Oct 15, 1993 - Division of Meteorology and Physical Oceanography. Rosenstiel School of Marine and Atmospheric Science. University of Miami, Miami, Florida ... various addenda to NOAA NESS Technical Memorandum 107 (Lauritson et ...
JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 98, NO. C10, PAGES 18,257-18,268, OCTOBER 15, 1993
Calibration of Advanced Very High ResolutionRadiometer Infrared Channels' A New Approach to Nonlinear Correction JAMESW. BROWN, OTIS B. BROWN, AND ROBERTH. EVANS Division of Meteorology and Physical Oceanography Rosenstiel School of Marine and Atmospheric Science University of Miami, Miami, Florida
A detailed reanalysisof the calibration proceduresfor the National Oceanic and Atmospheric Administration (NOAA) advanced very high resolution radiometer (AVHRR) based on thermalvacuum test data was performed as part of the National Air and SpaceAdministration/NOAA AVHRR PathfinderProject. This effort, a followup to work by Brown et al. (1985), was motivatedby the finding that the AVHRR instrumentson several NOAA platforms have been routinely operated outside the rangeof thermal-vacuumtest results, and thusone could not interpolatenonlinearcorrectionsdirectly from earlier methods.These new calibration procedurespermit calculationof nonlinear temperature correctionsfor any AVHRR operating temperature based on a second-orderpolynomial regression with a total calibration accuracy relative to an external calibration standardof less than two digital counts (_+0.2øC).Such an improvement is quite important to the absoluteaccuracy of surfacethermal fields, which are derived from these data utilizing various multichannelatmosphericwater vapor correction schemes.We find systematicdifferencesin the newly derived nonlinear correction results and those reported previously by Weinreb et al. (1990) and the original reference material in the various addenda to NOAA NESS Technical Memorandum 107 (Lauritson et al., 1979). Calibration results for various AVHRR
radiometers show instrument-similar
corrections for each band. Radiom-
eters on NOAA platforms 8-12 demonstratesimilar nonlinearities.
INTRODUCTION
Much interesthasbeen focusedrecently on the problemOf determiningaccurate global sea surface temperature (SST) fields for climatic use [Committee on Climate Change in the Ocean, 1983;Intergovernmental Panel on Climate Change, 1990]. Well-characterized SST fields are a necessity for understandingconceptual linkages between SST anomalies and large-scale meteorological response [Rasmusson and Wallace, 1983], surface flux calculations [Liu and Niiler, 1985], coupled model validation [e.g., Zebiak and Cane, 1987], "global warming" estimation [Strong, 1989], etc. There has been much debate as to whether present satellite infraredobservingsystemsare capableof deliveringdata of higher quality than shipsand if in fact such space-borne remote sensing systems can approach a root-mean-square (RMS) accuracy of 0.2øC for monthly unbiased estimates of SST on 1ø x 1ø areas [Strong, 1989;Reynolds et al., 1989]. Operationallyproducedglobal seasurfacetemperaturefields are derived in part from infrared radiancesmeasuredby the National Oceanic and Atmospheric Administration (NOAA) advanced very high resolution radiometer (AVHRR) [Schwalb, 1978; McClain et al., 1985]. Derived SST field accuracyis limited by a number of effects: sensordesignand calibration, atmospheric correction algorithms, data processing procedures, local variations in air-sea interaction, etc. However, the largest temperature biases are due to troposphericand stratosphericaerosols. In the presentwork we present an addendumto Ourearlier study of infrared radiometer calibration techniques [Brown et al., 1985]. This work is one element of a multifaceted program to derive accurate SST fields from satellite infrared observations
with
accuracies
commensurate
for
Copyright 1993 by the American GeophysicalUnion. Paper number 93JC01638. 0148-0227/93/93JC-01638505.00
climate
needs. This effort is motivated by our involvement in the National Air and Space Administration (NASA)/NOAA AVHRR Pathfinder Project, which is reprocessinga decadal global SST data set for use in climate analysis and modeling activities as a forerunner to the NASA Earth Observing System Project.
