NCAR/TN-364+STRNCAR TECHNICAL NOTE

September 1991

Preprocessing of AirbornePyranometer Data

Lutz BannehrAdvanced Study Program of the Office of the Director, andResearch Aviation Facility of the Atmospheric Technology DivisionNational Center for Atmospheric Research, Boulder, CO 80307-3000

Vince GloverResearch Aviation Facility of the Atmospheric Technology DivisionNational Center for Atmospheric Research, Boulder, CO 80307-3000

RESEARCH AVIATION FACILITYATMOSPHERIC TECHNOLOGY DIVISION

NATIONAL CENTER FOR ATMOSPHERIC RESEARCHBOULDER, COLORADO

I - LI _ _ I - - I -~~~~~~~~~~~~~~I

- ~ ~~ ~ ~~~~~~~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~~~ II-· I· I I

CONTENTS

List of Figures v

List of Tables vii

Abstract ix

Acknowledgements xi

1 PREFACE1

2 SHORT WAVELENGTH RADIOMETERS 3

3 OBSERVATIONS 4

4 CALIBRATION PROCEDURE 84.1 Astronomical Parameters. .............. 8

4.2 Relative and Diffuse Calibration Coefficient ................. 104.3 Applying the Individual Calibration Factors to the Raw Data . . . . . . . . . 14

5 CORRECTIONS 165.1 Correction for Aircraft Maneuvers . ................... 165.2 Installation of the Radiometer ... . . . . . . . . . . . 19

5.3 Incorporating the Diffuse Irradiance into the Correction Procedure . . . . . . . 22

5.4 Normalization to the Mean Air Mass ................... 26

6 CONCLUSIONS AND RECOMMENDATIONS 28

REFERENCES 30

APPENDIX A: Illustration of the correction scheme for the flight levels A and B 31

iii

LIST OF FIGURES

PAGE

43.1 Sketch of the flight pattern. The linear connections between the letters A, Band C denote the traverse sections (at three different levels designated A,Band C in the text) which were analyzed.

3.2 Unprocessed global irradiance data together with the pitch and roll anglesof the aircraft.

4.1 Relative calibration factor of the upward facing pyranometer.

4.2 Diffuse calibration coefficient for different anisotropy parameters b for theupward facing radiometer.

5.1 Illustration of the correction scheme for flight level C.

5.2 Pitch and roll variations during the observations at flight level C (216.7 hPa).

5.3 Comparison of misalignments of the upward looking pyranometer (traverse B).

5.4a Simulated ratio of diffuse to direct irradiance for different solaraltitudes and high loading of atmospheric constituents.

5.4b Simulated ratio of diffuse to direct irradiance for different solaraltitudes and low loading of atmospheric constituents.

v

5

12

14

17

18

21

23

24

LIST OF TABLES

PAGE

73.1 Statistics of the raw data. Static denotes the static pressure on theaircraft, pyra up is the measured global irradiance. Sun ele. andazimuth are the sun elevation and the azimuthal angle of the sun.The pitch, roll and heading are the attitude angles of theaircraft with respect to the earth.

4.1 Coefficients for the declination, equation of time and radius vector.

5.1 Percentage error in the global irradiance caused by a misalignment ofof the pyranometer.

vii

9

20

ABSTRACT

On the three research aircraft of the National Center for Atmospheric Research (NCAR),

Eppley pyranometers are employed to measure the up- and downwelling short wavelength

radiation fluxes in the atmosphere. The quality of the data used to investigate the radiation

budget and extinction of solar irradiance depends strongly on the calibration and correction

applied to the radiation data, accounting for (1) cosine response of the instruments, (2) ambient

temperature effects, (3) leveling of the radiometers, and (4) aircraft maneuvers during the

observations. This report makes suggestions about how the quality of the radiation data can be

enhanced by a more accurate calibration procedure and correction scheme. By considering the

recommnendations, data from the upward facing pyranometer can be improved by about 20%

*under clear sky conditions.

In order to improve the pyranometer data under cloudy conditions by the same percentage,

the diffuse irradiance must be measured in addition to the global irradiance.

ix

ACKNOWLEDGEMENTS

The authors wish to express their appreciation to the many people who contributed to and

supported this work. John DeLuisi and Donald Nelson of the Climate Monitoring and

Diagnostics Laboratory, NOAA/ERL/CMDL, made it possible to obtain a high quality calibration

of the pyranometer used in this study. John DeLuisi made the calibration facilities available and

Donald Nelson performed the calibration. Ronald Smith of Yale University generously provided

the data set, SMT1 1, used for verifying the methods developed in this Tech Note. The satellite

images used to verify the presence of clouds at the time and place of the SMT1 1 observations

were obtained through the research efforts of John Brown of the Forecast Systems Laboratory,

NOAA/ERL. Special thanks are due to Dave McFarland of the NCAR Research Aviation

Facility (RAF). He consulted with us numerous times on the characteristics of pyranometers and

other radiation instruments. Ronald Schwiesow and Darrel Baumgardner of the RAF reviewed

the draft of the technical note and made valuable suggestions on improving the quality of the

work.

This research has been supported by the National Science Foundation.

