satellite-sea-ice-edge-type [CDS]
Aspect: intercomparison_q01  |  Category: Satellite_ECVs
Section: Intercomparison of satellite multi-year sea ice extent estimates > Analysis and results > 1. Parameters, requests and functions definition > 1.2 Set Parameters
---
- set the years to use for the climatologies with `periods`. These years are also used to define the length of the time series.
- set `conc_threshold`, the concentration threshold to determine the presence of sea ice in the NERSC product.
- set the path to the NERSC ice age product with `NERSC_path`.

Define time periods
Concentration threshold to determine the presence of sea ice in the NERSC product
Define path to NERSC data


EQC Quality Assessment: "Intercomparison of satellite multi-year sea ice extent estimates"
Dataset: satellite-sea-ice-edge-type [CDS]
Aspect: intercomparison_q01  |  Category: Satellite_ECVs
Section: Intercomparison of satellite multi-year sea ice extent estimates > Analysis and results > 1. Parameters, requests and functions definition > 1.4 Functions to load and classify NERSC data
---
- `get_nersc_data` loads the NERSC data for a period corresponding to a set CDS data.
- `get_nersc_multiyear_ice` processes the NERSC data to produce a mask of multi-year sea ice.


EQC Quality Assessment: "Intercomparison of satellite multi-year sea ice extent estimates"
Dataset: satellite-sea-ice-edge-type [CDS]
Aspect: intercomparison_q01  |  Category: Satellite_ECVs
Section: Intercomparison of satellite multi-year sea ice extent estimates > Analysis and results > 1. Parameters, requests and functions definition > 1.5 Functions to produce time series
---
- `get_classification_mask` processes the CDS data to produce a mask of multi-year sea ice.
- `mask_outside_central_arctic` defines a mask based on a manually defined set of maximum latitudes. This mask is `False` if a pixel should be included in the calculation of MYI extent and error statistics and `True` if it shouldn't.
- `compute_spatial_sum` computes the area corresponding to a given boolean array on an equal-area grid.
- `compute_sea_ice_evaluation_diagnostics` computes the multi-year sea ice extent for the NERSC and the CDS products, the bias and the integrated ice type error between them.

grid cell area of sea ice edge grid
Mask for inside central Arctic
Masks for MYI
Fill variables


EQC Quality Assessment: "Intercomparison of satellite multi-year sea ice extent estimates"
Dataset: satellite-sea-ice-edge-type [CDS]
Aspect: intercomparison_q01  |  Category: Satellite_ECVs
Section: Intercomparison of satellite multi-year sea ice extent estimates > Analysis and results > 1. Parameters, requests and functions definition > 1.6 Functions to post-process and plot time series
---
- `rearrange_year_vs_monthday` groups a long time series by year and day of year.
- `split_dataset_ambiguous` splits a dataset into one dataset that depends on whether the ambiguous pixels in the CDS dataset are used, and another dataset that does not depend on this.
- `plot_against_monthday` plots the timeseries against the day-of-year by year, with a different colour for each year.


EQC Quality Assessment: "Intercomparison of satellite multi-year sea ice extent estimates"
Dataset: satellite-sea-ice-edge-type [CDS]
Aspect: intercomparison_q01  |  Category: Satellite_ECVs
Section: Intercomparison of satellite multi-year sea ice extent estimates > Analysis and results > 1. Parameters, requests and functions definition > 1.7 Functions to produce climatologies
---
- `compute_multiyear_ice_percentage` groups daily MYI masks by month and calculates the proportion of each month that a pixel contains MYI.
- `compute_cds_multiyear_ice_percentage` is a wrapper to call `compute_multiyear_ice_percentage` for CDS data.
- `compute_nersc_multiyear_ice_percentage` is a wrapper to call `compute_multiyear_ice_percentage` for NERSC data.


EQC Quality Assessment: "Intercomparison of satellite multi-year sea ice extent estimates"
Dataset: satellite-sea-ice-edge-type [CDS]
Aspect: intercomparison_q01  |  Category: Satellite_ECVs
Section: Intercomparison of satellite multi-year sea ice extent estimates > Analysis and results > 1. Parameters, requests and functions definition > 1.8 Functions to plot climatologies
---
- `plot_maps` plots multiple maps of either MYI percentage or the difference between the CDS and NERSC products.
- `plot_cds_maps` is a wrapper that calls `plot_maps` for CDS data.
- `plot_masked_data_cds` plots an example map to show the masked region used to calculate the time series.
- `plot_bias_maps` plots multiple maps of the difference between the CDS and NERSC products.

select a map to plot to illustrate the masked area

(section-2)=


EQC Quality Assessment: "Intercomparison of satellite multi-year sea ice extent estimates"
Dataset: satellite-sea-ice-edge-type [CDS]
Aspect: intercomparison_q01  |  Category: Satellite_ECVs
Section: Intercomparison of satellite multi-year sea ice extent estimates > Analysis and results > 2. Download and transform data
---
Here we download the sea ice type data and transform it to create the time series and climatology maps. The NERSC data should already be available locally.

Bias compared to NERSC product

(section-3)=


EQC Quality Assessment: "Intercomparison of satellite multi-year sea ice extent estimates"
Dataset: satellite-sea-ice-edge-type [CDS]
Aspect: intercomparison_q01  |  Category: Satellite_ECVs
Section: Intercomparison of satellite multi-year sea ice extent estimates > Analysis and results > 3. Results
---
The temporal evolution of multi-year sea ice extent over the Arctic is analysed using a combination of plots and maps. The plots help quantify and compare the temporal evolution of the Arctic multi-year sea ice extent provided by the two datasets, while the maps help explain the differences between the two datasets by identifying the regions where the two products differ the most.

(section-3.1)=


EQC Quality Assessment: "Intercomparison of satellite multi-year sea ice extent estimates"
Dataset: satellite-sea-ice-edge-type [CDS]
Aspect: intercomparison_q01  |  Category: Satellite_ECVs
Section: Intercomparison of satellite multi-year sea ice extent estimates > Analysis and results > 3. Results > 3.1 Temporal evolution of the total area covered by multi-year sea ice in the Arctic Basin
---
The map below shows the area over which the Arctic MYI extent is calculated to produce the plots. We should note that the MYI extent is computed over the Arctic Basin, therefore excluding the narrow straits and the Greenland Sea. This choice was made to ensure that the NERSC dataset was able to permit MYI in the selected region. For example, it may not be capable of advecting multi-year sea ice through narrow straits, such as the Nares Strait west of Greenland and the northern Canadian Archipelago.

The figure below consists of two plots. The plot on the left displays, for each boreal winter between October 1991 and April 2020, the daily area where the sea-ice type from the CDS dataset is set to ambiguous. The plot on the right follows the same structure, but shows the daily MYI extent as provided by the NERSC dataset.

The ambiguous MYI extent increases as each boreal winter progresses, with the rise accelerating in spring. This results from the CDS product performing better during the cold and stable mid-winter months than in the warmer spring months, when melting and other factors disrupt the distinction between classes. In addition, the CDS product uses drift tracking from the summer minimum to confirm the presence of MYI, and the error in this drift would also accumulate over the winter.

Interestingly, the ambiguous MYI extent does not experience a long-term change, despite the MYI extent decreasing over the period considered, as shown by the figure to the right and the ones below (introduced and discussed later).

The figure below consists of six plots, arranged in a grid of three rows and two columns. The first row displays the daily MYI extent for each boreal winter between October 1991 and April 2020, estimated from the CDS dataset. The second row shows the difference ("bias") between the CDS and the NERSC datasets, while the third row shows the corresponding integrated ice type error. The columns distinguish between the two definitions of multi-year sea ice for the CDS dataset. The right column shows the results based solely on the grid points labelled as "multi-year ice", whereas the left column shows results based on the grid points labelled as either "multi-year ice" or "ambiguous".

