Editing Openai/6938382f-f9e4-8003-a158-6d812c1bce84 (section)

===== 2.2 How he builds the ±4 W/m² LWCF “calibration error” =====

He pulls three main pieces together:
# TCF error from Jiang et al. 2012 (and related work) - CMIP5 models have ~±12.1% RMS error in global annual mean total cloud fraction, derived from 25-year means (1980–2004) compared to satellite datasets (MODIS, ISCCP2). Propagation_of_Error_and_the_Re… - Error patterns across models are strongly lag-1 autocorrelated and pair-wise correlated, so he argues they must be systematic theory errors, not random noise. Propagation_of_Error_and_the_Re…
# Conversion from cloud fraction error to LWCF error - Using Lauer & Hamilton (2013), he states CMIP5 models have ~±4 W/m² RMSE in long-wave cloud forcing (LWCF). Propagation_of_Error_and_the_Re… - This is consistent with their findings that model LWCF biases vs satellite climatologies are a few W/m² for multi-year means. American Meteorological Society Journals<ref>{{cite web|title=American Meteorological Society Journals|url=https://journals.ametsoc.org/view/journals/clim/26/11/jcli-d-12-00451.1.xml|publisher=American Meteorological Society Journals|access-date=2025-12-10}}</ref>
# Treating that ±4 W/m² as “annual average LWCF thermal flux calibration error” per year - He labels this as ±4 W/m² yr⁻¹, and calls it a “lower limit of resolution” for atmospheric forcing in CMIP5 models. Propagation_of_Error_and_the_Re… - He then compares this per-year flux “uncertainty” to the trend in GHG forcing (~0.035 W/m² per year) and notes the factor ~114 difference. Propagation_of_Error_and_the_Re…

Where this goes off the rails:
* The ±4 W/m² in Lauer & Hamilton is a climatological bias/RMSE of mean cloud radiative effect, not a year-to-year random error that gets re-drawn each year. It’s a systematic model bias in the multi-year mean spatial field. American Meteorological Society Journals<ref>{{cite web|title=American Meteorological Society Journals|url=https://journals.ametsoc.org/view/journals/clim/26/11/jcli-d-12-00451.1.xml|publisher=American Meteorological Society Journals|access-date=2025-12-10}}</ref>
* Frank effectively re-interprets that bias as a per-time-step random uncertainty that accumulates like a random walk. That’s not what Jiang/Lauer’s diagnostics represent, and it is not how climate models treat their fluxes internally.