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Modification of MODIS thermal infrared by LOWTRAN 7and global dataset Hiroshi Murakami

NASDA Calibration 4th Group, May 15, 2002

Outlines

We modified the MODIS L1B radiance to suit simulations by radiative transfer model LOWTRAN 7.

The following global data sets are used in this analysis: MODIS 5km resolution data (MOD02CSS),

weekly sea-surface temperature (SST) by Reynolds and Smith [1994], and Japan Meteorological

Agency (JMA) global objective analysis data (ANAL). Simultaneously, we derive coefficients of a

multi-channel SST (MCSST) scheme using simulated radiance and the input SST. Two-scene

comparisons with TRMM VIRS SST show that biases are 0°K and 0.3°K, and root mean square

differences (RMSD) are 0.76°K and 0.78°K. This scheme (a kind of global vicarious calibration) is

thought to be efficient for calibrating GLI thermal bands, especially in the early stage of the mission.

1. Objectives

The Tokai University Research and Information Center (TRIC) receives Earth-observation data by

MODIS on NASA Earth-observation satellite TERRA, and processes geometric and

radiometric-converted data (Level 1B data). Using the Level 1B data, the National Space Development

Agency of Japan (NASDA) Earth Observation Research Center (EORC) produces chlorophyll-a

concentration, normalized water-leaving radiance, and sea-surface temperature (SST) using ADEOS-2

GLI algorithms; testing the GLI algorithm is an objective in this operation. The SST data shows a bias

of −0.8°K around Japan due to the mismatch of the MODIS radiance and GLI algorithm. We will

therefore investigate how to improve the accuracy to suit our operations.

2. Data preparation

2.1 MOD02CSS data

Using MOD02CSS data produced by NASA from Version 3 MODIS L1B data, we made “binned

data” of 0.25° lat-lon grid. The binned data contains the clearest data sampled from MODIS channels 20,

29, 31, and 32 (see Table 1), and corresponding satellite zenith and azimuth angles (SAZ and SAA)

from about 120 scenes of MODCSS data on an ascending path from 75°N to 75°S on 13 September

2001. To avoid sun glint in ch30, we use only the ascending path (corresponding to nighttime in this

month). We resampled the binned data at 1.25° intervals to match grid points of JMA ANAL data.

The MODIS band response is represented by the center wavelength (λc) in this analysis to simplify

calculations. λc is calculated by the following equations using the MODIS relative band response (R(λ)

provided by the MODIS Characterization Support Team (MCST)). Results are listed in Table 1.

λc=∑i=1N-1 ( wi × λi

ave ) / ∑i=1N-1 wi (eq. 1)

2

wi=1/2 × ( R(λi)+ R(λi+1) ) × (λi+1−λi) (eq. 2)

λiave= (λi+1−λi) / (R(λi+1) − R(λi)) ×(sqrt( ( R(λi+1)2 + R(λi)2 )/2 ) − R(λi) ) + λi (eq. 3)

N: sample number of R(λ) and λ

Table 1 Center wavelength of MODIS ch20, 29, 31, and 32 calculated from MODIS relative response data

MODIS ch. ch20 ch29 ch31 ch32 λc [µm] 3.789 8.532 11.006 11.996

We use the following equation to convert from radiance to brightness temperature.

R=c1 / λc5 / (exp ( c2 / λc / T ) – 1 ) (eq. 4)

R: radiance [W/m2/str/µm], T: Brightness temperature [K],

λc: center wavelength [µm] of each band（see Table 1）

c1=119104272.3, c2=14387.75197

2.2 Weekly SST data by Reynolds and Smith [1994]

The National Meteorological Center (NMC) of the United States acquires and distributes global

1°×1° grid SST data (Reynolds and Smith, 1994). We linearly interpolated their weekly data (from 12 to

18 September, 2001) to a 1.25° spatial grid (to adjust to JMA ANAL grid).

2.3 JMA objective analysis data set

JMA provides objective analysis data (ANAL) (1.25° spatial and 18-vertical grids) to NASDA. We

use atmospheric profiles of the ANAL data (atmospheric temperatures, pressure, and humidity) at 12:00

on 13 September 2001 (UT) as input for the LOWTRAN 7 simulation.

