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ATMOSPHERIC AND ENVIRONMENTAL RESEARCH, INC.

CAMBRIDGE, MASSACHUSETTS
ADVANCED MOISTURE AND TEMPERATURE

SOUNDER (AMTS) STUDY

Final Report

NASA Contract NAS5-27629

Prepared by

L. D. Kaplan, R. G. Isaacs, R. D. Worsham, and G. DeBlonde

Atmospheric and Environmental Research, Inc.

840 Memorial Drive

Cambridge, Massachusetts 02139

Prepared for

Laboratory for Atmospheric Sciences

NASA Goddard Space Flight Center

Greenbelt, MD 20771

June 1985
TABLE OF CONTENTS

ABSTRACT 1

1. INTRODUCTION 2

2. AMTS SIMULATIONS 5

2.1 Simulation Methodology and Algorithms 5

2.1.1 Spectral Data 5

2.1.2 Line-by-Line Codes 6

2.1.3 Rapid Algorithm 6

2.2 Weighting Functions 7

2.3 Sensitivity Studies 12

2.4 Brightness Temperature Simulations 17

2.4.1 Atmosphere Sounding Sample Sets 15

2.4.2 Simulation Results 20

3. FIRST GUESS ALGORITHM 30,

3.1 Background 30

3.2 Retrieval of Integrated Column Amounts 32

3.3 Retrieval of Layer Amounts 33

3.4 Errors Due to Power Law Smoothing 38

3.5 Errors Due to Temperature Retrieval Errors 38

3.6 Corrections for Supersaturation Near the Surface 40

3.7 Summary of First Guess Results 42

4. RELAXATION ALGORITHM 46

4.1 Background and Discussion 46

4.2 Relaxation Equation 48

4.3 Effect of Noise in Temperature Sounding 48

4.4 Effect of Constraints on Relaxation 52

5. STATISTICAL RETRIEVAL OF WATER VAPOR 58

5.1 Background and Methodology 58

5.2 Comparison of Retrieval Simulation Results. 60

5.3 Contributions of Temperature and Water Vapor Channels ....62

6. SUMMARY AND CONCLUSIONS 69

ACKNOWLEDGEMENTS 70

MEETINGS ATTENDED 71

REFERENCES 72
LIST OF TABLES

Table No. Page

1 AMTS Narrow Bandpass Channels 4

2-1 Attributes of Atmospheric Sounding Sets Used in

Water Vapor Retrievals 18

2-2 Typical Sounding and Water Vapor Column Integral 19

2-3 Means, Standard Deviations, and RMS Variability of

Layer Water Vapor Abundances for Atmospheric Sample

Dependent Sets 21

3-1 Effect of Channel/Column Amount Assignment Method on

RMS Errors for Retrieval of Level Integrated Water

Vapor Column Amounts for Tropical Winter Soundings 34

3-2 Means, Standard Deviations, and RMS Variability of

Layer Water Vapor Abundances for Atmospheric Sample

Dependent Sets 35

5 AMTS and HIRS Temperature and Water Vapor Channels,

and Water Vapor Contribution to Temperature Channel

Brightness Temperatures 66

6 First Guess and Relaxation FUV and FOM Values 70

ii
LIST OF FIGURES

Figure No. Page

1-1 Schematic of moisture retrieval process including

first guess and relaxation codes 3

2-1 AMIS water vapor channel weighting functions at

equator for winter (1/1), spring (2/1), summer (3/1 8

2-2 Dependence of 1839.4 cm channel on season at

40°N latitude: winter (1/5), spring (2/5), summer

(3/5), and fall (4/5) 9

2-3 Spring AMIS water vapor channel weighting functions

for the equator (2/1), 20°N (2/3), 40°N (2/5), and

60°N (217) 10

2-4 AMTS channel weighting functions vs. column integrated water vapor for three model winter atmospheres

at the equator (1/1), 40°N (1/5), and 60°N (1/7) 11

2-5 Sensitivity of AMTS channels to local changes in layer

temperature and water vapor for a summer equatorial

atmospheric model 13

2-6 Sensitivity of AMTS channels to local changes in

layer temperature and water vapor for a spring midlatitude (40°N) atmospheric model 14

2-7a Dependence of AMTS channel sensitivity to layer

changes in temperature on season and latitude 15

2-7b Dependence of AMTS channel sensitivity to layer

changes in water vapor on season and latitude 16

2-8 RMS variability of atmospheric sample dependent sets 22

2-9 Simulated AMTS channel transmittance vs. brightness

temperature for dependent tropical winter (over

ocean only) atmospheres 23

2-10 Simulated AMTS channel brightness temperature vs.

integrated water vapor for dependent tropical winter

(over oceans only) atmospheres 25

2-11 Simulated HIRS channel transmittance vs. brightness ,

temperature for dependent tropical winter (over

ocean only) atmospheres 26

2-12 Simulated HIRS channel brightness temperature vs.

integrated water vapor for dependent tropical

winter (over oceans only) atmospheres 27

iii
List of Figures (cont'd)

Figure No. Page

2-13 Results of brightness temperature simulations for

dependent sets of atmospheric profiles 29

3-1 Schematic of first guess retrieval algorighm 31

3-2 Comparison of RMS error of first guess layer water

vapor values to climatology for tropical winter

atmospheres retrieved using: linear fit, channel

mean values, and multiple regression 37

3-3 RMS errors of first guess layer water vapor values

for tropical winter atmospheres retrieved 39

3-4 Effect of surface layer relative humidity adjustment for supersaturation on first guess RMS errors

for tropical winter atmospheres 41

3-5 Combined effect of surface layer relative humidity

adjustment and simulated temperature profile error

on first guess RMS errors for tropical winter

atmospheres 43

3-6 RMS errors of first guess layer water vapor values

for tropical winter, tropical winter (ocean only),

tropical summer, midlatitude winter, and midlatitude

summer atmospheres 44

4-1 Schematic of the relaxation program 47

4-2 Comparison of RMS error in water vapor retrieval

results for tropical winter (ocean only) atmospheres 49

4-3 Effect of relaxation constraints on tropical

summer water vapor retrievals using AMIS 51

4-4 Effect of temperature profile error and number of

relaxations on AMIS retrieval of layer water vapor

values for tropical winter atmospheres (ocean only) 53

4-5 Comparison of AMTS and HIRS first guess and

relaxed RMS errors in retrieved water vapor for

tropical winter (ocean only) atmospheres 54

4-6 Comparison of AMTS and HIRS first guess and relaxed

RMS errors in retrieved water vapor or midlatitude

summer atmospheres 56

4-7 Comparison of AMTS and HIRS first guess and relaxed

RMS retrieval errors for midlatitude winter atmospheres compared to climatology 57

iv
List of Figures (cont'd)

Figure No. Page

5-1 RMS errors for tropical winter ocean statistical

retrievals from simulated measurements by HIRS, AMTS,

AMSU-B, and SSMT/2, compared with climatology 61

5-2 Same as Figure 5-1 for midlatitude winter

statistical retrievals for HIRS, AMTS, and

climatology 61

5-3 RMS errors for tropical winter ocean AMTS and HIRS

statistical retrievals for combined temperature

and moisture channels, for temperature channels

only, for moisture channels only, and for climatology....63

5-4 Same as Figure 5-3, for midlatitude summer 64

5-5 Same as Figure 5-3, for midlatitude winter 65

5-6 RMS errors for TWO and MWM statistical retrievals

with all 19 AMTS temperature channels 68
ABSTRACT

Retrieval of tropospheric humidity profiles from satellite-based

upwelling radiances are shown to be improved by using physical methods for

obtaining first-guess profiles as well as for inverting the radiative transfer

equation by relaxation. The first guess is based on an empirically verified

hypothesis, from theoretical considerations, that the brightness temperature

corresponding to the radiance should be approximately equal to the actual

temperature at a channel-invariant optical depth provided that the surface and

stratospheric contributions to the radiance are small.

Even greater improvement of retrieved humidity profiles can be

accomplished by increasing the number of channels used and by selecting their

spectral location and bandpass to obtain sharper independent weighting

functions. For example, the AMTS system, with high resolution water channels

at 1650, 1700, 1839, 1850 and 1930 cm"1, is shown to be capable of reducing

the retrieved water vapor errors in 200 mb thick layers by a factor of two to

three relative to the HIRS-2 system errors. Expected AMTS errors in tropical

layer water content are particularly low, less than 20% at all levels, and of

the order of 10% or less in the middle troposphere.

Statistical retrievals were carried out and were generally better than

the physical retrievals in the lower and upper troposphere but were worse in

the middle troposphere. When all channels were used, AMTS gave slightly

better results than HIRS at all heights. The AMTS was distinctly better when

only the moisture channels were used. The results of these studies indicate

that the AMTS system is superior, but that it can be further improved by

meshing physical and statistical retrievals and by using more moisturesensitive channels in the 15 ym C02 band.

A test of the usefulness of new channels extending the height to which

atmospheric water vapor can be routinely retrieved will require confirming

measurements beyond the present radiosonde limits. ATMOS data should be

useful for this purpose.

-1-
1. INTRODUCTION

The aim of this effort was to optimize the selection of channels for the

Advanced Moisture and Temperature Sounder (AMTS). The initial emphasis was to

be on the water vapor channels, but the study was to include investigation of

the possibility of finding two ozone channels giving independent stratospheric

and tropospheric ozone distribution, and the dependence of temperature

retrievals on spectral resolution.

Work on the contract tasks had already begun before the effective

starting date with support from Jet Propulsion Laboratory. In particular, we

had found two superior water vapor channels, at 1650.1 and 1700.3 cm , to

replace the old upper troposphere channels at 1844.5 and 1889.57 cm . This

substitution gives sharp weighting functions evenly spaced throughout the

troposphere. A window channel at 875.0 cm" was found to be a better choice

than the one at 1203.0 cm which was redundant with the 1232 cm channel.

The search for a second, nonredundant ozone channel was unsuccessful, but the

location of the one channel was optimized to 1040.8 cm . The new channel

locations appeared in several reports (e.g., Chahine et al., 1984) and are

reproduced in Table 1.

Midway in the originally planned research period, NASA decided to

terminate AMTS studies. Because of this, almost all of the effort was devoted

to the water vapor channels, and even that investigation is incomplete with

interesting possibilities still to be pursued.

Section 2 of this report describes the data, algorithms, and methodology

used in the study, presents water vapor weighting functions and the results of

sensitivity studies, and shows the relationships between channel brightness

temperatures and transmittance or integrated water. These lead to a new

first-guess algorithm, which is introduced and investigated in Section 3.

Section 4 reports on simulated retrievals by relaxation, and shows that the

AMTS moisture channels are potentially capable of providing substantially

better retrievals than the HIRS channels. Figure 1-1 is a schematic of the

moisture retrieval process including first guess and relaxation codes.

Section 5 shows the results of retrieval simulations with statistical

regression, which again indicates advantages of the AMTS relative to HIRS and,

at least for clear-column radiances, relative to AMSU for tropospheric water

vapor retrievals. Section 6 includes a summary discussion and suggestions for

future investigations.

-2-
Atmospheric

Sounding

Data

Sets

Independent

-lemp

-Water Vapor

L-Surface Temp\

F*etr i eva I

Error

/Retrieved

I Temp Prof Ile/

Temp

Dependent

-lemp

-Water Vapor'

.-Surface TempV

Rapid

Simu 1 at ion

Algorithm

i

' 1

r

V

C

lnt

c

Wat

Integrated

Column

Water Vapor

(Synthetic ( j ( Noise Free |

Sensor Data1 I V Radiances I

First Guess

Algorithm

CActual Layer

Values )

(^Flrs t Guess \

V Layer Values r First Guess

RMS Error ,

Re Iaxat i on

Program

(

Relaxed \_

Layer Values J

Relaxed

RMS Error

Figure 1-1. Schematic of Moisture Retrieval Process Including First

Guess and Relaxation Codes

-3-
TABLE 1 AMTS NARROW BAND PASS CHANNELS

-a

c

ro

CO

No.