The comparison between the MYI extent from the CDS and the NERSC datasets yields comparable results, and the inclusion of the grid points labelled as "ambiguous" does not significantly alter the main conclusions. The results indicate that the spatial extent of multi-year sea ice in the Arctic has decreased since October 1991. Specifically, the October MYI extent dropped by approximately 1-2 million km$^2$ between the 5-year periods 1991-1995 and 2015-2019. A comparable result is found for the MYI extent in April. Selecting the ambiguous points does not significantly alter the results.

Both datasets also suggest that the MYI extent tends to decrease throughout each boreal winter. This is expected because MYI tends to be both exported and compressed through ridging as winter progresses (the reader is referred to [[4]](https://tc.copernicus.org/articles/17/1873/2023/) for a comprehensive explanation of sources and sinks of multi-year sea ice).

Despite their similarities, the datasets present some significant differences. Notably, the CDS dataset exhibits a slightly greater day-to-day variability compared to the NERSC dataset when the pixels labelled as "ambiguous" are included into the analysis. A thorough understanding of this discrepancy goes beyond the scope of this study. However, we hypothesize it to be partially attributed to atmospheric variability, which can affect the brightness temperature of sea ice and, therefore, the classification into first-year sea ice and multi-year sea ice. For example, warmer weather events pose a challenge to the classification of sea ice into ice types as they modify the surface of multi-year sea ice, making it appear similar to first-year sea ice (Product User Guide and Specification of the CDS dataset). This interpretation is corroborated by the day-to-day variability in the CDS dataset decreasing when the grid points labelled as "ambiguous" are not considered. The NERSC dataset on the other hand is based on relatively smooth, low-resolution sea ice concentration and drift products derived from lower-frequency (SSMIS) passive microwave measurements which are not as affected by atmospheric variability.


EQC Quality Assessment: "Intercomparison of satellite multi-year sea ice extent estimates"
Dataset: satellite-sea-ice-edge-type [CDS]
Aspect: intercomparison_q01  |  Category: Satellite_ECVs
Section: Intercomparison of satellite multi-year sea ice extent estimates > Analysis and results > 3. Results > 3.1 Temporal evolution of the total area covered by multi-year sea ice in the Arctic Basin
---
The NERSC dataset on the other hand is based on relatively smooth, low-resolution sea ice concentration and drift products derived from lower-frequency (SSMIS) passive microwave measurements which are not as affected by atmospheric variability.

The differences between the two datasets also appear in the four plots at the bottom, which show the temporal evolution of the bias and the integrated ice type error. Both diagnostics tend to progressively diverge from zero as each boreal winter evolves. This is not entirely surprising as at the end of summer, the Arctic by definition contains only multi-year ice, but the potential for mis-classification (by both the CDS and NERSC products) grows later in the winter as more FYI forms. With the NERSC product, the drift tracking algorithm will accumulate errors further into the winter; with the CDS product, the distinction between classes is disrupted in the spring months as warmer temperatures, melting, and dynamics (eg. increased deformation of FYI) disturb the emissivity of the sea ice.

The figure above indicates that the exclusion from the analysis of the pixels labelled as "ambiguous" leads to stronger decrease of multi-year sea ice extent throughout each boreal winter. This result better agrees with that provided by the NERSC dataset, with the exception of the month of April. In April, the penultimate subplot on the right shows a drop in the bias, especially during the first decade of the analysis, as indicated by the blue lines. Unfortunately, it is difficult to understand the causes behind this issue. On the one hand, the discrepancy might indicate that, in the month of April, some of the grid points labelled as "ambiguous" contain multi-year sea ice. On the other hand, it might indicate that the NERSC dataset interprets part of first-year sea ice as multi-year sea ice. This might occur because, as noticed in [[3]](https://tc.copernicus.org/articles/12/2073/2018/), the algorithm might prioritize small concentration of multi-year sea ice, therefore overstimating the age of sea ice at each pixel.

(section-3.2)=


EQC Quality Assessment: "Intercomparison of satellite multi-year sea ice extent estimates"
Dataset: satellite-sea-ice-edge-type [CDS]
Aspect: intercomparison_q01  |  Category: Satellite_ECVs
Section: Intercomparison of satellite multi-year sea ice extent estimates > Analysis and results > 3.2 Spatial and temporal evolution of the region covered by multi-year sea ice in the Arctic
---
- from Oct 1991 to Apr 2001 (10 boreal winters)
- from Oct 2001 to Apr 2011 (10 boreal winters)
- from Oct 2011 to Apr 2020 (9 boreal winters)


EQC Quality Assessment: "Intercomparison of satellite multi-year sea ice extent estimates"
Dataset: satellite-sea-ice-edge-type [CDS]
Aspect: intercomparison_q01  |  Category: Satellite_ECVs
Section: Intercomparison of satellite multi-year sea ice extent estimates > Analysis and results > 3.2 Spatial and temporal evolution of the region covered by multi-year sea ice in the Arctic > Maps of multi-year sea ice from NERSC dataset
---
The maps below visually complement the previous plots, illustrating the geographical distribution of multi-year sea ice in the Arctic, its evolution since the early 1990s, and the regions where the CDS and NERSC datasets diverge the most.

The initial set of maps refers to the NERSC dataset and displays, for each month and grid point, the percentage of days associated with multi-year sea ice across three distinct periods: from October 1991 to April 2001, from October 2001 to April 2011, and from October 2011 to April 2020. The figure comprises 21 maps, with each column corresponding to one of the three periods and each row to a different month.

Consistent with the plots above, the maps show a significant decline in the multi-year sea ice extent since 1991, as well as throughout the boreal winters. The decline in multi-year sea ice appears to have mostly occurred in the Beaufort Sea, the Chukchi Sea, and the Eurasian Basin. On the contrary, multi-year sea ice has consistently been present in the Canadian sector and in the Greenland Sea throughout the entire period. The presence of multi-year sea ice off the coast of Greenland is noticeable and presumably due to the advection of multi-year sea ice through the Fram Strait.


EQC Quality Assessment: "Intercomparison of satellite multi-year sea ice extent estimates"
Dataset: satellite-sea-ice-edge-type [CDS]
Aspect: intercomparison_q01  |  Category: Satellite_ECVs
Section: Intercomparison of satellite multi-year sea ice extent estimates > Analysis and results > 3.2 Spatial and temporal evolution of the region covered by multi-year sea ice in the Arctic > Maps of multi-year sea ice from CDS and "CDS - NERSC"
---
The Jupyter Notebook further presents four sets of maps. These are meant to help visualize the differences between the CDS and the NERSC datasets. Each set follows the same structure as the figure above. However, the first and the second sets of maps respectively show the percentage of multi-year sea ice provided by the CDS dataset for the case when the presence of multi-year sea ice is only detected using the pixels labelled as 'multi-year ice' and when the 'ambiguous' grid points are considered. The remaining sets of maps show the differences between the percentage of multi-year sea ice provided by the CDS and the NERSC datasets. The third set is produced only using the grid points of the CDS dataset that are classified as ‘multi-year ice’, whereas the one underneath uses the grid points classified as 'multi-year ice' and 'ambiguous'.

The inclusion of "ambiguous" data points primarily affects the magnitude of the difference, rather than the patterns. More precisely, when "ambiguous" values are included into the analysis, the grid points of the CDS dataset are more likely associated with multi-year sea ice and, therefore, the difference between the CDS and the NERSC datasets becomes more positive.

