We present a self-synchronizing and robust method for comparing the progression of the Covid-19 epidemics among multiple countries. In their growth phase the epidemics show power law rather than exponential law time dependences. They are similar enough for the earlier China outbreak to guide other countries projections. The delayed reaction of European countries is shown to produce a significantly worse outcome compared to China.

Abstract. Ice losses from the Greenland and Antarctic Ice Sheets have accelerated since the 1990s, accounting for a significant increase in global mean sea level. Here, we present a new 29-year record of ice sheet mass balance from 1992 to 2020 from the Ice Sheet Mass Balance Inter-comparison Exercise (IMBIE). We compare and combine 50 independent estimates of ice sheet mass balance derived from satellite observations of temporal changes in ice sheet flow, in ice sheet volume and in Earth’s gravity field. Between 1992 and 2020, the ice sheets contributed 21.0 ± 1.9 mm to global mean sea-level, with the rate of mass loss rising from 105 Gt yr-1 between 1992 and 1996 to 372 Gt yr-1 between 2016 and 2020. In Greenland, the rate of mass loss is 169 ± 9 Gt yr-1 between 1992 and 2020 but there are large inter-annual variations in mass balance with mass loss ranging from 86 Gt yr-1 in 2017 to 444 Gt yr-1 in 2019 due to large variability in surface mass balance. In Antarctica, ice losses continue to be dominated by mass loss from West Antarctica (-82 ± 9 Gt yr-1) and to a lesser extent from the Antarctic Peninsula (-13 ± 5 Gt yr-1). East Antarctica remains close to a state of balance (3 ± 15 Gt yr-1), but is the most uncertain component of Antarctica’s mass balance.

Background Classic epidemic curves – counts of daily events or cumulative events over time –emphasise temporal changes in the growth or size of epidemic outbreaks. Like any graph, these curves have limitations: they are impractical for comparisons of large and small outbreaks or of asynchronous outbreaks, and they do not display the relative growth rate of the epidemic. Our aim was to propose two additional graphical displays for the monitoring of epidemic outbreaks that overcome these limitations. Methods The first graph shows the growth of the epidemic as a function of its size; specifically, the logarithm of new cases on a given day, N(t), is plotted against the logarithm of cumulative cases C(t). Logarithm transformations facilitate comparisons of outbreaks of different sizes, and the lack of a time scale overcomes the need to establish a starting time for each outbreak. Notably, on this graph, exponential growth corresponds to a straight line with a slope equal to one. The second graph represents the logarithm of the relative rate of growth of the epidemic over time; specifically, log10(N(t)/C(t-1)) is plotted against time (t) since the 25th event. We applied these methods to daily death counts attributed to COVID-19 in selected countries, reported up to June 5, 2020. Results In most countries, the log(N) over log(C) plots showed initially a near-linear increase in COVID-19 deaths, followed by a sharp downturn. They enabled comparisons of small and large outbreaks (e.g., Switzerland vs UK), and identified outbreaks that were still growing at near-exponential rates (e.g., Brazil or India). The plots of log10(N(t)/C(t-1)) over time showed a near-linear decrease (on a log scale) of the relative growth rate of most COVID-19 epidemics, and identified countries in which this decrease failed to set in in the early weeks (e.g., USA) or abated late in the outbreak (e.g., Portugal or Russia). Conclusions The plot of log(N) over log(C) displays simultaneously the growth and size of an epidemic, and allows easy identification of exponential growth. The plot of the logarithm of the relative growth rate over time highlights an essential parameter of epidemic outbreaks.