Significantadvancesin operational infrared processing were the availability of multichannel infrared observations with the NOAA AVHRR platform/instrument and the utilization of multichannel correction algorithms [McClain, 1981] which parameterize atmospheric effects as a bulk correction to the temperature. This suite of techniques is based on earlier work by Anding and Kauth [1970], Shenk and Salomonson [1972], and Prabhakara et al. [1974] in which a linear relationship between water vapor attenuation and the apparent temperatures in selected infrared bands was deduced. Comparisons of conventional high-quality surfacedata from buoys and expendablebathythermographs with satellite-determined SST by McClain et al. [1985] find RMS
errors of 0.5ø-0.7øC
for various multichannel
AVHRR
algorithms. While major technical progresshas been made in the areas of AVHRR instrument development and atmospheric correction design, there has been no such agreement on basic radiometer calibration, which is a fundamental determinant of retrieval accuracy. Radiometer calibration can exhibit a dependence on internal operating temperature, radiometer age, storage methodology, etc., despite engineeringdesign to minimize such effects. Test data to ascertain the range of all these effects are lacking for the NOAA AVHRR instruments; however, there are extensive preflight data on the
variationof radiometercalibrationwith internaltemperature variation, the thermal vacuum test data. To quantify the operational instrumentalinternal temperature variability, NOAA 9 telemetry data were retrieved to extract internal target temperature as a function of time from
18,257
18,258
BROWN ET AL.' NONLINEAR CORRECTIONOF AVHRR
3O
INFRARED CHANNELS
estimation of SST. Algorithms in present use are quite sensitive to the input absolute temperatures. The AVHRR sensor is a payload on the NOAA satellite
platformswhich are in Sun-synchronous polar orbitsat altitudesof 833 to 870 km with ascendingpassesnear 0730 or cz2o4
.•r w,.....
1400 local
,,,r
,
I
i
,
I
,
i
Time (Years)
"sensor
Fig. 1. Time seriesplot of observed internal temperature for the AVHRR on NOAA 9. Starting and ending dates for the series are January 2, 1985, and December 8, 1988, respectively. The observed multiplicity of curves is due to sampling. Four passesper day (two adjacent day and night orbits covering the U.S. east coast) were retrieved for this analysis.
the Rosenstiel School of Marine and Atmospheric Science (RSMAS) east coast collection. Figure 1 presents a temperature record for internal target temperature over a 4-year interval
for NOAA
9 AVHRR.
There
are several
notable
features in this record: first, the overall range of the internal temperature goes beyond the published AVHRR calibration range [10ø to 20øC; i.e., Thermal-Vacuum Test results]; second, there are also large diurnal and weekly to seasonal time scale variations; and third, the annual cycle and longterm trend have a major influence on the time series. Thermal variations over single orbits also can be large as shown in Figure 6 of Brown et al. [1985]. Since the AVHRR is known to exhibit nonlinear errors of 1ø-4øC,dependenton internal operating temperature, it should be apparent from this record
that an accurate
method
of nonlinear
correction
is necessary for good brightness temperature estimation. Study of the sensor environmental telemetry for the AVHRR Pathfinder Project found that the AVHRR instruments on several NOAA platforms since 1981were routinely operated outside the range of the thermal-vacuum test resuits, and thus one could not interpolate nonlinear corrections directly from these data by any current method but would be forced to extrapolate a result. Therefore it was decided
to review
the thermal-vacuum
Sun time.
The
AVHRR
scans at a rate
of 360
swaths per minute with an effective ground resolution of 1.1 km (at nadir) in five coregistered spectral bands [Schwalb, 1978]. The AVHRR/2 bands (for NOAA 7) are numbered 1-5 and cover the spectral intervals 0.58-0.68, 0.725-1.10, 3.553.93, 10.3-11.3, and 11.5-12.5 txm, respectively. The AVHRR/1 instruments (for NOAA 6) have four distinct bands and cover the spectral intervals 0.58-0.68, 0.725-1.10, 3.55-3.93, and 10.5-11.5 txm. The sensingof SST through the atmospherein the thermal infrared is subject to environmental factors, which can affect the accuracy of the perceived temperature. This paper focuses on understanding sensor calibration and accurate
{ ..,
test data to ascertain
whether there were patterns to the nonlinearity behavior which would permit development of better extrapolation procedures. The question we readdress here is, Can higher-accuracy satellite brightness temperature estimates be made with present operational AVHRR observations? We believe the answer is yes, and in the present paper we demonstratenew results of an AVHRR sensor calibration study which suggests improvements in presently used procedures.