Compared to the NERSC dataset, the CDS product has less multi-year sea ice in the Greenland Sea, away from the coast of Greenland. Such a discrepancy might result from the difficulty of the NERSC dataset to well capture the impact of local dynamics on multi-year sea ice. Indeed, the drifts that were used to create the NERSC dataset have a daily temporal resolution. Thus, they might not fully represent the effects of the ocean since it is highly dynamic in the region. However, the discrepancy might also highlight issues with the CDS dataset as [[3]](https://tc.copernicus.org/articles/12/2073/2018/) showed the ability of the NERSC dataset to capture multi-year sea ice in the Greenland Sea through a comparison with Sentinel-1 SAR images, used as an independent dataset, on the 1st January 2016. Therefore, further analysis is necessary to determine what causes such a discrepancy and, therefore, which dataset most reliably provides information on multi-year sea ice in the region.

More difficult is to determine the quality of the two datasets in other sectors of the Arctic. For example, compared to the NERSC dataset, the CDS dataset shows higher percentages of multi-year sea ice in the Beaufort Sea, the Chukchi Sea, and the Eurasian Basin. We might speculate that, in the Eurasian Basin, the discrepancy might occur because the CDS dataset might overestimate the amount of MYI due to its binary classification, which labels a grid point as MYI even if contains substantial amount of FYI. In contrast, when analysing the NERSC dataset we have classified a pixel as MYI if the concentration of MYI is greater than the concentration of FYI, which may lead to there being less MYI in this product than in the one by CDS. However, further analysis, for example focusing on individual years, is needed to assess the causes behind these disagreements.


EQC Quality Assessment: "Intercomparison of satellite multi-year sea ice extent estimates"
Dataset: satellite-sea-ice-edge-type [CDS]
Aspect: intercomparison_q01  |  Category: Satellite_ECVs
Section: Intercomparison of satellite multi-year sea ice extent estimates > ℹ If you want to know more > Key resources
---
CDS dataset used:

* [Sea ice edge and type daily gridded data from 1978 to present derived from satellite observations](https://cds.climate.copernicus.eu/datasets/satellite-sea-ice-edge-type?tab=overview)

Additional resources:

* Section "SEA-ICE" in the [State of the Global Climate 2023](https://library.wmo.int/records/item/68835-state-of-the-global-climate-2023)
* [Learning material on sea ice provided by the National Snow and Ice Data Center](https://nsidc.org/learn/parts-cryosphere/sea-ice)
* [Arctic multi-year sea ice visualization](https://svs.gsfc.nasa.gov/4251) provided by NASA
* [Sea ice as a climate indicator](https://19january2021snapshot.epa.gov/climate-indicators/climate-change-indicators-arctic-sea-ice_.html  )
* [How sea ice is observed](https://www.metoffice.gov.uk/research/climate/cryosphere-oceans/sea-ice/measure)
* [NARVAL, a visualization portal for Earth observation and model data in the high-latitude oceans](https://narval.nersc.no), offers visualizations of various sea-ice variables

Code libraries used:

* [pandas](https://pandas.pydata.org/)
* [xarray](https://docs.xarray.dev/en/stable/)
* [matplotlib](https://matplotlib.org/)
* [cmocean](https://matplotlib.org/cmocean/)
* [cartopy](https://scitools.org.uk/cartopy/docs/latest/)
* [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: "Intercomparison of satellite multi-year sea ice extent estimates"
Dataset: satellite-sea-ice-edge-type [CDS]
Aspect: intercomparison_q01  |  Category: Satellite_ECVs
Section: Intercomparison of satellite multi-year sea ice extent estimates > ℹ If you want to know more > References
---
1. Maslanik, J., Stroeve, J., Fowler, C., and Emery, W.: Distribution and trends in Arctic sea ice age through spring 2011, Geophys. Res. Lett., 38, L13502, https://doi.org/10.1029/2011GL047735, 2011.
2. Meredith, M., Sommerkorn, M., Cassotta, S., Derksen, C., Ekaykin, A., Hollowed, A., Kofinas, G., Mackintosh, A., Melbourne-Thomas, J., Muelbert, M. M. C., Ottersen, G., Pritchard, H., and Schuur, E.: Polar Regions, in: IPCC Special Report on the Ocean and Cryosphere in a Changing Climate, edited by: Pörtner, H.-O., Roberts, D. C., Masson-Delmotte, V., Zhai, P., Tignor, M., Poloczanska, E., Mintenbeck, K., Alegría, A., Nicolai, M., Okem, A., Petzold, J., Rama, B., and Weyer, N. M., chap. 3, 203–320, Cambridge University Press, Cambridge, UK and New York, NY, USA, https://doi.org/10.1017/9781009157964.005, 2019.
3. Korosov, A. A., Rampal, P., Pedersen, L. T., Saldo, R., Ye, Y., Heygster, G., Lavergne, T., Aaboe, S., and Girard-Ardhuin, F.: A new tracking algorithm for sea ice age distribution estimation, The Cryosphere, 12, 2073–2085, https://doi.org/10.5194/tc-12-2073-2018, 2018.
4. Regan, H., Rampal, P., Ólason, E., Boutin, G., Korosov, A.: Modelling the evolution of Arctic multiyear sea ice over 2000-2018, The Cryosphere, 17, 1873-1893, https://doi.org/10.5194/tc-17-1873-2023, 2023.


EQC Quality Assessment: "Suitability of satellite sea ice thickness data for studying climate change"
Dataset: satellite-sea-ice-thickness [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Suitability of satellite sea ice thickness data for studying climate change > Quality assessment statement
---
These are the key outcomes of this assessment

- We find that the usefullness of satellite sea ice thickness data for the purpose of studying climate change is limited, since the time series are relatively short and the sea ice thickness variable has quite a lot of interannual variability. Note that this conclusion does not apply to other applications of this data like validation of models (bearing in mind biases and uncertainties in the data).