2.4 Land /waver percentage data from GMT

We first made 1/16° grid land/water flag data using land/water bit-map data (about 500-m resolution)

converted by the GLI processing system from GMT coastline data. Second, we counted the number of

land grids in each 1.25° grid, and defined the 1.25° grid as a land when the number exceeds ten percent

of the total. Because the atmospheric profiles above the ocean may differ from ones above land, we

analyzed only areas over the ocean defined by the land/water percentage data.

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3. Thermal radiance simulation by LOWTRAN 7

Using the data sets described in Chapter 2, we simulated thermal radiation using LOWTRAN 7 with a

thermal infrared surface albedo of 0.01 (i.e., emissivity is 0.99). Solar irradiance is not considered in

our simulation because we want to modify thermal infrared emitted from the ocean and use only

nighttime MODIS CSS data. The simulation and evaluation flows of this scheme are shown in Fig. 1.

Figure 1 Flowchart of radiance simulation and its evaluation

ch20 ch29

ch31 ch32

SAA SAZ

R&S SST ANAL press GMT land mask

ANAL temp

ANAL vapor

Atmospheric profile

Surface boundarycondition (SST) albedo=0.01

Setting viewing angle

MODIS CSS

LOWTRAN 7

Global 1.25° grid

ch20 ch29

ch31 ch32

Simulated radiance

Define ocean area

II. Derive MCSSTcoefficients

I. Comparison betweenMODIS and simulatedTIR radiance. Correction coefficients by SAZ

III. Calculation of MODISSST MODIS radiance→ MODIS corrected radiance→MODIS SST

MODIS SST

IV. Evaluation ofMODIS SST Bias=**, RMSE=**

ch20 ch29

ch31 ch32

JMA ANAL

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4. Results

4.1 Estimation of correction coefficients for MODIS observed radiance by fitting to LOWTRAN 7

simulated radiance (I in Fig. 1)

Figure 2 shows an example of the LOWTRAN 7 input and output. To consider the calibration

problem that depends on the scan-mirror angle, we converted SAZ according to the west-side and

east-side of scans using SAA (SAZ is converted to +SAZ when SAA>0, and −SAZ when SAA<0).

Figure 2 (a) Weekly SST byReynolds and Smith[1994]. (b) SAZ ofMODIS CSS data. (c)Simulated radiance ofch31 by LOWTRAN7. (d) Observedradiance of ch31 inMODIS CSS.

Input for LOWTRAN 7

Output of LOWTRAN 7

MODIS TIR observation

Com

pari

son

LOW

TRAN

7

Sim

ulat

ion

(a)

(b)

(c)

(d)

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We derived correction coefficients for the MODIS observed radiance by adjusting them to the

simulated radiance. Fig. 3 and Table 2 show the comparisons and the coefficients. LOWTRAN 7 does

not simulate thermal emission from cloud, so we exclude cloud areas detected by abnormal scatter and

two-band differences of brightness temperatures observed by MODIS.

Figure 3 Scatter diagram of MODIS observed radiance (x-axis) and simulated radiance by LOWTRAN 7 (y-axis). The four panels indicate each band ((a) ch20, (b) ch29, (c) ch31, (d) ch32). There were 10,172 samples. b1, a0, a1, c1 and c2 are coefficients of the least square fitting for (A) y=b1 x, (B) y=a0+a1 x, and (C) y=c1 x+c2 x2. Values in parentheses indicate intervals of 95% significance.

Table 2 Coefficients for correction from MODIS observed radiance to simulated radiance Eq. λc [µm] a0 a1 a2

(a) 3.789 − 0.9590 (±0.0021) − (b) 8.532 − 0.9991 (±0.0033) − (c) 11.006 − 1.0073 (±0.0037) −

A

(d) 11.996 − 1.0029 (±0.0044) − (a) 3.789 0.0144 (±0.0007) 0.9195 (±0.0020) − (b) 8.532 0.2134 (±0.0235) 0.9701 (±0.0032) − (c) 11.006 0.3114 (±0.0289) 0.9686 (±0.0036) −

B

(d) 11.996 0.4309 (±0.0316) 0.9455 (±0.0042) − (a) 3.789 − 1.0282 −0.1790 (b) 8.532 − 1.0365 −0.0050 (c) 11.006 − 1.0548 −0.0058

C

(d) 11.996 − 1.0715 −0.0091 a0, a1, and a2 are coefficients of the least square fitting to y=a0+a1 x + a2 x2. Values in parentheses indicate intervals of 95% significance.

