1. Introduction
Accurate radiometric calibration is a prerequisite for reliably inferring the fundamental geophysical parameters required for studying climate and weather systems. In general, radiometric measurements can be calibrated on the basis of prelaunch calibrations such as preflight tests in optical laboratories (e.g., Barnes et al. 1998). Even if prelaunch calibrations are flawless, the operation of a satellite sensor in space for a long duration may cause sensor degradation because of extraterrestrial solar radiation, aging of sensor optics, and molecular outgassing of the instrument. For this reason, it is necessary to closely monitor the calibration performance through the entire lifetime of the sensor.
To back up the onboard calibration system and monitor the calibration performance, alternative methods, such as the so-called vicarious calibration methods, are often used. The sensor calibration completely relies on vicarious methods if a sensor is not equipped with an onboard calibration device. This is especially true for geostationary meteorological satellites. The use of natural targets, such as bright deserts (Govaerts et al. 2004) and polar ice caps (Loeb 1997; Six et al. 2004), has been explored and demonstrated. Airborne observations can also provide useful information for calibration (Moeller et al. 2002, 2006) although an aircraft-based field campaign is usually financially costly. Intercalibration of a target sensor with sensors equipped with onboard calibration devices is another common approach for calibrating both infrared- and visible-channel sensors (Cao et al. 2005; Sohn et al. 2000, 2008; Minnis et al. 2002a,b; Heidinger et al. 2002; Wu and Sun 2005; Tobin et al. 2006; Gunshor et al. 2004).
This study focuses on the vicarious calibration for visible-channel sensors on the basis of deep convective clouds (DCCs). The spectral characteristics of these clouds are similar to those of white targets since cloud reflectance is nearly invariant over the visible spectrum. Clouds are abundant, particularly over the tropics, and meaningful statistics for the calibration can be obtained even for a short period. Most geostationary satellites are not equipped with onboard solar calibrators; however, they observe abundant DCCs. Hu et al. (2004) and Doelling et al. (2004) used DCCs to monitor visible-channel sensors based on an assumption that the distribution of broadband DCC albedo remains invariant over a month-long temporal scale. However, their methods are essentially intersatellite-calibration approaches because of a reliance on other well-calibrated broadband measurements of solar radiation.
In this study, the radiances reaching a visible-channel sensor aboard a satellite platform are simulated for scenes involving DCC targets without using the measurements from other solar sensors. It is assumed that the bidirectional reflectance associated with targeted DCCs can be accurately modeled if the optical properties of these clouds are known. The DCCs that overshoot the tropical tropopause layer (TTL) can be identified on the basis of a criterion specified in terms of infrared brightness temperature, and the characteristic optical properties of the selected DCCs can be determined. Furthermore, the inferred optical property information can be employed to simulate the top-of-atmosphere (TOA) radiances on the basis of state-of-the-art radiative transfer modeling capabilities. If these results are able to provide accurate and stable approximations to the measurements obtained at visible channels with an acceptable degree of uncertainty, the aforementioned DCC-based calibration method can be easily implemented for an absolute calibration and for monitoring visible-channel sensors.
The intent of this paper is to demonstrate the applicability of the DCC-based calibration method to solar channels (around 0.646 μm) and possibly extend it to other visible spectra (e.g., 0.4–1.0 μm). Once we adopt acquired optical properties of DCCs, this method is robust in the sense that it requires only infrared threshold brightness temperature for identifying DCCs that are abundant even within a daily time scale. The remainder of the paper is organized as follows: section 2 defines the DCCs and examines their optical characteristics from the operational Moderate Resolution Imaging Spectroradiometer (MODIS) cloud products. Section 3 presents the simulation of radiative transfer involving DCCs and the sensitivity of the MODIS band (0.646 μm) radiance to cloud optical thickness (COT) and effective particle radius. Section 4 examines whether the present DCC method is suitable for the solar-channel calibration. Section 5 gives the conclusions made from this study.
2. MODIS-retrieved optical properties of DCCs
DCCs are defined as highly convective clouds overshooting the TTL. When strong convective clouds overshoot the TTL extending from 14 to 19 km (Holton and Gettelman 2001), the temperature of the updrafting air decreases continuously with the ascent motion, following a near-dry adiabat because of the little amount of water vapor available within the air. Overshooting DCCs involve a strong upward motion that suppresses the exchange of air in the cloud with ambient air (Lattanzio et al. 2006), resulting in cloud-top temperatures lower than the tropopause temperature. On the other hand, because of generally increasing temperature with height above the tropopause, clouds spread from the convection centers have temperatures that are not very discernable from the tropopause temperature or are sometimes warmer than the tropopause temperature (e.g., Chung et al. 2008). Since the standard atmosphere shows that the tropopause temperature over the tropics is around 190 K, DCCs overshooting the TTL likely have their cloud-top temperatures lower than 190 K. Thus, the window-channel (10.8 μm) brightness temperature TB11 of 190 K can be used as a criterion for determining DCCs overshooting the TTL.