characterization." SENSOR CALIBRATION
Williamson [1977] presents a general methodology for calibration of satellite radiances; procedures used for the AVHRR are similar. Lauritson et at. [1979] give a detailed procedure for calibration of AVHRR radiances. To summarize, the calibration procedure is based on a linear fit between two measurements of radiance, one taken below and the other taken within the temperature range of interest [see Weinreb et at., 1990, Figure 3]. For the AVHRR, these two observations are of an internal target at •288 K and cold space at •3 K. Although the procedure is simple in concept, many practical difficulties arise because of sensor nonlinearities, measurement of internal target temperature, calculation of target radiance, internal reflections and emission in an instrument, etc. The following discussion treats these topics and presents a consistent methodology for deriving both a linear calibration and the nonlinear departure from this estimate. The basis for this methodology is the thermal vacuum test [ITT Aerospace Optical Division, 1982] data set. Prior to launch, the AVHRR instrument is operated in an evacuated test chamber with space radiances incident on the housing while viewing an external target, and both the external target and internal housing temperatures are varied to ascertain instrument performance over the design operating regime. AVHRR data acquisition is accomplished, as in space, by rotating the mirror in a cross-track direction at 6 rps. During a scan, the detectors view a window open to cold space, a warm internal target, and the external scene. Such an arrangement provides the two-point calibration discussed above for observed radiances [Schwatb, 1978]. The internal
target is monitored by four platinum resistance thermocouples (PRTs), which are used to estimate its emission temperature at AVHRR wavelengths. Following Lauritson et at. [1979], we convert the internal PRT counts to temperature using 4
T•rt(k)= Z aijxi BACKGROUND
The objective of this study is improvement of satellitedetermined brightness temperatures, which are used in the
(])
j=0
where-•i is the mean countfor the ith PRT and a ij are calibration coefficients for each thermocouple. The instru-
BROWN ET AL.' NONLINEAR CORRECTIONOF AVHRR
INFRARED CHANNELS
18,259
ment manufacturer, ITT, specifies that all PRTs shall be I i = C[p- SiL[p. (6) trimmedsuch that the a ij valuesare identicalwith an accuracyof _0.1 K. Theseaij valuesare derivedusing While the 3.7-/•m channel is quite linear in its response, the National Institute of Standards and Technology (NIST) traceable standards and represent the only onboard link to such a standard. ITT-supplied calibration is quadratic, i.e., j
10- to 11- and 11- to 12-/,•m channels are not. A number of methods have been proposed to deal with these nonlinearities: Lauritson et al. [1979] suggestusing a special negative
ranges from0 to 2. MeanPRTtemperature (T =0.25 Y./4= 1 L[p to minimize errors in the range 225-310 K; Weinreb et Ti) is used as the internal target temperature, althoughthere is no a priori reason for taking a simple mean as being the optimal predictor of internal target temperature, given that a gradient is normally present across the internal target. Now, we assume that the output of each AVHRR infrared channel count is proportional to input radiance [Lauritson et al., 1979], i.e.,
al. [1990] use lookup tables and modify the calibration of the onboard PRTs, etc. In this work a nonlinear correction vector will be derived to compensate for this behavior.
