Low Uncertainty Regional Climate Projections without Irrelevant Weather Details

Uncertainties in conventional (GCM) climate models, defined as the structural spread among com-
peting models, have increased for the first time in the latest AR6 report despite an exponential increase
in the modern computation power. The root problem is that these models are based in the weather
regime, that is, they spend unnecessary effort in calculating irrelevant weather details. This project
aims to produce precise regional projection using the Half Order Energy Balance Equation (HEBE): a
half order fractional derivative generalization of the standard Energy Balance Equation (EBE). HEBE
has the advantage of being a direct consequence of the continuum heat equation combined with energy-
conserving surface boundary conditions. A previous paper used Fractional EBE (FEBE) to model Earth
climate projections through 2100 on a global scale, and it yields significantly smaller uncertainty com-
pared to the CMIP6 MME. This project builds on a similar methodology, enhancing climate projection
with additional regional details and upgraded precision. The current results show that the parametric
uncertainty in HEBE’s temperature response is smaller than the internal variability at most locations,
at the exceptions of the high memory deep ocean regions near Pacific. HEBE’s regional hindcast ac-
curately reproduces ERA5 2mT series’ deterministic and stochastic patterns of regional temperature.
The global hindcast is also validated by various reanalysis datasets and instrumental records. The
direct year to year relative uncertainty (ratio between 90% confidence interval and best estimate) is
stable across time and marker scenarios, with most regions projecting values below 0.5 by 2100. On a
global scale, the parametric uncertainty in HEBE’s response temperature is negligible (±0.03K by 2100
using the SSP2-4.5 marker scenario). This effectively shows that HEBE’s projection is more precise
than its competitors even without taking period averages. The exceedingly low global uncertainty was
constrained by the large amount of regional information when taking the global averages. It should be
noted that the cited parametric uncertainty does not take into account systematic biases in HEBE and
in the input datasets. The most important source should be any errors in the forcings, especially con-
cerning aerosols. HEBE aims to provide a compelling and physically grounded alternative to complex
deterministic multi-model ensembles, offering a more precise, efficient, and interpretable means of pro-
jecting regional climate changes in the coming century. This positions it as a potentially valuable tool
for policy-relevant projections and adaptation planning, thereby showing the pertinency of fractional
derivative and Bayesian framework in atmospheric sciences.