Results with Neural Network Approximation for the NCAR CAM Long Wave Radiation Parameterization

NCAR, Mar 9, 2004 NNs for NCAR LWR 1

Results with Neural Network Approximation for the NCAR CAM Long Wave Radiation ParameterizationVladimir Krasnopolsky, University of Maryland & NOAA/NCEP

andMichael Fox-Rabinovitz, University of Maryland

Acknowledgments: William Collins, Phillip Rasch, Joseph Tribbia, Dmitry Chalikov


OUTLINE

INTRODUCTION: Motivation for the study:

new paradigm – combining deterministic GCM & statistical MLT (Machine Learning Techniques)

APPROACH: “NeuroPhysics” - NN Approximations for Model Physics

NCAR CAM-2 LWR:Accuracy and Performance of NN Approximation Comparison of CAM-2 Climate Simulations: two

10 Year Parallel Runs with the original LWR and its NN approximation

CONCLUSIONS & DISCUSSION


Distribution of Total Model Calculation TimePhysics vs. Dynamics (in %)

12%

66%

22%

Dynamics

Physics

Other

CAM-2 (T42 x L26): 3 x 3


Motivations for Applying NN to LWR

Calculations of model physics take about 70% of total time in CAM-2 Calculations of radiation, LW & SW, takes about 60% of model physics calculationsAll current improvements of CAM (and other GCMs) such as increasing resolution result in further increase of calculation time for physics including LWR (to 90+% for physics) Reexamination of model physics calculations seems to be a timely and urgent problem!


Generic Solution – “NeuroPhysics” Fast and Accurate NN Approximation for Parameterizations of Physics

Learning from Data

GCM

X Y

Parameterization

F

X Y

NN Approximation

FNN

TrainingSet …, {Xi, Yi}, … Xi Dphys

NN Approximation

FNN


Major Advantages of NNs Relevant for Approximating Model Physics:

NNs are very generic, accurate and convenient mathematical (statistical) models which are able to approximate model physics as complicated nonlinear input/output relationships (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 simple and fast. Training (only one for a model version!) is time consuming, application is NOT!NNs are well-suited for parallel processing


NNs for NCAR CAM-2 Long Wave Radiation

Parameterization


NN for CAM-2 Physics CAM-2 Long Wave Radiation

• Long Wave Radiative Transfer:

• Absorptivity & Emissivity (optical properties):

4

( ) ( ) ( , ) ( , ) ( )

( ) ( ) ( , ) ( )

( ) ( )

t

s

p

t t t

p

p

s

p

F p B p p p p p dB p

F p B p p p dB p

B p T p the Stefan Boltzman relation

0

0

{ ( ) / ( )} (1 ( , ))

( , )( ) / ( )

( ) (1 ( , ))

( , )( )

( )

t t

tt

dB p dT p p p d

p pdB p dT p

B p p p d

p pB p

B p the Plank function


Neural Network for NCAR LW Radiation NN characteristics

220 Inputs:Profiles: temperature; humidity; ozone, methane, cfc11, cfc12, & N2O mixing ratios, pressure, cloudiness, emissivity Relevant surface characteristics: surface pressure, upward LW flux on a surface - flwupcgs

33 Outputs:Profile of heating rates (26)7 LW radiation fluxes: flns, flnt, flut, flnsc, flntc, flutc, flwds

Hidden Layer: One layer with 90 neurons (may go up to 150-200)Training:

Training Data Set: Subset of about 100,000 instantaneous profiles simulated by CAM-2 for the 1-st yearTraining time: about 10 days (SGI workstation)Training iterations: 4,653

Validation on Independent Data:Validation Data Set (independent data): about 100,000 instantaneous profiles simulated by CAM-2 for the 2-nd year


NN Approximation Accuracy and Performance vs. Original Parameterization

Comparisons with ECMWF NN1)

Parameter Model Bias RMSE Mean Performance

HR(K/day)