- In limited regions, linear trends can explain a significant amount (greater than 0.5) of the variability in the satellite data, but even in those small regions the fits are not overly representative of the satellite estimates. That is, with the small number of years with data, how good the fits are is difficult to assess visually.
```


EQC Quality Assessment: "Suitability of satellite sea ice thickness data for studying climate change"
Dataset: satellite-sea-ice-thickness [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Suitability of satellite sea ice thickness data for studying climate change > Methodology
---
We consider the Level-3 [sea ice thickness dataset](https://cds.climate.copernicus.eu/datasets/satellite-sea-ice-thickness?tab=overview), which has two CDR (Climate Data Record) products:
- ENVISAT CDR (2002-2010)
- CryoSat-2 CDR (2010-2020)
CryoSat-2 also has an interim CDR (ICDR, covering 2020-2024) but we did not use this product in this notebook.

We fit linear trends to these two satellite products, and assess the goodness-of-fit using the $r^2$ and $p$-value statistics.
We do separate fits for each winter month (October-April), to all pixels with at least five years of data.
Maps of the mean, standard deviation and RMS (root mean sqare) uncertainty of the thickness, the fitted linear trend and the goodness-of-fit statistics are shown.
Note that the product uncertainty does not include biases and other errors. In the evaluations done ENVISAT was found to have a significant low bias while CryoSat-2 had a small positive bias (see the [Product User Guide, p5)](https://dast.copernicus-climate.eu/documents/satellite-sea-ice-thickness/level-3/v3-0/WP2-FDDP-2022-09_C3S2-Lot3_PUGS-of-v3.0-SeaIceThickness-products_v3.1_Final.pdf) for more details).

The "Analysis and results" section is structured as follows:

**[](section-1)**

**[](section-2)**

**[](section-3)**


EQC Quality Assessment: "Suitability of satellite sea ice thickness data for studying climate change"
Dataset: satellite-sea-ice-thickness [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Suitability of satellite sea ice thickness data for studying climate change > Analysis and results > 1. Parameters, requests and functions definition
---
- Define parameters and formulate requests for downloading with the EQC toolbox.
- Define functions to be applied to process and reduce the size of the downloaded data.
- Define functions to post-process and visualize the data.


EQC Quality Assessment: "Suitability of satellite sea ice thickness data for studying climate change"
Dataset: satellite-sea-ice-thickness [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Suitability of satellite sea ice thickness data for studying climate change > Analysis and results > 1. Parameters, requests and functions definition > 1.2 Set parameters
---
- Set the time range for ENVISAT data with `year_start_envisat` and `year_stop_envisat`
- Set the time range for CRYOSAT data with `year_start_cryosat` and `year_stop_cryosat`


EQC Quality Assessment: "Suitability of satellite sea ice thickness data for studying climate change"
Dataset: satellite-sea-ice-thickness [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Suitability of satellite sea ice thickness data for studying climate change > Analysis and results > 1. Parameters, requests and functions definition > 1.4 Post-processing functions
---
- `sort_time` sorts the dataset by month and year.
- `linregress_1d` fits a straight line to some training data (output and input).
- `get_stats` calculates some statistics over the year dimension (mean, standard deviation, RMS uncertainty) and also the coefficients of a linear fit (input is year) and goodness of fit statistics ($r^2$ value and $p$-value). It outputs a reduced dataset with no year dimension.
- `add_differences` adds the differences between the CryoSat-2 and ENVISAT statistics to the reduced dataset, and also reduces the spatial extent for better plotting.

get SIT statistics and create dataset
get linear fit of SIT vs year
remove areas with no data ever
ensure grid is contiguous after reducing area


EQC Quality Assessment: "Suitability of satellite sea ice thickness data for studying climate change"
Dataset: satellite-sea-ice-thickness [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Suitability of satellite sea ice thickness data for studying climate change > Analysis and results > 1. Parameters, requests and functions definition > 1.5 Plotting functions
---
- `plot_maps` plots monthly maps for a given variable.
- `plot_maps_trends` plots maps of the trend with the goodness-of-fit statistices, the $r^2$ and $p$ values.
- `plot_maps_valid_years` plots monthly maps of the number of valid years for each satellite.
- `check_fit` plots time series of the satellite thickness and error bars to compare to the linear fits for selected points.
- `check_fit_envisat` selects the example points to check the fits to the ENVISAT data.
- `check_fit_cryosat2` selects the example points to check the fits to the CryoSat-2 data.

Create plots
Loop over variables
plot a map showing the point locations
get the trend line
plot SIT time series and linear fit

(section-2)=


EQC Quality Assessment: "Suitability of satellite sea ice thickness data for studying climate change"
Dataset: satellite-sea-ice-thickness [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Suitability of satellite sea ice thickness data for studying climate change > Analysis and results > 2. Download and transform the data
---
This is where the data is downloaded, transformed using `monthly_weighted_linear_trend` and saved to disk by the EQC toolbox. If the code is rerun the transformed data is loaded from the disk.
The transformed data is then post-processed by `postprocess_dataset` after downloading or loading.

(section-3)=


EQC Quality Assessment: "Suitability of satellite sea ice thickness data for studying climate change"
Dataset: satellite-sea-ice-thickness [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Suitability of satellite sea ice thickness data for studying climate change > Analysis and results > 3. Results
---
In section [](section-3.1) we plot monthly maps showing the mean, variability and RMS uncertainty of sea ice thickness for the two satellites, and also plot the difference between the means for the two satellites to get an idea of the change in thickness going from the earlier to the later period.

In section [](section-3.2), we compute linear trends for the two satellites and test the goodness-of-fit of the linear fit.

(section-3.1)=


EQC Quality Assessment: "Suitability of satellite sea ice thickness data for studying climate change"
Dataset: satellite-sea-ice-thickness [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Suitability of satellite sea ice thickness data for studying climate change > Analysis and results > 3. Results > 3.1 Temporal mean and variability, and difference between satellite periods
---
Below we show the mean sea ice thickness for the two satellites ENVISAT (2002-2010) and CryoSat-2 (2010-2020), along with the difference between them.
The thickness in the CryoSat-2 product is higher at the coast north of Greenland and Canada and this extends to around the North Pole in earlier winter and a bit further later in the winter.
This pattern is consistent with the pattern in the ENVISAT thickness, but much of the area of interest is obscured by the large polar hole in that product.
However, looking at the difference in the means, there is a slight drop in thickness in the overlapping areas of thicker ice.
In general the mean thickness has dropped, with the exception of the area north of the Canadian archipelago (adjacent to the overlapping area of thicker ice) and in the Greenland Sea in the later winter months.

The two satellites have different biases (CryoSat-2 has a slight positive bias, while ENVISAT has a more significant negative bias) and accuracies so we should be be a little careful when comparing and trying to deduce temporal changes between them.
Given the satellite biases we can trust the reductions in thickness more than the increases in thickness. Moreover the increases in thickness also occur in regions of higher variability (plotted after the means and the difference in the means). Having said this we have used an 8-10 year averaging period so some of the variability will have been smoothed out.

Below we plot the standard deviations of the two satellite periods, and also the differences between them. For both the ENVISAT and the CryoSat-2 satellites, the variability is greatest in the areas with thicker and old ice, possibly since these areas are usually quite deformed due to ridging.
There is also high variability in the Greenland Sea, which is probably due in part to the highly dynamic nature of that area - the ice flows quite fast once it is exported through the Fram Strait. This exported ice can also be quite old and deformed with ridges which would also add to the variability. Looking at the differences, the variability has generally increased, with the exception of the area between the Beaufort Sea and the ENVISAT polar hole. This could be due to the higher resolution of the CryoSat-2 satellite, picking up smaller scale changes that ENVISAT cannot resolve, especially in regions of multi-year ice. CryoSat-2 also has less variability in the Labrador Sea Hudson bay from January to April, possibly since the ice there is generally more level, first-year ice.
Increased drift and deformation of the ice in latter years ([Rampal et al, 2009](https://doi.org/10.1029/2008JC005066)) may also be a factor.

Below we plot the RMS uncertainties of the two satellite periods, and also the differences between them. As with the variability, for both the ENVISAT and the CryoSat-2 satellites, the variability is greatest in the areas with thicker and old ice. It is also higher in coastal areas, possibly from a combination of more deformed ice, more uncertain snowfall and reference sea surface height, and radar signal contamination from land. Again like the variability, there is quite high uncertainty in the Greenland Sea. The uncertainty increases markedly as the winter progresses, possibly due to the ice becoming more deformed, and maybe higher errors in snow depth as more snow accumulates. In addition, once there starts to be surface melt melt ponds also start to interfere with the radar signal, which could also be increasing the April uncertainty.

Note that the uncertainties above do not include biases and other errors. In the evaluations done ENVISAT was found to have a significant low bias while CryoSat-2 had a small positive bias (see the [Product User Guide, p5)](https://dast.copernicus-climate.eu/documents/satellite-sea-ice-thickness/level-3/v3-0/WP2-FDDP-2022-09_C3S2-Lot3_PUGS-of-v3.0-SeaIceThickness-products_v3.1_Final.pdf) for more details).

(section-3.2)=


EQC Quality Assessment: "Suitability of satellite sea ice thickness data for studying climate change"
Dataset: satellite-sea-ice-thickness [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Suitability of satellite sea ice thickness data for studying climate change > Analysis and results > 3. Results > 3.2 Assessment of linear model for temporal variability
---
Before we show the trends and their goodness-of-fit statistics, we first plot maps showing the number of valid years for each pixel. The ENVISAT satellite generally has 8 valid years of data, with the exception of the marginal seas. CryoSat-2 has much less, possibly due to the smaller satellite footprint making it easier for the tracks to miss a given pixel. November/February/April mostly have 5/7/6 valid years, while other months have less than our minimum number of years (5). Hence we do not try to fit linear trends to October, December, January or March for the CryoSat-2 data.

For both satellite periods, we calcuated linear trends in sea ice thickness along with the goodness-of-fit statistices, the $r^2$ and $p$ values. The $r^2$ statistic measures the fraction of the variability explained by the linear trends and it is generally quite low, with the exception of a region between the Beaufort Sea and the polar hole in the ENVISAT data. This region also had the most significant reduction in sea ice variability. The $p$-value gives the probability of the data being explained by random variability around a zero trend. It tells a similar story to the $r^2$-value, in that it is generally quite high, with the exception of the same region in the ENVISAT data that had the higher r$^2$ value.

Below we plot the trend in the ENVISAT data for the month of February, along with the $r^2$ and $p$ values. The trend is about -10 cm/year in the region where the fit is acceptable. Other months are similar, in both the values and the region where the fit is acceptable. However, in general the linear fit to this data is explaining very little of the temporal variability.

Below we show three examples of the linear fits, at the positions shown on the map.

The first point has a high value of $r^2$ (0.79), and the fit is passing through all the error bars. It has a low $p$-value, so it is not well explained by random variations, but at the same time the behaviour is more of a step function than a linear decrease.

The second point has a borderline value of $r^2$ (0.46) and $p$-value (6.6%), so it is starting to be more explained by random variations (a common threshold is 5%). Visually the fit is not very representative of the data, and maybe a step function would be a better fit.

The third point has a very low value of $r^2$ and a high $p$-value or a high probability of being explained by random variability. With the exception of the first and last points, this series looks more like an increase followed by a decrease.
This example also shows the limitation of having such a short time series, in that removing possible outliers would leave very little data to work with.

In summary, for the ENVISAT data the region where linear fits are explaining a large fraction of the variability (as measured by $r^2$) is quite small, and even in those places a linear fit is still not overly convincing visually. The low number of data points also makes it hard to judge the fits visually.

Below we plot the trend in the CryoSat-2 data for the months with enough data, along with the $r^2$ and $p$ values. The regions where $r^2$ is reaching 0.5 and the $p$ value is below 0.1 are quite small and less coherent than for the ENVISAT data.
In general we can again say that the linear fits to the thickness data are explaining very little of the temporal variability.
November has the largest area of higher $r^2$ but the thickness in that month is more uncertain for physical reasons (the ice is still quite dynamic; leads and melt ponds may still be refreezing; new ice has lower freeboard so it is harder to measure) so we do not concentrate on that one.
Since melting is starting in April its thickness is also very uncertain, so we will now focus on the month of February, which also has the highest number of valid years (7).


EQC Quality Assessment: "Suitability of satellite sea ice thickness data for studying climate change"
Dataset: satellite-sea-ice-thickness [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Suitability of satellite sea ice thickness data for studying climate change > Analysis and results > 3. Results > 3.2 Assessment of linear model for temporal variability
---
we do not concentrate on that one.
Since melting is starting in April its thickness is also very uncertain, so we will now focus on the month of February, which also has the highest number of valid years (7).

Below we show three examples of the linear fits to the CryoSat-2 data for the month of February, at the positions shown on the map.
The first point has a higher value of $r^2$ (0.58), and a borderline $p$-value of 4.6%, so it is starting to have a significant chance of being explained by random variations.
The second point has a lower value of $r^2$ (0.37), so it is explaining less than half of the variability, and the $p$-value has increased to 15%.
The third point has a very low value of $r^2$ and a high $p$-value of 65%. While all of the fits are passing through all the error bars, it is difficult to decide visually if the fits are good ones due to the low number of points.


EQC Quality Assessment: "Suitability of satellite sea ice thickness data for studying climate change"
Dataset: satellite-sea-ice-thickness [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Suitability of satellite sea ice thickness data for studying climate change > ℹ If you want to know more > Key resources
---
Introductory sea ice materials:
- [Role of sea ice in the climate](https://marine.copernicus.eu/explainers/why-ocean-important/sea-ice)
- [Sea ice as an indicator of climate change](https://climate.copernicus.eu/climate-indicators/sea-ice#)
- [Observing sea ice with satellites](https://www.metoffice.gov.uk/research/climate/cryosphere-oceans/sea-ice/measure)

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: "Suitability of satellite sea ice thickness data for studying climate change"
Dataset: satellite-sea-ice-thickness [CDS]
Aspect: trend-assessment_q01  |  Category: Satellite_ECVs
Section: Suitability of satellite sea ice thickness data for studying climate change > ℹ If you want to know more > References
---
1. Tilling, R. L., Ridout, A., & Shepherd, A. (2018). Estimating Arctic sea ice thickness and volume using CryoSat-2 radar altimeter data. Advances in Space Research, 62(6), 1203-1225, [ https://doi.org/10.1016/j.asr.2017.10.051 ](https://doi.org/10.1016/j.asr.2017.10.051).

2. Müller, F. L., Paul, S., Hendricks, S., and Dettmering, D. (2023). Monitoring Arctic thin ice: a comparison between CryoSat-2 SAR altimetry data and MODIS thermal-infrared imagery. The Cryosphere, 17, 809–825, [ https://doi.org/10.5194/tc-17-809-2023 ](https://doi.org/10.5194/tc-17-809-2023).

3. Rampal, P., J. Weiss, and D. Marsan (2009). Positive trend in the mean speed and deformation rate of Arctic sea ice, 1979–2007, J. Geophys. Res., 114, C05013, [ https://doi.org/10.1029/2008JC005066 ](https://doi.org/10.1029/2008JC005066).


EQC Quality Assessment: "Long-term global Eddy Kinetic Energy trends from satellite observations"
Dataset: satellite-sea-level-global [CDS]
Aspect: consistency_q01  |  Category: Satellite_ECVs
Section: Long-term global Eddy Kinetic Energy trends from satellite observations
---
Production date: 4-11-2025

Produced by: Joan Armajach and Blanca Fernández-Álvarez - IMEDEA (CSIC-UIB) [[webpage]](https://imedea.uib-csic.es/)


EQC Quality Assessment: "Long-term global Eddy Kinetic Energy trends from satellite observations"
Dataset: satellite-sea-level-global [CDS]
Aspect: consistency_q01  |  Category: Satellite_ECVs
Section: Long-term global Eddy Kinetic Energy trends from satellite observations > Quality assessment questions
---
* **Can we assess the long-term variability of global ocean Eddy Kinetic Energy using satellite altimetry?**

Global ocean circulation is both a cause and consequence of fluid interactions occurring across a wide range of spatial scales, from millimetres to more than 10,000 km [[1]](https://doi.org/10.1146/annurev.fluid.40.111406.102139). For ocean circulation, most of the available energy is expressed as kinetic energy (KE), which is a suitable index for measuring the intensity of ocean currents [[2]](https://doi.org/10.1126/sciadv.aax7727). Mesoscale variability, which ranges from tens to hundreds of kilometers depending on latitude [[3]](https://doi.org/10.1175/1520-0485%281998%29028<0433:GVOTFB>2.0.CO;2), contains nearly all of the ocean’s KE and represents the dominant signal in ocean circulation [[4]](https://doi.org/10.1029/2005GL024633). About 90% of the total KE is associated with the mesoscale activity, called Eddy Kinetic Energy (EKE) [[1](https://doi.org/10.1146/annurev.fluid.40.111406.102139), [5](https://doi.org/10.1038/s41598-025-06149-9)]. Meanders, eddies, fronts and jets are examples of mesoscale features that contribute a large part of the transport of heat, mass and chemical constituents in seawater [[6]](https://doi.org/10.1029/2007GL030812). Consequently, the dynamics of mesoscale features has a notable impact on the surface circulation and oceanic biogeochemistry, spanning local and global scales [[7]](https://doi.org/10.1175/JTECH-D-17-0010.1). To study the evolution of the EKE, gridded satellite sea level anomaly (SLA) products are widely used [[8]](https://doi.org/10.3389/fmars.2019.00703). Over the last two decades, satellite altimetry has significantly improved our ability to observe and understand ocean circulation at the mesoscale, providing global, high-resolution, and regular monitoring capabilities [[9](https://doi.org/10.1016/j.asr.2021.01.022), [10](https://doi.org/10.1016/j.asr.2011.09.033)]. At present, over 30 years of altimetric EKE time series are available, and several studies have reported a strengthening trend per decade in some energetic regions (e.g., [[5](https://doi.org/10.1038/s41598-025-06149-9), [11](https://doi.org/10.5194/egusphere-2025-4651), [12](https://doi.org/10.1038/s41558-021-01006-9)]). In long-term studies from satellite observations, we need to consider that gridded energy levels can vary depending on the data processing and the number of the altimeter missions [[13]](https://doi.org/10.1007/s10712-023-09778-9). As highlighted in [[13]](https://doi.org/10.1007/s10712-023-09778-9), a consistent sampling over time from the 2-satellite configuration is recommended for the evaluation of long-term EKE.

This notebook aims to assess the performance of sea level data from satellite observations to estimate the global EKE trends over 1993-2022, following [Barceló-Llull et al. (2025)](https://doi.org/10.1038/s41598-025-06149-9).


EQC Quality Assessment: "Long-term global Eddy Kinetic Energy trends from satellite observations"
Dataset: satellite-sea-level-global [CDS]
Aspect: consistency_q01  |  Category: Satellite_ECVs
Section: Long-term global Eddy Kinetic Energy trends from satellite observations > Quality assessment statement
---
These are the key outcomes of this assessment

* At the global level, mesoscale activity has intensified over the last decade. Most of this strengthening is consistently concentrated in regions characterized by high Eddy Kinetic Energy (EKE) in both the vDT2021 and vDT2024 datasets.

* When comparing the sea level products distributed through the Climate Data Store (CDS), the vDT2021 dataset produces higher EKE both in the global ocean and in high-EKE regions throughout the studied period. Nevertheless, in regions such as the Kuroshio Extension (KExt), these differences between versions are much smaller. This demonstrates that a two-satellite constellation can properly capture mesoscale activity. A constellation with a stable number of satellites ensures the long-term stability of the data record, as is the case for this product, making it a suitable tool for this type of study.

* In general, we recommend using the vDT2024 version, as it incorporates new input L2P (Level-2 Plus) altimeter standards compared to the older version (vDT2021). The L2P products serve as the main input for the altimeter-derived sea level production system, providing the necessary information to compute the along-track Sea Level Anomalies (SLA), while applying the same updated corrections and models for the altimeter missions.
```