1

2

3

4

<u

c

c

<0

JZ

o

No.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

iy

20

21

22

23

24

25

26

27

28

-C

J_>

•— Ol

OJ C

C OJ

C i —

<o o>

-C >

o <o

—y

X(ym)

16.476

16.046

15.929

15.765

15.466

15.282

15.025

14.996

14.967

r- %

tO C

J- CU

4-> 3

O cr

O) O)

Q. SC/> Ll_

utcnr1)

606.95

623.20

627.80

634.30

646.60

654.35

665.55

666.85

668.15

14.9381 669.45

11.429

9.608

8.120

6.060

5.881

5.437

5.403

5.181

4.19b

4.191

4.187

4.184

4.180

4.176

4.125

3.992

3.822

3.723

875.00

1040.80

1231.60

1650.10

1700.30

1839.40

1850.90

1930.10

2384. OU

2386.10

2388.20

2390.20

2392.35

2394.50

2424.00

2505.00

2616.50

5— C

o> o

S <TJ-- 0 si -l->

Q. 4-> 3

1 o"~

<4- QJ 0

r— 0. W 5 ">£

Au(cm'1)

0.50

0.50

0.50

0.50

0.50

0.50

0.50

0.50

0.50

0.50

0.7b

1.00

1.00

1.30

1.30

1.50

1.50

1.50

2.UU

2.00

2.00

2.00

2.00

2.00

2.50

2.50

2.50

2686.00) 2.50

Equivalent Scene

Blackbody Temperature

Above Atmosphere

min

230

229

218

211

202

195

197

194

198

199

231

198

231

220

216

232

233

232

214

222

229

231

232

232

232

232

232

232

Tstd

263.83

260.15

236.51

226.46

219.66

219.68

222.69

223.38

254.00

233.04

285.00

256.26

285.40

--

--

259.32

266.90

280.28

229.56

240.97

254.69

265.88

273.30

276.20

281.38

285.22

286.57

286.53

max

Main

Channel

Function

286 )

283 V CLOUD FILTERING

260 )

256

248

255

266

279

300

285

TEMPERATURE

PROFILE

UPPER ATMOSPHERE

327 H2U/SST

290 OZONE

327 H20/SST

261 I H00 PROFILE

255 f 2

282 )

289 V H20 PROFILE

315 )

274

299

313

321

325

326

TEMPERATURE

PROFILE

LOWER ATMOSPHERE

331 AIR-SURFACE AT

342 )

354 } SKIN SURFACE

364 ) TEMPERATURE

-4-
2. AMTS SIMULATIONS

2.1 Simulation Methodology and Algorithms

As a prerequisite to our channel optimization studies, a variety of

computational tools were implemented on AER's in-house Harris computer. These

codes provided the capabilities to: (1) generate and maintain files of

spectral data for desired atmospheric absorbers and wavenumber intervals, (2)

accurately evaluate channel atmospheric transmission, weighting functions, and

emergent radiances and brightness temperatures using the line-by-line (LBL)

approach and spectral data obtained in (1) above, and (3) perform efficient

sensor radiance/brightness temperature simulations using a "rapid" atmospheric

transmittance algorithm based on the LBL results. Since none of the codes

referred to above were written on Harris compatible machines each required

program conversion, testing, and where possible, comparison with test cases.

The models described above were exercised to perform a variety of

calculations during the current reporting period including: (1) water vapor

channel brightness temperature simulations, (2) evaluation of channel

weighting functions, and (3) sensitivity analyses. The theme of these studies

has been the investigation of the response of selected water vapor channels to

changes in temperature and moisture profile.

2.1.1 Spectral Data

Our spectral data base is the most recent version of the AFGL compilation

of absorption line (molecules 1-7) and trace gas (molecules 8-28) parameters

obtained from AFGL (Rothman et al., 1983). Two separate programs were used to

access this data and generate input files for calculations with Susskind's

(1978) LBL code and the AFGL FASCODE (Smith et al., 1978), respectively. In

the former case, formatted spectral data "BFILES" have been generated for use

in the following wavenumber regions: 0-100, 500-900, 600-1400, 1250-2400,

2100-2900 cm"1. (The first of these was used in a modified version of the LBL

code which we have used to perform microwave simulations.) Binary spectral

data sets for FASCODE were prepared using our converted version of AFGL's

"BCDMRG" program which provides the added capability to select trace gases of

interest and mejrge them by wavenumber into the desired data set.

-5-
2.1.2 Line-by-line Codes

We used our converted version of Susskind's LBL code for exact calculations of channel transmittance and weighting function profiles and to

simulate sensor-incident radiances. This code originally came to us in CDC

compatible FORTRAN format, accompanied by an update file providing for radiance calculations, a Gaussian filter function, and the nitrogen and water

vapor continua. Since our system does not include update file capabilities,

these changes were hand edited into the source code using a complete listing

for guidance and previous model runs for verification. Modified versions of

this code were written to: (1) perform sensor channel sensitivity analyses

(described in 2.3 below), (2) calculate transmittance and weighting functions

over narrow (0.1 cm ) band passes to aid in the search for optimum channel

locations, and (3) extend the infrared code to the 0-100 cm spectral region

for microwave simulations. This last task largely involved changes in

spectral data format, substitution of the van Vleck-Weisskopf line shape, and

specification of the microwave water vapor continuum expression used by Gaut

and Reifenstein (1971).

Additionally, we obtained and converted the high resolution fast atmospheric signature code (FASCODE) developed at AFGL (Smith et al., 1978) for

eventual use in our simulations. The version is denoted FASCOD1C (Clough,

1983). Test cases provided have been successfully verified and comparisons

with the Susskind (i.e., project) LBL code described above carried out.

2.1.3 Rapid Algorithm

The rapid algorithm for modeling atmospheric transmittance and radiance

described by Susskind et al. (1982) has been obtained in addition to required

input data sets including winter and summer extrapolated radiosonde profiles

(i.e., the Phillips data) and transmittance functions for the HIRS/MSU and

AMTS/MSU. This code has been converted to run on the Harris computer and

results compare favorably to sample output of brightness temperatures

generated by the simulation program which were provided by NASA.

(Discrepancies are on the order of the Gaussian noise added in the

simulation.) Additionally, favorable comparisons were made to previous

calculations using the LBL code. Modifications have been made to the rapid

simulation code to: (1) evaluate weighting function profiles using a method

analogous to that in the project LBL code, (2) perform sensitivity analyses to

-6-
layer water vapor and temperature variations (described below),

(3) accommodate the recently supplied transmittance function coefficients for

the new AMIS channels (i.e., 875, 1650.1, 1700.3 cm"1 at nadir including

appropriate changes to the water vapor continuum self broadening

coefficients), and (4) accept climatological model profiles (from the "WPOT"

data set) in addition to the radiosonde profiles (read by subroutine

"FIDRAD").

2.2 AMIS Channel Weighting Functions

Weighting functions were evaluated for a subset of the thirty-two

seasonally (l=winter, 2=spring, 3=summer, 4=fall) and latitudinally (1=0°,

2=10°, 3=20°, ..... 8=70°) dependent atmospheres from Rodgers (1967) supplied

as the "WPOT" climatological data set. Figure 2-1 illustrates these results

for the AMIS water vapor channels as a function of season at the equator.

Results for the seasonal variation of the channel at 1839.4 cm at latitude

40° are illustrated in Figure 2-2. Among other features, a shift of peak

sensitivity pressure level with seasonal water vapor variation is evident.

The variation of AMTS water vapor weighting functions with latitude is

illustrated in Figure 2-3. These calculations were done for a spring

atmosphere at the equator, 20°N, 40°N, and 60°N. The change in shape of

individual channel weighting functions and shifting of weighting function peak

pressure levels to higher pressures at higher latitudes is notable. In a

practical context, these results emphasize that individual channels are

sensitive to water vapor at pressure levels which differ systematically in the

course of a satellite orbit. As has been suggested by other investigators,

for this reason it is useful to consider water vapor weighting functions in an

alternative coordinate system based on integrated absorber amount (Chahine,

1970; Rosenkranz et al., 1982; Rosenberg et al., 1983). This is further

illustrated in Figure 2-4 which plots channel weighting functions, WF^,

defined as:

WF. =- (2.D

i

vs. column integrated water vapor, V- , for three model January atmospheres for

latitudes: (a) 0°, (b) 40°N, and (c) 60°N. In this representation weighting

functions remain approximately constant among model atmospheres.

-7-
ORIGINAL PAGE IS

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Figure 2-2. Dependence of 1839.4 cm"1 channel on season at 40°N

latitude: winter (1/5), spring (2/5), summer (3/5),

and fall (4/5) .

-9-
WEIGHT FUNCTION

8.511 I 283 1.689

ORIGINAL PAGE 13

OF POOR QUALITY, WEIGHT FUNCTION

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(2/1), 20°N (2/3), 40°:i (2/5), and 60°N (2/7).

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2.3 Sensitivity Studies

The computational efficiency of the rapid simulation algorithm provided

an opportunity to perform a variety of sensitivity studies which would not

ordinarily be undertaken using a time consuming LBL approach. An example is

the set of sensitivity calculations described below.

The purpose of these calculations was to examine the sensitivity of the

AMTS water vapor channels to specified changes in temperature and water vapor

abundance at individual layers within the atmosphere. The results of this

exercise provide a direct indication of the sensor-incident signal available

due to specified changes in the layer values of atmospheric temperature and

moisture. Water vapor abundance and temperature were increased by triangular

functions with maxima of 20% and 2K, respectively, and 50 mb half-width at

half-height, centered within seven 200 mb layers located at 200, 350, 500,

650, 800, 900, and 1000 mb. The algorithm employed was to: (1) select a

baseline (i.e. unperturbed) model atmospheres from the "WPOT" data set

[designated as (i/j) where 1=1,4 is the season and j=l,8 is the latitude, as

above], (2) simulate corresponding brightness temperatures for each water

vapor channel (i.e., 875, 1231.6, 1650.1, 1700.3, 1839.4, 1850.9, 1930.1

cm"-'-), (3) increment temperature within the first layer (i.e., centered at 200

mb) and reevaluate channel brightness temperatures, and (4) subtract the set

of brightness temperatures obtained in step (3) from that of step (2) for the

brightness temperature change due to the perturbation at this pressure

level. Steps (3) and (4) are then successively repeated for each layer (i.e.,

six more times). The process is then repeated for layer water vapor

perturbations, resulting in a total of fifteen simulations of the channel

set. These calculations with the rapid algorithm compared quite favorably

with those reported earlier for a standard atmosphere performed using the LBL

code. Due to the time savings it was possible to accomplish the analysis for

sixteen model atmospheres (four seasons and latitudes of 0, 20, 40, and

60°). For example, temperature and water vapor sensitivity results for

summer, equatorial and spring, midlatitude atmospheric models are shown in

Figures 2-5 and 2-6, respectively. There is notable variation of channel

sensitivity to both season and latitude. These variations are most apparent

comparing the entire set of results for temperature and water vapor. These

are illustrated in Figures 2-7a and b, respectively.

-12-
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TEMPERRTURE CHRNGE

Figure 2-5. Sensitivity of AMTS channels to local changes in layer

temperature and water vapor for a summer equatorial

atmospheric model.

-13-
TEMPERRTURE SENSITIVIT Y (2/5)

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Figure 2-6. Sensitivity of AMIS channels to local changes in

layer temperature and water vapor for a spring

midlatitude (40°N) atmospheric model.

-14-
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-16-
2.4 Brightness Temperature Simulations

2.4.1 Atmospheric Sounding Sample Sets

Simulated AMTS water vapor channel brightness temperatures are desired

both to investigate the relationship between emergent radiances and various

properties of the atmospheric water vapor profile and to provide synthetic

satellite sensor data for use in subsequent retrieval studies. For these

purposes it was desired to work with actual atmospheric soundings rather than

climatological data sets such as those described in Section 2.2. The sample

of sounding data chosen for this purpose was the Phillips (1984) winter/summer

radiosonde set used in the AMTS/HIRS comparison study. The extrapolated

profiles supplied by NASA were used instead of the actual incomplete

soundings. From among the available 1600 soundings, four sets of 200

atmospheres each were selected corresponding to tropical winter (TW) and

summer (TS) and midlatitude winter (MW) and summer (MS), respectively. Within

each set the first 100 soundings were designated as the dependent (D) subset

to be used as climatology, while the second 100 soundings were designated the

independent (I) subset. Brightness temperatures generated from the dependent

subset were calculated without adding instrumental noise to provide a basis

for relating brightness temperature variations to changes in the vertical

distribution of atmospheric water vapor. Noisy brightness temperatures

generated from the independent set were subsequently used as synthetic

satellite sensor data to test our retrieval methods. Additionally, the

tropical winter (TW) set was specially processed to provide a fifth set

including soundings over ocean only. In order to accomplish this, the first

two-hundred tropical winter soundings over the ocean were identified and

alternately sorted into dependent and independent sets. The attributes of the

various sample sets described above including sounding header number,

approximate latitude range, and land/ocean flag are summarized in Table 2-1.