Lutz Bannehr

September 1991

xi

1 PREFACE

In recent years, concern about the impact of human activity on our climate has grown

considerably. Accurate data on parameters such as net short wave and long wave radiation,

heating rate, and absorption and scattering by the atmospheric constituents are needed to provide

input data for general circulation models. Airborne investigations are undertaken in order to

study the radiation budget and extinction of incoming solar irradiance by using UV-radiometers,

pyranometers and pyrgeometers. However, operating such radiometers on research airplanes to

obtain high quality data is not a simple task, because these instruments are designed for ground-

based operations. Their performance suffers drastically when used on aircraft due to extreme

atmospheric conditions as well as aircraft maneuvers. Therefore, the results of the measurements

and the conclusions drawn from them are very dependent on the quality of the data used.

Reliable values for the flux divergence derived from airborne radiation measurements can only

be obtained by performing calibrations and corrections carefully so that uncertainties are

minimized.

For calibration, the pyranometers are sent to the manufacturer, Eppley Laboratories. One

calibration coefficient is given for all zenith angles. By considering the cosine response of the

pyranometers, the accuracy of the global and reflected radiation data can be slightly enhanced.

Applying corrections to the upward facing pyranometer to compensate for the inclination of the

instrument during airborne observations improved the data by almost 12% as will be

demonstrated in Section 5.1. This correction is the main contribution to reducing uncertainty.

Another important factor, especially if the investigations are carried out at low solar altitude, is

that the pyranometer should be aligned as closely as possible with the aircraft inertial navigation

system. Radiative transfer calculations indicated that a misalignment of ±2° can cause an error

of about ±9% at a sun elevation of 25°.

In this report, the global irradiance data of flight SMTll, performed on January 19, 1989,

will be analyzed. It will be shown how the accuracy of the shortwave radiation data can be

1

improved when the necessary calibrations are performed and corrections are applied to thecollected data. The correction procedure for the reflected radiation data is not as critical as for

the global irradiance data. Hence, rather then analyzing the time series of the upwelling radiation

data in detail, only some comments will be made on how they can be improved.

Future work is required to enhance the quality of the radiometer data further. The

development of a shading device to measure the diffuse irradiance from aircraft in addition tothe global irradiance is essential in order to correct the data properly. Also, more development

effort is necessary in order to correct pyranometers for temperature sensitivity as is done withpyrgeometers.

2

2 SHORT WAVELENGTH RADIOMETERS

The description of pyranometers given here is by no means complete, and the interested

reader is referred to the undated brochure by Eppley Laboratory Inc. cited in the Reference

section. The shortwave radiometers or pyranometers operated at NCAR have a viewing angle

of 2I stearadians. This type of instrument is used to measure the downwelling or global

irradiance in the solar spectrum (0.30 to 4.0 pm). The actual spectral response of the

pyranometer is from 0.285 to 2.80 pm. These instruments, made by Eppley Laboratories, are

generally flown on NCAR aircraft in pairs and can be mounted in a boat-shaped container. One

is installed on top of the aircraft's fuselage facing upward. The global irradiance G as received

by the upward facing pyranometer sensor is:

G = I sin(O) + D (2.1)

where I is the direct irradiance, 0 is the solar altitude, and the diffuse irradiance is denoted with

D. The other pyranometer is mounted under the aircraft's body, facing downward. This

radiometer allows measurement of the upwelling or reflected radiation. Both radiometers use

thermopiles as sensors. Different spectral bandwidths are obtainable by using hemispherical glass

filters. The instruments are compensated for the non-linearity of the thermopile response for

temperatures between -20 to +40°C within ± 1%. The cosine response of the radiometers is,

according to the manufacturer, ±1 % for solar altitudes between 20° to 90° and ±3% for sun

elevations between 10° to 20°. The l/e time response of these instruments is 1 second.

3

3 OBSERVATIONS

The flight used to discuss the correction scheme was performed on January 19, 1989,

between 16:18 and 18:37 GMT with the NCAR Sabreliner aircraft. The acronym for this

particular flight is SMTll. The flight pattern is shown in Figure 3.1.

45.8

44.9

0)* 44.1

4:.

-

43.1

42.2

-70.1 -69.4 -68.7 -68.0 -67.3 -66.6

ALON (deg )

Figure 3.1 Sketch of the flight pattern. The linear connections between the letters A, B and C denote the traversesections (at three different altitude levels designated AB and C in the text) which were analyzed.

4

Figure 3.2 shows the time series of the global irradiance, the pitch angle and roll angle of

the aircraft during the observation of the SMT1 1 flight. The data were collected at a rate of 50

Flight SMT11 -1/19/89-800

700CM

I

IE

600uc

4C-'= 500

s-L.c.

- 400

0-D

300

200

6

4

: 2IL1

0

cr0

-2

-4

0 1000 2000 3000 4000 5000 6000

Samples

Figure 3.2 Unprocessed global irradiance data together with the roll and pitch angles of the aircraft.