EQC Quality Assessment: "Long-term global Eddy Kinetic Energy trends from satellite observations"
Dataset: satellite-sea-level-global [CDS]
Aspect: consistency_q01  |  Category: Satellite_ECVs
Section: Long-term global Eddy Kinetic Energy trends from satellite observations > Methodology
---
Satellite Altimerty based sea level datasets are distributed by the [Copernicus Marine Environment Monitoring Service (CMEMS)](https://marine.copernicus.eu/) and the [Copernicus Climate Change Service (C3S)](https://climate.copernicus.eu/). In this assessment, we use [the Sea level gridded data from satellite observations](https://cds.climate.copernicus.eu/datasets/satellite-sea-level-global?tab=overview) provided by the [CDS](https://cds.climate.copernicus.eu/). This product is designed for climate applications and is based on a consistent and stable altimeter constellation to ensure the long-term stability of the ocean observing system. The constellation of the C3S product comprises more than 10 satellites, configured to ensure that two altimeters are always active. Of the satellites, one is always the active reference altimetry mission. Although there are changes over time, each replacement mission follows the same orbit, ensuring consistency. The other, known as the secondary mission, is a complementary satellite that provides significant information for estimating mesoscale signals. All the necessary information can be found in the [Product User Guide and Specification (PUGS)](https://confluence.ecmwf.int/display/CKB/Sea+Level+version+DT2024%3A+Product+User+Guide+and+Specification#SeaLevelversionDT2024:ProductUserGuideandSpecification-section4.2.2).