For each individual sounding, values of temperature (K), water vapor and

ozone local column densities (cm~2) are given at 64 pressure levels. The

surface temperature is taken as that at the 1000 mb level. Table 2-2

illustrates a sample sounding taken from the TO set. Included is the column

integral of water vapor from the top of the atmosphere to a particular

pressure level (cm~2). For each individual sounding, column water vapor

densities were calculated for five layers corresponding to pressure level

-17-
Table 2-1

Attributes of Atmospheric Sounding Sets

Used in Water Vapor Retrievals

Atmosphere Sample*

Sounding

Numbers

Latitude

Range

Land (L)/

Ocean (0)

Tropical Winter (TW)

D 1001-1100 -28/-12

I 1101-1200 -28/+8

Midlatitude Winter (TW)

D 1451-1550 +32/+4S

I 1551-1650 +42/+4S

Tropical Summer (TS)

D 2001-2100 -30/-12

I 2101-2200 -287+8

Midlatitude Summer (MS)

D 2451-2550 +32/+4S

I 2551-2650 +427+48

Tropical Winter

(Ocean only)

L/0

L/0

L/0

L/0

L/0

L/0

L/0

L/0

D

I

1001-1317

1002-1318

-28/+2S

-28/+28

0

0

*Dependent set (D) - first-guess formulation

Independent (I) - retrieval application

-18-
Table 2-2

Typical Sounding and Water Vapor Column Integral

PRESSURE

1 .00

2.00

3.00

4 .00

5.00

6.00

7.00

8.00

9.00

10.00

15.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

100.00

110.00

120.00

130.00

140.00

150.00

160.00

170.00

180.00

190.00

200 . 00

220.00

240.00

260.00

280.00

300.00

320.00

340.00

360.00

380.00

400.00

425.00

450.00

475.00

500.00

525.00

550.00

575.00

600.00

625.00

650.00

675.00

700.00

725.00

750.00

775.00

800.00

825.00

850.00

875.00

900.00

925.00

950.00

9 7 5 . 00

1000.00

TEMPERATURE WATER

274.727 0.681700E+17

257.724 0.681700E+17

246.825 0.681700E+17

240.710 0.681700E-H7

236.087 0.681700E+17

233.349 0.681700E+17

231 .233 0.681700E+17

228.563 0.681700E+17

226.210 0.681700E+17

224.677 0.681700E+17

219.095 0.340850E+18

214.789 0.340850E+18

210.520 0.681700E+18

204.069 0.681700E+18

199.089 0.681700E+18

195. 132 0.681700E+18

196.043 0.681700E+18

196.587 0.681700E+18

196.891 0.681700E+18

195.024 0.681700E+18

195.429 0. 100962E+19

199.316 0.144276E+19

202.892 0.200122E+19

206.202 0.270678E+19

209.285 0.358291E+19

212.186 0.465471E+19

215.180 0.594897E+19

218.003 0.749409E+19

220.673 0.932014E+19

223.206 0. 1 14588E+20

227.846 0.306525E+20

231 .974 0.438028E+20

235.771 0.607579E+20

239.735 0.821791E+20

243.597 0. 108779E+21

247.210 0. 141319E+21

250.602 0. 180613E+21

253.800 0.227524E+21

256.825 0.282963E+21

259.695 0.347894E+21

263.086 0.541933E+21

265.959 0.682689E+21

268.674 0.849036E+21

271 .250 0.104386E+22

273.701 0. 127020E+22

276.098 0.153123E+22

278.410 0.183029E+22

280.623 0.234674E+22

282.745 0.292633E+22

284.784 0.356968E+22

286.746 0.427707E+22

288.637 0.504860E+22

290.462 0.588423E+22

292.477 0.671308E+22

295.196 0.727340E+22

297.829 0.756085E+22

300.381 0.775532E+22

302.856 0.784346E+22

305.260 0.781247E+22

307.596 0.764972E+22

309.744 0.761635E+22

311.815 0.779832E+22

313.833 0.797453E+22

315.800 0.810376E+22

INTEGRAL

0.681700E+17

0.136340E+18

0.204510E+18

0.272680E+18

0.340850E+18

0.409020E+18

0.477190E+18

0.545360E+18

0.613530E+18

0.681700E+18

0.102255E+19

0. 136340E+19

0.204510E+19

0.272630E+19

0.340850E+19

0.409020E+19

0.477190E+19

0.545360E+19

0.613530E+19

0.681700E+19

0.782662E+19

0.926938E+19

0. 1 12706E + 20

0.139774E+20

0.175603E+20

0.222150E+20

0.281640E+20

0.356581E+20

0.449782E+20

0.564370E+20

0.870895E+20

0. 130892E+21

0.191650E+21

0.273829E+21

0.382608E+21

0.523927E+21

0.704540E+21

0.932064E+21 .

0.121503E+22 >

0. 156292E + 22 ,

0.210485E+22 ]

0.278754E+22 |

0.363658E+22 [

0.468044E+22 !

0.595064E+22 >

0.748187E+22 .

0.931216E+22

0. 1 16589E + 23

0.145852E+23

0.181549E+23

0.224320E+23

0.274806E+23

0.333648E+23

0.400779E+23

0.473513E+23

0.549121E+23

0.62S675E+23

0.705109E+23

0.783234E+23

0.859731E+23

0.935895E+23

0.101388E+24

0.109362E+24

0. 117466E + 24

-19-
intervals of: (1) less than 200 mb, (2) 200-300 mb, (3) 300-500 mb, (4) 500-

700 mb, and (5) 700-1000 mb. A"sixth layer value (less than 1000 mb) was

defined to provide the total integrated water vapor column. For each of the

dependent sets of atmospheres, layer water vapor statistics were evaluated to

provide a climatology for retrieval comparison purposes. These statistics are

given in Table 2-3 and include layer mean values, standard deviations and

fractional RMS variabilities (may be expressed as percent by multiplying by

100). The RMS values can be considered as a measure of the climatological

variation of layer water vapor column densities for each set of atmospheres

against which to measure a given retrieval method. They are plotted in Figure

2-8. For example, if the mean water vapor density for each layer were chosen

as a first-guess retrieved value, the RMS error of the method evaluated over

the set would be the variability shown in Figure 2-8. While the properties of

the climatologies illustrated are generally reasonable (i.e. least variability

near the surface for tropical case over the ocean and most for midlatitude

winter cases), the decrease of variability at higher levels is most likely an

artifact of filling missing upper level values in the original incomplete

soundings with climatology.

2.4.2 Simulation Results

Rapid algorithm AMTS water vapor channel simulations were performed using

the selected sounding sample sets described above in order to investigate

relationships between resultant channel brightness temperatures, atmospheric

transmittances, and water vapor profile. Brightness temperatures were

calculated for each dependent sounding set without adding instrumental

noise. The results of these simulations were used to generate scatter

diagrams to test a few basic hypotheses. Early in the course of the

simulation modeling it was observed that the calculated i channel

transmittance to space, T*, from the pressure level in the model atmosphere

with local physical temperature, T(p), equal to the simulated channel

brightness temperature, T ,-was approximately constant, i.e.:

T

i[p(T = T£)] « const (2.2)

This constant was ~0.50 for channels not affected by surface contributions or

the tropopause. Figure 2-9, for example, illustrates a scatter plot of T, vs.

-20-
Table 2-3

Means, Standard Deviations, and RMS Variability of Layer

Water Vapor Abundances for Atmospheric Sample Dependent Sets

Atmosphere Sample

Tropical Winter

Midlatitude Winter

Tropical Summer

Midlatitude Summer

Tropical Winter

(ocean only)

Layer

1

2

3

4

5

6

1

2

3

4

5

6

1

2

3

4

5

6

1

2

3

4

5

6

1

2

3

4

5

6

Pressure

Range (mb)

< 200

200-300

300-500

500-7000

700-1000

< 1000

< 200

200-300

300-500

500-700

700-1000

< 1000

< 200

200-300

300-500

500-700

700-1000

< 1000

< 200

200-300

300-500

500-700

700-1000

< 1000

< 200

200-300

300-500

500-700

700-1000

< 1000

Mean

0.5737E+20

0.3492E+21

0.5039E+22

0.2198E+23

0.9198E+23

0.1194E+24

0.4341E+20

0.1954E+21

0.2133E+22

0.8421E+22

0.3438E+23

0.4517E+23

0.4882E+20

0.2519E+21

0.3128E+22

0.1288E+23

0.6894E+23

0.8526E+23

0.5115E+20

0.2739E+21

0.3481E+22

0.1483E+23

0.6772E+23

0.8636E+23

0.5588E+20

0.3295E+21

0.4594E+22

0.2044E+23

0.1013E+24

0.1267E+24

SDEV

0.1182E+20

0.1414E+21

0.2926E+22

0.1263E+23

0.3047E+23

0.4352E+23

0.8663E+19

0.8361E+20

0.1355E+22

0.5714E+22

0.1914E+23

0.2382E+23

0.1029E+20

0.1125E+21

0.2112E+22

0.8734E+22

0.3185E+23

0.4018E+23

0.9153E+19

0.1049E+21

0.2053E+22

0.8675E+22

0.2612E+23

0.3419E+23

0.1068E+20

0.1272E+21

0.2613E+22

0.1188E+23

0.2884E+23

0.4018E+23

RMS

0.2050E+00

0.4030E+00

0.5777E+00

0.5715E+00

0.3296E+00

0.3626E+00

0.1985E+00

0.4257E+00

0.6320E+00

0.6751E+00

0.5541E+00

0.5247E+00

0.2095E+00

0.4445E+00

0.6718E+00

0.6746E+00

0.4596E+00

0.4690E+00

0.1780E+00

0.3811E+00

0.5869E+00

0.5816E+00

0.3838E+00

0.3938E+00

0.1901E+00

0.3842E+00

0.5658E+00

0.5785E+00

0.2833E+00

0.3155E+00

-21-
(S

E>

CD

DC

ID

CD

(D

LU

CC

CL

IS)

CD

0.20

RMS

0.10 0.60 0.80

I I I

CLIMflTOLOGT

T

TROPICflL WINTER

MJDLBTITUDE WINTER

M10LRTITUDE SUMMER

TROP. WINTER IDCEflN ONLY)

I

IS)

IS

S)

OJ

00

. I

CC

a

CO

LU

CC

to

CD

IS)

S)

CD

0.20 0.40 0.60 0.80

Figure 2-8. RMS Variability of Atmospheric Sample Dependent Sets

-22-
o

in

UJ

in

cn

en

tn

1 I I I I

TROPICR L WINTE R (flMTS)

1231

875

1930

1650

 1839

1850

1700

I

215.0000 230.0000 2M5.0000 260 0000 275.0000 290.0000 305.0000

BRIGHTNESS TEMPERflTURE

Figure 2-9. Simula-ted AMIS channel transmittance vs. brightness

temperature for dependent tropical winter (over

ocean only) atmospheres.

-23-
T

1 for the five AMIS water vapor channels (1700.3, 1650.1, 1839.4, 1850.9,

1930.1 cm"1) and two surface channels (875.0, 1231.8 cm"1) calculated for the

TW (ocean only) set of soundings. The pressure level, p(T = T?" ), for each

channel, i, was identified for each sounding using the corresponding

temperature profile assumed as known. Note that with the exception of points

near temperatures of about 215 K and 290 K due to the exception noted above

(from the 1700 cm and 875, 1231.8 cm channels, respectively), most

channels whose weighting functions peak in mid-atmosphere cluster about T *

0.50.

This observation led to exploring the relationship between channel

tness temperature T*

5

 b

level Ui[Cm *] defined as:

brightness temperature T* , and integrated water vapor column density to the

b

U.[p(T = T)] = / n(p) H(p) dlnp (2.3) *

_ o

where n[cm ] is the local water vapor number density and H[cm] is the local

scale height. This relationship is illustrated in Figure 2-10. Notably, each

water vapor channel corresponds to a relatively fixed integrated column

density (with some channels exhibiting an apparently linear dependence

on T, ). As expected, the magnitude of the integrated water vapor column

b

sensed by each channel increases as the peak of its characteristic weighting

function approaches the surface (cf. Figure 2-1). The surface channels are

clustered in the upper right hand corner. This observation suggests that a

first order profile may be constructed by assigning a channel specific

integrated column water vapor amount to a pressure level defined by the

channel brightness temperature and a knowledge of the temperature profile.