5

v I i1 M vI 1 AA a Mvy kV Y I

\v

8

I10

6

a-

2

07000

I » » . . i . I I I . I . ...... !s I.......IIV V II

. . . . .. . . . . . . . . . . . . .A.I

1

d a

. . . . . . . .I . . q I I I I I . . g . . . . . . . . .

i

II I MIA. AAlk AA

Hz and averaged over one second. One second is equivalent to one sample in Figure 3.2. The

strong influence of pitch and roll movements on the global irradiance can be clearly seen. In

situations where the pitch and roll angles are large, the instrument senses not only the

downwelling radiation but also receives a large proportion of the upwelling radiation. Since it

is not possible to distinguish clearly between the two different signals, no correction can be

applied to the radiation data and the data are rejected for further processing. Hence, the analyzed

observations are divided into several sections. The criterion for the current analyses is that the

radiometric data are excluded where the pitch or roll angles exceed ±6°. Therefore, runs without

ascents, descents, or turns are used for the processing. To circumvent the problem of differential

heating of the pyranometer, which causes an error in the output signal, only data 20 seconds after

reaching the cruising altitude are chosen. The values selected are divided in the three consecutive

levels A, B and C at mean pressure levels of 315.25, 238.81 and 216.74 hPa. Due to the nature

of the flight operations and the constraints on the aircraft attitude, given above, each processed

time series has a different length. The selected data for level A are between samples 1600 and

2350, for level B between 3250 and 4100, and for level C between 4900 and 6200. Some basic

flight statistics of the SMT1 1 are given in Table 3.1, such as the average value, MEAN, for each

level, the minimum, MIN, and maximum, MAX, as well as the standard deviation, SDEV.

6

Table 3.1 Statistics of the raw data. Static denotes the static pressure on the aircraft, pyra up is the measured

global irradiance. Sun ele. and azimuth are the sun elevation and the azimuthal angle of the sun. The angles

pitch, roll and heading are the attitude angles of the aircraft with respect to the earth.

LEVEL A iMEAN M IN MAX SDEVStatic [hPa] 315.25 314.75 316.09 0.284

Pyra up [Wm- 2] 572.51 551.14 583.86 5.725

Sun ele. [0] 26.54 25.94 27.15 0.353

Azimuth [0] 183.43 181.87 185.07 0.926

Pitch [0] 3.27 2.73 3.97 0.191

Roll [] 0.58 - 2.15 1.61 0.727

Heading [0] 187.21 183.40 192.72 3.645

LEVEL B

Pressure [hPa] 238.81 237.82 239.45 0.246

Pyra up [Wm 2] 584.12 577.07 594.85 4.136

Sun ele. [0] 24.56 23.46 25.62 0.626

Azimuth [0] 190.64 188.89 192.37 1.00

Pitch [0] 3.61 3.09 4.15 0.184

Roll [] 0.61 - 0.03 1.44 0.334

Heading [°] 353.74 352.93 354.44 0.334

LEVEL C

Pressure [hPa] 216.74 216.13 217.39 0.299

Pyra up [Wmn2] 450.73 434.44 467.88 6.918

Sun ele. [°] 24.01 23.46 24.50 0.301

Azimuth [0] 198.66 195.78 201.52 1.656

Pitch [0] 4.20 3.41 4.76 0.179

Roll [°] 0.61 - 0.50 3.55 0.593

Heading [] 188.19 180.61 189.44 1.467

7

4 CALIBRATION PROCEDURE

4.1 Astronomical Parameters

The solar position is a basic input quantity for the equations determining the effect of the

cosine response of a pyranometer and for the correction of the pyranometer data to the horizontal.

Generally, the sun position is not measured directly, but calculated from the time and place where

the observations were carried out. During the airborne observations the geographic longitude and

geographic latitude are obtained from the aircraft's Inertial Navigation System (INS). From these

data plus information about the solar declination and the equation of time, the sun elevation and

azimuth are determined. The well-known equation for the true solar elevation 0 (without

accounting for refraction) and the sun's azimuth a are given below.

0 = arcsin(sin4 sin 5 + cos4 cos coscK) (4.1)

K = (t- 12) + g + X (4.2)

. a sin(s) * sin0 - sin)a = arcsm Cos ---Cos- (4 .3)

cost cos0

The azimuth a is positive from south to west and negative to the east.

The angle 4 is the geographic latitude of the observer, 6 the declination of the sun, and K the

local hour angle of the sun. In Equation 4.2, t is the local time, and X is the difference between

the local longitude and the reference meridian of the time zone. The equation of time is given

8

by g. Both the declination § and the equation of time are functions depending on the day of the

year and are found in the astronomical almanac. For the present investigation the functions are

approximated by Fourier series (Equation 4.4) with five coefficients (Bannehr, 1985) as listed in

Table 4.1.

The extraterrestrial flux intensity Io depends on the sun-earth distance RV (given in relative

distance) and varies throughout the year. The daily value of the flux density is obtained by

applying the squared inverse of RV to Io, which for the mean sun-earth distance is assigned the

value of 1367 Wm 2. The radius vector is also approximated by the periodic function of Equation

4.4.

() A ( 2nnt 3. 2 tnt--- + a n cos + b n

+ Sm'2 : 365 36

Table 4.1 Coefficients for the declination, equation of time and radius vector.

Coef. Declination Eqn. of time Radius vector

ao 0.79020 0.01238 1.00017

a, -22.92297 0.37852 -0.01663

a2 - 0.38859 -3.58074 -1.1968 E-4

a3 - 0.15527 -0.08528 1.5769 E-5

a4 - 0.00987 -0.13513 -1.6053 E-5

as - 0.00390 0.00992 1.2649 E-5

bl 3.92260 -7.36616 -1.1282 E-3

b2 0.04504 -9.22933 1.5840 E-6

b3 0.08285 -0.25052 1.7095 E-5

b4 0.00511 -0.12434 2.0198 E-5

b 0.00373 0.01718 2.3071 E-5.L -

(4.4)

9

The earth's atmosphere refracts the sunlight so that the sun appears slightly higher than it would

without an atmosphere. Therefore, when the radiation data are corrected, the refraction has to

be considered. The refraction term has to be added to the true solar elevation.