The regression lines are close to the y=x line for all bands in Fig. 3. However, the 95% confidence

level indicates that a1 of equation (A) is significantly different from one for bands (a) and (c), and a0

and a1 of (B) are significantly different from zero and one for bands (a), (b), (c) and (d). MCST has

reported that the scan-mirror reflectance of MODIS changes according to the scan angle. This has been

corrected in L1B operation but the scan-angle dependent error may still remain a little. Ratios of

simulated radiance to observed radiance are plotted against SAZ in Fig. 4.

(a) (b) (c) (d)

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Figure 4 Ratios of simulated radiance to MODIS-observed radiance plotted against SAZ. The x-axis represents SAZ separated into left and right sides of the scan (see text 4.1). The four panels indicate the bands. (a) ch20. (b) ch29. (c) ch31. (d) ch32. There were 10,172 samples. d0, d1, and d2 are regression coefficients of y=d0+d1×SAZ+d2×SAZ2 (Table 2 B), e0 and e2 are those of y= e0+e2×SAZ2 (Table 2 A).

There is a weak correlation with SAZ in ch20 (a) and ch31 (c) of Fig. 4, but the relation does not

seem to depend on the sign of the SAZ (i.e., it looks symmetric). This suggests that the relation may

arise not from the correction error of the scan-mirror angle but from errors in our simulation depending

on air mass. The SST estimation accuracy was better using the coefficients in Table 3 (A) than using

those in Table 2 (see Fig. 7). As an empirical result, we propose a set of correction coefficients (Table

3A) that is symmetric to SAZ.

Table 3 MODIS TIR correction coefficients

Eq. λc [µm] r0 r1 r2 (a) 3.789 0.9704 − −0.1556E-5 (b) 8.532 1.0007 − −0.0331E-5 (c) 11.006 1.0066 − 0.0928E-5

A

(d) 11.996 1.0041 − −0.0104E-5 (a) 3.789 0.9704 −0.1911E-4 −0.1566E-5 (b) 8.532 1.0007 0.1883E-4 −0.0320E-5 (c) 11.006 1.0066 −0.0341E-4 0.0927E-5

B

(d) 11.996 1.0041 −0.0398E-4 −0.0106E-5 radcorrected=radoriginal × (r0 + r1 × SAZ+ r2 × SAZ2) (SAZ: [degree])

The coefficients do not simply represent the calibration error because they include systematic errors

of simulation by LOWTRAN 7, errors in input datasets, and errors due to representing the band spectral

response by the center wavelength. We can only say that SST estimation can be improved using the

correction coefficients and MCSST coefficients that are derived from simulated radiance and SST used

as the boundary condition for the simulation.

(a) (b) (c) (d)

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4.2 Estimation of MCSST coefficients (II in Fig. 1)

Figure 5 Regression of input SST and output brightness temperature of LOWTRAN 7. The x-axis represents SST estimated by Reynolds and Smith 1994; the y-axis, SST derived from simulated radiance by LOWTRAN 7. These were 19,825 data samples.

Coefficients in (a), (b), and (c) indicate regression coefficients for equations A, B and C below. SST= a0 + a1 T3 + a2 (T3−T4) + a3 (T3−T4) ams (eq. A) SST= a0 + a1 T3 + a2 (T3−T4) + a3 (T3−T4) ams + a4 (T3−T2) +a5 (T3−T2) ams (eq. B) SST= a0 + a1 T3 + a2 (T3−T4) + a3 (T3−T4) ams + a4 (T1−T3) +a5 (T1−T3) ams (eq. C) ams= 1 / cos( SAZ × π / 180) – 1

Figure 5 shows regression coefficients for equations A, B, and C using brightness temperatures that are calculated by eq. 4 with simulated sensor noise (random noise) of standard deviation of 0.1°K added. Table 4 shows the coefficients and Root Mean Square Error (RMSE) of the estimated SST from input SST.

Table 4 Regression coefficients for each equation Equation a0 a1 a2 a3 a4 a5 RMSE [K]

eq. A −4.7704 1.0175 2.8780 0.9911 0 0 0.68 eq. B −8.0545 1.0386 2.7635 1.1746 −1.0748 0.2044 0.57 eq. C −3.1763 1.0159 1.1779 1.0735 1.0423 −0.1307 0.40

4.3 Estimation and evaluation of MODIS SST (III and IV in Fig. 1)

We estimate SST using 1.25°-grid MODIS radiance (see section 2.1) corrected by factors of Table 3A

and MCSST coefficients of Table 4B. The SST estimation is validated by comparison with the weekly

SST data estimated by Reynolds and Smith [1994] that was used for the LOWTRAN 7 simulation input.