An analogous set of scatter diagrams was generated for the three water

vapor channels (1484.4, 1363.7, 1217.1 cm) and window channel (897.7 cm )

of the TOVS HIRS-2 sounder. These are illustrated in Figures 2-11 and 2-12,

respectively. Intercomparison with the previous two figures indicate

relationships with behavior which is quantitatively similar to that noted for

the AMTS. Most differences between the AMTS and HIRS results are likely due

to the number of channels and spacing of integrated water vapor column amounts

sensed by each instrument's channel set. For example, the AMTS has more water

vapor channels including one (at 1700 cm) which senses a column about a

factor of ten less (i.e., higher in the atmosphere) than the highest HIRS

channel (at 1484 cm"1).

-24-
cc »-

UJ -

cr

°LLJ 0 i

cr

cc

o

o

i i i i i i r

TROPICPL NINTE R (flMTS)

' .- 875,1231

1930

1850 •;

1839

1650

1700

I I

215 0060 230 0B00 215 0008 260 OOP0 275 6000 290 0000 305.0003

BRIGHTNESS TEMPERRTURE

Figure 2-10. Simulated AMIS channel brightness temperature

vs. integrated water vapor for dependent tropical

winter (over oceans only) atmospheres.

-25-
1 I 1 I I I

TROPICflL WINTE R (HIRS)

897

1217

1363

1484

215 0008 230 0000 2M5 0000 260.0000 275 0008 290 0800 305 000B

BRIGHTNESS TEMPERflTURE

Figure 2-11. Simulated HIRS channel transmittance vs. brightness

temperature for dependent tropical winter (over

ocean-only) atmospheres

-26-
cc -

LU -

Q

LU

t—

CC

cc

o

I I I I I

TROPICR L NINTE R (HIRS)

897

1217

1363

1484

215 0000 230 0000 215 0000 260 0000 275 0083 290 0030 305 0000

BRIGHTNESS TEMPERflTURE

Figure 2-12. Simulated HIRS channel brightness temperature

vs. integrated water vapor for dependent tropical

winter (over oceans only) atmospheres.

-27-
The success of the first order approach described above will depend to a

great extent on how invariant the specific integrated column water vapor

amount is for each channel. Figure 2-13 illustrates the AMIS brightness

temperature integrated water scatter diagrams analogous to Figure 2-10 above

for each of the sample atmospheric profile sets. Qualitatively, it is notable

that when these four plots are superimposed, channels cluster for the most

part in their own characteristic domains, i.e. the association of an

integrated column for each channel is only weakly dependent on season and

latitude. Exceptions are largely attributable to surface effects. It is

notable, however, that the individual scatter diagrams differ in detail.

Specifically, the separation notable for individual channel brightness

temperature/integrated water curves of the TW (ocean only) set (Figure 2-10)

and the TO set presented here (Figure 2-13b), becomes somewhat less distinct

for the channels affected by the lower atmosphere and surface (upper right

hand corner of each scatter diagram). This is particularly evident for the

midlatitude winter results (Figure 2-13d) where the lowest three water vapor

channels (1839, 1850, 1930) and surface channels (875, 1231) tend to blend

together. Additionally, the remarkable "bullet" pattern noted for the highest

peaking channel at 1700 cm"1 (in the lower left hand corner of each scatter

diagram) is destroyed in going from tropical (Figure 2-13a,b) to midlatitude

soundings (Figure 2-13c,d). This is likely due to differences in variances of

the height of the tropopause.

-28-
ORIGINAL PA£E [3

Of POOR QUALITY

_

3

O

5

O

.j

I I ill ) 1

•"3) T ropic.nl bunmer

"

.

* -• ,

1 I t 1 1 i I

o

a

0

- 5

cc -

UJ —

c

a 3

UJ •

^ i

o

o

_J B

at

e

1 1 1 1 1 1 1

(b) Tropical Winter

"

.

- ~>

i i t i i i " i

BRICMldESS TEHPERfllURE BRIGHTNESS TEMPERHTURE

S

I i I 1 1 1 1

(c) MidlJCicude Summer

— -^ * -

-

--'T. <.. -.

-;'„'

,11111 1

us ••» i» •"• "*

 law

 ?*• «••• "5 Mia rta aaia ia:> aaa«

S

cr

0

UJNTEGRfl T

JSBI 21

O

o

2

1 1 1 1 1 I I

(d) Midlatitude Winter

' t "*

if - ,; x

'^

 f i "

^->::~

"r

i i i i i i i

BRIGHTNESS TEMPERATURE BRIGHTNESS TEMPERHTURE

Figure 2-13. Results of brightness temperature simulations for

dependent sets of atmospheric profiles: (a) Tropical

Summer, (b) Tropical Winter, (c) Midlatitude Summer,

and (d) Midlatitude Winter.

-29-
3. DEVELOPMENT OF A FIRST GUESS RETRIEVAL ALGORITHM

3.1 Background

The brightness temperature simulation results described in the previous

section (§2.4.2) suggest that to first order, each AMTS water vapor channel

senses an essentially constant column of water vapor related to an

approximately constant value of transmittance or, alternatively, optical

depth. This notion is conceptually supported by the water vapor channel

weighting functions calculated as functions of integrated column density

(Equation 2.1) illustrated in Figure 2-4. Furthermore, the pressure level

corresponding to this integrated column is approximately that for which the

local temperature is equal to the channel's brightness temperature. Thus,

given a knowledge of both the temperature profile, T(p) (from a temperature

retrieval, for example) and the water vapor channel brightness temperatures,

it should be possible to infer the vertical distribution of water vapor by

assigning the specified column amount for each channel, U-, to that pressure

level described above, i.e.,

U [p(T = Ty] = U. (3.1)

and producing a smooth profile by interpolation. In practice, problems are

introduced by a variety of necessary operations including: (1) determining an

integrated column amount to assign to each channel, (2) interpolating between

pressure levels both to produce a smooth integrated column profile and provide

layer amounts for specified pressure level boundaries from column amounts,

(3) extrapolating above the lowest pressure level and below the highest

pressure level (the latter occasionally leading to supersaturation in the

surface layer), and (4) assigning a pressure level to each channel for a given

retrieval due to errors in the associated temperature profile.

In this section, the development of a novel first guess water vapor

profile retrieval algorithm based on the above hypothesis is described.

Figure 3-1 illustrates a schematic of the first guess retrieval algorithm.

The retrieved layer values are obtained from synthetic noisy water vapor

channel brightness temperature data obtained from the independent sets of

atmospheric soundings (see 2.4.1) using the rapid algorithm. The method is

tested and verified by comparing retrieved layer values with those of the

-30-
Independent

Sounding

Set

 9

Retrieval

Temperature

Profile

c

Retrieved

Surface

Temperature

/ Actual Layer

I Values

Dependent

Sounding

Set

(Noise Free j

Radiances ^1

c

ActuaI

Profiles

I J

>

„

Integrated

Water/Brightness

Temperature

Relat ionshi p

\

First Guess

Column

Retrieve 1

1 r

Column- i

to-Layer

Conversion

(

First Guess \

Layer Values J

First Guess

RMS Errors

Figure 3-1. Schematic of First Guess Retrieval Algorithm

-31-
actual soundings and evaluating RMS error statistics over the entire ensemble

of soundings. Possible solutions to the problems enumerated above are also

described.

3.2 First Guess Retrieval of Integrated Column Amounts

A basic consideration is the selection of a reasonable method to assign a

column integrated water vapor amount to each AMIS channel based on the

brightness temperature simulation results for the dependent sounding sets

illustrated in Figure 2—13. Three candidate approaches were investigated

using: (a) the mean value of the column integrated water vapor for each

channel, (b) a linear fit of the log of the column integrated water vapor, U^.

for the ic^ channel with the channel brightness temperature I* of the form

b

log U. = a. T* + b. (3.2)

i i b i

and (c) a multiple regression equation based on the channel brightness

temperature and other presumed known parameters (such as the height of the

tropopause). Each method was evaluated by applying the selected channel

specific values to retrieve integrated column amounts for each channel using

noisy synthetic brightness temperatures calculated for the independent set and

examining the resulting RMS error. The RMS error for the i channel

integrated column amount evaluated over the set of N = 100 independent

soundings was defined as:

RMS(i) =^-L- {N'1 I [U(i,j) - U(i,j)]2}

1/2

 (3.3)

where U(i,j) and U(i,j) are, respectively, the retrieved and actual column

integrated water vapor amounts for the i channel and j sounding

and U(i) is the channel mean value. It is important to note that the

quantities being retrieved here, the U(i,j) , are not referenced to a fixed

pressure level since even for a given channel, this will vary among the

soundings with the vertical distribution of water vapor and temperature. This

is simply a test of the potential for using the results of the forward problem

to infer the column values sensed by each channel. The sources of error were

the channel-dependent instrumental noise introduced in the generation of

synthetic brightness temperature, 1.5 K of assumed temperature retrieval

-32-
uncertainty, and the choice of method assumed above. Results are given in

Table 3-1 for the tropical winter set of soundings corresponding to Figure 2—

13b. For channels not influenced by the surface and upper atmosphere, the

simple linear fit appears to perform adequately. As might be expected,

channels with distinct linear patterns in the scatter diagram (e.g., 1650.1

cm"*) produce the best retrievals, while those influenced by the surface

(875.0, 1231.8 cm"1) are least accurate.

Applying the linear fit approach to the dependent sounding set

simulations illustrated in Figure 2-13 results in the regression and

correlation coefficients summarized in Table 3-2. These regression

coefficients are subsequently used as the basis for retrieving channel

integrated water vapor values from synthetic channel brightness temperature

data generated from the independent set of soundings. Some measure of the

potential success of this approach is provided by the individual channel

correlation coefficients which should be greater than about 0.4 for this

sample size to suggest statistically significant linear dependence.

3.3 First Guess Retrieval of Layer Amounts

u

Using the approach described above, each channel associates a column

water vapor amount with a pressure level. Using the water vapor channels and

one surface channel, for example, six points along the integrated water vapor

profile are determined. The pressure levels associated with these points vary

with each sounding, however, and therfore it is convenient to provide for

calculating a continuous profile. This also facilitates retrieving layer

amounts within fixed pressure increments.

A piecewise smooth integrated column profile is evaluated using segments

individually fit as:

U(P) =

 u ( P ) <P/P > fo r P j

 < p < P . . (3.4)

where the power law experiment A.: is given for each segment by:

ln[U(p )/U(p ,)]

A. -- , 3 . - 2±±— (3.5)

Values are extrapolated above the lowest pressure value (for the 1700 cm )

and to the surface.

-33-
Table 3-1

Effect of Channel/Column Amount Assignment Method on

RMS Errors for Retrieval of Level Integrated

Water Vapor Column Amounts for Tropical Winter Soundings

Channel

1650.1

1700.3

1839.4

1850.9

1930.1

875.0

1231.8

Means

.0601

.1796

.1046

.1614

.1809

.2329

.2687

Linear

.0468

.1803

.08941

.1543

.1642

.2367

.2842

Multiple

.0468

.3339

.08941

.1543

.2304

.2516

.2961

-34-
Table 3-2

Means, Standard Deviations, and RMS Variability of Layer

Water Vapor Abundances for Atmospheric Sample Dependent Sets

Atmosphere Sample

Tropical Winter

Midlatitude Winter

>

Tropical Summer

Midlatitude Summer

AMTS Channel

1650.1

1700.3

1839.4

1850.9

1930.1

875.0

1231.8

1650.1

1700.3

1839.4

1850.9

1930.1

875.0

1231.8

1650.1

1700.3

1839.4

1850.9

1930.1

875.0

1231.8

1650.1

1700.3

1839.4

1850.9

1930.1

875.0

1231.8

Regression

a

i

-.682894E-02

-.207474E-02

-.881106E-02

-.127429E-01

-.115886E-01

-.104205E-01

-.971928E-02

-.794979E-02

-.641433E-02

-.399605E-02

-.359382E-02

0.210679E-01

0.255938E-01

0.237758E-01

-.680776E-02

-.987208E-02

-.996337E-02

-.139610E-01

-.101513E-01

0.280548E-01

0.310113E-01

-.483858E-02

-.151727E-01

-.496142E-02

-.798210E-02

-.658089E-02

0.138860E-01

0.159077E-01

Coefficients

0.223116E+02

0.201019E+02

0.240791E+02

0.255050E+02

0.259446E+02

0.260061E+02

0.258259E+02

0.225060E+02

0.213317E+02

0.227093E+02

0.229308E+02

0.165564E+02

0.153525E+02

0.158645E+02

0.222915E+02

0.218247E+02

0.243636E+02

0.258160E+02

0.254136E+02

0.145925E+02

0.137363E+02

0.218171E+02

0.232295E+02

0.230231E+02

0.241753E+02

0.243887E+02

0.187229E+02

0.181412E+02

Correlation

Coefficient

0.698516E+00

0.740448E+00

0.662491E+00

0.609532E+00

0.564673E+00

0.418703E+00

0.316401E+00

0.647118E+QO

0.921094E+01

0.149386E+00

0.113795E+00

0.675599E+00

0.771720E+00

0.764807E+00

0.644311E+00

0.335425E+00

0.556745E+00

0.472715E+00

0.205299E+00

0.463431E+00

0.518697E+00

0.663063E+00

0.141038E+00

0.468682E+00

0.513617E+00

0.205369E+00

0.374975E+00

0.430633E+00

-35-
Results of the first guess algorithm using AMIS and the three integrated

column amount selection methods described in the previous section are shown in

Figure 3-2. Layer water vapor column accounts (cm~2) were retrieved from the

independent set of TW atmospheres using regression coefficients (Table 3-2)

derived from the dependent set (Figure 2-13b). In determining pressure levels

for each channel, temperature retrieval error of 1.5 K was assumed at all

levels. RMS percent errors were evaluated for five retrieval layers

corresponding to: (a) 0-200 mb, (b) 200-300 mb, (c) 300-500 mb, (d) 500-700

mb, and (e) 700-1000 mb, and are plotted at each layer's average pressure.

