[also, this reference is somewhat old now; I haven't checked if this problem has been addressed in more recent models]
There is evidence[1] that the climate model software doesn't handle floating point properly (which is, unfortunately, a very common problem).
"... there exist differences in the results for different ... parallel
libraries, and optimization levels, primarily a result of the treatment
of rounding errors ... the ensemble spread due to the differences in
software system is comparable to the ensemble spread due to the
differences in initial conditions ..."
Rounding errors on different hardware, operation ordering, and optimization level screams that the software isn't properly handling[2] IEEE 754 floating point. This could be a serious problem in an iterated model that is chaotically sensitive to initial conditions (hence the use of ensemble forecasting)./* regardless, we need a lot thorium reactors ASAP */
[1] http://journals.ametsoc.org/doi/abs/10.1175/MWR-D-12-00352.1
[2] (pdf) https://ece.uwaterloo.ca/~dwharder/NumericalAnalysis/02Numer...
Further, what's your source on your last statement, that global temperatures are dropping?
The NOAA does adjust the data (and continues to do so) based on various factors like time of observation (TOBS), urban heat island effect (UHI). As well as infilling data when a station drops or they don't have the coverage.
As for the global temp dropping. That is most likely based on the satellite data showing a slight decrease (the hiatus).
[1] https://stevengoddard.wordpress.com/2015/08/17/the-majority-...
I guarantee you they'd be happy to prove America wrong on the world stage, so there's an incentive for them to be accurate.