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).

[1] To examine the suitability of GPS radio occultation (RO) observations as a climate benchmark data set, this study aims at quantifying the structural uncertainty in GPS RO-derived vertical profiles of refractivity and measured refractivity trends obtained from atmospheric excess phase processing and inversion procedures. Five years (2002)(2003)(2004)(2005)(2006) of monthly mean climatologies (MMC) of retrieved refractivity from the experiment aboard the German satellite CHAMP generated by four RO operational centers were compared. Results show that the absolute values of fractional refractivity anomalies among the centers are, in general, 0.2% from 8 to 25 km altitude. The median absolute deviations among the centers are less than 0.2% globally. Because the differences in fractional refractivity produced by the four centers are, in general, unchanging with time, the uncertainty of the trend for fractional refractivity anomalies among centers is ±0.04% per 5 years globally. The primary cause of the trend uncertainty is due to different quality control methods used by the four centers, which yield different sampling errors for different centers. We used the National Centers for Environmental Prediction reanalysis in the same period to estimate sampling errors. After removing the sampling errors, the uncertainty of the trend for fractional refractivity anomalies among centers is between À0.03 and 0.01% per 5 years. Thus 0.03% per 5 years can be considered an upper bound in the processing scheme-induced uncertainty for global refractivity trend monitoring. Systematic errors common to all centers are not discussed in this article but are generally believed to be small.

[1] To examine the claim that Global Positioning System (GPS) radio occultation (RO) data are useful as a benchmark data set for climate monitoring, the structural uncertainties of retrieved profiles that result from different processing methods are quantified. Profile-to-profile comparisons of CHAMP (CHAllenging Minisatellite Payload) data from January 2002 to August 2008 retrieved by six RO processing centers are presented. Differences and standard deviations of the individual centers relative to the inter-center mean are used to quantify the structural uncertainty. Uncertainties accumulate in derived variables due to propagation through the RO retrieval chain. This is reflected in the inter-center differences, which are small for bending angle and refractivity increasing to dry temperature, dry pressure, and dry geopotential height. The mean differences of the time series in the 8 km to 30 km layer range from À0.08% to 0.12% for bending angle, À0.03% to 0.02% for refractivity, À0.27 K to 0.15 K for dry temperature, À0.04% to 0.04% for dry pressure, and À7.6 m to 6.8 m for dry geopotential height. The corresponding standard deviations are within 0.02%, 0.01%, 0.06 K, 0.02%, and 2.0 m, respectively. The mean trend differences from 8 km to 30 km for bending angle, refractivity, dry temperature, dry pressure, and dry geopotential height are within AE0.02%/5 yrs, AE0.02%/5 yrs, AE0.06 K/5 yrs, AE0.02%/5 yrs, and AE2.3 m/5 yrs, respectively. Although the RO-derived variables are not readily traceable to the international system of units, the high precision nature of the raw RO observables is preserved in the inversion chain.

High quality observations of the atmosphere are particularly required for monitoring global climate change. Radio occultation (RO) data, using Global Navigation Satellite System (GNSS) signals, are well suited for this challenge. The special climate utility of RO data arises from their long-term stability due to their self-calibrated nature. The German research satellite CHAllenging Minisatellite Payload for geoscientific research (CHAMP) continuously records RO profiles since August 2001 providing the first opportunity to create RO based climatologies for a multi-year period of more than 5 years. A period of missing CHAMP data from July 3, 2006 to August 8, 2006 can be bridged with RO data from the GRACE satellite (Gravity Recovery and Climate Experiment). We have built seasonal and zonal mean climatologies of atmospheric (dry) temperature, microwave refractivity, geopotential height and pressure with 10°lat-itudinal resolution. We show representative results with focus on dry temperatures and compare them with analysis data from the European Centre for Medium-Range Weather Forecasts (ECMWF). Although we have available only about 150 CHAMP profiles per day (compared to millions of data entering the ECMWF analyses) the overall agreement between 8 and 30 km altitude is in general very good with systematic differences \0.5 K in most parts of the domain. Pronounced systematic differences (exceeding 2 K) in the tropical tropopause region and above Antarctica in southern winter can almost entirely be attributed to errors in the ECMWF analyses. Errors resulting from uneven sampling in space and time are a potential error source for single-satellite climatologies. The average CHAMP sampling error for seasonal zonal means is \0.2 K, higher values occur in restricted regions and time intervals which can be clearly identified by the sampling error estimation approach we introduced (which is based on ECMWF analysis fields). The total error of this new type of temperature climatologies is estimated to be \0.5 K below 30 km. The recently launched Taiwan/U.S. FORMOSAT-3/COSMIC constellation of 6 RO satellites started to provide thousands of RO profiles per day, but already now the single-satellite CHAMP RO climatologies improve upon modern operational climatologies in the upper troposphere-lower stratosphere and can act as absolute reference climatologies for validation of more bias-sensitive climate datasets and models.

.[1] Observation of the atmospheric climate and detection of changes require high quality data. Radio Occultation (RO) using Global Positioning System (GPS) signals is based on time measurements with precise atomic clocks. It provides a long-term stable and consistent data record with global coverage and favorable error characteristics. Highest quality and vertical resolution is given in the upper troposphere and lower stratosphere (UTLS). RO data exist from the GPS/Met mission within 1995-1997, and continuous observations are available since 2001. We give a review on studies using RO data for climate monitoring and change detection in the UTLS and discuss RO characteristics and error estimates, climate change indicators, trend detection, and comparison to conventional upper-air data. These studies showed that RO parameters cover the whole UTLS with useful indicators of climate change, being most robust in the tropics. Refractivity is most sensitive in the lower stratosphere (LS) and tropopause region, pressure/geopotential height and temperature over the UTLS region. An emerging climate change signal in the RO record can be detected for geopotential height of pressure levels and for temperature, reflecting warming of the troposphere and cooling of the LS. The results are in agreement with trends in radiosonde and ERA-Interim records. Climate model trends basically agree as well but they show less warming/cooling contrast across the tropical tropopause. (Advanced) Microwave Sounding Unit LS bulk temperature anomalies show significant differences to RO. Overall, the quality of RO climate records is suitable to fulfill the requirements of a global climate change monitoring system.

