A Linear Inverse Model for Improved Model Guidance of CPC’s Week 3-4 Operational Temperature Outlooks

We present a machine learning approach called a linear inverse model (LIM) that generates year-round real-time forecasts to support NOAA Climate Prediction Center Weeks 3-4 US temperature outlooks. The LIM is an observationally based, stochastically-forced empirical-dynamical model, whose state-dependent predictability is explainable through eigenanalysis of its operator. We use JRA-55 reanalysis for the period 1958-2016 to construct LIMs based on bimonthly periods, which are subsequently blended across adjacent months to yield seamless deterministic and probabilistic predictions year-round. Explicitly predicted variables include tropical heating and sea-surface temperature, tropospheric and stratospheric geopotential heights, mean sea level pressure, tropospheric streamfunction, and North American root zone soil moisture and 2m temperature. These LIMs are updated relative to an earlier version run at CPC, most notably by the adding two new variables (sea-surface temperature and soil moisture), extending the training period back to 1958, and by defining the anomalies relative to a “fair-sliding mean”, which acts to remove the trend component and reduce apparent long-term changes in covariability.

Ten-fold cross-validated LIM skill is evaluated for the entire training period. Additionally, we compare skill of the LIM retrospective forecasts (starting in 2017, after the LIM training period), using both deterministic and probabilistic measures, to that of real-time ECMWF IFS forecasts for the same period (2017-present). On average, the skill of the LIM is comparable to that of the IFS; over the United States and Alaska (the regions of interest for the official outlook), for the years 2017-2021, two category 2m temperature Heidke skill score of the LIM is 0.28, whereas the IFS skill is 0.27. However, skill has notable seasonality, with IFS skill slightly better skill during spring and LIM skill better during summer to early fall, and regionality, with IFS skill higher in the Northeast and LIM skill higher in the Southwest. Additionally, the LIM’s inclusion of soil moisture enhances its warm season skill; while the variance of soil moisture is regional, its effect in the LIM is to increase temperature skill across the entire CONUS.

Lessons learned from transitioning the LIM to an operational environment will be discussed, including: (1) How to leverage, for forecasters’ use, the LIM’s ability to identify forecasts of opportunity by predicting its own skill, particularly important when exploiting the relatively small amount of Weeks 3-4 skill; and (2) Decomposing the forecast into LIM eigenmodes representing key dynamical processes, including ENSO and stratospheric sudden warmings, to support forecasters’ physical understanding of their operational predictions.