To examine the optical properties of DCCs, the cloud products, visible-band radiances, and infrared brightness temperatures (TB11) from the Aqua MODIS measurements acquired in January 2006 over tropical ocean and land (30°N–30°S, 90°W–90°E) are binned. A MODIS pixel is identified as a DCC target if the surrounding 9 × 9 MODIS pixels show a standard deviation (STD) of TB11 less than 1 K and if the target is located within a spatially homogeneous cloud. In addition, a spatial homogeneity criterion of the visible reflectance is applied. A pixel is selected if the STD of the 0.646-μm reflectance for the surrounding 9 × 9 pixels normalized by their mean value is less than 0.03. Targets are selected only if both the criteria are satisfied. This selecting process effectively eliminates pixels near cloud edges or those associated with rapidly changing smaller-scale cloud plumes. In this study, 4249 DCC targets are selected for January 2006. Among the selected 4249 targets, 3160 targets are located over land, whereas 1089 targets are over ocean and coastal areas. It is noted that selected targets are generally located along the intertropical convergence zone (ITCZ).
Figure 1 shows the frequency distributions (given in %) of the MODIS 0.646-μm-channel reflectance, MODIS-derived COT, and cloud effective radius (re) for selected targets. Note that reflectance [or bidirectional reflectance factor (BRF)] is defined by πR0.646/F0 cosθ0, where R0.646 and F0 are measured radiance and incoming solar irradiance at the 0.646-μm band, respectively, and θ0 is the solar zenith angle (SZA). COT and effective radius are obtained from MODIS cloud products in the collection 5 version (King et al. 1997, 2006). All those MODIS cloud and radiance parameters are provided with a 1-km resolution. The measured reflectance at 0.646 μm, COT, and effective radius for 4249 DCC pixels are binned with increments of 0.05, 1, and 1 μm, respectively. The frequencies of these quantities are calculated for each bin.
It is shown that most selected pixels have reflectances larger than 0.9, implying that the DCCs determined from the criterion of TB11 ≤ 190 K represent optically thick clouds. On the other hand, about 90.8% of the 4249 DCC pixels show a COT value of 100. Since the MODIS cloud algorithm retrieves COT up to 100, actual COTs of DCCs could be larger than 100. Among the 4249 DCC pixels, only 9.2% show COTs smaller than 100, which are likely to be associated with moderately thick clouds originating from convection centers in the TTL layer in the late stage of convection development. Note that an explanation of the mechanism of the DCC evolution in the TTL can be found in Luo et al. (2008). It is evident from Fig. 1 that the histogram of the MODIS-based effective particle radii for the DCCs shows a narrow distribution with the maximum frequency at about 20 μm.
Using the MODIS quality assurance information, we further examine the COT characteristics of DCCs with COTs of 100. The MODIS COT algorithm does not provide quantitative values for COT greater than 100 (in this case COT is marked as “100”); however, quality assurance data provide additional information about the COT range that clouds may have. With the MODIS quality assurance information, selected pixels are classified into three categories, namely, COT < 100, 100 ≤ COT < 150, and COT ≥ 150. The relative fraction of each category is shown in Fig. 1d. As expected, 9.2% of the pixels belong to the first category (COT < 100), 20.8% of the pixels belong to the second category (100 ≤ COT < 150), and 70% of the pixels belong to the third category (COT ≥ 150). The DCCs defined in this study are mainly represented by clouds whose optical thicknesses are greater than 100 (here about 90.8%). Furthermore, more than 70% of selected DCC pixels have COTs greater than 150.
In this study, the optical properties of overshooting DCCs are represented in terms of COT = 200 and effective radius = 20 μm. This assumption is based on the fact that the effective radii for DCCs show a sharp peak around 20 μm and that the percentile frequency of DCCs shows COT ≥ 150 for more than 70% of the total cases.