These layers were chosen both to correspond to lower atmospheric pressure

level increments used in the reporting of the operational water vapor products

supported by the HIRS-2 sensor (Smith et al., 1979; NOAA, 1981) and to explore

the potential for increased vertical resolution in the upper atmosphere from

the AMTS. The points plotted at 1000 mb correspond to the RMS errors of the

total integrated water vapor column. The RMS error for each layer k evaluated

over the set of N = 100 independent soundings was defined as:

i _i N » 91/ 9

RMS(k) = —I- {N I [u(k,j) - udc.jHn1 (3.6)

u(k) j=l

4*.

where u(k,j) and u(k,j) are, respectively, the retrieved and actual water

vapor amounts for the ktn layer and j1-*1 sounding and u(k) is the layer mean

value.

For comparison purposes, the RMS variation of the dependent set of

atmospheres is also shown as climatology. The algorithm appears to provide a

reasonable first guess water vapor profile based on improvement over

climatology throughout most of the atmosphere.

Comparing the three column amount selection methods, both the mean and

linear fit appear to be equally applicable. The latter was retained to

perform subsequent calculations. Problems are evident in retrieving the

surface layer (plotted at 850 mb) and that above 200 mb (plotted at 100 mb).

An important source of error introduced in the process of retrieving layer

values is that due to the power law interpolation method and subsequent

extrapolation, especially to the surface. This is in addition to the effects

of instrumental noise and errors in the retrieved temperature profile. These

factors are discussed in the sections to follow.

-36-
0.20

RMS

0.40

ERROR

0.60 0.80

i I I r

TROPICflL NINTE R

CO

19

6J

GJ

«9

S

OC (9

cn

en

LU

cc

CE

5

(9

(9

g

G)

19

ei

G)

00

A iWflR REGRESSION FIT

+ HEHN INTECRH7ED HRTER

X HULT1PLE REGRESSION FIT

I

(\J CD

a cc

s ID

gen

en

CC

H

IS

to

CD

IS

(3

CD

.20 0.40

RMS

0.60

ERROR

0.80

Figure 3-2. Comparison of RMS errors of first guess layer water vapor

values to climatology for tropical winter atmospheres retrieved

using: linear fit, channel mean values, and multiple regression

-37-
It should be noted that the data set was extrapolated from 300 mb or

greater pressure to climatological mean values at 100 mb. These and

subsequent results, therefore, are unfortunately not helpful in testing the

usefulness of the 1700 cm~l channel.

3.4 Errors Due to Power Law Smoothing

The numerical device of power law smoothing of the retrieved integrated

column water vapor amounts between pressure levels and extrapolation beyond

this domain introduces some error in the first guess procedure. From Table

3-1, for example, it may be noted that RMS errors in retrieving integrated

column amounts near the surface for the TW sample set using the linear fit

method are between 16 and 29% using the 1930.1 and 1231.8 cm~l channels,

respectively. In Figure 3-2, however, retrieval accuracy for the layer

nearest the surface (i.e. 700-1000 mb) is reduced to about 40%. To isolate

the errors due to smoothing (both interpolation and extrapolation) on first

guess retrieval errors, the exact column amounts from the independent TW set

were input as retrieved values to the layer fitting scheme and RMS errors of

the resultant layer values were calculated. Additionally, to eliminate

temperature error effects the exact temperature profiles were used for each

sounding (i.e., 0.0 K temperature error). The results are shown in Figure

3-3. (In this and subsequent like figures the first guess curve refers to a

linear fit.) While there is a small amount of RMS error introduced in the

highest layer retrieval (< 200 mb) due to extrapolation, most of the effect is

apparent in the lowest two layers (i.e. 500-700 mb, 700-1000). The middle two

layers (i.e. 200-300 mb, 300-500 mb) are hardly affected. The magnitude of

the RMS error due to extrapolation to the surface for the lowest layer is

about 10%. As will be discussed in Section 3.6, much of this error is

attributable to soundings with relatively dry layers at the surface.

3.5 Errors Due to Uncertainties in the Temperature Profile

The first guess procedure for each water vapor channel is based on

identifying that pressure level within a given sounding where the brightness

temperature is equal to the actual level temperature. Since retrieved

temperature profiles must be used to accomplish this in practice, their

associated errors critically constrain the potential accuracy of the first

guess moisture retrieval process. This is illustrated by a second curve in

-38-
0.20

RMS

0.M0

ERROR

0.60 0.80

a

(3

s

E>

s

fU

CC

ID

o->

CD

LU

CC

CD

IS

EJ

U3 —

CD —

TROPTCflL NINTE R

0.y0

RMS

0.60

ERROR

0.80

Figure 3-3. RMS errors of first guess layer water vapor values for tropical

winter atmospheres retrieved using: true integrated column

amounts and temperature profiles, true integrated column amounts

and simulated temperature profile errors of 1.5 K, and simulated

integrated column amounts and temperature profiles (i.e. first

guess).

-39-
Figure 3-3 derived by repeating the calculation discussed in the previous

section, however, now including a temperature profile retrieval error of 1.5

K.

Comparing this curve to the previous results (no error in column amounts

or temperature profiles) and to the first guess curve (errors in both column

amounts and temperature profiles), it can be observed that in the upper three

layers, much if not all of the RMS error in the water vapor retrieval is due

to uncertainties associated with the temperature retrieval. In the lowest

layer about a quarter of the error each is attributable to extrapolation and

temperature error while about half is due to uncertainties in obtaining the

water vapor amounts themselves. In the remaining layer (centered at 600 mb),

these factors contribute about one third each to the RMS error.

3.6 Corrections for Supersaturation in the Surface Layer

An examination of individual water vapor soundings within the TW set -

indicated that surface layer values were occasionally quite overestimated by

the first guess retrieval due to extrapolation of the column profile to the

surface (as noted in Section 3.4). In order to circumvent this situation

where possible, a method was developed to test the near surface layer in each

first guess retrieval for Supersaturation (i.e. relative humidity of greater

than 100%) and correct if necessary by reducing the layer water vapor amount

accordingly. The algorithm calculates relative humidity from the water vapor

amount given by the first guess profile in the lowest layer between 975 and

1000 mb and an assumed surface temperature, Ts- If this layer is

supersaturated the power law exponent in the fit for the lowest surface layer

is reduced to bring the relative humidity to a value less than 100%.

Conceptually, the surface temperatures should be available from one of the

AMIS super window channels to an accuracy of about 1.5 K (Chahine et al.,

1984).

The results of testing the surface layer correction are shown in Figure

3-4. The previous first guess results with no relative humidity correction

are included for comparison." Four cases were considered corresponding to:

(1) assuming a constant value for the surface temperature (300 K), and

retrieving surface temperature with errors of (2) 0.0 K, (3) 1.5 K, and (4)

2.0 K, respectively. The retrieved surface temperatures were the actual 1000

mb temperatures with an added random error. Correcting for Supersaturation

-40-
0.20

RMS ERROR

0.M0 0.60 0.80

CO

IS

Q

(\J

CC Q

P

LU

CC

G>

CD <s»

> ^

cr

is

Q

CO

I I I

TROPICflL HINTE R

I

0.20 0.M0

RMS

0.60

ERROR

O NO RH CORR

A TS = 300 K

+ 2.0 K TS ERROR

1.5 K TS ERROR

0.0 K TS ERROR

o

IS

IS

IS

is CC

DC

Q_

is (_D

'

D

>

CE

IS

(3

CD

0.80

Figure 3-4. Effect of surface layer relative humidity adjustment for

supersaturation on first guess RMS errors for tropical

winter atmospheres.

-41-
does improve the surface layer results by a few percent even when a constant

surface temperature is assumed. Using a simulated retrieved surface

temperature value does better still. Notably, this improvement is relatively

independent of the surface temperature retrieval accuracy. Using the 1.5 K

surface temperature retrieval accuracy value, an almost 12% relative

improvement can be realized in retrieving the surface layer water vapor.

Figure 3-5 illustrates the combined effect of relative humidity

correction and uncertainty in the retrieved temperature profile on the RMS

error of the layer water vapor retrieval. The first guess curve includes 1.5

K temperature profile error, but no relative humidity correction near the

surface. The relative humidity correction adopted assumes a 1.5 K error in

surface temperature retrieval. Consistent with the discussion in Section 3.5,

the effect of temperature profile error reduction from 1.5 to 1.0 K is chiefly

noted in the upper atmosphere.

3.7 Summary of First Guess Results

The first guess water vapor retrieval algorithm was applied to each of

the five atmospheric sounding sample independent sets defined in Table 2-1.

The format adopted as the standard algorithm for this purpose included the

linear fit of column integrated values from the respective dependent set

(§3.2), power law smoothing of the retrieved integrated profile (§3.3), an

assumed temperature profile error of 1.5 K (§3.5), and the relative humidity

correction of the surface layer values with an assumed surface temperature

retrieval error of 1.5 K (§3.6). Results are given in Figure 3-6 (climatologies for comparison are shown in Figure 2-8) and can be understood largely

on the basis of the scatter diagrams illustrated in Figure 2-13 upon which the

first guesses are based. The high RMS errors for the upper levels of the

midlatitude atmospheres (MS, MW) are probably in large part due to an extrapolation of the profiles above the values given by the 1700 cm~^ channel to

tropical rather than the appropriate midlatitude values. The RMS error

minimum for both the layers centered at 250 mb (for the tropical atmospheres

sets) and at 400 mb for all of the sets is undoubtedly due to the influence of

the 1650.1 and 1839.4 channels in providing accurate column amounts. For the

two surface layers (centered at 600 and 850 mb, respectively), RMS error is

related to the degree of scatter in the log integrated water/brightness

temperature fit for the channels peaking in the lower atmosphere. The RMS

-42-
0.20

RMS

0.40

ERROR

0.60 0.80

LoJ

OC

ID

CO

CO

LU

CC

Q_

CD

>

cr

is

si

(S

O

CD

I I I I

TROPTCflL NINTE R

0.20 0.40

RMS

0.60

ERROR

0.80

Figure 3-5. Combined effect of surface layer relative humidity adjustment

and simulated temperature profile error on first guess RMS

errors for tropical winter atmospheres.

-43-
0.20

RMS ERROR

0.40 0.60 0.80

IS)

s

CO £ —

CC s

——^ * 01 5

CO

LU

CC

Q_

" E>

CE

Q

(3

CO

0.20 0.40

RMS

0.60

ERROR

0.80

Figure 3-6. RMS errors of first guess layer water vapor values for

tropical winter, tropical winter (ocean only), tropical

summer, midlatitude winter, and midlatitude summer atmospheres.

-44-
error performance in the surface layer by atmospheric set is that given by the

ability of the 1930.1 cm~l channel to retrieve column integrated amount within

the context of the first guess method, i.e. in order of increasing accuracy:

midlatitude winter, tropical summer, midlatitude summer, and tropical

winter. The specially processed tropical winter set using soundings over the

ocean probably does best mostly because it has the least number of soundings

with dry lower layers. In order to improve the first guess algorithm in the

lower atmosphere, especially for the midlatiude soundings, it will be necessary to investigate more advantageous column retrieval approaches.

