1

Optimal Channel Selection

2

Redundancy

“Information Content”

vs.

“On the diagnosis of the strength of the measurements in an observing system

through the use of metrics that measure the amount of information contained within its

observations”

3

Blue a priori state space

Green state space that also matches MODIS visible channel (0.64 μm)

Red state space that matches both 0.64 and 2.13 μm channels

Yellow state space that matches all 17 MODIS channels (only a factor of 2 better resolution)

Recall the Liquid Cloud Problem

Prior State Space 0.64 μm (H=1.20)

LW

P (

gm

-3)

Re (μm)

LW

P (

gm

-3)

Re (μm)

0.64 & 2.13 μm(H=2.51)

17 Channels(H=3.53)

4

Measurement Redundancy

Using multiple channels with similar sensitivities to the parameters of interest merely adds redundant information to the retrieval.

While this can have the benefit of reducing random noise, it cannot remove biases introduced by forward model assumptions that often impact both channels in similar ways as well.

IWP = 100 gm-2 Re = 16 μm Ctop = 9 km

5

The information content of individual channels in an observing system can be assessed via:

where kj is the row of K corresponding to channel j.

The channels providing the greatest amount of information can then be sequentially selected by adjusting the covariance matrix via:

Channel Selection

Tj 2 j a j

1H log 1 k S k

2

Tl

1a

1l kkSS

6

Method

Evaluate Sy

Compute K Establish prior information Evaluate the information content of each channel, Hj, with

respect to the a priori, Sa

Select the channel that provides the most information and update the covariance matrix using the appropriate row of K

Recompute the information content of all remaining channels with respect to this new error covariance, S1

Select the channel that provides the most additional information Repeat this procedure until the signal-to-noise ratio of all

remaining channels is less than 1: j 2H = 0.5 log 1+1 0.5

7

Measuring Stick Analogy

The first channel selected provides the greatest number of divisions of the measuring stick.

Each subsequent channel further refines the resolution of the observing system until none of the remaining channels contains enough information to further resolve state space.

Full range of a priori solutions

3

Channel 3: Refinement to final resolution H3 = 1, Hf = 5.16

1

Channel 1: Biggest resolution increase H1 = 2.58

Channel 2: Most improvement relative to new resolution H2 = 1.58

2

8

Optimizing Retrieval Algorithms

GOAL: Select optimal channel configuration that maximizes retrieval information content for the least possible computational cost by limiting the amount of redundancy in the observations

APPROACH: Use Jacobian of the forward model combined with appropriate error statistics to determine the set of measurements that provides the most information concerning the geophysical parameters of interest for the least computational cost

9

MODIS Cloud Retrievals Revisited

y

1 1 dYSNR=

σ X dX

IWP = 100 gm-2 Re = 16 μm Ctop = 9 km

x = (IWP, Tc, Re, α)

10

Information Spectra

Relative to the a priori, the 11 μm channel provides the most information due to its sensitivity to cloud height and its lower uncertainty relative to the visible channels.

Once the information this channel carries is added to the retrieval, the I.C. of the remaining IR channels is greatly reduced and two visible channels are chosen next.

IWP = 100 gm-2 Re = 16 μm Ctop = 9 km

11

Unrealistic Errors

When a uniform 10% measurement uncertainty is assumed, the visible/near-IR channels are weighted unrealistically strongly relative to the IR.

IWP = 100 gm-2 Re = 16 μm Ctop = 9 kmIWP = 100 gm-2 Re = 16 μm Ctop = 9 km

10 %

12

Thin Cloud (IWP = 10 gm-2)

For very thin clouds, the improved accuracy of IR channels relative to those in the visible increases their utility in the retrieval.

IWP = 10 gm-2 Re = 16 μm Ctop = 9 kmIWP = 100 gm-2 Re = 16 μm Ctop = 9 km

13

Larger Crystals (Re = 40 μm)

At large effective radii, both the visible and IR channels lose sensitivity to effective radius. Two IR channels are chosen primarily for retrieving cloud height and optical depth.

IWP = 100 gm-2 Re = 40 μm Ctop = 9 kmIWP = 100 gm-2 Re = 16 μm Ctop = 9 km

14

High Cloud (Ctop = 14 km)

The enhanced contrast between cloud top temperature and the surface increases the signal to noise ratio of the IR channels.

IWP = 100 gm-2 Re = 16 μm Ctop = 14 kmIWP = 100 gm-2 Re = 16 μm Ctop = 9 km

15

Ancillary Cloud Boundary Info.

With CloudSat cloud boundaries, the information content of the IR channels is much lower and the optimal channels reduce to those in the Nakajima and King (1990) algorithm.

