Multi-year trend errors in sub-seasonal reforecasts

Multi-year trends in sub-seasonal reforecasts that are inconsistent with observed trends constitute a time- or state-dependent bias in either the physical forecast model or the forecast initialization data and methods, regardless of whether the observed trends are due to climate change or slow internal variability. These reforecast trend errors degrade the skill diagnosed from the reforecasts and point to deficiencies of the sub-seasonal forecasting system in representing a changing mean state. However, detection and quantification of these trend errors is non-trivial because of often high levels of sub-seasonal to interannual variability in combination with weak trends. Here, we propose methods to assess the robustness and importance of trends in observations, and detect when trends in sub-seasonal reforecasts are inconsistent with the observed trends. As a concrete example, we pick surface air temperature (SAT) trends in Northern Hemisphere winter, and assess consistency of trends in ECMWF 47R1 reforecasts at different lead times for the 20-year period 2000-2019 with the ERA5 reanalysis trend. We find that some regions - even for this relatively short period - exhibit positive SAT trends in ERA5 that are significantly different from zero, robust against small changes in the period and relatively large when compared to interannual variability. Among these regions are the Tropical Warm Pool and the Eurasian Arctic. In the latter region, the reforecasts clearly underrepresent the observed warming trend of about 2 K per decade at longer lead times: for lead times beyond three weeks, the reforecast trend is only about 1 K per decade, with a 95% confidence interval from 0.5 to 1.5 K per decade. We discuss potential reasons for this specific trend error, with the aim to provide guidance for future improvements in the physical forecast model and data assimilation methods.