-45-
4. RELAXATION OF FIRST GUESS RETRIEVALS

4. 1 Relaxation Algorithm

Although the first guess algorithm described in the previous section

produces skillful retrievals throughout much of the atmosphere, it is

desirable to take advantage of the sensitivity of the selected water vapor

channel set to further reduce remaining errors. This is of particular value

for the layers above 200 mb for which the first guess does not provide much

improvement over climatology. In order to accomplish this objective, the

first guess layer water vapor values were used to start an iterative retrieval

process based on the relaxation method (Chahine, 1968, 1970). The particular

algorithm adopted is summarized in Figure 4-1.

The relaxation algorithm was formulated to retrieve atmospheric water

vapor profiles (i.e. layer column values as described in §3.3 above) from

A «

noisy simulated sensor brightness temperatures, Tr~ , [or equivalently their

radiances R^T1)] calculated from the independent set of soundings. The six

b

AMTS channels (or alternatively, the four HIRS channels) used in the first

guess algorithm were also used as input for the relaxation code. A retrieved

A A

temperature profile, T(p) , and surface temperature, T , were also assumed

5

known, each with 1.5 K of retrieval error (2.0 K for HIRS). For each

attempted retrieval, the relaxation process was started using the first guess

integrated water vapor profile, UO(P), obtained using the methodology

described in Section 3.2 above and the rapid algorithm (Susskind et al., 1982)

* A A

to evaluate radiances for each channel, R [U (p), T(p), T ]. The need for

o o s

subsequent relaxations was based on examining the residuals for each channel

given by:

. R1 - RW)

A =

 n . .. b (4.D

Two formats were used in this decision: (a) without constraints or (b) with

constraints. In the former cases, a fixed number of relaxations (say three or

ten) were employed, regardless of the residual values. For the latter cases,

relaxation of a particular channel was terminated when either the residuals

increased or when they were reduced below a predetermined noise threshold.

The following sections discuss the relationship used to relax water vapor

values during the retrieval process, the effect of temperature profile errors

-46-
cFirst Guess

Layer VaIues

Layerto-Level

Conversion

Rapid

Algorithm

G nth Relax j

Simulated Data 7

C

Relaxed J

Layer Values J

CActual Layer

Values

Relaxed

RMS

Error

Columnto-Layer

Conversion

Adjust

Surface

Values

Relaxation

Equation

YES

RH \_ NO

Correct i on

Figure 4-1. Schematic of the Relaxation Program

-47-
and the use of various constraints to terminate channel relaxation, and

finally retrieval results for both AMIS and HIRS for the atmospheric sounding

sets defined above.

4.2 The Relaxation Equation

The relaxation equation adopted for determining the water vapor column to

pressure level p(T = T ) from the i channel radiance was

(4.2)

n ' n

where T is the channel transmittance for the ntn relaxation. It is

n

partially based on the assumption of a random strong line

1/2

relationship (T. « exp(-a.U )) between transmittance and integrated water

vapor, resulting in:

Vl = V1 + ln[R>/l]/l - O. (4.3)

4.3 Factors Influencing Relaxation Results

Although the volume of our relaxation tests has been limited in scope,

five factors have been identified which apparently influence the accuracy of

resultant water vapor retrievals. In approximate order of increasing

importance as they influence retrieval accuracy these are: (1) temperature

profile error, (2) number of iterations, (3) constraints used to terminate the

relaxation process, (4) accuracy of first guess profile, and (5) water vapor

channel set. To some extent, these factors are interrelated. For example,

the number of iterations taken for a specific channel depends on the decision

method used to terminate relaxing (if there is one). The water vapor channel

sets (or alternatively, the sensor chosen) fixes the magnitude of temperature

profile error and, as described in Section 3, also determines the accuracy of

the first guess. It has also been noted previously that the first guess

accuracy depends on the sample set of atmospheric soundings chosen for

retrieval (i.e. midlatitude vs. tropical, etc.)

The effectiveness of the relaxation algorithm applied to the tropical

winter set and AMTS instrument is illustrated in Figure 4-2. Here the

ensemble RMS error was evaluated over the set of 100 independent TW soundings

-48-
0.20

RMS

0.40

ERROR

0.60 0.80

fS>

E>

CQ S

CO

CO

UJ

OC

Q_

cr

£3

(3

CO

T T I

TROPICAL WINTER AMTS

JX - CUM.

lELSXED - 3X - 1ST

iELRXED - 1 OX - NO ONST.

I I

E)

IS)

s>

CO

UJ

DC

is

cr

(S

IS)

CO

0.20 0.140

RMS

0.60

ERROR

0.60

Figure 4-2. Comparison of RMS error in water vapor retrieval results for

Tropical Winter (ocean only) atmospheres relaxed using climatology as a first guess (3 iterations), and the first guess

results as a first guess (for both three and ten iterations),

-49-
for layer water vapor profiles relaxed using: (a) climatology (i.e., the mean

profile from the dependent TO set) as first guess (relaxed three times with

constraints), (b) the first guess as first guess, and (c) the first guess but

relaxed ten times with no constraints. The assumed temperature profile error

for AMTS was 1.5 K. Both the variability of the dependent sounding set (i.e.

climatology) and the first guess retrieval are included for comparison, for

this set of soundings, the relaxation method significantly improves the

accuracy of water vapor retrievals obtained using the first guess algorithm

alone. Notably, the relaxed results obtained using the first guess as the

starting water vapor profile are somewhat better than those similarly obtained

starting with climatology.

The best results overall are those relaxed ten times for each channel

without terminating relaxation in any channel (i.e. no constraints). The

figure of ten relaxations was chosen for convenience and does not represent

the result of an optimized relaxation procedure. The degree of improvement

noted for this case is uniform for each layer compared to the initial first

guess results. This is not true for the cases performed with individual

channel relaxations terminated when either the residuals increased or were

determined to be below a numerical noise value (i.e. the constrained cases).

These errors in the upper atmosphere increased with each relaxation.

The effect of these relaxation termination constraints is illustrated in

Figure 4-3 for the AMTS instrument applied to the independent set of soundings

for tropical summer. Three relaxations were done with and without individual

channel relaxation termination. For comparison climatology, the corresponding

first guess retrieval, and results for ten relaxations (without the

contraints) are also included. Note that accuracy at upper levels is reduced

by terminating the relaxation of individual channels. Examination of the

residuals for these channels indicates that they relax very early in the

process (i.e. within one or two iterations). Terminating relaxation of these

channels in subsequent iterations, however, allows noise to build up (i.e.

their residuals actually increase) decreasing their impact on the retrieval

accuracy. The effect of such noise can also be seen in the ten times

relaxation results for the level values centered at 600 mb. There an increase

in the number of iterations from three to ten actually increases the RMS error

slightly although there is improvement over much of the profile, especially

for the layers nearest the surface. In general, applying the relaxation

-50-
0.20

RMS ERROR

0.40 0.60 0.80

T

TROPICni SUMMER

ts

(3

IS)

E>

CD

LiJ

CC

ID

cn

CO

LU

cc

CE

is

ts

to

C3

(3

(3

00

Q<+X«|

CUMfllOLOGY :

TR5T GUESS

tELftXED 3X -

1ELHXED 3X -

RELAXED I0X

H/ CONSTS.

H/0 CONS75.

- H/0 CONS1S.

I

is

IS L£l

K) CC

CO

LU

CC

CC

is

is

is

is

oo

0.40 0.60

RMS ERROR

0.80

Figure 4-3. Effect of relaxation constraints on tropical summer water

vapor retrievals using AMTS.

-51-
algorithm to AMIS, we have observed that the number of iterations required for

residuals to stabilize at a minimum value is least for upper layers, greatest

near the surface, and intermediate for the middle layers.

The effect of temperature profile retrieval accuracy on relaxation

results is illustrated in Figure 4-4. Temperature profile error affects the

water vapor retrieval relaxation process through the assignment of channeldependent integrated column amounts to specific pressure levels based on

comparison of brightness temperatures to the assumed temperature profile.

Curves for three relaxations and temperature profile errors of 0.0 K, 1.5 K,

and 2.5 K are illustrated. The first guess input profile illustrated for

comparison was obtained assuming 1.5 K temperature profile error as is that

for ten relaxations. As expected RMS error in layer water vapor retrieval

increases with increasing error in the temperature profile at all levels.

Notably, however, the spread in RMS water vapor error from 0.0 to 2.5 K

temperature error is not great, i.e. temperature error does not greatly affect

the relaxation results. Except for the level centered at 400 mb, for example,

increasing the number of relaxations from three to ten improves the retrieval

accuracy at all levels above that obtainable with no temperature profile

error.

4.4 Comparison of AMTS and HIRS Instruments

First guess results for the AMTS and HIRS-2 instruments were used as

initial guesses for the relaxation algorithms to provide the basis of an

instrument comparison. Relaxation results were calculated for the tropical

winter (ocean only), midlatitude summer, and midlatitude winter atmospheric

sounding sets.

Figure 4-5 compares relaxations for HIRS-2 and AMTS using corresponding

first guess inputs. For the same number of relaxations (term with no

constraints), AMTS outperforms HIRS-2. Comparing the first guess and relaxed

RMS error statistics for each instrument, the improvement due to relaxation of

the first guess is quite nonuniform for HIRS. Accuracy in the upper layers is

markedly improved while that"near the surface responds little. As remarked

earlier, it is much more uniform for AMTS. A possible explanation of this

discrepancy is the applicability of the relaxation equation used at each

iteration (cf. Section 4.2) to the specific spectral properties of each

instrument's channels. It is likely that the assumptions used in deriving the

-52-
RMS ERROR

0.20 0-4 0 0.60 0.80

T

TROPICAL WINTER AMTS

G>

E3

EJ

LL)

CC

ID

CO

CO

LU

CC

is

E>

CC

03 (D CLIMflTOLOGT

A FIRST GUESS

+ 3 RELflX - 0.0 K

X 3 RELflX - 1.5 K

O 3 RELflX - 2.5 K

10 RELflX - 1.5 K

I

IS)

s f ^

^QQ

S

CD

LU

CC

s

cr

IS)

SI

IS)

O

03

0.20 0.M0

RMS

0.60

ERROR

0.80

Figure 4-4. Effect of temperature profile error and number of relaxations

on AMTS retrieval of layer water vapor values for tropical

winter atmospheres (ocean only).

-53-
0.20

"1

RMS ERROR

0.40 0.60 0.80

TROPICAL WINTER

E>

E>

OQ

LU

DC

ID

co

CO

LU

cc

O

Q

Q

IS

(\J

is

E)

ID

(3

ta

C3

CD

<5>

(3

IS)

CO

CO

LU

OC

CE

El

CO

O CLIHftTOLOGT

^ HIRS - FIRST GUESS

+ ftHTS - FIRST GUESS

X HIRS - RELflXED - 10X

<>> flHTS - RELflXE 10X

0.20 0.M 0

RMS

0.60

ERROR

0.80

Figure 4-5. Comparison of AMTS and HIRS first guess and relaxed RMS

errors in retrieved water vapor for tropical winter

(ocean only) atmospheres.

-54-
relaxation criteria (i.e., random strong lines) is most applicable to the most

opaque HIRS-2 channels, i.e. those affecting the retrieval of upper layers.

Additionally, most of the information available from the HIRS-2 channels

affecting the lower atmosphere, is probably already in the first guess.

Analogous results for the midlatitude summer sounding set is shown in

Figure 4-6. In this case the better HIRS first guess in the layer near the

surface gives it an advantage in the subsequent relaxation processes.

Throughout much of the rest of the atmosphere, however, the converse is true,

with the relaxed AMTS results providing more accurate retrievals. As as noted

in the discussion of Figure 4-5, the upper layer HIRS results relax

considerably over those of the first guess while those near the surface change

little.

Finally, Figure 4-7 compares HIRS and AMTS for the midlatitude winter

sounding set. As noted previously, first guesses for this set are not

particularly good due to the poor column integrated water/brightness

temperature relationships derived from the dependent set. Like the MS set

results above (with the exception of the layer centered at 250 mb), the AMTS

first guess results are slightly better in the upper layers, while HIRS better

predicts the surface layer values. Upon relaxing a like number of times (in

this case six with constraints), RMS errors increase in the lower atmosphere

for the HIRS instrument while decreasing for the AMTS.

-55-
0.20

RMS ERROR

0.M0 0.60 0.80

o

G>

IS

S

O

(\J

CC E>

ID a*

cn ^

en

LJ

CC

CD

E5

E»

10

(3

E)

C3

o

03

T I I I

MIDLflTITUDE SUMMER

O CLIMflTOLOGY

A HIRS - FIRST GUESS

+ flMTS - FIRST GUESS

X HIRS - RELflXED - 3X

O flMTS - RELflXED - 3X

I I

E>

IS)

a

CD

LU

CC

G '

s CD

<*>

CE

00

0.20 0.40

RMS

0.60

ERROR

0.80

Figure 4-6. Comparison of AMT9 and HIRS first guess and relaxed RMS

errors in retrieved water vapor or midlatitude summer

atmospheres.

