or theory-based machine learning to distinguish from
the pure data-driven approaches.
There are two options to include physical rules
into data-driven machine learning models, of which
the overview is given in Fig.5. The first option is to
enforce physical consistency through adding a regu-
larization term in the loss function. Such an approach
is based on data-driven machine learning. The second
option is to use a CTM for generating output which
is then used as input for a machine learning system.
The latter one combines knowledge of physics (for-
mulated in terms of physical parametrization) with
data-driven machine learning.
Figure 5: The combination of data assimilation and ma-
chine learning system.
Option 2 uses the mechanism depicted in Fig.1(b)
which represents the model-based & data-driven
baseline forecasts, the configuration of the extended
system. CTM
t
0
+i
gives the baseline forecasts of i
hours in advance from the CTMs. The meteorolog-
ical forecast W
W
W
t
0
+i
is also used as input.
Finally, we believe that integration of machine
learning, data assimilation and physics-based numer-
ical models can be applied to many other problems
in scientific and engineering fields. For instance, con-
sider another air quality modeling application, predic-
tions of visibility. Currently, conventional numerical
models are insufficient to produce accurate visibility
predictions, e.g., (Clark et al., 2008), due to the com-
plexity and inability to fully quantify the influence of
many factors. In (Deng et al., 2019), LSTM has been
used to learn to predict the visibility based on local
meteorological measurements such as wind and hu-
midity. A promising extension would be to combine
weather and air quality predictions with current mea-
surement data to further improve the visibility fore-
cast accuracy. Yet another auspicious application of
the integrated framework is to use machine learning
techniques to estimate errors of (physics-based) nu-
merical models. It is known that an error quantifica-
tion of the numerical model is essential for the suc-
cess of data assimilation. However, there is usually
little knowledge about these errors. Machine learn-
ing can be applied to estimate of an error model using
measurement data and twin-experiments. A quality-
assured error model can further enhance the effective-
ness of the data assimilation.
REFERENCES
Caldwell, P. M., Bretherton, C. S., Zelinka, M. D., Klein,
S. A., Santer, B. D., and Sanderson, B. M. (2014).
Statistical significance of climate sensitivity predic-
tors obtained by data mining. Geophysical Research
Letters, 41(5):1803–1808.
Chen, G., Li, S., Knibbs, L. D., Hamm, N. A. S., Cao, W.,
Li, T., Guo, J., Ren, H., Abramson, M. J., and Guo, Y.
(2018). A machine learning method to estimate PM2.5
concentrations across China with remote sensing, me-
teorological and land use information. Science of The
Total Environment, 636:52–60.
Clark, P. A., Harcourt, S. A., Macpherson, B., Mathison,
C. T., Cusack, S., and Naylor, M. (2008). Prediction
of visibility and aerosol within the operational Met
Office Unified Model. I: Model formulation and vari-
ational assimilation. Quarterly Journal of the Royal
Meteorological Society, 134(636):1801–1816.
Deng, T., Cheng, A., Han, W., and Lin, H. X. (2019). Vis-
ibility forecast for airport operations by LSTM neural
networks. Proc. ICAART.
Fan, J., Li, Q., Hou, J., Feng, X., Karimian, H., and Lin, S.
(2017). A Spatiotemporal Prediction Framework for
Air Pollution Based on Deep RNN. ISPRS Annals of
Photogrammetry, Remote Sensing and Spatial Infor-
mation Sciences, IV-4/W2:15–22.
Hey, T., Tansley, S., and Tolle, K. (2009). The Fourth
Paradigm: Data-Intensive Scientific Discovery. Mi-
crosoft Research.
Jia, X., Karpatne, A., Willard, J., Steinbach, M., Read, J.,
Hanson, P. C., Dugan, H. A., and Kumar, V. (2018).
Physics Guided Recurrent Neural Networks For Mod-
eling Dynamical Systems: Application to Monitoring
Water Temperature And Quality In Lakes.
Jin, J., Lin, H. X., Heemink, A., and Segers, A. (2018).
Spatially varying parameter estimation for dust emis-
sions using reduced-tangent-linearization 4DVar. At-
mospheric Environment, 187:358–373.
Karpatne, A., Atluri, G., Faghmous, J. H., Steinbach, M.,
Banerjee, A., Ganguly, A., Shekhar, S., Samatova, N.,
and Kumar, V. (2017). Theory-guided Data Science:
A New Paradigm for Scientific Discovery from Data.
IEEE Transactions on Knowledge and Data Engineer-
ing, 29(10):2318–2331.
Keller, C. A., Evans, M. J., Kutz, J. N., and Pawson, S.
(2017). Machine learning and air quality modeling.
2017 IEEE International Conference on Big Data (Big
Data), pages 4570–4576.
Lazer, D., Kennedy, R., King, G., and Vespignani, A.
(2014). The Parable of Google Flu: Traps in Big Data
Analysis. Science, 343(6176):1203–1205.
Li, X., Peng, L., Hu, Y., Shao, J., and Chi, T. (2016).
Deep learning architecture for air quality predic-
tions. Environmental Science and Pollution Research,
23(22):22408–22417.
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