Global Positioning System (GPS) radio occultation (RO) has provided continuous observations of the Earth's atmosphere since 2001 with global coverage, all-weather capability, and high accuracy and vertical resolution in the upper troposphere and lower stratosphere (UTLS). Precise time measurements enable long-term stability but careful processing is needed. Here we provide climate-oriented atmospheric scientists with multicenter-based results on the long-term stability of RO climatological fields for trend studies. We quantify the structural uncertainty of atmospheric trends estimated from the RO record, which arises from current processing schemes of six international RO processing centers, DMI Copenhagen, EUM Darmstadt, GFZ Potsdam, JPL Pasadena, UCAR Boulder, and WEGC Graz. Monthly-mean zonal-mean fields of bending angle, refractivity, dry pressure, dry geopotential height, and dry temperature from the CHAMP mission are compared for September 2001 to September 2008. We find that structural uncertainty is lowest in the tropics and mid-latitudes (50° S to 50° N) from 8 km to 25 km for all inspected RO variables. In this region, the structural uncertainty in trends over 7 yr is <0.03% for bending angle, refractivity, and pressure, <3 m for geopotential height of pressure levels, and <0.06 K for temperature; low enough for detecting a climate change signal within about a decade. Larger structural uncertainty above about 25 km and at high latitudes is attributable to differences in the processing schemes, which undergo continuous improvements. Though current use of RO for reliable climate trend assessment is bound to 50° S to 50° N, our results show that quality, consistency, and reproducibility are favorable in the UTLS for the establishment of a climate benchmark record

[1] Global Navigation Satellite System-based radio occultation (RO) measurements promise to become a valuable observational basis for climate research, numerical weather prediction, and atmospheric process studies, thanks to their unique combination of global coverage, high accuracy and vertical resolution, and long-term stability. Concerning the quality of the RO-derived atmospheric profiles, performance simulation studies and first data analysis results from the current CHAMP satellite mission are encouraging but also reveal weaknesses of present RO retrieval chains at high altitudes (above 30 km). This study aims at providing, first, understanding of these weaknesses and, second, mitigation by an advanced retrieval scheme. We first evaluated present state-of-the-art high-altitude RO retrieval algorithms. We found clear superiority for using statistical optimization involving background information over using exponential extrapolation and a sensitivity of RO retrieval products to biases in background information calling for sensible bias mitigation. Exploiting these findings, an advanced high-altitude retrieval scheme is presented, which focuses on minimizing residual retrieval biases in the upper stratosphere and thereby on optimizing the climate monitoring utility of retrieved profiles. Applied to a large ensemble of simulated occultation events, the advanced scheme proved to be effective. The scheme is currently under evaluation with real data from the CHAMP mission. It will then serve as part of a processing chain generating RO-based global climatologies of refractivity, geopotential height, temperature, and humidity based on RO data from CHAMP, SAC-C, GRACE and other future satellites carrying RO instruments.

[1] Radio occultation (RO) observations using the Global Navigation Satellite System (GNSS) globally provide high quality atmospheric data which can support the advancement of climate monitoring and modeling as well as the improvement of numerical weather prediction. In order to make optimal use of the data, e.g., via data assimilation systems, the characterization of measurement errors is of importance. Within this context we present results of an empirical error analysis based on quasi-realistically simulated GNSS RO data. The study is based on an end-to-end forward-inverse simulation involving (1) modeling of the neutral atmosphere and ionosphere, (2) simulation of RO observations, (3) forward modeling of excess phase observables including realistic observation system error modeling, and (4) retrieval of atmospheric parameters. Occultation observations were simulated for one day from which an ensemble of 300 occultation events was chosen, with 100 events in each of three latitude bands (low, middle, high). Phase path profiles were computed showing a realistic rms error of the ionosphere corrected phase paths of 2-3 mm at mesospheric and stratospheric heights at 10 Hz sampling rate. Atmospheric profiles were retrieved by applying a dry air retrieval in the stratosphere and an optimal estimation retrieval in the troposphere. The retrieved profiles were referenced to the ''true'' co-located ones of the analysis field of the European Centre for Medium-range Weather Forecasts (ECMWF). We empirically estimated bias profiles and covariance matrices (standard deviations and correlation functions) for the retrieval products such as bending angle, refractivity, pressure, geopotential height, temperature, and specific humidity. Results include the refractivity error showing a relative standard deviation of 0.1-0.75% and a relative bias of <0.1% at 5-40 km height. Temperature exhibits a standard deviation of 0.2-1 K at 3-31 km height and a bias of <0.1-0.5 K below 33 km and of <0.1 K below 20 km. Simple analytical error covariance formulations are presented for refractivity, as deduced from the empirically estimated covariance matrices. The reasonably realistic error estimates presented are a good basis for further retrieval algorithm improvements and for proper specification of observational errors in data assimilation systems.Citation: Steiner, A. K., and G. Kirchengast (2005), Error analysis for GNSS radio occultation data based on ensembles of profiles from end-to-end simulations,