-56-
RMS

0.20 0.M0

ERROR

0.60 0.80

i i i i r

MIDLflTITUDE NINTE R (OCERN ONLY)

E)

E) E)

E)

E>

E>

Q

OJ

DC

ID

CO

CO

LiJ

DC

Q_

CD

>

CT

IS

IS

Q

CO

E>

E)

CO

LU

DC

E)

E)

El

cc

<D CLIMflTOLOG.Y

A H]RS (FIRST GUESS)

+ flMTS (FIRST GUESS)

X HJRS (RELflXED 6X)

O RHTS (RELflXED 6X)

E)

<a

E)

E)

00

0.20 0.140

RMS

0.60

ERROR

0.80 1.00

Figure 4-7. Comparison of AMIS and HIRS first guess and relaxed RMS

retrieval errors for midlatitude winter atmospheres

compared to climatology.

-57-
5. STATISTICAL RETRIEVAL OF WATER VAPOR

5.1 Background and Methodology

As the last stage in this abbreviated effort, the first guess and relaxed

physical retrieval simulations described above were compared with statistical

retrieval simulations, described in this section. The statistical moisture

profile retrievals were obtained based on inverting the independent samples of

simulated sensor brightness temperatures calculated using the simulation code

described in the previous sections and implementing an inversion technique

based on an approach to obtaining geophysical parameters from radiometric data

discussed by Rodgers (1966), Staelin (1967), Gaut (1967), Waters and Staelin

(1968) and Gaut (1968). It is similar to the procedure outlined in Westwater

and Strand (1965). The method is reviewed by Rodgers (1976). The essential

element of the scheme is to choose, in a statistical sense, the most probable^

combination of atmospheric and surface properties which produces the set of

measured radiometric data values. It is a general statistical regression

technique which minimizes the mean square error between the estimated and

observed values of the parameter of interest. This method is also similar to

that used operationally for obtaining microwave temperature profiles from the

SSM/T (Rigone and Stogryn, 1977; Grody et al., 1984) and proposed as the basis

of an approach to millimeter moisture retrieval by Rosenkranz et al. (1982).

As applied in our retrievals, layer water vapor abundances obtained from the

dependent sample set of radiosondes were regressed directly against the

respective brightness temperatures obtained by stimulation. Retrievals were

accomplished by using these regression statistics and simulated sensor

brightness temperatures for the independent sample to obtain analogous layer

abundances. The parameter retrieved was the absolute abundance of water vapor

(molecules cm~2) in six layers corresponding to 0-200, 200-300, 300-500, 500-

700, 700-850 mb, and 850-1000 mb, respectively.

More precisely, the technique consisted of calculating and using the

eigenvectors of covariance matrix of the data set (here brightness

temperatures) with itself and of the parameter set (here layer integrated

water vapor) with itself (see Smith and Woolf, 1976). An individual retrieval

of layer integrated water vapor in the six layers from n channel brightness

temperatures was obtained from:

-58-
u = Dt (5.1)

with

D = (UT)(T*A* (5.2)

where

rs

is a vector giving an estimate of the profile of integrated water

vapor in each of six layers

is a vector whose components are n brightness temperatures

water vapor at six levels for s atmospheric samples (r=6)

T brightness temperatures for n channels for s samples

T* selected eigenvectors of TTC

A* diagonal matrix whose elements are corresponding eigenvalues

The eigenvectors having relatively small eigenvalues (compared with the

largest eigenvalue) can be discarded since they represent noise. In the

algorithm employed, only eigenvectors of the covariance matrix of the data set

with itself have the potential to be discarded. The advantage of the method

is that by truncating the sequence of eigenvalues, one reduces the condition

number of the matrix, and therefore also the sensitivity to noise. (As it

turns out, none of the eigenvalues of the covariance matrix of the parameter

set with itself are small enough to be discarded using a criteria of 10 .

Thus all of them need to be retained.) In this method, if none of the eigenvectors are discarded, the problem reduces to that of solving the least

squares fit problem, i.e.

D = (5.3)

A quantitative measure of retrieval accuracy was obtained by comparing

inferred layer water vapor abundances to those in the actual profiles (the

error) and evaluating the fractional root mean square (RMS) error over the

ensemble of retrievals. The RMS error for each layer k evaluated over the set

of N = 100 independent soundings was again defined as:

-59-
of N = 100 independent soundings was again defined as:

M

i _i " * 71/ 9

RMS(k) = —!- (N I [u(k,j) - u(k,j)] } ' (5.4)

u(k) j=l

where u(k,j) and u(k,j) are, respectively, the retrieved and actual water

vapor amounts for the k layer and j sounding and u(k) is the layer mean

value. For comparison, the same statistic was evaluated assuming the mean of

the ensemble as the best estimate climatological retrieval for each sounding,

i.e. by replacing u by u itself. The ratio of the fractional RMS error of the

retrievals to that of climatology provides a direct measure of retrieval

effectiveness. The former quantity should always be less than the latter.

(When this is not true the retrieval process itself has usually added too much

noise.) The fraction of unexplained variance (FUV), an often used statistic,

is the square of this ratio. When the two quantities are equal, the FUV is *

unity and no information has been gained from the retrieval process. When the

FUV is zero, the retrieval is perfect.

5.2 Comparison of Retrieval Simulation Results

Figure 5-1 compares the RMS fractional errors for simulated statistical

retrievals of tropical winter ocean (TWO) soundings from measurements by AMTS,

HIRS, AMSU-B, and SSMT/2 instruments. It is seen that, at pressures greater

than 750 mb, errors are nearly equal for all four instruments and less than

those resulting from physical retrievals, as shown in Figure 4-5. At

pressures less than 750 mb, the infrared retrievals are more accurate than the

millimeter wave retrievals but become generally less accurate than the

physical retrievals, at least in the case of AMTS. The almost identical error

profiles for AMTS and HIRS statistical retrievals are in marked contrast to

the systematic superiority of physical retrievals for AMTS relative to those

for HIRS for tropical simulations. Similar results were found in tropical and

midlatitude summer simulations.

RMS errors for AMTS and" HIRS midlatitude winter statistical retrieval

simulations are shown in Figure 5-2. Again, the error profiles are almost

identical, AMTS being only marginally better. In this case, however, the

statistical retrievals are better than the physical retrievals at all levels,

as can be seen by comparing Figure 5-2 with Figure 4-7.

-60-
0*002

(9N)

0'00fi 0*009 0-00 9

CO

cn

ca

CM

is

z:

<z

<n

a:

cc

o

cc

QJ

CC

I—

LU

CC

_J

<r

ca

(S

cn

0

es

0*00 2 0'00fi

(9N)

0*009 0*008

Jj

0)

4J »

C co

•H pi

5 M

4J CO •

i-H cfl 60

T) > O

•H 0) •-!

g -H O

H 4J

o

4-4

r-l

1

in

CO

cfl

0)

cO

0)

!-i

rH

CO

0

•H

4J

CO

•H

4-1

Cfl

4-1

g

•H

i-l

0

""O

C

cfl

ft

CO

H

23

co co

I

u-i

t>o

•H

CO

cn

CM

to

cn

Q

01

CM

0'002 0'00fi 0*009

caw)3ynss3U d

0*00 8

§

cfl

0)

•H

CO G.

pi g

M O

PS O

CN

CO

O

•r-l CU

ft M

O

VJ t-l

4J CO

o

CO

o

CU C

cfl

cn cu

<^H ^ S o

I

in

d

oo

cu cn

g-g ^

3 (0 60

CO O

cfl

01

6

0)

4-1

cd

C3 Cfl

w 6

o

3 cn ji

E H u

•H S -H

-61-
One implication of the above comparisons is that water vapor retrievals from

AMIS measurements should be generally equal to or better than from HIRS or AMSU,

at least for clear conditions. Supplementary microwave measurements would be

desirable for overcast conditions, but our studies have found that the presence

of clouds seriously degrades retrievals from measurements near 183 GHz, and

requires extra channels to minimize cloud effects (Isaacs et al., 1985).

Another implication is that best results can be obtained by physical

retrieval methods in the tropical and/or summer middle troposphere. Statistical

retrievals seem to be generally more useful in the lower troposphere, and at all

levels in middle (and presumably high) latitudes. It is still possible, however,

that improved physical retrievals would result from the use of channels other

than those used in this study. Some support for this possibility comes from the

following examination of the separate contributions of the temperature and water

vapor channels to the statistical retrievals.

5.3 Contributions of Temperature and Water Vapor Channels

The results reported for statistical retrievals from AMIS and HIRS in

Figures 5-1 and 5-2 were obtained with the use of all the temperature channels,

as well as the water vapor channels, in contrast to the physical retrievals

reported earlier, for which only the water vapor channels were used, with the

temperature assumed known within an RMS standard error. This approximates the

way in which the physical and statistical retrievals would be done in practice,

except that the temperature retrievals would be done first for a physical inversion, then water retrieval, then iteration.

Statistical inversion does not use a priori information except in the sense

that it is included in the regression coefficients. Some insight into the

information content of individual channels or sets of channels can be gained by

examining the effect on RMS fractional errors of eliminating them in the statistical retrievals. This is illustrated for AMTS and HIRS tropical winter ocean

statistical retrievals in Figure 5-3. The curves are, from left to right, for

retrievals with the combined set of temperature and moisture channels as in

Figure 5-1, for the temperature channels only, for the moisture channels only,

and for climatology. Qualitatively similar results are shown in Figures 5-4 and

5-5, respectively, for summer and winter midlatitude retrievals. The temperature

channels, labelled T and TQ, and moisture channels, labelled WV, are listed in

Table 5, and consecutively numbered.

-62-
(9W 3SdnSS3Ud

0*002 0*00Fi 0*009 0*008

01

0*002 0*00Fi 0*00 9

caw)3ynss3y d

0*009

01

0*002 0*00 h

(8W)

0*009 0 '008

, — I

CO

O

•H

4-1

CO

•H

4J

CO

4-1

CO

sM

EC

•"O

C

cfl

C/l

tJH

<£

C

CO

cu

o

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t-i

CU

4J

C

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iH

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cx

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4-1

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M-l

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-63-
(9W)3UflSS3U d

0-008 0'00fl 0-009 0-00 8

I

to

GJ

CO

IS

10

8

<3

0'002 0'00fi

(aw )

0'009 0-008

OD

CO

ru

to

IS

CO

(LI

•O

W

•H

4J

n)

iH

T)

•H

S

u-i

en

a

-<r

in

0)

60

•H

OJ

0'002 0'00fi 0*009 0*008

-64-
0-002

(9N)

0-00F) 0'009 0-009

0-002 0'00fl

(GN)

0-009 0-00 8

0*00 2 0-00F)

(9N)

0-009 0-00 8

t-l

0)

4-1

c

•H

0)

3

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01

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-65-
Table 5

AMIS and HIRS/MSU Temperature and Water Vapor Channels, and Water Vapor

Contribution to Temperature Channel Brightness Temperatures

AMTS HIRS/MSU

No.

(1)

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

«-i

607.0

623.2

627.8

634.3

646.6

654.4

665.6

666.8

668.2

669.4

875.0

1231.6

1650.1

1700.3

1839.4

1850.9

1930.1

2384.0

2386.1

2388.2

2390.2

2392.4

2394.5

2424.0

2505.0

2686.1

Funct- ATB

i

(C)

ion TWO MWM

T 3.9 0.9

T 3.7 1.2

T 0.3 0.1

T

T

T

T

T

T

T

WV

WV

WV

WV

WV

WV

WV

T

T

T

T

T

T

TG

TG

TG 0.4 0.1

cm 1

668.4

679.2

691.1

703.6

716.0

732.4

748.3

897.7

1027.9

1217.1

1363.7

1484.4

2190.4

2212.7

2240.1

2276.3

2511.9

2671.2

50.3 GHz

53.7 GHz

55.0 GHz

58.0 GHz

Function

T

T

T

T

T

T

T

WV

TG> 03

WV

WV

WV

T

T

T

T

T

T

TG

T

T

T

ATB

i

(C)

TWO

0.4

1.1

2.7

, 4-6

2.0

1.0

0.6

0.3

0.2

2.6

-16.0

-0.3

-66-
The AMIS moisture channel results are distinctly superior to those from

HIRS, supporting the previous conclusion that the similar results from the

physical retrievals are probably due to more moisture information in the AMIS

channels. It is interesting that the statistical retrievals are considerably

improved when the temperature channels are included, and particularly striking

that use of the temperature channels alone give better results than use of the

moisture channels alone. Part of the explanation, of course, is that the

radiances in the moisture channels are functions of both the temperature and

moisture distributions, and that there are more temperature channels than

moisture channels. The question remains, however, as to whether the water

vapor information in the temperature channels is mostly due to the well-known

correlation between moisture and temperature in the atmosphere or to water

absorption/emission in the temperature channels.