THERMAL
The
instrument
VACUUM
manufacturer
DATA
validates
an
individual
AVHRR sensor'sperformance during a mandated test series at space conditions [ITT Aerospace Optical Division, 1982] with Ci as the count, L i as the incident radiance, and Si, Ii that is performed prior to acceptance by the U.S. Governas the slope and intercepts, respectively, for the ith channel. ment. The instrument is operated according to a regime Typically, the instantaneous count values reported are which approximates normal conditions expected during noisy, so an average value is used for this calculation: flight; external target temperature is varied from 175 to 320 K RSMAS uses block averages of 500 lines. In the following (10-K increments from 175 to 295 K and 5-K increments procedure we assume the use of average values. from 295 to 320 K), while internal target temperature is The spaceandinternaltargetcountsC? andc/t for a scan cycled from 10øto 20øC(or 25øCin specific instances) in 5øC can be used to derive a calibration slope and intercept if one increments. The calibration specification requires that exterassumes that sensor response is approximately linear in nal target temperature be stabilized to ---0.5 K before mearadiance. Specifically, surements are taken. Calculated error in the internal target radiation temperature is +0.39 K [ITT Aerospace Optical c7Division, 1982]. Estimates of relative error must have this random error component combined with them for an absoC i = SiL i q- I i
(2)
Si=Lip_L[
(3)
lute error
whereSi is the slopefor the ith channel,C[p and Cit are averagespaceandinternaltargetcounts,andL[P andL [ are the respective space and internal target radiances. The total radiance L T for a body of temperature T can be defined
as
LT =
•w •2
e(V)BT(v)W(v ) dv
(4)
1
where w i are the zero limits of the spectralresponsefunction W(v), and B T(V) is the Planck black body function for temperature T, wavenumber v, and emissivity e(v). The Planck black body function is given by
estimate.
Data which document the external target temperature, internal operating environment, and observed space and internal target temperatures are recorded; 360 scans are saved for each internal operating temperature-external tem-
perature pair. A calibration set for an instrument consistsof at least 48 runs, a total of approximately 75 megabytes of data. A guide to these data, with measured spectral response functions, PRT calibrations, etc., is produced for each instrument [cf. ITT Aerospace Optical Division, 1978a, b, 1979, 1980; 1982]. These data are archived on magnetic tapes at NOAA National Environmental Satellite and Data Information Service (NESDIS).
-1
_1) (1.43879v
BT(V) = 1.1910659 X10-5v 3 exp T
(5)
The present calculations assume that the internal and external target emissivities are 1.0; published estimates are 0.995 and 0.999327 for the internal and external targets, respectively [ITT Aerospace Optical Division, 1982]. Several different
methods exist for numerical
evaluation
of
(4) [see Lauritson et al., 1979]. The method used in the present study consists of the following steps: convert temperature to spectral radiance using the black body function, multiply spectral radiance by the particular window transmittance function given in Appendix B of NESS Technical Memorandum 107 for the instrument in question, and integrate this weighted spectral radiance over the entire window using Simpson's rule to obtain total sensed radiance. Once the calibration slopes have been found, the intercepts are given by
ANALYSIS
The thermal vacuum test data for a given sensor are analyzed in the following manner. For each data run, mean counts and standard deviations are computed for the external and internal target PRTs and space and back scan (internal target and external target) data. Histograms of data are made, and bins within 1 standard deviation of the largest bin are used to compute mean and RMS values. PRT data are converted to temperatures using the ITT-specified quadratic calibration coefficients. Radiances are computed from these temperatures for the internal and external targets using (4) and (5). The methodology outlined in (1)-(6) is applied to generate a sensor-estimated two-point or linear radiance. Sensor-measured radiances and PRT-based external target radiances are converted to temperature using the inverse of
(5). The nonlinearcorrectionTnl is definedas Thi= Text- Tlin
(7)
18,260
BROWN ET AL.' NONLINEAR CORRECTIONOF AVHRR
Channel
INFRARED CHANNELS
4
ci
A
A
A
o
o
[]
o
o
ri
o
10C
ß
15C
A
20C
o
'•
' 200
I 220
'
I 240
'
! 260
'
External
I 280
Target
'
I 300
'
I 320
25C ß
340
(K)
Fig. 2. Differencesbetween measuredand two-point linear fit predictedexternal target temperaturesfor NOAA 7 radiometer channel 4. Curves are derived from the thermal vacuum test data for the 10ø, 15ø, 20ø, and 25øC internal target temperature plateaus.