As previously mentioned, we follow the same methodology as in [[5]](https://doi.org/10.1038/s41598-025-06149-9) to estimate EKE time series and trends over the global ocean. In addition, we quantify EKE in regions of high mesoscale activity, as performed in that study. The authors used the vDT2018 and vDT2021 two-satellite products from C3S to compare them with the vDT2021 all-satellite product provided by CMEMS. The latter uses all available satellites, ranging from 2 to 7 over the altimetric period.

In this study, the vDT2024 version of the satellite gridded sea level observations available in the Climate Data Store is compared with the vDT2021, in order to evaluate how the new version resolves the EKE relative to the previous one. The TOPEX-A instrument drift correction for 1993-1998, which has been quantified in many studies (e.g., [[14]](https://doi.org/10.1038/NCLIMATE2635)), has not yet been computed in the vDT2024 data. In contrast, the vDT2021 product implements this correction as a separate variable (not directly included in the SLA estimate).

The analysis and results are organised in the following steps, which are detailed in the sections below:

**[](section-1)**
 * Set up the python environment and import required libraries
 * Define the startup parameters
 * Define request for satellite altimetry, using both vDT2021 and vDT2024 datasets available from CDS

**[](section-2)**

**[](section-3)**

**[](section-4)**

**[](section-5)**
 * High EKE regions
 * Area-weighted mean EKE time series
 * EKE trends


EQC Quality Assessment: "Long-term global Eddy Kinetic Energy trends from satellite observations"
Dataset: satellite-sea-level-global [CDS]
Aspect: consistency_q01  |  Category: Satellite_ECVs
Section: Long-term global Eddy Kinetic Energy trends from satellite observations > Analysis and results > 1. Data selection and setup > Define startup parameters
---
For this study, we select the period from 1993 to 2022. Moreover, we apply a mask to include only latitudes between 65°S and 65°N, ensuring that satellite observations remain consistent and are not affected by sea ice.

Global region


EQC Quality Assessment: "Long-term global Eddy Kinetic Energy trends from satellite observations"
Dataset: satellite-sea-level-global [CDS]
Aspect: consistency_q01  |  Category: Satellite_ECVs
Section: Long-term global Eddy Kinetic Energy trends from satellite observations > Analysis and results > 1. Data selection and setup > Define data request for satellite altimetry (vDT2021 and vDT2024)
---
Here, we define the data request for the global gridded daily sea level products for each version (vDT2021 and vDT2024) using the [CDS API client](https://cds.climate.copernicus.eu/how-to-api).

(section-2)=


EQC Quality Assessment: "Long-term global Eddy Kinetic Energy trends from satellite observations"
Dataset: satellite-sea-level-global [CDS]
Aspect: consistency_q01  |  Category: Satellite_ECVs
Section: Long-term global Eddy Kinetic Energy trends from satellite observations > Analysis and results > 2. Eddy Kinetic Energy (EKE) computation
---
To compute EKE, we apply the specific formula:

$$
EKE = \frac{1}{2} (u_a^2 + v_a^2) \quad \text{(cm² s⁻²)}
$$

where $u_a^2$ and $v_a^2$ refer to the zonal and meridional components of the geostrophic velocity anomalies, respectively. These variables are derived from the gridded SLA field. The computation is based on a 9-point stencil width [[15]](https://doi.org/10.1029/2011JC007367) for latitudes outside the ±5°N band. In the equatorial band, the Lagerloef method [[16]](https://doi.org/10.1029/1999JC900197) is applied, using the β plane approximation.