3. Radiative transfer calculation for DCC targets
a. Radiative transfer model
For the visible-channel calibration, TOA radiances are simulated under cloudy conditions by using the Discrete Ordinates Radiative Transfer (DISORT) model (Stamnes et al. 1988), and are compared with the measured counterparts. This radiative transfer model (RTM) fully accounts for the multiple scattering of radiation by particles in the atmosphere and the computational time depends on the number of streams used for the radiation field. The bulk phase function for a cloud shows a strong forward peak and thousands of Legendre polynomials may be needed to fully account for the phase function (King 1983; Nakajima and Tanaka 1988; Hu et al. 2000) in the radiative transfer simulation. To reduce the computational burden without degrading computational accuracy, the delta-fit method (Hu et al. 2000) is used to truncate the phase function in the forward directions. Additionally, the delta transmission associated with the scattering of radiation by ice crystals is taken into account in this study. The technical details of truncating the phase function can be found in Yang et al. (2000).
The bulk scattering properties for ice particles (Baum et al. 2005a,b; hereafter referred to as the Baum scattering model) are used to specify cloud optical properties in the RTM. The Baum scattering model provides band-averaged scattering properties such as the extinction efficiency (Qext), asymmetry factor (g), phase function [P(Θ)], single-scattering albedo (SSA), and fraction of delta transmitted energy ( fd) for 18 effective radii from 5 to 90 μm with a 5-μm interval. Note that only the optical properties of ice particles are considered here. This is because the DCCs in this study have their cloud tops generally located above the tropopause and the upper parts of clouds consist of nonspherical ice particles.
To prescribe the altitude and thickness of a DCC, the cloud-top and cloud-base heights are assumed to be 15 and 1 km, respectively, resulting in a geometric thickness of 14 km. This assumption is reasonable because convectively active clouds overshooting the TTL are usually thicker than 10 km (Chung et al. 2008; Luo et al. 2008).
One of the advantages of using DCC for the TOA radiance calculation is to minimize the influences of the surface and atmosphere on the TOA visible radiances because the reflection from a deep cloud layer should be much larger than the contributions from the surface and the molecular scattering above the cloud, as shown in the appendix. With an expected insignificant influence of the atmosphere, atmospheric thermodynamic conditions can be represented in terms of the standard tropical profile (McClatchey et al. 1972). The optical thickness related to the gaseous absorption is calculated from the correlated-k-distribution method (Kratz 1995; Kratz and Rose 1999) by using the tropical standard profile. Pressure profiles are also used for calculating the optical thickness associated with Rayleigh scattering. The total optical thickness for each layer is the sum of the optical thicknesses associated with gaseous absorption, Rayleigh scattering, and clouds.
An oceanic bidirectional reflectance distribution function (BRDF) model adopted from the Santa Barbara Disort Radiative Transfer (SBDART; Ricchiazzi et al. 1998) is used for considering the variations of reflectance, including sun glint, with the viewing geometry. For the BRF calculation, satellite viewing zenith angle (VZA), the viewing azimuth angle (VAA), the SZA, and the solar azimuth angle (SAA) are used for the RTM inputs.
b. Use of DCCs for the visible-channel calibration
To examine the feasibility of using DCCs to calibrate the visible-channel sensor, we first study the sensitivity of the TOA radiance (or reflectance) to the variation of COT for an effective radius of 20 μm. The variation of reflectance at 0.646 μm with respect to COT change is obtained from the model simulation (Fig. 2). Simulations are carried out only for ice clouds whose effective radii are assumed to be 20 μm. Flux reflectances (or albedos) are simulated for SZA = 30° whereas the bidirectional reflectance is calculated for SZA = 30°, VZA = 20°, and a relative azimuth angle (RAA) of 30°. These solar and viewing geometries are used for the sensitivity test only. The influences of various viewing geometries are examined in more detail with Figs. 3 and 4, while influences of SZA variations on BRF are found in Table A1 of the appendix.
It is shown that both flux and bidirectional reflectance increase rapidly with the increase of COT, reaching up to 80% of reflectance at approximately COT = 30. When COT further increases the slope decreases slowly and reflectivity approaches its asymptotic value, especially with COTs greater than 200. However, the increase seems to continue even at COT around 400. In spite of the monotonically increasing tendency of reflectance in the given range of COT, reflectances for COTs larger than 200 appear not to be significantly sensitive to the COT change, suggesting that the TOA radiance for DCC targets can be simulated within a specified uncertainty range when typical values for the optical properties of DCCs are used in the radiative transfer simulation.
To quantify the uncertainty range of the simulated TOA radiance by assuming COT = 200 and re = 20 μm to be typical for the optical properties of DCCs, the TOA BRFs are simulated with three COT values (COT = 100, 200, and 400) for various viewing geometries (0° ≤ VZA ≤ 60°, 0° ≤ RAA ≤ 180°, and fixed SZA = 30°) and re = 20 μm. The top panels of Fig. 3 show the TOA BRFs simulated for three COTs (100, 200, and 400). For the viewing geometries, VZA and RAA are presented in the radial and tangential directions, respectively. The term RAA = 0° indicates the forward scattering of sunlight, whereas RAA = 180° indicates the backward scattering.