ECMWF 0.2 0.45 8

times faster

NCAR

Clear /

Total

2. 10-

5 /

3. 10-5

0.15

/

0.38

-1.40 1.98 80

times faster

OLR(W/m2)

ECMWF 0.8 1.9

NCAR 0.01 1.7 240.5 46.9

1)ECMWF NN approximation consists of the battery of 40 NNs Operational at ECMWF since October 2003


Errors and Variability Profiles

Bias - dashedRMSE - Solid

Bias and RMSE profiles in Bias and RMSE Profiles in K/day

Bias = 3. 10-5 K/dayRMSE = 0.38 K/day

PRMSE = 0.29 K/day

PRMSE = 0.25 K/day


Errors and Variability Profiles (NASA)Bias and RMSE profiles in Bias and RMSE Profiles in K/day

Statistics

For HRs

Orig. vs. NN

K/day

Bias 2.10-4

6.10-4

RMSE 0.62

0.47

PRMSE 0.52

0.38

PRMSE0.34

0.27


NN Approximation Accuracy: Typical

HR in K/d

NN

HR

K/d

Bia

s in

R

MS

E in

HR in K/dHR in K/d

Err

or

Dis

trib

uti

on

Error in K/d

Level Statistics

For HRs

Orig.

K/day

NN

K/day

Min Val. -7.7 -8.2

Max Val. 6.1 5.2

Mean -0.779 -0.778

0.27 0.26

Bias - 1.10-3

RMSE - 0.145

P 626 mb


Zonal Mean – Approximation Bias

-0.1

0.

0.05

0.1

-0.05

K/day


PRMSE = 0.47 & 0.34 K/day

Individual Profiles

PRMSE = 0.18 & 0.10 K/day PRMSE = 0.16 & 0.08 K/day

Black – Original ParameterizationRed – NN with 90 neuronsBlue – NN with 150 neurons


PRMSE = 0.14 & 0.07 K/day

Individual Profiles

PRMSE = 0.11 & 0.06 K/day PRMSE = 0.05 & 0.04 K/day

Black – Original ParameterizationRed – NN with 90 neuronsBlue – NN with 150 neurons


NCAR CAM-2: 10 YEAR EXPERIMENTS

CONTROL: the standard NCAR CAM version (available from the CCSM web site) with the original Long-Wave Radiation (LWR) (e.g. Collins, JAS, v. 58, pp. 3224-3242, 2001)

LWR/NN: the NCAR CAM version with NN approximation of the LWR (Krasnopolsky, Fox-Rabinovitz, and Chalikov, to be submitted in March 2004; and Fox-Rabinovitz, Krasnopolsky, and Chalikov, to be submitted in April 2004)


CONSERVATION PROPERTIES (Global Annual Means)

Parameter Differences

(original LWR parameterization - NN Approximation) in %

Mean Sea Level Pressure (hPa)

0.001

Temperature 0.002

Surface Temperature (K)

0.03

Total Precipitation (mm/day)

0.3

Outgoing LWR – OLR (Wt/m2)

0.3

Total Cloudiness (fractions 0.1 to 1.)

1.