where T extis the recordedexternaltargettemperatureand between scene temperatures and the linearly estimated tem-
Tlinis thecomputed brightness temperature fromtheradi- peratures,i.e., the nonlinearity, show a very tight clustering ometer using the method outlined in (1)-(6). T ext is monitored using PRT sensorssimilar to those specifiedfor the AVHRR internal target; i.e., one expects the accuracy of
of base plate curves about a single parametric shape. A least squares fit is performed on an edited data set to reduce the effect of spuriouspoints. That is, we parameter-
these temperatures to be comparable [seeBrown et al., 1985, for more information]. Figure 2, a compilation of several such runs for the NOAA 7 satellite radiometer, illustrates the
ize thenonlinear correction T?l for a givenrescaled scene temperature T• as
computeddifferences Tnl betweenthe two temperature determinations.The positive trends and magnitudesof the differences for temperatures above •280 K present an immediate problem to computationof accuratesurfacetemperatures. Our solution to this problem is a systematicstudy of the error field over an instrument's operating range. Weinreb et al. [1990] pointed out that the nonlinearity
T•l= a0+ a1ßT• + a2ßT•2
(9)
a0, a l, and a2 are the derived least squaresfit coefficients. Data points are removed from considerationfor the final fit if they lie more than 2 standard deviations from the preliminary fit line. Outlying points are removed and a quadratic polynomial is fit to channels4 and 5 of each data set. The fit shows an RMS
of 0.1øC for the NOAA
7 observations
in
correctionmust be zero by definitionwhen the external Figure 3. The magnitude of the RMS is consistent with the
target temperature matches the internal target temperature. This behavior is clearly evident in the NOAA 7 observations plotted in Figure 2, which suggestsa correlation between base plate temperature and curve shape. We hypothesize that the nonlinearity magnitudes are invariant relative to base plate temperature (also noted by Weinreb et al., 1990). To test this assumption,the external scenetemperaturewas
known PRT calibration and the digitizer quantitization error for these channels.
To test the quality of the coordinate transformation processas an extrapolation procedure, the 30øCinternal target temperature data set was withheld from the above calculation during the estimation of the fit shown in Figure 3.
Differences are computed betweenTt!in+ T?1 and the
rescaledfor each set of data as "two-point scenetempera- observed 30øCthermalvacuumtest data, whereT?1 is ture-base plate temperature," i.e.,
T• = T[in-- •i'
(8)
generated from the 10ø-25øCfit coefficients evaluated at a 30øCinternal target temperature. These differences are presented in Figure 4; the mean d•erence is -80øC. The magnitudeof the derived mean nonlinear correction
We have developed a method which derives an analytical form for the nonlinear corrections required for each NOAA AVHRR instrument. The method is based on rescaling sensed scene brightness temperature by the internal target temperature. These curve fits permit the computation of nonlinearity corrections at any base plate temperature directly, with no need for a table lookup or an interpolation. The same method can be used for either interpolation or
fluctuates about zero with
a range from -0.15-0.13øC (mean is -0.02øC); the standard deviation of the correction varies from 0.08-0.31øC, with a mean value of 0.22øC. This analysis suggeststhere is no statistically quantifiable bias or correlation with internal target temperature observable in the channel 3 thermal vacuum test data for the radiometer data sets currently available.
AVHRR/1
Channel
4
Tiros N Noaa 6 Noaa 8 Noaa 10 ß
00
I
-e0
'
I
-60
Two
'
I
'
-40
Point
I
-20
-
Internal
o Target
='o (K)
Fig. 9. Fitted channel4 nonlinearcorrectioncurves (differencesbetween measuredand predictedtwo-point linear) for various NOAA AVHRR/1 instruments. Curves are coded for TIROS-N and NOAA 6, 8, and 10 instruments.
BROWN ET AL.' NONLINEAR CORRECTIONOF AVHRR
INFRARED CHANNELS
18,265
[] []
z
[]
& [] E!
Noaa 9
©
Noaa 11
&
-1
ß
-100
i -80
ß
i
ß
-60
Two
i
ß
-40
Point
i -20
-Internal
ß
i
ß
i
0
Target
Noaa 12 ß
20
40
(K)
Fig. 10. Differences between RSMAS and NESDIS fitted channel 4 nonlinear correction curves for various NOAA AVHRR/2 instruments. Curves are coded for NOAA 9, 11, and 12 instruments.
extrapolation. Testing of this approach for the NOAA 7 instrument demonstratesthat it accurately models the radiometer responseto internal temperature variation. Since the least count quantizing error, or digitizing resolution, for NOAA 7 AVHRR channel 4 is _+0.1 K at 300 K, the total calibration error relative to the external temperature standard for this radiometer is reduced to one digital count with this new method. Errors for other instruments listed in Table
1 vary from this level to approximately twice its magnitude, i.e., two digital counts. Review of the thermal vacuum test data for the complete radiometer set suggeststhat much of the increase may be due to variation in test methodology rather than instrumental
differences.
