The Earth climate system is out of energy balance, and heat has accumulated continuously over the past decades, warming the ocean, the land, the cryosphere, and the atmosphere. According to the Sixth Assessment Report by Working Group I of the Intergovernmental Panel on Climate Change, this planetary warming over multiple decades is human-driven and results in unprecedented and committed changes to the Earth system, with adverse impacts for ecosystems and human systems. The Earth heat inventory provides a measure of the Earth energy imbalance (EEI) and allows for quantifying how much heat has accumulated in the Earth system, as well as where the heat is stored. Here we show that the Earth system has continued to accumulate heat, with 381±61 ZJ accumulated from 1971 to 2020. This is equivalent to a heating rate (i.e., the EEI) of 0.48±0.1 W m ⁻² . The majority, about 89 %, of this heat is stored in the ocean, followed by about 6 % on land, 1 % in the atmosphere, and about 4 % available for melting the cryosphere. Over the most recent period (2006–2020), the EEI amounts to 0.76±0.2 W m ⁻² . The Earth energy imbalance is the most fundamental global climate indicator that the scientific community and the public can use as the measure of how well the world is doing in the task of bringing anthropogenic climate change under control. Moreover, this indicator is highly complementary to other established ones like global mean surface temperature as it represents a robust measure of the rate of climate change and its future commitment. We call for an implementation of the Earth energy imbalance into the Paris Agreement's Global Stocktake based on best available science. The Earth heat inventory in this study, updated from von Schuckmann et al. (2020), is underpinned by worldwide multidisciplinary collaboration and demonstrates the critical importance of concerted international efforts for climate change monitoring and community-based recommendations and we also call for urgently needed actions for enabling continuity, archiving, rescuing, and calibrating efforts to assure improved and long-term monitoring capacity of the global climate observing system. The data for the Earth heat inventory are publicly available, and more details are provided in Table 4.

A new algorithm for classification of sea ice types on Sentinel-1 Synthetic Aperture Radar (SAR) data using a convolutional neural network (CNN) is presented. The CNN is trained on reference ice charts produced by human experts and compared with an existing machine learning algorithm based on texture features and random forest classifier. The CNN is trained on two datasets in 2018 and 2020 for retrieval of four classes: ice free, young ice, first-year ice and old ice. The accuracy of our classification is 90.5% for the 2018-dataset and 91.6% for the 2020-dataset. The uncertainty is a bit higher for young ice (85%/76% accuracy in 2018/2020) and first-year ice (86%/84% accuracy in 2018/2020). Our algorithm outperforms the existing random forest product for each ice type. It has also proved to be more efficient in computing time and less sensitive to the noise in SAR data. The code is publicly available.

A satellite database including 16 555 satellite images and ice charts displaying the area of Isfjorden, Hornsund, and the Svalbard region has been established with focus on the time period 2000–2014. 3319 manual interpretations of sea ice conditions have been conducted, resulting in two time series dividing the area of Isfjorden and Hornsund into "fast ice" (sea ice attached to the coastline), "drift ice", and "open water". The maximum fast ice coverage of Isfjorden is > 40 % in the periods 2000–2005 and 2009–2011 and stays < 30 % in 2006–2008 and 2012–2014. Fast ice cover in Hornsund reaches > 40 % in all considered years, except for 2012 and 2014, where the maximum stays < 20 %. The mean seasonal cycles of fast ice in Isfjorden and Hornsund show monthly averaged values of less than 1 % between July and November and maxima in March (Isfjorden, 35.7 %) and April (Hornsund, 42.1 %), respectively. A significant reduction of the monthly averaged fast ice coverage is found when comparing the time periods 2000–2005 and 2006–2014. The seasonal maximum decreases from 57.5 to 23.2 % in Isfjorden and from 52.6 to 35.2 % in Hornsund. A new index, called "days of fast ice" (DFI), is introduced for quantification of the interannual variation of fast ice cover, allowing for comparison between different fjords and winter seasons. Considering the time period from 1 March until end of the sea ice season, the mean DFI values for 2000–2014 are 33.1 ± 18.2 DFI (Isfjorden) and 42.9 ± 18.2 DFI (Hornsund). A distinct shift to lower DFI values is observed in 2006. Calculating a mean before and after 2006 yields a decrease from 50 to 22 DFI for Isfjorden and from 56 to 34 DFI for Hornsund. Fast ice coverage generally correlates well with remote-sensing sea surface temperature and in situ air temperature. An increase of autumn ocean heat content is observed during the last few years when the DFI values decrease. The presented sea ice time series can be utilized for various climate effect studies linked to, e.g. glacier dynamics, ocean chemistry, and marine biology.

In this paper, we evaluate the neXtSIM sea ice model with respect to the observed scaling invariance properties of sea ice deformation in the spatial and temporal domains. Using an Arctic setup with realistic initial conditions, state-of-the-art atmospheric reanalysis forcing and geostrophic currents retrieved from satellite data, we show that the model is able to reproduce the observed properties of this scaling in both the spatial and temporal domains over a wide range of scales, as well as their multi-fractality. The variability of these properties during the winter season is also captured by the model. We also show that the simulated scaling exhibits a space–time coupling, a suggested property of brittle deformation at geophysical scales. The ability to reproduce the multi-fractality of this scaling is crucial in the context of downscaling model simulation outputs to infer sea ice variables at the sub-grid scale and also has implications for modeling the statistical properties of deformation-related quantities, such as lead fractions and heat and salt fluxes.

The intensity of a Sentinel-1 Terrain Observation with Progressive Scans synthetic aperture radar image is disturbed by additive thermal noise, particularly in the cross-polarization channel. Although the European Space Agency provides calibrated noise vectors for noise power subtraction, residual noise contributions are significant when considering the relatively narrow backscattering distribution of the cross-polarization channel. In this paper, we investigate the characteristics of noise and propose an efficient method for noise reduction based on a three-step correction process comprised of azimuth descalloping, noise scaling and interswath power balancing, and local residual noise power compensation. The core idea is to find the optimal correction coefficients resulting in the most noise-uncorrelated gentle backscatter profile over a homogeneous region and to combine them with the scalloping gain for a reconstruction of the complete 2-D noise field. Denoising is accomplished by subtracting the reconstructed noise field from the original image. The performance improvement in some applications by adopting the denoising procedure shows the effectiveness of the proposed method.

We present a new brittle rheology and an accompanying numerical framework for large‐scale sea‐ice modeling. This rheology is based on a Bingham‐Maxwell constitutive model and the Maxwell‐Elasto‐Brittle (MEB) rheology, the latter of which has previously been used to model sea ice. The key strength of the MEB rheology is its ability to represent the scaling properties of simulated sea‐ice deformation in space and time. The new rheology we propose here, which we refer to as the brittle Bingham‐Maxwell rheology (BBM), represents a further evolution of the MEB rheology. It is developed to address two main shortcomings of the MEB rheology and numerical implementation we were unable to address previously: excessive thickening of the ice in model runs longer than about one winter and a relatively high computational cost. In the BBM rheology and numerical framework these shortcomings are addressed by demanding that the ice deforms under convergence in a purely elastic manner when internal stresses lie below a given compressive threshold. Numerical performance is improved by introducing an explicit scheme to solve the ice momentum equation. In this paper, we introduce the new rheology and numerical framework. Using an implementation of BBM in version two of the neXtSIM sea‐ice model (neXtSIMv2), we show that it gives reasonable long term evolution of the Arctic sea‐ice cover and very good deformation fields and statistics compared to satellite observations.