Refr(0) = (4.5)exp (h / 27000) tan (45)

Refr(0) denotes the refraction for a certain solar altitude, given in minutes of arc. The aircraft's

flight altitude is h in feet above sea level.

Equation 4.5 for the determination of the refraction (Nautical Almanac, 1981) is suitable for

aircraft observations. It is accurate to within ±0.2' for solar altitudes >10°. Since the refraction

increases with decreasing solar altitude, the error caused by disregarding the correction increases

accordingly. Modeling has been carried out to investigate this error, assuming clear sky

conditions. For a sun elevation of 20° the deviation found was less than 2.5 Wm' 2. A

comparable error could occur as a consequence of drift in the inertial navigation system on the

aircraft, since a position error on the order of minutes of arc is possible.

4.2 Relative and Diffuse Calibration Coefficient

The calibration of the broadband pyranometers is identical to the calibration procedure

performed by Bannehr (1990) for spectral radiation measurements.

As mentioned in the Preface, the pyranometer response is represented by a single calibration

coefficient, which assumes a perfect instrument response with no variations with the solar zenith

angle. Only in this case can the an the calibration factor be specified by one coefficient K' (millivolts

per Watt per square meter). The deviation of the radiometer response from an ideal cosine

10

response is generally caused by non-ideal sensor surface properties and/or optical effects of the

glass hemispheres, which produce different calibration factors for different solar elevations. This

deviation from Lambert's cosine law will be referred to further on as the relative calibration. The

relative calibration is dependent upon the difference between the measured global and diffuse

signal of a pyranometer compared with the direct signal of a reference device (for example, a

pyrheliometer for broad band studies). Multiplying the relative calibration by the direct

calibration factor of the reference instrument for a particular zenith angle converts the

pyranometer signal into the same scale as the reference device. The relative calibration is given

by:

K'(0) = G-D (4.6)sinO I

G = global signal of the instrument to be calibratedD = diffuse signal of the instrument to be calibratedI = direct signal of the reference instrument0 = observed solar altitude (true solar altitude plus refraction)

Strictly speaking, K'(0) applies only to the direct beam signal. For the diffuse signal, a diffuse

calibration coefficient must be derived from the radiance distribution and the cosine response.

The upward facing pyranometer used on the Sabreliner aircraft was calibrated under clear sky

conditions on 3 July 1991. The World Meteorological Organization (Frohlich and London, 1986)

recommends that the calibration of pyranometers should be repeated at least once a year or even

more frequently if unusual performance of the instrument is detected. The pyranometer was set

up, leveled, and the signal was recorded in two-minute averages. At the same time, direct and

diffuse irradiance measurements were collected by a pyrheliometer and a pyranometer equipped

with a shading band. The relative calibration factor K'(0) for sun elevations between 9° and 72°

was then determined according to Equation 4.6 and illustrated by Figure 4.1.

11

1.03

L- 1.02o

.L-s0

LL- I Nl

c0

.1.

0

.- 1.0000

0 0.99. 0

: 0.98

0 10 20 30 40 50 60 70 80 90

Sun Elevation [ ]

Figure 4.1 Relative calibration factor of the upward facing pyranometer.

The pyranometer shows small deviations from an ideal cosine response. For the present case

the deviation of the cosine response of the pyranometer from ideal is less than ±1% and better

than the specification provided by the manufacturer, Eppley Laboratories. The absolute

pyranometer calibration coefficient derived by Eppley Laboratories on 31 October 1988 was 8.00

E-6 V/Wm' 2, which deviates from the calibration coefficient retrieved on 3 July 1991 by 1.7%.

This small change in the calibration coefficient over a time period of almost 3 years can be

expected. Assuming that only the mean value of the calibration coefficient has changed between

the two calibrations, while the cosine response curve has remained constant, for a more precise

data evaluation the calibration factor K'(9) has been approximated by a bicubic spline function

(Press et al., 1989). It should be pointed out that the good cosine response of the instrument

used in this example is not necessarily representative for other instruments and therefore must

be investigated for each instrument. The error caused by using only a single calibration

coefficient instead of incorporating the full cosine response of the pyranometer results in about

±5.5 Wm' 2 for the current investigation.

12

No. 12127. ... I . . . I , , I , . a. _,!.. ! . I I I I t

I I I I I -if 11 5 I I . . I I I . I I I I . . I I I I I I I I I I I I I I I F I I I I

-i

I

The diffuse component of the measured global signal must be treated differently from the direct

signal. Assuming there are no azimuthal dependencies, the relative diffuse calibration factor P'

can be written as

2

fK'(O) L(O) sin20 dOP / 0 (47)

L( ( + b..1 si

where b is a non-dimensional anisotropy parameter.

For an isotropic sky radiance distribution, the value of b is equal zero. A value of 10

corresponds to a strongly anisotropic radiance distribution. An illustration of the change in the

diffuse calibration factor with increasing anisotropy parameter b for the upward facing radiometer

is given in Figure 4.2. For the evaluation of flight SMT11 an anisotropy parameter b = 3 was

assumed.

13

1.03

a--- 1.020

._-

a 1.0100c

4-0

.Q

o 0.99

(0

0.98

0 Q7

0 2 4 6 8 10

Anisotropy Factor b

Figure 4.2 Diffuse calibration coefficient for different anisotropy parameters b for the upward facing radiometer.

