Emulations of Long Wave

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Development of Fast and
Accurate Neural Network
Emulations of Long Wave
Radiation for the NCEP Climate
Forecast System Model


V. Krasnopolsky, M. Fox
-
Rabinovitz, S. Lord, Y.
-
T. Hou,

and A. Belochitski,


Acknowledgments:
Drs. H.
-
L. Pan, S. Saha, S. Moorthi, and M. Iredell

for their useful consultations and discussions. The research is supported
by the NOAA CPO CDEP CTB grant NA06OAR4310047.

NOAA 32nd Annual

Climate Diagnostics and Prediction Workshop, Oct. 22
-
26, 2007, Tallahassee, FL

OUTLINE


CTB project: Transferring the developed Neural Network
(NN) methodology applied to physics of NCEP CFS


Goals: (a) improving computational efficiency of radiation
of the CFS model, (b) providing a practical opportunity for
using new more sophisticated and time
-
consuming
radiation and other physics components for the CFS model


NN applications to the CFS model:

Development of NN
emulations for LW and SW radiation of the CFS model (SWR


work in progress)


Background information on the NN approach


Development of NN emulations of LWR

(Long
-
Wave
Radiation) for the CFS model and evaluation of their
accuracy

vs. the original LWR


Validation of NN emulations

of LWR through the CFS model
run using the LWR NN emulations vs. the control run using the
original LWR


Conclusions and plans

Background


Any parameterization of model physics is
a relationship or
MAPPING

(continuous or
almost continuous) between two vectors: a
vector of input variables,
X
, and a vector of
output variables,
Y
,



NN is a
generic approximation

for
any

continuous or almost continuous mapping
given by a set of its input/output records:

SET = {
X
i
,
Y
i
}
i

= 1, …,N


Neural Network

Y = F
NN
(X)

Continuous Input to Output Mapping

Neuron

Major Advantages of NNs:

NNs are
generic,
very

accurate and convenient

mathematical (statistical) models which are able
to
emulate numerical model components
, which are
complicated nonlinear input/output relationships
(continuous or almost continuous mappings ).

NNs are
robust

with respect to random noise and fault
-

tolerant.

NNs are
analytically differentiable

(training, error and
sensitivity analyses):
almost free Jacobian!

NNs are
well
-
suited for parallel and vector processing

NNs emulations are
accurate and fast but there is

NO FREE LUNCH
!


Training is a complicated and time consuming nonlinear
optimization procedure;
however, training should be done
only once for a particular application!


NN Emulations of Model Physics
Parameterizations


Learning from Data

GCM

X

Y

Parameterization

F

X

Y

NN Emulation

F
NN

Training

Set

…, {
X
i
,
Y
i
}, …

X
i


D
phys

NN Emulation

F
NN

CFS Model: LWR NN emulation


NN dimensionality and other parameters
:


591 inputs: 12 variables (pressure, T, moisture,
cloudiness parameters, surface emissivity, gases
(ozone, CO2)


69 outputs: 6 variables (heating rates, fluxes)


Dimensionality of the NN training space: 50,000 to
100,000


Training and testing data sets are produced by
saving inputs and outputs of LWR during 2
-
year
T126L64 CFS simulations; half of the data is used
for training and another half for validation or NN
accuracy estimation vs. the original LWR


Number of neurons for NN versions: 50 to 150

NN Approximation Accuracy

for Heating Rates (
on independent data set
) vs. Original
Parameterization (all in K/day),
Mean HR =
-
1.88,

HR
= 2.28

Parameterization

NN

Bias

(
K/day
)


PRMSE
(
K/day
)


LWR

NN75

1.5 10
-
3

0.37

NN95

4. 10
-
3

0.28

NN200

0.3 10
-
3

0.21

NN Computational Performance:

LWR NN emulations are
two
orders of magnitude faster

than the original LWR


Overall

CFS model computational

performance:

~30% faster

when using LWR NN emulations vs. the original LWR

Profiles of RMSE for NNs, in K/day

Individual HR Profiles for NN75

Global and time mean Seasonal & Daily
T
-
850 Temperatures and their Differences

Max Difference = 0.06 K

Max Difference = 0.1 K

Top of Atmosphere Upward LWR Flux Differences

Season 2:

0
-
5 W/m², max 10
-
20 W/m²


Season 4:

0
-
5 W/m², max 10
-
20 W/m²


Differences between the
seasonal

(1
-

4) CFS runs with
NN LWR emulation and with the original LWR


Field


Mean



Max


Top of Atm. Upward LWR Flux (in W/m²)



0


0.5



10


20


Surface Downward LWR Flux (in W/m²)



0


0.5



10


20


Zonal mean T (in K)


0


0.5

1.5


2.5

Zonal mean U (in m/s)


0


1


2

Zonal mean V (in m/s)


0


0.1

0.2


0.4

T
-
500 (in K)


0


1


2
-

3

Relative Humidity (in %)


0


2



4
-

6

NOTE
-
1: For seasons 1
-
4 the mean and maximum differences are about the same,
i.e. the differences

are not increasing

during seasonal CFS model integrations.

NOTE
-
2: The differences are
within the uncertainty

of observations or reanalysis

Day
-
2: Differences between CFS runs with NN LWR
emulation and with the original LWR



Field


Mean


Max

Upward Top of Atmosphere LWR Flux

(in

W/m**2)


0
-

2



10
-

20


Surface Upward LWR Flux

(in

W/m**2)


0
-

2



10
-

20

T
-
850 (in K)



0


0.2

0.5


1.5


U
-
850

(in m/s)


0
-

0.1


0.5


1


Day Seven: T
-

850 Differences (in K): 0


1, max 2
-

3

Multi
-
year Mean Upward Top of Atmosphere LWR Flux (in W/m²)

Differences: 0
-
5, max 10
-
20

Recent Journal and Conference Papers

Journal Papers:




V.M. Krasnopolsky, M.S. Fox
-
Rabinovitz, and A. Beloshitski, 2007, “Compound Parameterization for a Quality Control of Outliers a
nd
Larger Errors in NN Emulations of Model Physics",
Neural Networks
, submitted.



V.M. Krasnopolsky, M.S. Fox
-
Rabinovitz, and A. Beloshitski, 2007, “Decadal climate simulations using accurate and fast neural ne
twork
emulation of full, long
-

and short wave, radiation.
Mon. Wea. Rev.,

accepted.



V.M. Krasnopolsky, 2007, “Neural Network Emulations for Complex Multidimensional Geophysical Mappings: Applications of Neural

Network Techniques to Atmospheric and Oceanic Satellite Retrievals and Numerical Modeling”,
Reviews of Geophysics
, in press



V.M. Krasnopolsky, 2007: “Reducing Uncertainties in Neural Network Jacobians and Improving Accuracy of Neural Network Emulati
ons

with NN Ensemble Approaches”,
Neural Networks
, Neural Networks, 20, pp. 454
-
46



V.M. Krasnopolsky and M.S. Fox
-
Rabinovitz, 2006: "Complex Hybrid Models Combining Deterministic and Machine Learning
Components for Numerical Climate Modeling and Weather Prediction",
Neural Networks
, 19, 122
-
134



V.M. Krasnopolsky and M.S. Fox
-
Rabinovitz, 2006: "A New Synergetic Paradigm in Environmental Numerical Modeling: Hybrid Models
Combining Deterministic and Machine Learning Components",
Ecological Modelling
, v. 191, 5
-
18


Conference Papers;



V.M. Krasnopolsky, M. S. Fox
-
Rabinovitz, Y.
-
T. Hou, S. J. Lord, and A. A. Belochitski, 2007,


Development of Fast and Accurate Neural
Network Emulations of Long Wave Radiation for the NCEP Climate Forecast System Model”, submitted to the NOAA 32nd Annual
Climate Diagnostics and Prediction Workshop



V.M. Krasnopolsky, M. S. Fox
-
Rabinovitz, Y.
-
T. Hou, S. J. Lord, and A. A. Belochitski, 2007, “Accurate and Fast Neural Network
Emulations of Long Wave Radiation for the NCEP Climate Forecast System Model”, submitted to 20th Conference on Climate
Variability and Change, New Orleans, January 2008




M. S. Fox
-
Rabinovitz, V. Krasnopolsky, and A. Belochitski, 2006: “Ensemble of Neural Network Emulations for Climate Model Physic
s:
The Impact on Climate Simulations”,
Proc.,

2006 International Joint Conference on Neural Networks,
Vancouver, BC, Canada, July 16
-
21, 2006, pp. 9321
-
9326, CD
-
ROM


Conclusions


Developed NN emulations of LWR for the CFS model show
high accuracy and computational efficiency
. Due to a near
zero bias, NN errors are not accumulating in time during model
integrations.