IWP = 100 gm-2 Re = 16 μm Ctop = 9 kmIWP = 100 gm-2 Re = 16 μm Ctop = 9 km

CloudSat

16

Channel Selection Histogram

Dark blue – conservative scattering visible channels

Light blue – absorbing visible/near IR channels

Green – water vapor Yellow – 3.78/4.05 μm Orange – IR window Red – CO2 slicing

17

With CloudSat Cloud Boundaries

With ancillary cloud boundary information, fewer MODIS channels provide information above the level of background noise.

IR channels are selected less often due to the much better a priori cloud placement.

18

The Five Channel Algorithm

When the complete ensemble of cases is examined and a list of all channels selected are compiled, a five channel retrieval algorithm emerges as optimal for the widest range of scenes.

11 μm 0.646 μm 4.05 μm

2.13 μm 13.34 μm Total

19

Traditional Approaches

The Nakajima and King (1990) and split-window (Inoue, 1985) approaches each exhibit information content over part of the solution space but the combination of the two is required to provide maximum information over the full range considered.

Split-window (IR) 11 μm 11.92 μm 0.646 μm

4.05 μm 2.13 μm Total

Nakajima and King (Vis) 2.13 μm 0.646 μm 11 μm

4.05 μm 13.34 μm Total

20

CloudSat’s Impact

In the absence of cloud boundary information from CloudSat, infrared radiances from MODIS add significant additional information concerning cloud top height.

Without CloudSat

11 μm 0.646 μm 4.05 μm

2.13 μm 13.34 μm Total

With CloudSat

11 μm 0.646 μm 4.05 μm

2.13 μm 13.34 μm Total

21

Optimizing A New Observing System

This distribution of IWP represents one of the largest uncertainties in climate models and a gap in current observing systems.

Model IWP Sensitivity to a Doubling of CO2

22

The SIRICE Concept

The Sub-millimeter & Infrared Ice Cloud Experiment (SIRICE) offers the unique capability to measure a component of the water cycle that we know little about – the amount of ice in the atmosphere.

Microwave - Precipitation

Microwave – Liquid Water Path

Infrared – Thin cloudsSolar – Top of clouds

SIRICE – Ice Water Path

23

The Infrared Cloud Ice Radiometer

Goal: Design a new IR radiometer with two or three optimal bands between 7-14 μm for retrieving IWP and effective diameter.

De = 50 μm IWP = 150.4 gm-2 Tc = 223 K

24

Error Characterization

Error analyses include the following assumptions:

– PSD shape– Crystal habit– Surface T– Surface ε– Cloud geometric thickness– q profile

Measurement error of 0.5 K also assumed on each channel

Wavelength (μm)

Total Water Vapor SFC Properties

Err

or (

K)

Cloud Thickness Crystal Properties Measurements

25

Importance of Error Analysis (AGAIN!)

Measurement ErrorOnly (σ = 0.5 K)

Info

rmat

ion

(b

its)

Wavelength (μm)

Info

rmat

ion

(b

its)

Wavelength (μm)

26

ARM Cases

To establish the optimal channels for global retrievals 10,000 high cloud scenes are generated from statistics acquired at the ARM TWP and SGP sites to establish approximate global cloud statistics.

Cloud properties are retrieved from radar and lidar measurements. While there are uncertainties in these products, it is hoped that they provide a realistic representation of the observed distribution.

IWP

Fre

qu

ency

IWP (gm-2) Dme (μm)

Dme

Fre

qu

ency

27

Optimal Channels

Selected AnytimeSelected First

Wavelength (μm)Wavelength (μm)

13.6 μm

10.9 μm

28

Synthetic Retrievals

Modeled radiances for all 141 channels are employed to test a number of possible wavelength combinations in an optimal estimation inversion framework:

– Retrieval vector x = (LWP, De);– xa = (120 gm-2, 75 μm), σa = (2000 gm-2, 200 μm); – xtruth = (75 gm-2, 50 μm);– y = various combinations of channels between 7 and 14 μm.

0

F(x)ySF(x)yxxSxx

xx

Φ 1y

Ta

1a

Ta

29

Synthetic Retrievals

Information Used

IWPIWP Bias

σIWP De De Bias σDeComputation

Time*

All 141 Channels

76.56 1.56 5.7 53.14 3.14 4.8 10.6 days

Ten Channels 76.97 1.97 20.2 53.46 3.46 17.1 18.6 hours

Optimal Channels

76.61 1.61 28.7 53.08 3.08 25.2 7 hours

Split-Window 77.73 2.73 42.6 54.01 4.01 37.01 4.6 hours

Single Channel 96.84 21.84 166.5 75.19 25.19 199.3 3.6 hours

* Time to process a 100x100 array or 10,000 pixels on a 1.4 GHz Linux PC.

xa = (120 gm-2, 75 μm), xtruth = (75 gm-2, 50 μm), σa = (2000, 200)