4.3 Applying the Individual Calibration Factors to the Raw Data

The raw radiation data from both pyranometers need to be calibrated. Only the diffuse

calibration factor P' has to be applied to the downward facing pyranometer. The calibration of

an upward facing pyranometer is slightly more complex. The direct component I (Equation 4.9)

is obtained by subtracting from the measured global signal G' the diffuse signal D' and applying

the relative calibration coefficient K'(0) (accounting for the non ideal cosine response of the

instrument) to the direct signal. Since the diffuse irradiance D' is not recorded during the

observations, this component will be estimated by means of radiative transfer calculations and

is discussed in Paragraph 5.3. The diffuse calibration factor P' is applied to the estimated diffuse

signal (Equation 4.10). Now, the calibrated signals are in the same scale as the reference

pyrheliometer.

14

I I I t -- - I -- I I * I 2 I. I . 1 I I I I

. .l l I i

G I - D/sin0

D = D P'

G = IsinE + D

(4.9)

(4.10)

(4.11)

Upon adding the direct and diffuse signals to obtain the global signal, the preprocessing is

complete.

15

5 CORRECTIONS

5.1 Correction for Aircraft Maneuvers

The downward facing radiometer, used to measure the reflected radiation, requires no special

correction scheme because the received signal is only diffuse. Again, more complex is the data

treatment of the upward facing pyranometer. Deviations from straight and level flight make it

necessary to correct the direct radiation data of the upward facing pyranometer for excursions

from the horizontal. The aircraft inertial navigation system provides all the required parameters,

and a geometrical correction for the inclination of the pyranometer can be computed for every

data point. The correction factor which has to be applied to the data is given as follows:

sinO,F = sin- (5.1)

cosO, sin sin( -h) - cos sinp cos( - h)+ sinO cos [cosa

F = correction factor (the direct signal must be multiplied by this quantity)- = solar altitudec = roll angle of the aircraft (positive for left wing up)P = pitch angle (positive for nose up)h = aircraft heading

= azimuthal angle of the sun

Equation 5.1 contains the implicit assumption that the incoming radiation signal is direct

only. If not, this equation is no longer valid, and it would incorrectly determine the direct signal

and thus the global signal.

An example of the correction scheme is given for flight SMT11, level C, in Figure 5.1.

For this example it was assumed that the measured solar irradiance was only direct. The upper

time series shows the computed correction factor determined from Equation 5.1. The second

16

Fliaht SMT11 Level C -1/19/89-

0 100 200 300 400 500 600 700 800 900 1000 111

_A._

0 100 200 300 400 500 600 700 800 900 1000 1101S&mp Ies

Figure 5.1 Illustration of the correction scheme for flight level C.

00 1200 1300

0 1200 1300

17

1 .20

1.18

1.16

o 1.14d

L

<) 1.12

1.10

1 .08

1.06

480

N 470

a 460u

d

- 450LL

440.0

430

N 530

:520

510i- 510

L

- 500

-

O 490

480

_ __ ,--~~~~~~~~~I .M.- -1 I . -- .- - .I I - I

A A-

time series shows the global uncorrected but calibrated data. In the third time series, the

correction factor is applied to the data of the global irradiance time series above. Figure 5.1

explicitly shows how the global irradiance data are smoothed by applying the derived correction

factor to the raw data. Furthermore, the data are not only smoothed but the mean is shifted up

by 60.3 Wm-2 in the present case. The standard deviation was derived after the trend has been

removed by low pass filtering. It was reduced from 4.164 to 0.924 after the correction factor was

applied to the time series. The difference between maximum and minimumn after low pass

filtering decreased at the same time from 27.3 to 7.1 Wmn2. Using the corrected time series as

a reference, the error caused by ignoring the correction for any aircraft maneuvers was as high

as 11.8%.

Figure 5.2 shows the pitch and roll angles of flight SMT11 at 37000 feet. In this figure

6

5

L

4

f.Q1

3

2

2

L

t1

01

0

-1

Flight SMT11 Level C -1/19/89-. .. .. . ... . . . .. .. .I . . . . . . .... . , . . ..

I. . .

" I.. . . . . . .. .. .

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300Samplem

Figure 5.2 Pitch and roll variations during the observations at level C (216.7 hPa).

18

0 100 200 300 400 500 600 700 600 900 1000 1100 1200 1300.. . . . I . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

I-

the average roll angle is not zero as it should be for a correct INS installation. The results given

in this section demonstrate that an INS misalignment does not influence the effectiveness of the

correction scheme. Similar figures are produced for the traverses A and B. They are found in

Appendix A.

5.2 Installation of the Radiometers

The upward facing instrument is installed on top of the fuselage where the obstructions by

the aircraft are minimized. However, depending on the heading of the aircraft and the solar

position, the radiometer signal can be slightly affected by the aircraft's tail. This should be kept

in mind for the data evaluation.

The installation of the downward facing radiometer is not complicated. Apart from adjusting

it to the mean pitch angle of the aircraft during the observation no special considerations are

required.

Simulations have shown the importance of aligning the upward facing radiometer as close

as possible to the inertial navigation system of the aircraft, because the pitch angle, roll angle,

and aircraft heading provide the input parameters for the correction (Equation 5.1). Even small

deviations cause significant uncertainties when the radiometer data are corrected for the

radiometer inclination during the flight. The order of the error depends on the atmospheric

loading and more strongly on the solar altitude. The error increases for low solar altitudes.

Radiative transfer calculations were performed to investigate this potential error source.

