Using Stochastic Techniques to analyze AIRS data€¦ · Larrabee Strow, Philip Sura ... SST, sea...

Overview Data Analyzing Time Series Quantiles and Extremes Conclusions

Using Stochastic Techniques to analyze

AIRS data

Sergio De-Souza Machado, Andrew TangbornLarrabee Strow, Philip Sura⇤

Department of Physics, JCETUniversity of Maryland Baltimore County (UMBC)

⇤ Florida State University, Tallahasee, FL

AIRS Science Team MeetingOctober 2017Greenbelt, MD

1

Overview


Outline

AIRS has given us 15+ years of high qualityTop-Of-Atmosphere radiance data

retrievals (L2, L3), assimilation,climate studies (radiance trends, L2/L3 trends)

We use data to study variability via PDFs of observations

Talk summarizes JAMC May 2017 paper

Newer work

2


Motivation

(1) The high resolution AIRS spectra allow us to probedifferent regions of the atmosphere (eg surface, strat T(z),trop T(z), trop WV(z), UT WV(z), stratospheric ozone)

Climate studies with AIRS data now feasible eg trace gas rates,T(z) and WV(z) rates

(2) Progress in speed/accuracy of scattering RTAs allow us tocompare AIRS observational data with GCM model fields; firstmoment (biases) and second moment (standard deviations)give primary indications of NWP and/or GCM accuracy

(3) Variability of observational and model data can be furtherstudied using higher order PDF moments (third = skewness,fourth = kurtosis)Gaussian : skewness = 0, kurtosis = 3

3


PDF Moments

Sharply peaked distribution (less in the tails) : Kurtosis > 3Wider distribution (more in the tails) : Kurtosis < 3"More stuff on the left" or "tail extending to right : Skewness > 0"More stuff on the right" or "tail extending to left : Skewness < 0

4


Earlier stochastic analysis of atmospheric/ocean data

Use stats from "microphysical" locations (eg over multiplegridboxes) to look for "macroscopic" relationshipSST, sea level heights, 300 mb vorticity shows that

K � 3/2S

2 � r

power law behavior in tails pdf (x) = x

�↵ for large x

5


Advances in stochastic modeling

This can be modeled!Take dynamics (forcing, linear terms, nonlinear terms) equationsand separate out into slow and fast scales; the nonlinearinteraction of fast scales leads to a SDE

Multiplicative noise in stochastically forced models reproducesnon-Gaussian statistics and power law behavior in PDF tails

dx

dt

= a(x(t))+ b(x(t))⌘(t)

where a = deterministic slow processes, while b⌘ represents statedependent multiplicative noise [as opposed to state independentadditive noise [a(x(t))+ ⌘(t)]; ⌘(t) is Gaussian white noise

6


Advances in stochastic modeling

Linearizing the equation x = <x> + y (y is the anomaly) we get

dy

dt

= �Ay(t)+ [G + Ey(t)]⌘(t)

where the same noise ⌘(t) multiplies the additive noise G and themultiplicative noise Ey(t) hence Correlated and AdditiveMultiplicative noise (CAM)

Time dependent probability distribution function can be derivedfrom SDE, from which the K � 3

2S

2 + B relationship and power lawtails pdf (x) = x

�↵ for large x can be derived

7

Data


Applications to AIRS data

Radiative transfer for any AIRS channel is a convolution overmultidimensional phase space (includes T (z),WV(z), othertrace gases, surface temp, clouds etc)

Allsky PDFS are extremely non-Gaussian, evidence ofdeviations from Gaussian in the tails (cold tail = clouds)

So limit to clear sky PDFs

Do the obs/cal show K � 3/2S

2 � r? where r is an offsetarising from reducing the dynamical equations to a scalar

8


AIRS data and SARTA calcs

CLEAR SKY

use AIRXBCAL data , filtered for clear scenes

co-locate ERA geophysical, ran off SARTA clear forOcean/Night/Season

collect 10+ years of data into 4�bins, make PDFs for handfulof channels strat/trop T (662,754 cm�1), ozone (1024 cm�1),window (1231 cm�1) and trop/strat WV (1344,1420 cm�1)

compute S,K, look for extremes

Reduce effects of seasonal cycle by concentrating on DJF andremoving mean

9


Clear Sky : 662 and 754 cm�1

(a) 662 cm�1 (b) 754 cm�1

(c) 662 cm�1 (d) 754 cm�1

(e) 662 cm�1 (f) 754 cm�1

10



(a) 1024 cm�1 (b) 1231 cm�1

(c) 1024 cm�1 (d) 1231 cm�1

(e) 1024 cm�1 (f) 1231 cm�1

11



(a) 1344 cm�1 (b) 1420 cm�1

(c) 1344 cm�1 (d) 1420 cm�1

(e) 1344 cm�1 (f) 1420 cm�1

12


Global maps 1420 cm�1 Skewness

Night time DJF, boxed less than 500 observations are removed

OBS skew

Longitude [deg]-150 -100 -50 0 50 100 150

Latit

ude [deg]