Two pieces of evidence supporting the latter cause are a much smaller

improvement of statistical microwave retrievals by inclusion of the less

moisture-sensitive temperature channels, and a marked deterioration of the

retrieval when the most moisture-sensitive AMIS channels (channels 1 and 2,

see Table 5) are removed. The moisture sensitivity is shown in Table 5 by the

columns labelled AT^(C), representing the increase in brightness temperature

when the specific humidity is decreased by 99 percent at all levels. The

effect of this temperature channel moisture sensitivity is shown in Figure 5-6

for TWO and MWM AMTS retrievals. The curves are, from left to right

respectively, retrievals from all 19 temperature channels, a pair of almost

identical retrievals with channels 1 and 2 missing, and with 1, 2, 3, and 28

missing, and finally climatology.

Evidently, the CC^ absorption is helping to provide sharper effective

water vapor weighting functions, even in the lower layers. The possibility of

using these channels to improve physical moisture retrievals, therefore, seems

well worth investigating. The possibility of finding even better new moisture

channels in the 15 \i CC^ band seems even more promising, since the temperature

channels were deliberately chosen to minimize rather than maximize the effect

of water vapor.

-67-
0*002

(9N)

0*00fi 0'009 0*009

I

CO

en

cc

1

CO

ts>

cn co

H ^1

c

en a

°C ^rH .C

c\j

S

0*002 0'00fi

(9W )

0*00 9 0*009

en

cn

CC

03

CO

OJ

C3

•H «

S 60

CO -H

rH W

CO CO

> -H

cu e •

•H >,

»-l CM 60

W O

CD tl iH

H C O

CO -U

t-l cfl

ca rH e O -H

•H CO ^H

W rH O

CO <D

•H C M

W C O

nj cfl IH

w ^3

co o -a

2 J3 cfl

S 60

•a c

C « -H

CO CO CO

i-H CO

O 0) -H

Ctt CO

t-l X Cv4

O CJ

4-1 T)

0) C

M cd

4J «

cd ro

CO

O

CX CN

VO

I

m

eo

•H

0*002 0*00h 0*009 0*009

-68-
6. SUMMARY AND CONCLUSIONS

A two-step method has been developed to retrieve water vapor profiles

from satellite radiance data employing a physically-based first guess

initialization of an inversion of the radiative transfer equation by

relaxation. The approach has been applied to synthetic radiance data

calculated for water vapor channels of the HIRS and AMIS instruments for

ensembles of seasonally and latitudinally dependent radiosondes. Results of

these simulated retrievals are summarized in Table 6 for the two sounding sets

corresponding to the most and least successful performance, i.e. tropical

ocean winter (TWO) and midlatitude winter (MW), respectively. For each layer

and instrument the fraction of unexplained variance (FUV) has been evaluated

corresponding to both first guess retrievals alone and those obtained after

subsequent relaxation. The FUV values correspond to the ratio of variance *

remaining after retrieval to that of the original climatology. Meaningful

values lie between 0 and 1, corresponding to perfect and perfectly useless,

retrievals, respectively. To compare the two instruments, the ratio of FUVs

for HIRS and AMTS is included to provide a figure of merit (FOM) indicating

the relative ability of the AMTS to decrease the unexplained variance. The

FOM is unity when the instruments perform equally and greater than unity when

AMTS outperforms HIRS.

From these values it is notable that even the first guess procedure alone

provides skillful retrievals for layers in the middle atmosphere. The

greatest reduction in variance occurs for the AMTS-based retrievals in the

300-500 mb layer. Using relaxed retrievals, the FUV is reduced even

further. From the FOM values, it appears that the high resolution AMTS water

vapor channels are capable of reducing the unexplained variance by factors of

at least 1.5 and usually greater than 2.0 relative to the HIRS-2 system.

The results of statistical inversion simulations show that better

retrievals should be obtainable in the lowest and highest layers, where the

simulated physical retrievals were the poorest, and where better retrieval

algorithms and/or better channels seem to be required. The use of moisturesensitive channels in the 15 ym C02

 band to retrieve low layer water vapor

seems particularly promising.

-69-
Table 6. First Guess and Relaxation FUV and FOM Values

First Guess

Sounding Set:

(a)

(b)

Layer

TWO

< 200

200-300

300-500

500-700

700-1000

MW

< 200

200-300

300-500

500-700

700-1000

FUV

(HIRS)

1.50

0.81

0.21

0.37

0.63

25.12

0.72

0.28

1.26

1.53

FUV

(AMTS)

1.24

0.15

0.08

0.14

0.90

8.50

0.25

0.07

0.35

0.13

FOM

1.2

5.4

2.6

2.6

0.7

2.9

2.9

4.0

3.6

11.8

FUV

(HIRS)

0.90

0.03

0.17

0.32

0.55

5.52

0.08

0.16

1.33

1.77

Relaxed

FUV

(AMTS)

0.27

0.02

0.02

0.06

0.31

1.19

0.04

0.05

0.30

0.77

FOM

3.3

1.5

8.5

5.3

1.8

4.6

2.0

3.2

4.4

2.3

The usefulness of the 700 and 650 cm~^ channels to obtain water

retrievals in the upper troposphere and lower mid-latitude and polar

stratosphere cannot be adequately tested against radiosonde measurements

because radiosondes do not measure water vapor above about the 300 mb level.

Hopefully, the new ATMOS data will provide measurements at these heights

against which to test retrievals from the new channels, which promise to

extend the height to which the atmosphere is routinely sounded for water

vapor.

ACKNOWLEDGEMENTS

The authors wish to thank Dr. Moustafa T. Chahine of Jet Propulsion

Laboratory for his continuing interest and helpful discussions, and for

support of this work prior to the effective starting date. We also wish to

thank Dr. Joel Susskind of NASA/GSFC for the use of his rapid algorithm

routine and other codes and data for HIRS/AMTS simulations.

-70-
MEETINGS ATTENDED

Dr. Kaplan attended the NASA/IFAORS Review of Instrument Development in

the Global Scale Process Research Program held in Washington, D.C. on

September 26 and 27, 1983, and presented a report on "AMIS Studies", with

emphasis on the I^O channels including the weighting functions and sensitivity

analysis of the new set of channels. He also attended the Fifth AMS

Conference on Atmospheric Radiation held in Baltimore, MD, October 31 to

November 4, 1983, and co-chaired a session on Radiation and GCM. A paper

entitled "Retrieval of Humidity Profiles from Satellite Radiance Measurements"

by L. D. Kaplan and R. G. Isaacs was presented at the Workshop on Advances in

Remote Sensing Retrieval Methods, held in Williamsburg, VA, October 30 to

November 2, 1984. It will appear in Advances in Remote Sensing Retrieval

Methods, published by A. Deepak Publishing and edited by A. Deepak, H. E.

Fleming, and M. T. Chahine. Reprints will be sent when they are available.

-71-
REFERENCES

Chahine, M. T., 1968: Determination of the temperature profile in an

atmosphere from its outgoing radiance. J. Opt. Soc. Amer., 58, 1634-1637.

Chahine, M. T., 1970: Inverse problems in radiative transfer: Determination

of atmospheric parameters. J. Atmos. Sci., 27, 960-967.

Chahine, M. T., N. L. Evans, V. Gilbert, and R. D. Raskins, 1984:

Requirements for a passive IR advanced moisture and temperature sounder.

Appl. Opt., 23, 7, 979-989.

Clough, S. A., 1983: Preliminary Instructions for FASCOD1C (rev. 1).

AFGL/OPI, 27 September 1983, 26 pp.

Gaut, N. E., and E. C. Reifenstein III, 1971: Interaction model of microwave

energy and atmospheric variables. ERT Tech. Rep. No. 13, Environmental

Research and Technology, Inc., Waltham, MA, 167 pp.

^.

Isaacs, R. G., G. Deblonde, R. D. Worsham, M. Livshits, 1985: Millimeter wave

moisture sounder feasibility study: The effect of cloud and precipitation

on moisture retrievals. AFGL TR-85-0040, Air Force Geophysics Laboratory,

Hanscom AFB, Bedford, MA 01731.

Gaut, N. E., 1967: Studies of Atmospheric Water Vapor by Means of Passive

Microwave Techniques, Ph.D. Thesis, Dept. of Meteor. M.I.T., Cambridge,

MA.

Gaut, N. E., 1968: Research Laboratory of Electronics Tech. Report No. 467,

M.I.T., Cambridge, MA.

NOAA, 1981: NOAA Polar Orbiter Data (TIROS-N and NOAA-6) Users' Guide. NOAAEDIS-NCC-SDSD, Washington, DC.

Phillips, N. A., 1984: Results of Comparative Simulation Studies on AMTS and

HIRS Conducted by NASA and NOAA (to be published).

Rigone, J. L. and A. P. Stogryn, 1977: Data processing for the DMSP microwave

radiometer system. In Proc. Eleventh International Symp. Remote Sensing

of the Environment. Univ. of Michigan, Ann Arbor, MI, pp. 1599-1608.

Rodgers, C. D., 1966: A Discussion of Inversion Methods, Memo 66.13,

Clarendon Laboratory, Oxford University.

Rodgers, C. D. , 1967: The radiative heat budget of the troposphere and lower

stratosphere. MIT Department of Meteorology, Report No. A2, Cambridge,

MA.

Rosenberg, A., D. B. Hogan, C. K. Bowman, 1983: Satellite Moisture Retrieval

Techniques. Vol. 1: Technique Development and Evaluation. CR 83-01(a),

Naval Environmental Prediction and Research Facility, Monterey, CA 93940.

-72-
Rosenberg, P. W., M. J. Konichak, and D. H. Staelin, 1982: A method for

estimation of atmospheric water vapor profiles by microwave radiometry.

J. Appl. Meteor.. 21, 1364-1370.

Rosenkranz, P. W., M. J. Komichak, and D. H. Staelin, 1982: A method for

estimation of atmospheric water vapor profiles by microwave radiometry.

J. Appl. Meteorol.. 21, 1364-1370.

Rothman, L. S., R. R. Gamache, A. Barbe, A. Goldman, J. R. Gillis, L. R.

Brown, R. A. Toth, J.-M. Flaud, and C. Camy-Peyret, 1983: AFGL atmospheric line parameters compilation. Appl. Opt., 22, 2247-2256.

Smith, H. J. P., D. J. Dube, M. E. Gardner, S. A. Clough, F. X. Kneizys, and

L. S. Rothman, 1978: FASCODE - Fast atmospheric signature code (spectral

transmittance and radiance).

Smith, W. L., H. M. Woolf, C. M. Hayden, D. Q. Wark, and L. M. McMillan,

1979: The TIROS-N operational vertical sounder. Bull. Am. Meteorol.

Soc., 60, 1177-1187.

Smith, W. L., and H. M. Woolf, 1976: The use of eigenvectors of statistical

covariance matrices for interpreting satellite sounding radiometer observations. J. Atmos. Sci., 33, 1127-1140.

Staelin, D. H., 1967: Quarterly Progress Report No. 85, Research Laboratory

of Electronics, M.I.T., Cambridge, MA, April 15, pp. 15-16.

Susskind, J., and J. E. Searl, 1978: Synthetic atmospheric transmittance

spectra near 15 pm and 4.3 \im. J. Quant. Spectrosc. Radiat. Trans., 19,

195-215.

Susskind, J., J. Rosenfield, D. Reuter, and M. T. Chahine, 1982: The GLAS

physical inversion method for analysis of HIRS-2/MSU sounding data. NASATM-84936, 101 pp.

Waters, J. W. and D. H. Staelin, 1968: Quarterly Progress Report No. 89.

Research Laboratory of Electronics, M.I.T., Cambridge, MA, April 15, pp.

25-28.

Westwater, E. R. and 0. N. Strand, 1965: Application of Statistical

Estimation Techniques to Ground-Based Passive Probing of the Tropospheric

Structure, ESSA Technical Report No. IER 371/1TSA 37.

-73-