Zonal Mean Vertical Distributions and

Differences Between the Experiments


NCAR CAM-2 Zonal Mean Heating Rates

10 Year Average

(a)– Original LWR Parameterization

(b)- NN Approximation(c)- Difference (a) – (b),

contour = 0.1 K/day

all in K/day


NCAR CAM-2 Zonal Mean U10 Year Average



contour 1 m/sec

all in m/sec


NCAR CAM-2 Zonal Mean V10 Year Average



contour 0.1 m/sec

all in m/sec


NCAR CAM-2 Zonal Mean Temperature

10 Year Average



contour 1K

all in K


NCAR CAM-2 Zonal RMSE for Heating Rates10 Year Average


(b)- NN Approximation(c)- RMS Difference (a) – (b),

contour 0.1K/day

all in K/day


NCAR CAM-2 Zonal RMSE for Temperature10 Year Average


(b)- NN Approximation(c)- RMS Difference (a) – (b),

contour 1K

all in K


Horizontal Distributions of Model Diagnostics


NCAR CAM-2 Surface Pressure 10 Year Average



all in hPa

Mean Min Max

(a) 1011.48 -3.912 -0.871

(b) 1011.42 - 3.766 -0.926

(c) -0. 06 -2. 31 1.87


NCAR CAM-2 Total Cloudiness

10 Year Average


(b)- NN Approximation

(c)- Difference (a) – (b),

all in fractions

Mean Min Max

(a) 0.607 0.079 0.950

(b) 0.614 0.070 0.952

(c) 0.007 -0.085 0.086


NCAR CAM-2 Total Precipitation

10 Year Average


(b)- NN Approximation(c)- Difference (a) – (b), all in mm/day

Mean Min Max

(a) 2.275 0.022 15.213

(b) 2.288 0.029 14.578

(c) 0.121 -1.189 1.184


NCAR CAM-2 FLNT(OLR)10 Year Average


(b)- NN Approximation(c)- Difference (a) – (b)

all in W/m2

Mean Min Max

(a) 234.43 133.62 299.50

(b) 236.73 136.69 301.60

(c) 2.29 -6.10 11.94


NCAR CAM-2 LWR Heating Rates

(near 850 hPa)10 Year Average


(b)- NN Approximation(c)- Difference (a) – (b)

all in K/day

Mean Min Max

(a) -1.698 -3.912 -0.871

(b) -1.697 - 3.766 -0.926

(c) -0. 001 -0. 418 0.615


Horizontal Distributions of Model Prognostics


NCAR CAM-2 Temperature (near 850 hPa)

10 Year Average


(b)- NN Approximation(c)- Difference (a) –

(b)

all in KMean Min Max

(a) 251.08 231.84 298.24

(b) 250.99 232.47 298.10

(c) -0.09 -1.05 0.81


NCAR CAM-2 Temperature (near 200 hPa)

10 Year Average



(b)

all in KMean Min Max

(a) 213.87 231.84 298.24

(b) 213.97 232.47 298.10

(c) 0.11 -0.78 2.45


NCAR CAM-2 U(near 850 hPa)

10 Year Average



(b)

all in m/sec

Mean Min Max

(a) 0.64 -13.56 17.74

(b) 0.58 -13.04 17.25

(c) -0.06 -1.46 1.29


NCAR CAM-2 U(near 200 hPa)

10 Year Average



(b)

all in m/sec

Mean Min Max

(a) 16.35 -14.57 45.18

(b) 15.87 -14.60 44.51

(c) -0.48 -2.71 2.17


CONCLUSIONS:The proof of concept: Application of MLT/ NN for fast and accurate approximation of model physics has been successfully demonstrated for the NCAR CAM LWR parameterization. NN approximation of the NCAR CAM LWR is 80 times faster and very close to the original LWR parameterizationThe simulated diagnostic and prognostic fields are very close for the parallel NCAR CAM climate runs with NN approximation and the original LWR parameterizationThe conservation properties are very well preservedA solid scientific foundation is laid for development of MLT/NN approximations for other NCAR CAM physics components or a complete set of MLT/”Neuro-Physics”. Such a focused effort will result in a complete reexamination of the model physics calculations.


OTHER POTENTIAL FUTURE DEVELOPMENTS

The effort can be extended in the future to reexamination of calculations for: other CCSM components; and chemical and physical components of chemistry transport modelsMLT/NN can be applied for future development of new more sophisticated and time consuming parameterizations and even superparameterizationsMLT/SVM approximations should be explored and compared to those of NNA feasibility study on MLT approximation of model dynamics will be conducted Developing MLT approximations for other time-consuming “bottleneck” procedures (e.g., solvers, iterations, inversions, transformations, etc.)

Documents

Results with Neural Network Approximation for the NCAR CAM Long Wave Radiation Parameterization