Assuming a total aerosol optical depth T=0.1, an atmospheric water vapor content ppw=l1.5 cm,

an ozone mass 03=0.3 cm, and a surface albedo w=0.12, Table 5.1 shows the percentage error

for different solar altitudes and pyranometer misalignment of ±2°.

19

Table 5.1 Percentage error in global irradiance caused by a misalignment of the pyranometer.

Nominal Solar Tilted(±2° )

Altitude (°) Error (%)

10 ±26.5

30 t 7.2

50 3.3

70 t 1.4

90_24.57 9.3

Figure 5.3 shows the shift of the corrected radiometer data if the instrument is aligned

accurately within ±2°. For the given example, flight SMT1 1, the mean solar altitude was 24.57°.

At this solar altitude a misalignment of ±2° can produce an uncertainty of about 9.3%. Provided

that the solar altitude is 65° for the same misalignment, the error in the global irradiance is of

the order of 2%.

20

600

C<i

4

- 550

Lo s

40

500

4500 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850

Samples

Figure 5.3 Comparison of misalignments of the upward facing pyranometer (traverse B).

Since there is currently no technique available to retrieve the unknown misalignment in pitch

and roll angles, a numerical iterative procedure was developed to account for any possible

misalignment when the pyranometer is installed on the aircraft. The idea is based on the fact that

the global irradiance received by the sensor of the radiometer under clear skies and at a fixed

altitude is almost independent of the direction in which the aircraft flies. Only trends due to

changing solar altitude are expected. For the case where the instrument is not properly aligned,

systematic changes in the global irradiance signal will occur when the aircraft flies in different

directions. Fortunately, a flight pattern was available where the heading changed from 302° to

333° and then to 69°, so that data at one altitude and three different directions are accessible to

derive the pitch and roll misalignment errors, Ap and Ar. The method uses Equation 5.1 as a

basis, which corrects the radiometer data by the factor F for the deviation from a straight flight

during the observations. The correction factor F is derived from the observed quantities (sun

elevation, azimuth, pitch and roll angles of the aircraft) and assumed values for delta pitch, Ap,

21

A. ! n6D50

and delta roll angles, Ar for the whole traverse and is applied to the radiometer data. The

corrected time series is low-pass filtered to remove any trends due to changing solar altitude.

The data are stored temporarily. Then the low pass filtered time series is subtracted from the

unfiltered time series to obtain a series of higher frequency residuals. The standard deviation is

determined and stored together with the assumed delta pitch and delta roll angles. This procedure

is repeated between two defined Ap and Ar bounds, namely ±3°. The actual delta pitch and delta

roll angles are found by searching for the smallest standard deviation of the corrected time series.

The delta pitch and delta roll angles retrieved by the numerical procedure were Ap=-0.48° and

Ar=-0.08°. By adding these values to the recorded pitch and roll angles, the pyranometer is

aligned with respect to the aircraft inertial system. The numerical procedure was also tested

using only two flight legs and the results were unsatisfactory. It was found that satisfactory

results are achievable only if all three flight traverses are utilized in the delta pitch and delta roll

determination.

5.3 Incorporating the Diffuse Irradiance into the Correction Procedure

Currently, there is no instrumentation or shading device installed on the aircraft that allows

the measurement of diffuse irradiance. Therefore it is not possible to separate the direct

irradiance from the global irradiance which is stringently necessary to correct properly for aircraft

attitude changes. For the case that the observations have been carried out under conditions of

clear skies, a vertical profile of the ratio of diffuse irradiance to global irradiance can be

estimated from a radiation model, and thus the diffuse irradiance can be estimated. For the

present investigation such simulations for different atmospheric conditions have been undertaken.

The model used is Forgan's (1989) simple multi-layer spectral radiation model for clear skies.

It provides the upwelling and downwelling radiation fluxes for n defined pressure levels. The

simulations are performed for two different cases, each with 9 layers between surface pressure

and 100 hPa and five different solar altitudes between 10° and 90°. The first case used a high

total aerosol optical depth of 0.25 and a high total atmospheric precipitable water of 3.0 cm. The

second case used a low total aerosol optical depth of 0.10 and a low total ppw value of 0.5 cm.

22

The value of 0.12 was assigned for the surface albedo for both cases. Figure 5.4a and Figure

5.4b show the results of the simulations.

Figure 5.4a Simulated ratio of diffuse to direct irradiance for different solar altitudes, heights and high loading ofatmospheric constituents.

23

0

Figure 5.4b Simulated ratio of diffuse to direct irradiance for different solar altitudes, heights and low loading of

atmospheric constituents.

These two graphs show the variability of the ratio of diffuse to global irradiance D/G(O) for

high and low aerosol loading and water vapor for different sun elevations and pressure levels

under clear sky conditions. These data are used now to obtain an estimate of the diffuse

irradiance D' for each flight level.

