Problem: predict thermodynamic state of the atmosphere (an open spatiallly-distributed thermodynamic system)
making the use of  (incomplete indirect) data acquired with a  stationary upward-looking ground-based radiometer.

Reformulating the problem:
    a) parametrize a large stochastic system/data series
    b)  using observation of  one stochastic  vector process,  predict another vector process.
Solution: neural network trained with avalable data sets/corresponding snapshots of the dynamic system states;
incorporating (when possible) theoretical models of links between observed processes  and system states of interest.

COIF-NN: Cloud Onset Instant Foreteller - Neural Network

Predicting cloud/fog onsets with ground-based (FTIR-) radiometer data via COIF-NN
COIF-NN - cloud onsets' instant foreteller - neural network

Training set  for the COIF-neural network  has been composed  with avaiable
pairs of
downwelling  infra-red  radiation spectra (ground-based AERI ),and
radiosonde observations (RAOB)  of atmospheric temperature and humidity profiles (ARM Archive)
Validation  of   time/altitude of cloud onsets has been performed with laser backscatter (LIDAR Ceilometer) data.

Lidar dataPredicted gap evolution
Figure  1. Lidar data & Predicted gap evolution
"Gap"= difference between actual- and dewpoint-temperature profiles: an onset occurs when  the  "gap" reaches "0"
Prediction has started at 0:29 GMT, driven by the operator of evolution which has been estimated over the time window  (Oct. 3) 21:00 - (Oct. 4) 0:22 GMT. Note, that with respect to the lidar backscatter data a cloudbase was detected at altitude 1.1 km about 3 hours GMT.
Figure  2. Prediction of  IR- spectrum evolution  (the fisrt 4 spectral parameters are displayed)

Predicted IR-spectrum evolution

Figure  3. Predicted evolution of IR-spectrum
Gennady Ryzhikov
aka Геннадий Рыжиков

The 2nd example