This analytic approach can also be an effective way of assessingthe quality of a given thermal vacuum test run. If one assumes that correct data should lie on the fitted line, then differences can arise only from either instrument construction or test anomalies. The data-editing criterion noted
earlieris an exampleof suchuse. Review of Table 1 and Figures 6-9 suggestsseveral areas of improvement in AVHRR thermal vacuum test procedures and calibration practices. First, it is important to characterize another instrument as well as the AVHRR/2 prototype used on NOAA
differences
7 to ascertain
between
NOAA
whether
the observed
familial
7 and the other instruments
are
characteristicof expected instrumentalvariation, are particular to NOAA 7, or are a function of the test procedure. Second, the step sizes in internal and external temperatures permit only a coarse estimate of the nonlinear variation; finer scale variations are masked by the 5øC increment for operating temperature and by the 10 K step for external target temperature. Third, the thermal vacuum test procedure should have added quality assuranceto reduce the magnitude and frequency of anomalous observations. Finally, there do not currently exist instrumental data which can be used to characterize the effect of aging on radiometer per-
formance: given the time between instrument construction, test, flight, and flight lifetimes of AVHRR instruments, this is a major unknown. The present results show a consistentbehavior in the error functionals
for all tested
AVHRR
instruments.
Nonlinear
error is correlated with internal operating and external environmental temperatures. The stability of the AVHRR instrument is much better than specification in that sensor calibration is reproducible to -+0.26 K over a wide range of operatingtemperatures(10ø--25øC) for most instrumentsand internal temperature plateaus. The procedures presently used operationally do not exploit these inherent accuracies, nor are they optimal for mappingof the error field. Figures 10, 11, and 12 compare our results with the published NOAA NESDIS nonlinear corrections and calibration procedures [Hamilton, 1986a, b; Popham, 1988;
Brown,1991].Differencesare approximately zero for T• = 0; i.e., both corrections show minimal correction at external scene temperatures equivalent to the internal target temperatures, as expected. However, the differencesshow disper-
sionfor T• > 0. Thereis alsoevidencefor a sinusoidalvariationand positivecorrelationwith T• in the difference between the present results and the NOAA NESDIS results (see Figures 10 and 11). Mean and RMS values for the differencesrange from -0.16 øto 0.18øC and from 0.08ø to 0.49øC, respectively. The linear atmosphericcorrection algorithm combines two far-infrared AVHRR channels to estimate SST [Anding and Kauth, 1970]'
Tsst= a + [3T4 + T(T4 - Ts)
(10)
Systematic offsetsin brightnesstemperature due to calibration errors will have two effects in the linear atmospheric correction algorithm: an overall offset proportional to/3. T 4 and a temperature-dependentoffset of value 3" (T4 -- Ts)Using typical values for/3 (0.99) and 3' (2.67), the channel 4
18,266
BROWN ETAL.' NONLINEAR CORRECTION OFAVHRR INFRARED CHANNELS
y.
o
:3
[]
tO
Noaa 9
ß Noaa 11 &
I
-100
I
-80
I
-60
I
-40
Two
Point
I
-20
-
I
0
Internal
Noaa 12
20
Target
4
!•
(K)
Fig. 11. Differences between RSMASandNESDISfittedchannel 5 nonlinear correction curves forvarious NOAA AVHRR/2 instruments. Curves are coded for NOAA 9, 11, and 12 instruments.