D' = G. () * D (5.2)G(0)

In Equation 5.2, the estimated diffuse irradiance is D'. Gm(O) denotes the measured global

24

Sun Elevation

0 10*30v 50

... . . .7.Q...........0 90

ppw = 0.50 cmT = 0-10a = 0.12

200

ci,L 600

o_

CL

c-

800

1000

0.001 0.01 0.1 1

Rotio Diffuse to Globol Irrodionce

I - . . I .7 I I . I I I I . r---r -I- r-

i

III

I- - - -

I . -. . . . I . . . . I - - A. . . I. . . . . . . . . . ..

irradiance. The ratio of diffuse to global irradiance is given by D/G(0). By subtracting from the

measured global irradiance G. the estimated diffuse irradiance, the direct irradiance I for the

actual solar altitude is obtained. The correction factor F (Equation 5.1) is now applied to the

direct signal and the diffuse irradiance is added to the corrected time series. Since the flight

levels A, B and C of SMT1 1 were in the lower stratosphere, the diffuse irradiance for clear sky

conditions is small and was estimated from the multi-layer radiation model as 7.5% (for level A)

of the total irradiance at the solar altitude of 26.5°. No significant differences are found by

incorporating the diffuse irradiance into the correction. However, it must be emphasized that

for most occasions the assumption of completely clear skies is not appropriate. Even thin cirrus

clouds in the area of the observations cause a strong increase in the forward scattering direction

or diffuse irradiance. This can lead to higher or lower global irradiance than is found under clear

sky conditions.

Under clear skies, the global irradiance increases with height due to decreasing extinction of

the solar radiation. In the present investigation, the mean corrected values for the global

irradiance derived are for level A 620.3 Wm`2, for level B 537.9 Wm' 2 and for level C (highest

flight leg) 511.0 Wm'2. Obviously, the expected increase of the global irradiance with increasing

height does not occur and shows a reversed behavior. This feature might be caused by changing

solar altitude with time, not including the real diffuse irradiance but using only an estimate in

the correction procedure, changing location for the observations, or a combination of all three.

Since the diffuse irradiance was not measured during mission SMTI 1, no statement about this

parameter can be made, and therefore no information about clouds is available from

measurements on the aircraft. The observed global irradiance is treated as a direct signal only.

Changes of the global irradiance due to the different locations at the altitudes flown are regarded

as small and will not be discussed further. The change of the solar elevation has a strong effect

on the global irradiance, even if the observations are carried out over a short period of time.

This effect is only small around noon. Therefore, to derive the solar heating rate or the

absorption of a layer, the radiation data must be normalized to a mean solar altitude before the

radiation fluxes can be computed. The required normalization will be discussed in the following

paragraph.

25

5.4 Normalization to the Mean Air Mass

After the calibration is performed and the attitude variations of the aircraft have been taken

into account, the data are referenced to a standard air mass of the flight before the flux

divergence can be calculated. The standard air mass for the correction will be referred to as the

middle air mass of the flight. Four assumptions are made:

1) The total optical depth T, is constant during the observations,

2) the ratio of direct to diffuse irradiance I/D is constant for each level

and independent of the sun elevation 0, and hence

3) the albedo ac is constant during the flight.

4) A further assumption required is that the water vapor absorption can be

described by the law of Lambert-Bouguer-Beer

I' = Iie t -ine osine (5.3)

trot = -ln(4) sinOt (5.4)

D=(ll -i /(5.5)

G' = I; sin + D (5.6)

U. = a, Gil (5.7)

26

0i is the mean solar altitude of the flight level and Q0 is the middle solar altitude of the flight as

a whole. ty is the total optical depth, 1 is the extraterrestrial flux density, and Ii, Di, and Gi are

the direct, diffuse and global radiation. By calculating Di', G1' and U,' for each level, the data

are converted into the same referenced solar altitude O. U1' denotes the reflected radiation.

Using the mean corrected global irradiance data and normalizing them to the mean solar

altitude of 24.57° (mean solar elevation of the analyzed data set) yields for level A 576.3 Wm'2

(lowest cruising level), for level B 537.9 Wm'2 and for level C 522.3 Wm' 2. Despite having all

corrections applied, the radiation data still do not increase with height for the three flight levels

as can be expected from the model (clear sky conditions). This result can be caused by the

limited accuracy achievable with the pyranometer and/or the presence of clouds in the area of

observation, enhancing the diffuse and global irradiance. An agreement better than 1.5% is

achieved between the observed global irradiances and model results for level B. For level C the

observed values are 3.0% smaller than the modeled fluxes. For level A the measured global

irradiance deviates by 10.3%. This large difference in the global irradiances can be explained

by the presence of cirrus clouds in the region of observation, which were indicated in the satellite

picture on this day. From the data analysis and modeling results, the clouds appear to be below

flight level B. The assumption of a clear sky is therefore applicable, so the modeled ratio of

diffuse to global irradiance cannot be used to derive the diffuse irradiance and it is not

incorporated in the correction procedure illustrated here. If the true diffuse irradiance is not

known, the applied correction (Equation 5.1) leads to false results. This example illustrates the

importance of measuring the diffuse irradiance explicitly and not deriving it implicitly by

radiative transfer calculations that presume certain atmospheric conditions.

27

6 Conclusions and Reconunendations

The procedure described for the calibration and correction of pyranometer data in this

technical note is aimed at improving of the current basic data treatment. The observed error in

the pyranometer cosine response was less than 1% for solar altitudes between 9° to 72°. Ignoring

cosine corrections the data results in an error of about ±5.5 Wm- 2 for the current investigation.

The calibration should be repeated at least once a year to detect and compensate for drifts of the

instruments.

The correction technique for the upward facing pyranometer that accounts for aircraft

maneuvers improved the accuracy of the radiometer data drastically. The absolute deviation was

reduced by 11.7 Wm"2 on average for all three levels and showed the smoothing effect of the

correction. More significant, however, was the shift of the mean global irradiance values. For

level C the shift was as high as 60.3 Wmn2. When applying the correction factor to the radiation

data, it must be realized that such a correction cannot be performed for large inclinations of the

aircraft. For large pitch or roll angles the pyranometer receives in addition to the downwelling

radiation also upwelling radiation, for which it is not possible to correct. It is suggested that data

should be used only if the pitch and roll angles of the aircraft are within ±6°.