(a) (b) (c)

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Figure 6 Comparison of estimated SST from MODIS radiance (y-axis) and SST determined by Reynolds and Smith [1994] (x-axis). (a), (b), and (c) represent equations A, B, and C using corrected radiance. (d) represents eq. B without radiance correction.

The regression error in Table 4 and RMSE in Fig. 6 demonstrate that eq. C has the best accuracy.

However, we adopt eq. B because T3 (3.789µm) is influenced by solar reflectance in the daytime and

the GLI standard algorithm uses eq. B in the pre-launch algorithm version. Figs. 6b and 6d indicate that

both bias and RMSE are improved by the radiance correction using the coefficients in Table 3A.

(a) (b) (c) (d)

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Figure 7a shows that the SST estimation has a bias of −0.8°K when radiance is not corrected. Fig. 7b

(7c) shows that radiance corrections using a constant (not using a constant) do not make a large

difference in bias and RMSE. Fig.s 7b and 7d show that correction by SAZ (coefficients of Table 3A) is

effective around the scan edges.

(a)

(b)

(d)

Figure 7 SST estimationsapplying severalradiance-correction factors. Original radiance andgeometries are sampledfrom MODIS CSS data(see Section 2.1). TheMCSST formula of eq. Bis used for all cases.Colors indicatedeviations from SSTderived by Reynolds andSmith [1994]. (a) shows the estimationerror without radiancecorrection; (b) the errorwith coefficients of Table2A, (c) the error withcoefficients of Table 2B,and (d) the error withcoefficients of Table 3A.

(c)

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4.4 Comparison of VIRS SST and MODIS SST (III and IV in Fig. 1)

We evaluated the new SST estimates using input data of the SST regression in the previous section.

We then evaluated the new SST data using TRMM VIRS SST observed on the same day. VIRS SST data

has a higher spatial resolution (0.125°) than Reynolds and Smith's SST. The VIRS SST was evaluated

by the TAO array; the RMSD was 0.68°K from the TAO SST.

(See http://www.eorc.nasda.go.jp/TRMM/imgdt/day_vrs/virs_sst.pdf)

Figure 8 SST by (a) TRMM VIRS and (b) MODIS SST without radiation correction using MCSST

coefficients of Table 4B in the East China Sea (from 120°E to 134°E, and from 24°N to 41°N).

The MODIS SST spatial patterns generally agree

with ones of VIRS SST, but the MODIS SST is

−0.6°K lower than the VIRS SST. This indicates that

the MODIS SST needs radiance correction. The bias

looks similar to that of Figs. 6b and 7a.

Figure 9 Scatter diagram for (a) and (b) inFig. 8. The x-axis indicates VIRS SST, and they-axis, MODIS SST.

(a) (b)

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Figure 10 Same as Fig. 8, except for applying radiance correction coefficients from Table 3A to (b).

Using the radiation correction coefficients of Table 3A and MCSST coefficients of Table 4B closes

bias to zero and decreases RMSD to 0.76°K. The RMSD suggest that the accuracy of the

radiance-corrected MODIS SST is as good as the VIRS SST considering RMSD between VIRS SST and

TAO SST is 0.68°K.

(a) (b)

Figure 11 Scatter diagram for (a) and (b)in Fig. 10. The x-axis indicates VIRS SST, and the

y-axis, MODIS SST.

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Figure 12 Same as Fig. 10, except for the area (from 134°E to 142°E, and from 30°N to 37°N) and day

(3 October 2001).

Figure 12 compares in another date and area. The bias between the radiance-corrected MODIS SST

and VIRS SST is 0.3°K, and the RMSD is 0.78°K. The bias looks a little large, but the scatter diagram

in Fig. 13 suggests as good agreement as in Fig. 11.

(a) (b)

Figure 13 Scatter diagram for (a) and(b) in Fig. 12. The x-axis indicates VIRS SST, and the

y-axis MODIS SST.

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5. Summary and Discussion

5.1 Analysis results

We found that satellite observed thermal-infrared radiance could be calibrated globally by numerical

simulation using simultaneous surface and atmospheric datasets to suit the SST estimations. However,

the adjustment includes not only calibration errors, but also representation errors resulting from MODIS

band representation by the center wavelength, and systematic errors in the simulation and its input data

sets. Systematic errors of water vapor content or air temperature in the input atmospheric profile will

strongly influence the simulated radiance. However, we can estimate SST with good accuracy (RMSD

from VIRS SST is 0.76°K or 0.78°K) when we use MCSST coefficients derived using the same

LOWTRAN 7 inputs and outputs, because this scheme passes all these errors to the correction

coefficients.