-80

-60

-40

-20

0

20

40

60

80

-0.5

0

0.5

1

1.5

2

ERA skew

Longitude [deg]-150 -100 -50 0 50 100 150

Latit

ude [deg]

-80

-60

-40

-20

0

20

40

60

80

-0.5

0

0.5

1

1.5

2

13


Global maps 1420 cm�1 Kurtosis

Night time DJF, boxed less than 500 observations are removed

OBS exkurt

Longitude [deg]-150 -100 -50 0 50 100 150

Latit

ude [deg]

-80

-60

-40

-20

0

20

40

60

80

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2ERA exkurt

Longitude [deg]-150 -100 -50 0 50 100 150

Latit

ude [deg]

-80

-60

-40

-20

0

20

40

60

80

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

14


Some observations

The 6 different channels probe different regions/constituentsof atmosphere

They show K vs S

2 behavior that can be modeled bystochastic CAM theory

Negative skewness in obs =) ?? cloud contamination; butalso have negative skewness in SARTA clear sky calcs

Offset of curves from zero is indication of correlations (ie wereduced fluid eqns to a single scalar)

Strat T(z) channels have skew/exK between -1 and +1(quiescent); MERRA/ERA stats similar

1231 cm�1 channel has most of its data above K vs 1.5 S

2 sostrong CAM forcing

Power law tails in some grid boxes (not shown in this talk)

15

Analyzing Time Series


Clear sky stochastic time series

Weather is short time scales, Seasonal Cycles (driven by periodicsolar insolation), Climate is much longer time scales.Other climate processes (eg El Nino) have in between time scales

We are already familiar with auto-regressive processesTaking this to a bigger picture, some climate phenomena/timeseries can be regarded as having a “memory” ie daily fluctuationsimpact seasonal fluctuations impact long term climate phenomena

Use equations that embrace a wide range of temporal scalesslow/fast Stochastic Eqns!

16


Clear sky stochastic time series

“A unified nonlinear stochastic time series analysis for climatescience”, Moon and Wettlaufer, 2017, Nature Scientific Reports

dx(t)dt

= a(t)x(t)+N(t)⌘(t)+ F(⌧)

a(t) is seasonal (slow freq), N(t) ⌘(t) is noise ⇥ Weiner process, F isslow forcingNext page shows preliminary analysis of 14 years of area weightedBT1231 clear sky observations, yielding damping and noise

17


Clear sky stochastic time series analysis

Units on left panel are in /year, right panel are in KelvinRemember this is clear sky, so have problems at polar regionsAlso have ability to generate error estimatesPlan to adapt this to CAM forcing (tricky! tricky!)

18

Quantiles and Extremes


Quantiles

Quantiles from 14 years of tropical AIRS observations

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Quantile

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

K/y

ear

180

200

220

240

260

280

300

320

BT

1231 o

bs

(K)

quant K/yr

BT1231 obs

UMBCERAAIRS

Black curve (right axis) shows the mean observed BT1231 quantileGreen curve = d/dt(obsBT1231) quantile (K/year)Red curve = d/dt(calcBT1231) quantile (K/year) (SARTA 2Slab,ERA)Quantiles ⇠ 1 : extreme hot events +ve so getting hotterQuantiles ⇠ 0 : thick, high clouds +ve so are cloud tops movinglower? Less thick? 19


Extremes

Pick off 100 hottest points daily, look at the extreme distributionsBlack curve is the (GEV) extreme distribution for a typical yearThe other curves are the � between extremes from(2015/09-2016/08) and (2002/09-2003/08) for OBS, ERA andUMBC retrievalsHottest points are getting hotter

295 300 305 310

BT1231 obs

-6

-4

-2

0

2

4

6

pd

f

10 -3

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

Ob

s G

EV

pd

f

ObsUMBCERA

Different channels show different GEV distributions(shapes/parameters)

20

Conclusions


Conclusions

Hyperspectral sounder channels show evidence of stochasticforcing, which can be explained using a CAM model

K � 3/2S

2 � r

power law behavior in tails pdf (x) = x

�↵ for large x

JAMC paper establishing this published May 2017“Non-Gaussian Analysis of Observations from the AtmosphericInfrared Sounder Compared with ERA and MERRA Reanalyses”J.Appl.Met. and. Clim, 2017https://doi.org/10.1175/JAMC-D-16-0278.1

Plan to continue work on more climate related studiesSpectral trends (see Larrabee’s talks)Time series analysis : damping and forcing constantExtremesNeural Net for cloud height estimations

21

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Using Stochastic Techniques to analyze AIRS data€¦ · Larrabee Strow, Philip Sura ... SST, sea...

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