error appearsas an offsetof 0.3-0.7 K in the resultingSST estimate; error due to nonlinear errors between the split window channels,althoughsmaller(•0.1 K), is magnifiedto
sayit wouldprobablybe reflectedin largerRMS co_mparison values with in situ observations. In the case of either no
correction or limited validity range for the correction, one
a similar level by the multiplier % In somecasesthesetwo errors may cancel for a specifictemperaturerange. Historically, NOAA NESDIS either has not applied a nonlinearcorrection,hasapplieda correctionwith a limited
wouldexpectday-nightbiasesin retrievedSST to be correlatedwith internaltargettemperature,sincethe correctionis
rangeof validity,orhasapplie d a possibly incorrect value.It
tions for positivevalues(Figure 1 illustratesday-nightinstrumenttemperature variationsfor NOAA 9). Sincethereis apparentlyalso a drift toward higher internal operating
is difficultto generalizethe effect of an incorrectvalue for the nonlinear correction on the retrieved SST other than to
highlyasymmetricabout T•/ = 0, with small nonlinear correctionsfor negative values and large nonlinear correc-
a a a a a a
a 13
a
a
a
a
a a
aaaa
a a
n
[] [] [] a []
a
a
a a a a 13a
a ß
00
I
-80
'
I
-60
Two
'
I
-40
Point
'
I
-20
-Internal
'
I
0
Target
'
I
20
Noaa '
10
I
40
(K)
Fig. 12. Differences between RSMASandNESDISfittedchannel 4 nonlinear correction curves for theNOAA10 AVHRR/1
instrument.
BROWNET AL.: NONLINEAR CORRECTIONOF AVHRR
temperaturesover the life of a given instrument,one would also expect a time-dependenttemperaturebias in the multichannel
SST formulation.
CONCLUSIONS
This
work
was initiated
in order
to derive
a reliable
method of computing nonlinear correctionsfor the AVHRR instrumentsoperated outside the thermal-vacuumtest envelope. We develop a consistentmethod in this paper for the calibration
of the NOAA
AVHRR
instrument
based on ITT
thermal-vacuum test data which parameterize the nonlinear dependenceof the two-point calibration on internal operating temperature.Resultsfor a numberof radiometersshowa similar form of responsedeparture from a two-point linear calibration
for variations
in differences
between
external
sceneand internal target temperatures. An unexpectedbenefit of the new approachis that it is computationally simpler to implement than methods currently in use. Calibrations done according to the method outlined in (2)-(8) have a relative error of approximately one digital count over the oceanic temperature range, with no observable temperature-dependent bias. ITT Aerospace Optical Division [1982] states that the errors due to external target calibration to a NIST standard, external target disequilibrium, and gradients have an uncertainty equivalent to the sum of the absolute value of the individual errors, i.e., -+0.37 K. The square root of the sums of the squares, i.e., the root-sum-square(rss) error, of these individual errors yields an expected error of -+0.15 K. The system error estimates derived from the thermal vacuum test data in the present work show maximum levels of -+0.2 K. That is, there is very good agreementbetween an rss estimate of the various ITT Aerospace Optical Division [1982] error estimates and the current result, which leads us to conclude that the ITT summationof absoluteerrors shouldbe an upper limit for the error and that methodologicallyconsistentcalibrations, such as is the case with NOAA 7, can produce substantially improved calibration at the -+0.15 K level. Combining this estimate of relative error (-+0.2 K) with the calculated error in the internal target radiation temperature (-+0.39 K [ITT Aerospace Optical Division, 1982]), using the rss method, yields an absolute radiometer calibration error of -+0.44 K. Acknowledgments. The authors would like to acknowledgethe assistanceof Guillermo Podesta for his helpful comments on the statisticalmeasures.We especiallywish to thank M. Weinreb of the NOAA NESDIS Calibration Group. He and his group graciously provided the AVHRR thermal vacuum test data, helpful comments, and support. Support of the Orificeof Naval Research under grant N00014-89-J-1144, NASA under grant NAGW-273 and contract NAS5-31361, and NOAA under contracts NA90RAH00075 and NA16RC0057-01 is gratefully acknowledged. This research is a contribution from the NASA-NOAA AVHRR Pathfinder Project. REFERENCES
Anding, D., and R. Kauth, Estimation of sea surface temperature from Space, Remote $ens. Environ., 1,217-220, 1970. Brown, O. B., J. W. Brown, and R. H. Evans, Calibration of advanced very high resolution radiometer infrared observations, J. Geophys. Res., 90, 11,667-11,677, 1985. Brown, S., Amendments to NOAA technical memorandum 107 appendix B for NOAA-D, NOAA Tech. Memo. NE$$107, Natl. Environ. Satell. Data and Inf. Serv., Suitland, Md., 1991. Committee on Climate Change in the Ocean, Proceedingsof the
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(Received March 4, 1992; revised March 11, 1993' accepted March 17, 1993.)