If the upward facing pyranometer is misaligned by ±2° compared to the aircraft inertial

navigation system, the error in the global irradiance can be up to ±11% for a solar altitude of 20°

according to radiative transfer calculations. Therefore, care should be taken to eliminate this

uncertainty. The numerical procedure described can be used to derive the pitch and roll angle

misalignment errors and therefore to account for this source of uncertainty. The downward

facing pyranometer should be adjusted to the mean pitch angle of the aircraft in order to

minimize the detection of the downwelling radiation.

The main recommendation concluded from the data analysis is that the diffuse irradiance

should be measured in addition to the observed global irradiance in order to make a more

28

efficient use of the correction procedure. Diffuse irradiance could be obtained by designing a

rotating or flipping shading device. Including the diffuse irradiance in the group of radiometric

quantities has some further benefits. Namely, by measuring the global and diffuse irradiance,

the direct irradiance, and therefore the total optical depth can be determined, which is an

important input parameter for climatological models.

A matter not discussed in this technical note should be mentioned, as some future work is

still necessary. The pyranometer output is known to be sensitive to differential heating between

the dome of the instrument and the cold junction of the thermopile. This effect for pyrgeometers

has been discussed by many scientists. According to Albrecht and Cox (1977), the error of the

long wavelength radiation can be reduced by 60 Wm'2. For this technique, the dome and the sink

temperatures of the pyrgeometer are measured in addition to the radiometer output. Since the

pyranometer and pyrgeometer are identical instruments apart from the spectral filtering

mechanism, a similar correction procedure can be derived for the pyranometers if the dome and

sink temperatures of the pyranometer are measured.

29

REFERENCES

Albrecht, B. and Cox, S.K.: 1976, Procedure for Improving Pyrgeometer Performance,J. Appl. Meteor., 16, 188-197

Bannehr, L.: 1985, Die Extinktion der direkten Solarstrahlung im aktinometrischenSpektralbereich, Diplomarbeit, Freie Universitat Berlin, 85 pp.

Bannehr, L.: 1990, Airborne Spectral Radiation Measurements in South Australia, Ph.D. Thesis,Flinders University of South Australia, 180 pp.

Eppley Laboratory Inc.: (no date), Instrumentation for the Measurement of the Components ofSolar and Terrestrial Radiation, Newport, R.I. 02840, USA, 12 pp.

Forgan, B.W.: 1979, The Measurement of Solar Irradiance: Instrumentation and Measurementin the Adelaide Region, Ph.D. Thesis, Flinders University of South Australia, 380 pp., 1979

Forgan, B.W.: 1989, Personal Communication

Frollich, C. and London, J. (ed.): 1986, Revised Instruction Manual on Radiation Instrumentsand Measurements, WCRP Publications Series No. 7, WMO/TID-No. 149

Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.I.: 1989, Numerical Recipes,Cambridge University Press, 702 pp.

30

APPENDIX A

Illustration of the correction scheme for the flight levels A and B

31

Flight SMiT11 Lovel A -1/19/89-

0 50 100 150 20 2 250 300 350 400 450 500 550 600 650 700 750Samp les

32

1 .16

1 .14

1.12

o 1 .10

L

uJ 1.08

1 .06

1 .04

1 .02

, 590

a 580u

a 570LL

- 560

0

550

540i

650

c 640

f-

630

4

- 620

LI.

- 610

0-05 600

590

.-- .-- --- --- --- --- -- - --- - -- --

& Md,2

I

Flight SMT11 Level A -1/19/89-

50

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750

Samples

33

5

Io

A4

UC

3

20 50 100 150 200 250 300 350 400 450 500 550 600 650 700 7

U

3-1

-2-21

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Flight SMT11 L.vel B -1/19/89--- ------- ------. . . . . . . . . . . . . . . . . . . . .. . I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I., ..

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850

0 50 100 '150 200 250 300 350 400 450 500 550 600 650 700 750 800 850

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850Sump es

34

1 .00

.98

.96

.94

.92

.90

.88

.86

L0u

0119

600

590Cc

- 580L

L

- 570

-0

K60

550

560

3

550

C

' 540d

L-.4

- 530

-o

520

r10 I

. . . . . . . . . . . . . . . -. . . . . . . . . . . . L . .- . ..- .. .. . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . I I , I I I . I I I I . I I I I . . . . . .. . .. . .. . . . . . . . . . . .. . .. . . I . . . .

.. ... .... ... . . . ... .. .. .. .. . ... ... .... ... . . . .. . . .. . .. . . . . . .... .

,- - - - - -- - - - - . . . . . . . . . . . . . . . . . . . . . . | . . .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . s. . O r. . . .r.

. .. . . . . .. I I . . . . . . . . .. . . ... I -. . . . . 1 I · 1 ·· ii t -. i · Il · · I . _. .- · I I I· 1 L I-. ..

I

dL 4 a"1

;; i; Lo -

e

E-M

;IV Ii

--------- - -- -- --- --- --- --

Flight SMTI! Level 8 -1/19/89-0

Samples

35

0

5

a

o

-c4L

0I

04

E.

3

2

3

2

U

g1

0I.

0

-1

500 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 600 8

. . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .7 777 7I I ~r7 77 7 7I T 17

Pi/"J