In this part, we download the datasets according to the request, integrating the function that computes EKE once all the data are available. Chunks are necessary to manage large volumes of information. Finally, we concatenate the EKE data along the dimension "version".

```text
version='vdt2021'
```

```text
100%|██████████| 360/360 [02:10<00:00,  2.77it/s]
```

```text
version='vdt2024'
```

```text
100%|██████████| 360/360 [01:55<00:00,  3.13it/s]
```

(section-3)=


EQC Quality Assessment: "Long-term global Eddy Kinetic Energy trends from satellite observations"
Dataset: satellite-sea-level-global [CDS]
Aspect: consistency_q01  |  Category: Satellite_ECVs
Section: Long-term global Eddy Kinetic Energy trends from satellite observations > Analysis and results > 3. Definition of high EKE regions
---
As described in [[5]](https://doi.org/10.1038/s41598-025-06149-9), specific areas with high mesoscale activity due to their ocean dynamics are referred to as high EKE regions. To identify these high-intensity regions, the 90th spatial percentile of the mean EKE over the full period (1993-2022) is computed.

Temporal mean of EKE
Define high EKE regions (90th percentile)

Once we have identified the areas with high EKE activity, we define these regions using the latitude and longitude bounds for each region. These regions are: Brazil-Malvinas Confluence (BMC), Loop Current (LC), Gulf Stream (GS), Great Whirl and Socotra Eddy (GWSE), Agulhas Current (AC), Kuroshio Extension (KExt), and East Australian Current (EAC).

For the regions with high EKE, we apply a function that fills holes, removes small regions using a threshold, and smooths contours. This results in well-defined regions and the minimisation of the spurious inclusion of small patches.

We create a dataset with the masks of all individual high EKE regions, previously defined as "regions". First, we generate a binary global mask based on the mean EKE, where values of 1 mean that the threshold (90th percentile) is exceeded, and values of 0 represent otherwise. Once done, we extract the high EKE regions and apply the smoothing function. Then, we concatenate all the regional masks along the dimension named "region" to differentiate each one.

Additionally, we integrate new masks, one composed of all high EKE regions combined (named "high EKE"), another representing the global mask without NaN values of EKE (named "no ice"), and finally a mask representing the tropical band (named "tropical"), excluding the regions that are already included in "high EKE" mask.

Global mask (1 for high EKE, 0)
All individual high EKE regions
All high EKE regions combined ('high EKE') and global ('no ice')
Tropical mask

(section-4)=


EQC Quality Assessment: "Long-term global Eddy Kinetic Energy trends from satellite observations"
Dataset: satellite-sea-level-global [CDS]
Aspect: consistency_q01  |  Category: Satellite_ECVs
Section: Long-term global Eddy Kinetic Energy trends from satellite observations > Analysis and results > 4. EKE time series and trends computation
---
In this section, we calculate the area-weighted mean for the spatial averages using latitude weighting. This process is applied to all the masks.

Compute time series of EKE for all masks

Here, we define the regions used in the test (no ice, high EKE, KExt, and GS) and the dictionaries to store the original time series and a 12-month rolling mean over a continuous period to smooth fluctuations in the data.

Regions for the test
12-month rolling mean
Store time series in dictionaries

```text
----------------
no ice
----------------

----------------
high EKE
----------------

----------------
KE
----------------

----------------
GS
----------------
```

For the computation of EKE trends, we implement the Theil-Sen estimator, a non-parametric method for fitting a line to sample points. This regression algorithm is more robust to outliers compared to ordinary least-squares regression, which is sensitive to them. To assess the significance of trends, we use the Mann-Kendall test. However, the presence of serial correlation in time series can affect the results [[17]](https://doi.org/10.1023/B:WARM.0000043140.61082.60). Therefore, we employ the modified Mann-Kendall test proposed by [[17]](https://doi.org/10.1023/B:WARM.0000043140.61082.60), which accounts for this autocorrelation.

Furthermore, we convert the trends, initially in cm² s⁻² month⁻¹ to cm² s⁻² year⁻¹ using a factor to facilitate the comparison of the results.

Function to compute trends (Mann-Kendall test)
Multply by the factor 12 months to convert trends per month to trends per year

In this case, we calculate the trends over different periods of the EKE time series, starting each trend in a different year between 1993 and 2013 (inclusive) and ending in the last year of the study (2022). The MK test is applied to each EKE time series for every region and version. As before, we create new dictionaries to store all trends and p-values.