Validation of NN emulations for LWR through CFS model runs
using the NN emulations vs. the CFS model run with the
original LWR show a
close similarity

of the runs, namely the
differences are
within the

uncertainty of observational data
and/or reanalysis for seasonal predictions, climate
simulations, and short
-

to medium
-
range forecasts
.


Obtaining small and not accumulating in time differences
between the NN and control runs is crucially important for the
CFS model as a
complex nonlinear system



Near
-
term plans: Development of SWR NN emulations is in
progress. Using SWR NN emulations will increase the
o
verall
CFS model computational performance by ~
60
-

70%



Opportunity for using new more sophisticated and time
-
consuming radiation and other physics components


Future developments: Other model physics components


Potential applications of the NN approach to GFS and DAS

Additional Plots

5/31/2007; GFDL

V. Krasnopolsky & M. Fox
-
Rabinovitz, Neural Networks for
Model Physics

18

NN
-

Continuous Input to Output Mapping

Multilayer Perceptron:

Feed Forward, Fully Connected

Input

Layer

Output

Layer

Hidden

Layer

Y = F
NN
(X)


Jacobian !

Neuron

t
j

Top of Atmosphere Upward LWR Flux
Global Seasonal and Daily Differences

U Zonal Mean
Differences

Season 1: 0


1 m/s, max 3
-

4 m/s

Season 2: 0


1 m/s, max 2 m/s

Season 3: 0


1 m/s, max 2 m/s

Season 4: 0
-

1m/s, max 2 m/s

T Zonal Mean
Differences

Season 1: 0


0.5 K, max 1.5
-
2 K

Season 2: 0


0.5 K, max 1.5
-
2.5 K

Season 3: 0


0.5 K, max 1.5
-
2 K

Season 4: 0


0.5 K, max 2
-
3 K

V Zonal Mean
Differences

Season 1: 0


0.1 m/s, max 0.2
-

0.4 m/s

Season 2: 0


0.1 m/s, max 0.2
-

0.3 m/s

Season 3: 0


0.1 m/s, max 0.2
-

0.4 m/s

Season 4: 0
-

0.1m/s, max 0 .2
-

0.4 m/s

Day Two: Upward Top of Atmosphere LWR Flux)


Differences near 0
-

2 W/m
2
, a few minor max of 10
-

20 W/m
2

Orig.
-

NN

Day Two:
T
-
850


Differences near 0


0.2 K, max 0.5


1.5 K

Day Two: U
-
850

Differences 0
-

0.1 m/s, max 0.5


1 m/s


Day Seven:
T
-
850

Differences near 0.


1.0 K, max 2
-

3 K

2
-
Year Mean OLR (Upward Top of Atmosphere LWR Flux), in W/m²


Differences 0
-
5 W/m², max 10
-
20 W/m²

Near term (FY07 and Year
-
2 of the project)

science plans


Completing work on LWR NN emulation


Generating more representative data sets


Continuing training and validation of LWR NN emulations for the
CFS model


Continuing experimentation and validation of seasonal climate
predictions with LWR NN emulations


Refining the NN methodology for emulating model physics


Work on an NN
ensemble

approach aimed at improve accuracy
of NN emulations


Develop a compound parameterization for
quality control

(QC)
and for dynamical adjustment of the NN emulations


Refining experimentation and validation framework


Continuation of development of NN emulations for the CFS model
radiation block


Analysis of CFS
SWR
, generating initial training data sets, and
developing initial SWR NN emulations


Initial experiments with
SWR

NN emulation for the CFS model


Initial development of the project
web site

and its link to a relevant
NCEP and/or CTB web sites

Future (FY08 and Year
-
3 of the project) science plans



Completing work on
SWR

NN emulation for the CFS model


-

Training and validation of SWR NN emulations

-

Performing seasonal climate predictions with SWR NN
emulation


Performing extensive CFS seasonal climate predictions with
developed NN emulations for the CFS
full radiation block

(LWR & SWR), and validating their overall impact
computational efficiency


Completing the
transition

of the developed NN radiation
products into the NCEP operational CFS


Completing development of the
project web site

and using it
for interactions with potential NCEP users and other users in
educational and research communities


Preparation for
future

developments: other CFS model physics
components, and potential applications to other NCEP systems
like GFS and climate predictions