5.2 Discussion of correction errors

In normal vicarious calibration, we acquire accurate observations on the ground and in the

atmosphere, simulate TOA radiance using these observations, and compare the results with satellite

observations at specific points (see Fig. 14a). In this analysis, we use 100-km-scale, general-use datasets,

and compare satellite observations to them globally (see Fig. 14b).

Figrure 14 Vicarious calibration schemes using (a) ground observation and (b) global-scale simulation.

Estimated errors are indicated in italics. The errors are summed by Etotal2=E1

2+E22 …

1×1 km

Radiative-transfer simulation

Ground observation （1 m scale）

TOA radiance at observed point

1×1 km satellite observations

Vi-cal Assumption of 1×1 km ≈ 1 m

Representative grids

Radiative-transfer simulation 100km scale

grid data 100km-scale

TOA radiance1×1 km

satellite observations

Vi-cal

Assumption of 100×100 km≈1×1 km

Error 0.1°K

+error 0.5°K (due to Input

Error 0.51°K

+error 0.5°K (spatial pattern)

Error 0.71°K

Error 0.1°K

+error 0.5°K

Error 0.51°K

+error 2°K

Error 2.1°K

(a) Normal vicarious calibration using ground observations

(b) Vicarious calibration of 100km scale

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The calibration error of a point in Fig. 14b seems to be larger than that in Fig. 14a. However, scheme

(b) can easily obtain many more than 10,000 points as shown in Fig. 3. In contrast, it is difficult to

obtain many accurate observations on the ground and in the atmosphere. For Ocean Color and

Temperature Scanner (OCTS) on ADEOS-I, we could only obtain 86 points one year after the launch

(Sakaida et al., 1998). Assuming errors are independent, errors can be reduced by the sample number as

follows.

Etotal=Eeach/sqrt(N)

N: data number

The total calibration error can be estimated for schemes (a) and (b) as follows.

(a) 0.71°K/sqrt(60)=0.09°K

(b) 2.1°K/sqrt(10000)=0.02°K

These indicate that (b) is more accurate than (a) when we have many points in scheme (b).

5.3 Importance of this scheme in GLI calibration activities

We will be able to have more ground observation points in the GLI activities than the OCTS activities

because JMA will automatically provide GTS data that includes many ground observations. However,

we will still not have enough observations in the early stage of the calibration activities. In contrast, we

will easily obtain more than 10,000 points from a single day of global observations for scheme (b). The

sample points of scheme (b) are uniformly distributed and may explain the relative characteristics of

GLI related to scan angle, tilt angle, observation local time, and long-term observation during the

mission.

We have to carefully consider systematic errors due to errors of input data and assumptions in

LOWTRAN 7. If our objective is only SST estimation, we can avoid the problem by using consistent

MCSST coefficients. However, the GLI mission seeks to use thermal infrared data for many other

objectives: cloud properties, atmospheric water vapor, surface emissivity over land, and so on. In the

GLI calibration activities, we should implement and compare both schemes (a) and (b), because they

complement each other with respect to acquisition of ground obsrvation data in each calibration phase.

Acknowledgement

MODIS L1B data and MOD02CSS data are developed and provided by NASA. VIRS SST data are

provided by the EORC TRMM project. JMA ANAL data are provided by JMA based on a

NASDA−JMA agreement. NASDA calibration members gave me kind and useful advice. I deeply

appreciate these data providers and collaborators.

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References

Murakami, H., Sea Surface Temperature Estimation using Visible and Infrared Scanner (VIRS), http://www.eorc.nasda.go.jp/TRMM/imgdt/day_vrs/virs_sst.pdf, 1999.

Reynolds, R. W. and T. M. Smith, Improved global sea surface temperature analyses, J. Clim, 7, 929-948, 1994.

Sakaida, F., M. Moriyama, H. Murakami, H. Oaku, Y. Mitomi, A Mukaida and H. Kawamura, The sea surface temperature product algorithm of the Ocean Color and Temperature Scanner (OCTS) and its accuracy, J. Oceanogr., 54, 437-442, 1998.