Abstract. Human-induced atmospheric composition changes cause a radiative imbalance at the top of the atmosphere which is driving global warming. This Earth energy imbalance (EEI) is the most critical number defining the prospects for continued global warming and climate change. Understanding the heat gain of the Earth system – and particularly how much and where the heat is distributed – is fundamental to understanding how this affects warming ocean, atmosphere and land; rising surface temperature; sea level; and loss of grounded and floating ice, which are fundamental concerns for society. This study is a Global Climate Observing System (GCOS) concerted international effort to update the Earth heat inventory and presents an updated assessment of ocean warming estimates as well as new and updated estimates of heat gain in the atmosphere, cryosphere and land over the period 1960–2018. The study obtains a consistent long-term Earth system heat gain over the period 1971–2018, with a total heat gain of 358±37 ZJ, which is equivalent to a global heating rate of 0.47±0.1 W m−2. Over the period 1971–2018 (2010–2018), the majority of heat gain is reported for the global ocean with 89 % (90 %), with 52 % for both periods in the upper 700 m depth, 28 % (30 %) for the 700–2000 m depth layer and 9 % (8 %) below 2000 m depth. Heat gain over land amounts to 6 % (5 %) over these periods, 4 % (3 %) is available for the melting of grounded and floating ice, and 1 % (2 %) is available for atmospheric warming. Our results also show that EEI is not only continuing, but also increasing: the EEI amounts to 0.87±0.12 W m−2 during 2010–2018. Stabilization of climate, the goal of the universally agreed United Nations Framework Convention on Climate Change (UNFCCC) in 1992 and the Paris Agreement in 2015, requires that EEI be reduced to approximately zero to achieve Earth's system quasi-equilibrium. The amount of CO2 in the atmosphere would need to be reduced from 410 to 353 ppm to increase heat radiation to space by 0.87 W m−2, bringing Earth back towards energy balance. This simple number, EEI, is the most fundamental metric that the scientific community and public must be aware of as the measure of how well the world is doing in the task of bringing climate change under control, and we call for an implementation of the EEI into the global stocktake based on best available science. Continued quantification and reduced uncertainties in the Earth heat inventory can be best achieved through the maintenance of the current global climate observing system, its extension into areas of gaps in the sampling, and the establishment of an international framework for concerted multidisciplinary research of the Earth heat inventory as presented in this study. This Earth heat inventory is published at the German Climate Computing Centre (DKRZ, https://www.dkrz.de/, last access: 7 August 2020) under the DOI https://doi.org/10.26050/WDCC/GCOS_EHI_EXP_v2 (von Schuckmann et al., 2020).

Abstract. 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.

Abstract. Human-induced atmospheric composition changes cause a radiative imbalance at the top-of-atmosphere which is driving global warming. This Earth Energy Imbalance (EEI) is a fundamental metric of climate change. Understanding the heat gain of the Earth system from this accumulated heat – and particularly how much and where the heat is distributed in the Earth system – is fundamental to understanding how this affects warming oceans, atmosphere and land, rising temperatures and sea level, and loss of grounded and floating ice, which are fundamental concerns for society. This study is a Global Climate Observing System (GCOS) concerted international effort to update the Earth heat inventory, and presents an updated international assessment of ocean warming estimates, and new and updated estimates of heat gain in the atmosphere, cryosphere and land over the period 1960–2018. The study obtains a consistent long-term Earth system heat gain over the past 58 years, with a total heat gain of 393 ± 40 ZJ, which is equivalent to a heating rate of 0.42 ± 0.04 W m−2. The majority of the heat gain (89 %) takes place in the global ocean (0–700 m: 53 %; 700–2000 m: 28 %; > 2000 m: 8 %), while it amounts to 6 % for the land heat gain, to 4 % available for the melting of grounded and floating ice, and to 1 % for atmospheric warming. These new estimates indicate a larger contribution of land and ice heat gain (10 % in total) compared to previous estimates (7 %). There is a regime shift of the Earth heat inventory over the past 2 decades, which appears to be predominantly driven by heat sequestration into the deeper layers of the global ocean, and a doubling of heat gain in the atmosphere. However, a major challenge is to reduce uncertainties in the Earth heat inventory, which can be best achieved through the maintenance of the current global climate observing system, its extension into areas of gaps in the sampling, as well as to establish an international framework for concerted multi-disciplinary research of the Earth heat inventory. Earth heat inventory is published at DKRZ (https://www.dkrz.de/) under the doi: https://doi.org/10.26050/WDCC/GCOS_EHI_EXP (von Schuckmann et al., 2020).

The ability to find and recognize patterns in high-dimensional geophysical data is fundamental to climate science and critical for meaningful interpretation of weather and climate processes. Archetypal analysis (AA) is one technique that has recently gained traction in the geophysical science community for its ability to find patterns based on extreme conditions. While traditional empirical orthogonal function (EOF) analysis can reveal patterns based on data covariance, AA seeks patterns from the points located at the edges of the data distribution. The utility of any objective pattern method depends on the properties of the data to which it is applied and the choices made in implementing the method. Given the relative novelty of the application of AA in geophysics it is important to develop experience in applying the method. We provide an assessment of the method, implementation, sensitivity, and interpretation of AA with respect to geophysical data. As an example for demonstration, we apply AA to a 39-year sea surface temperature (SST) reanalysis data set. We show that the decisions made to implement AA can significantly affect the interpretation of results, but also, in the case of SST, that the analysis is exceptionally robust under both spatial and temporal coarse-graining.

From time to time atmospheric flows become organized and form coherent long-lived structures. Such structures could be propagating, quasi-stationary, or recur in place. We investigate the ability of Principal Components Analysis (PCA) and Archetypal Analysis (AA) to identify long-lived events, excluding propagating forms. Our analysis is carried out on the Southern Hemisphere mid-tropospheric flow represented by geopotential height at 500hPa (Z500). The leading basis patterns of Z500 for PCA and AA are similar and describe structures representing (or similar to) the Southern Annular Mode (SAM) and Pacific South American (PSA) pattern. Long-lived events are identified here from sequences of 8 days or longer where the same basis pattern dominates for PCA or AA. AA identifies more long-lived events than PCA using this approach. The most commonly occurring long-lived event for both AA and PCA is the annular SAM-like pattern. The second most commonly occurring event is the PSA-like Pacific wavetrain for both AA and PCA. For AA the flow at any given time is approximated as weighted contributions from each basis pattern, which lends itself to metrics for discriminating among basis patterns. These show that the longest long-lived events are in general better expressed than shorter events. Case studies of long-lived events featuring a blocking structure and an annular structure show that both PCA and AA can identify and discriminate the dominant basis pattern that most closely resembles the flow event.