Retrieval of water vapour vmr isolines

AMSU-B brightness temperatures

from

Peter Mills

Bredbeck 2004

Sixth annual workshop on radiative transfer

Retrieving isolines from AMSU-B

- motivation

- technique

- results from simulation

- quantification of errors

- results from real data

- further work

Why do we want to retrieve isolines?

- contour advection: ability to resolve the structure

of an advected, conserved tracer to a very fine scale

- consider: if we inject a blob of dye into a flow field, how

do the edges of that blob evolve forward in time?

Contour advection is an adaptive algorithm that, given

a velocity field, predicts the evolution of a single isoline

of a conserved tracer.

How do we retrieve isolines?

Consider: is the vmr greater than, or less than the value of the isoline?

→ classification problem:

- given a set of sample points,

- with each point is associated a given class, j

- what is the class of a test point, ?

- usually expressed as a

conditional probability:

- class is that supplying the

maximum value of P

}

training data

Consider the following tautology:

- immediately suggests a numerical method of

estimating the probability density function (pdf)...

Estimating the probability density function (pdf):

- weighted average of sample points in the class

- weight is a function of the distance from the test point

where:

- are the samples belonging to class j

- is a variable parameter

- N is the normalization coefficient:

where:

- V is the number of variables

- n is the total number of samples

Estimating the probability density function (pdf):

where:

- i is the index of the variable

-	is the standard deviation of the ith variable

-	is a weighting coefficient

- the double braces ( ) denote a modified Cartesian metric:

→ takes care of vector spaces that are not isotropic

Estimating the probability density function (pdf):

Advantage: can resolve arbitrary functional dependences

(to a resolution given by )

Advantage: makes use of statistical tendencies in the data

A

B

atmospheric state:

(P = 0.01)

atmospheric state:

(P = 0.0005)

produces

measurement state:

class 1

class 2

C

given:

C

class 1

we choose

∈

∈

produces

Gauging the accuracy

Confidence rating for a given classification:

where:

-	is the total probability at point

- j is the “winning” class

- Nc is the number of classes

The classification data

AMSU-B: high horizontal resolution, only five channels

→ perfect for our classification scheme!

- the five AMSU-B channels:

89 ± 0.9 150 ± 0.9 183 ± 1 183 ± 3 183 ± 7 GHz

- throw in temperature and temperature lapse rate

- “training” data:

100000 ECMWF profiles randomly chosen in time and space

Chan. 16	Chan 17.	Chan. 18	Chan. 19	Chan. 20

COURTESY OF:

Everybody's favourite radiative transfer simulator!

Radiative transfer simulations...

assumptions:

- full nadir

- constant surface emissivity (0.6)

- clear sky (no scattering)

test 1:

- 2000 points randomly selected from the training data

- ECMWF sigma level 36

- vmr threshold of 0.0005

- sf = 0.071

results:

- accuracy: 99.6%

- r = 0.99

Test scenarios

test 2:

- data from an ECMWF field for a single date

- ECMWF sigma level 36

- vmr threshold of 0.0005

- sf = 0.71

results:

- see next slide...

Test scenarios

- heavy yellow is the true isoline

- yellow dots show retrieved

- shading indicates confidence

r = 0.80

accuracy: 90 %

Classification accuracy versus confidence rating

Converting a confidence rating to a confidence interval

- obtained by line integral

- heavy black line shows retrieved, red is true isoline

- fine black lines show 50% and 90% confidence intervals

- broken line is 1 “standard deviation”

Sensitivity to different parameters

- decreasing sf produces more optimistic confidence ratings

- optimal value for sf

- retrieval not so sensitive to vmr or vertical level

→ cannot be made into a “well-posed problem”

Test 3:

- AMSU-B channels 17, 18 and 19 + T and T-lapse

- collocated radiosondes supply vmr

- 400 hPa vertical level

- vmr threshold of 0.0005

- sf = 0.35

results:

- accuracy: 84.5%

- r = 0.66

Application to real data

Notes

- scheme works better with three channels than five

- scheme works just as well with only one channel

as with three!

Sources of error

- variations in surface emissivity

- collocation errors

- cloud contamination

- measurement errors

BT simulations with collocated radiosonde profiles

Questions

Why does the scheme work so much better with data sampled

from the training set than with a real field?

Why doesn't the scheme work as well with real data as with

simulated data?

Using simulated data, the more variables the better,

while for real data, the converse seems to be the case. Why?

Improving the classification scheme

- adaptive scheme to find optimal sf for trial point

- optimise this by selecting terms supplying most weight first

- advantage of our scheme over k-nearst neighbours: analytic derivatives

→ can be used to find class borders

- why does confidence rating change with sf?

→ error bounds on estimate of PDF

- similar scheme can be applied directly to estimate values of a field

(and with quite good results—see next slide)

Improving the results

- correct the collocation errors using trajectory calculations

- use simulated BT's to retrieve real data?

- knowledge of surface emissivity

- apply scheme only to a limiting case

- shading is retrieved

- lines are ECMWF (“true”)

r = 0.94

As classification problem:

r = 0.79

accuracy: 87%

2004-05-29T20:01:44