Years for the test
Updated dictionary keys
Lists to save results for high EKE regions, global ocean, Kuroshio Extension (KExt) and Gulf Stream (GS)
Global ocean
High EKE regions
Kuroshio Extension (KExt)

```text
1993

----------------
no ice
----------------
----------------
high EKE
----------------
----------------
KE
----------------
----------------
GS
----------------

1994

----------------
no ice
----------------
----------------
high EKE
----------------
----------------
KE
----------------
----------------
GS
----------------

1995

----------------
no ice
----------------
----------------
high EKE
----------------
----------------
KE
----------------
----------------
GS
----------------

1996

----------------
no ice
----------------
----------------
high EKE
----------------
----------------
KE
----------------
----------------
GS
----------------

1997

----------------
no ice
----------------
----------------
high EKE
----------------
----------------
KE
----------------
----------------
GS
----------------

1998

----------------
no ice
----------------
----------------
high EKE
----------------
----------------
KE
----------------
----------------
GS
----------------

1999

----------------
no ice
----------------
----------------
high EKE
----------------
----------------
KE
----------------
----------------
GS
----------------

2000

----------------
no ice
----------------
----------------
high EKE
----------------
----------------
KE
----------------
----------------
GS
----------------

2001

----------------
no ice
----------------
----------------
high EKE
----------------
----------------
KE
----------------
----------------
GS
----------------

2002

----------------
no ice
----------------
----------------
high EKE
----------------
----------------
KE
----------------
----------------
GS
----------------

2003

----------------
no ice
----------------
----------------
high EKE
----------------
----------------
KE
----------------
----------------
GS
----------------

2004

----------------
no ice
----------------
----------------
high EKE
----------------
----------------
KE
----------------
----------------
GS
----------------

2005

----------------
no ice
----------------
----------------
high EKE
----------------
----------------
KE
----------------
----------------
GS
----------------

2006

----------------
no ice
----------------
----------------
high EKE
----------------
----------------
KE
----------------
----------------
GS
----------------

2007

----------------
no ice
----------------
----------------
high EKE
----------------
----------------
KE
----------------
----------------
GS
----------------

2008

----------------
no ice
----------------
----------------
high EKE
----------------
----------------
KE
----------------
----------------
GS
----------------

2009

----------------
no ice
----------------
----------------
high EKE
----------------
----------------
KE
----------------
----------------
GS
----------------

2010


EQC Quality Assessment: "Long-term global Eddy Kinetic Energy trends from satellite observations"
Dataset: satellite-sea-level-global [CDS]
Aspect: consistency_q01  |  Category: Satellite_ECVs
Section: Long-term global Eddy Kinetic Energy trends from satellite observations > Analysis and results > 5. Plotting and discussion of results > High EKE regions
---
Here, we prepare the high EKE and tropical masks as binary masks for proper visualisation. For the tropical mask, we apply "add_cyclic_point" to avoid discontinuity at 180° longitude. We also exclude these masks when graphing to represent only the individual high EKE regions.

Define high EKE regions


EQC Quality Assessment: "Long-term global Eddy Kinetic Energy trends from satellite observations"
Dataset: satellite-sea-level-global [CDS]
Aspect: consistency_q01  |  Category: Satellite_ECVs
Section: Define tropical region (reindexing to avoid discontinuity at 180° when plotting)
---
Define a mask with only the individual high EKE regions

Once the masks have been treated, we display the corresponding graphs in a layout of two subplots.

General parameters
Mean eke (Subplot A)
Tropical band
High EKE regions
Map mean EKE
High EKE regions (Subplot B)

This figure shows a global map of the temporal mean EKE at each grid point over 1993-2022, using only the vDT2024 dataset. The green contours delimit the regions with high EKE activity (over the 90th percentile), and the blue line marks the tropical band. These areas contain most of the mesoscale activity, which averages zero in the remainder part of the globe.

In the other global map, we represent the exact high EKE regions (covering 5% of the global ocean) along with their corresponding acronyms. As a first observation, the largest regions (in terms of area) with high mesoscale activity occur in AC, KExt, and GS. In contrast, LC and EAC are the smallest regions.


EQC Quality Assessment: "Long-term global Eddy Kinetic Energy trends from satellite observations"
Dataset: satellite-sea-level-global [CDS]
Aspect: consistency_q01  |  Category: Satellite_ECVs
Section: Define tropical region (reindexing to avoid discontinuity at 180° when plotting) > Area-weighted mean EKE time series
---
In this section, we plot the EKE time series (in cm² s⁻²) over the global ocean and the high EKE regions, including the Kuroshio Extension and the Gulf Stream, covering the altimeter period 1993 to 2022.

General parameters

##### Global region

Global ocean and high EKE

The two subplots show the evolution of EKE in the global and high EKE regions. The color blue represents the vDT2024 version and the color red the vDT2021 version. The thinner lines show the raw (untreated) data, whilst the thicker lines indicate the data after applying an annual rolling mean. Regarding the results, notable differences are observed when comparing the two versions. For both the global ocean and high EKE regions, vDT2021 exhibits higher values throughout the entire period than vDT2024. One possible reason is the methodology used in producing each version, including the metrics, procedures, and equations implemented, resulting in more accurate data in the current version (vDT2024), as mentioned in the [Algorithm Theoretical Basis Document](https://dast.copernicus-climate.eu/documents/satellite-sea-level/vDT2024/C3S2-D312b-WP2-FDDP-SL-v3.0-202411-ATBD-of-vDT2024-v1_Final.pdf). For the global region, the rolling mean values are around 190-250 cm² s⁻² approximately. However, focusing on the high EKE regions, the values increase markedly, reaching up to 1150 cm² s⁻². These regions, as observed, demonstrate high mesoscale activity.

##### Mesoscale High-Activity Regions

Kuroshio Extension and Gulf Stream

Following [[5]](https://doi.org/10.1038/s41598-025-06149-9), two specific areas were selected and compared: the KExt and the GS. Similarly to the previous plot, we have two timeseries for each version (red for the vDT2021 and blue for the vDT2024), with the older version showing higher energy than the newer one. The difference is larger in the GS than in the KExt. When we compare the energy in both areas, both versions point towards an increase in EKE in the KExt. Both versions also capture the variability in the timeseries, with higher seasonal variability in the GS.


EQC Quality Assessment: "Long-term global Eddy Kinetic Energy trends from satellite observations"
Dataset: satellite-sea-level-global [CDS]
Aspect: consistency_q01  |  Category: Satellite_ECVs
Section: Define tropical region (reindexing to avoid discontinuity at 180° when plotting) > EKE trends
---
For these plots, we first defined a specific marker and text style to distinguish non-significant trends in the bar plots. Non-significant trends are shown in italics, with oblique grey hatching.

Marker (hatching) and text style (italic) for non-significant trends
Global ocean
High EKE regions
Kuroshio Extension (KExt)

##### Global region

Global ocean
High EKE regions

In this case, we can observe the EKE trends over different periods, progressively shortening the intervals to study the trends. For the global ocean, the trends are larger over shorter timescales, reaching a maximum trend of 0.87 cm² s⁻² year⁻¹ (vDT2024) and 1.14 cm² s⁻² year⁻¹ (vDT2021) from 2012 to 2022. Looking in more detail, the initial trends computed with a starting year prior to 2000 show a slight decrease, resulting in non-significant trends for both datasets and even negative trends in the case of vDT2024, for which, if we consider the whole period, the EKE trend is not significant (whereas it is for vDT2021). This behaviour changes drastically after 2000, with a constant increase, revealing an intensification of the mesoscale activity globally.

For the high EKE regions, we can clearly see a substantial increase throughout the full period for both datasets. In this case, all trends are significant, although vDT2021 displays larger values than vDT2024. For the older version, the trend over 2012-2022 is 6.1 times larger than the trend during 1993-2022, increasing from 2.58 cm² s⁻² year⁻¹ to 15.75 cm² s⁻² year⁻¹. However, for the latest version, the trend is 6.5 times larger, from 2.29 cm² s⁻² year⁻¹ to 14.89 cm² s⁻² year⁻¹. This suggests that over the last two decades, EKE activity has become stronger and more energetic, especially in the high EKE regions, with a particularly high rate of increase in the most recent periods.

In [[5]](https://doi.org/10.1038/s41598-025-06149-9), the vDT2021 all-sat product from CMEMS is used to compare with the vDT2021 two-sat product from C3S. That study suggests that differences in trends between the two products are partly related to the number of satellites included in the all-sat product.

##### Mesoscale High-Activity Regions

Kuroshio Extension

Here, we focus on the regions where the mesoscale activity exhibits more significant positive EKE trends. This intensification is concentrated mainly in the Kuroshio Extension (KExt) and the Gulf Stream (GS). Regarding the KExt region, the computed trends show a progressive increase for both datasets. The vDT2021 presents higher values than vDT2024, but these differences are small compared with the other regions. Only the trend over 1999-2022 is not statistically significant for either version. As mentioned before, this fast increase occurs primarily in the last decade. For the period 2013-2022, the EKE trend for vDT2024 is 61.65 cm² s⁻² year⁻¹ and for vDT2021 is 61.99 cm² s⁻² year⁻¹, while over the entire 30-year period the trends are 8.23 cm² s⁻² year⁻¹ and 8.69 cm² s⁻² year⁻¹, respectively. This region is crucial for ocean circulation and mid-latitudes air-sea interactions and is one of the major western boundary currents [[18]](https://doi.org/10.1016/j.dynatmoce.2024.101497). As reported by [[19]](https://doi.org/10.1007/s10236-023-01565-9), the decadal variability of EKE in this region is linked to the Pacific Decadal Oscillation (PDO).


EQC Quality Assessment: "Long-term global Eddy Kinetic Energy trends from satellite observations"
Dataset: satellite-sea-level-global [CDS]
Aspect: consistency_q01  |  Category: Satellite_ECVs
Section: Define tropical region (reindexing to avoid discontinuity at 180° when plotting) > EKE trends
---
]](https://doi.org/10.1007/s10236-023-01565-9), the decadal variability of EKE in this region is linked to the Pacific Decadal Oscillation (PDO).

In the Gulf Stream (GS), the general trend shows a gradual increase. Over the 30 years, the EKE trends are 2.12 cm² s⁻² year⁻¹ for vDT2024 and 2.51 cm² s⁻² year⁻¹ for vDT2021, both of which are statistically non-significant. In the most recent decade, the trends have increased notably, reaching 18.09 cm² s⁻² year⁻¹ and 20.33 cm² s⁻² year⁻¹, respectively. This corresponds to an increase in the EKE trend of 8.5 and 8.1 times faster than over the entire 30-year period. The GS plays an important role due to its contribution to the Atlantic Meridional Overturning Circulation (AMOC) [[20]](https://doi.org/10.1002/2015RG000493). [[21]](https://doi.org/10.1175/2010JCLI3310.1) reported that the path of the GS is associated with the strength of the AMOC.