For all three COT cases, the maximum reflectance is observed in the direction of VZA = 30° and RAA = 180°, indicating the dominant backward scattering by the cloud layer. Other maximum areas are noted near the nadir viewing direction (VZA = 0°) and the reflectance appears to generally decrease with increasing VZA. Figure 3 also shows that cloud reflectance depends strongly on the viewing geometry (e.g., reflectance for COT = 100 changes from 0.82 to 1 in the range of 0° ≤ VZA ≤ 60°), implying that a cloud layer cannot be treated as a Lambertian surface.
The BRF changes associated with COT changes from 100 to 200 and from 200 to 400 are given in the bottom panels of Fig. 3. The maximum difference of BRFs up to 0.05 is observed at the nadir view when COT increases from 100 to 200, and the difference decreases with the increase of the viewing angle. Relatively small maximum differences (up to 0.025) are noted again over the nadir view when COT changes from 200 to 400.
The uncertainty range of BRFs caused by changes in effective radius is also examined. TOA BRFs are simulated with COT = 200 and three effective radii (10, 20, and 30 μm) for the same viewing geometry used for Fig. 3. Results are given in the top panels of Fig. 4. For all three re cases, the maximum reflection occurs at backward direction (VZA = 30° and RAA = 180°) where sunlight is coming, as in the case shown in Fig. 3.
Also shown in Fig. 4 are BRF changes with respect to the effective radius variation from 10 to 20 μm and from 20 to 30 μm (the bottom two panels of Fig. 4). Forward scattering tends to be increased while backward scattering is decreased with respect to particle size, as the asymmetry factor and SSA decrease. However, in the exact backward direction (VZA = 30° and RAA = 180°), maximum peak sharpens for larger particle size. Except in the backward direction, the overall differences in BRFs for both cases appear to be less than 0.02 when the VZA is smaller than 40°. Considering that the actual range of the effective radii for DCCs is narrower as shown in Fig. 1 (i.e., observed effective radii are from 15 to 25 μm), the uncertainties caused by using 20 μm for the effective radii for all DCCs are not significant. These results are consistent with an interpretation based on Mie theory. When the size parameter (α = 2πr/λ, where r is particle size and λ is wavelength) becomes large (e.g., α = 100), the scattering efficiency converges to 2 if there is no absorption (Liou 2002). For size parameters around 200 at a wavelength of 0.646 μm, a nearly invariant scattering efficiency can be expected in spite of the nonsphericity and absorption of cloud particles.
Possible uncertainties induced by modeling are shown in the appendix. It is noted that surface, atmosphere, and aerosol have negligible impact on the simulation errors while COT and effective radius are main factors in determining the simulation accuracy. With 100 ≤ COT ≤ 400 and 10 μm ≤ re ≤ 30 μm, maximum simulation errors are estimated to be around 5% when fixed cloud parameters (COT = 200 and re = 20 μm) are used for the simulation of BRF under DCC conditions.
The present results suggest that visible reflectances associated with DCC clouds can be simulated with fixed cloud optical properties with uncertainties around 5% and may be acceptable for the visible-channel sensor calibration. This capability is important because only the identification of DCCs is required for the calibration of a visible-channel sensor. Furthermore, since many meteorological satellites [e.g., Geostationary Operational Environmental Satellite (GOES), Meteosat, and Multifunctional Transport Satellite (MTSAT)] are equipped with onboard blackbody calibrators for thermal infrared channels, the well-calibrated infrared band measurements can provide information for determining DCCs, which in turn can be used for the calibration of solar sensors aboard the same platform.
4. Solar-channel calibration using DCC targets
In this section we will examine the possibility of calibrating a satellite-borne solar sensor by simulating the TOA radiances for DCC pixels on the basis of the radiative transfer calculations described in section 3. With the fixed optical properties of DCCs, radiances at a visible channel can be simulated and the calibration coefficients can be derived by regressing estimated digital counts to simulated radiances. In this study, the MODIS visible-channel (0.646 μm) radiances are simulated and the theoretical results are compared with the observations. This method provides an efficient approach to evaluate the accuracy of a calibration algorithm using DCC targets because the MODIS sensors are equipped with the onboard calibration system and are well calibrated (Xiong and Barnes 2006; Minnis et al. 2008).
The MODIS data acquired from January to June 2006 on both Terra and Aqua are used for examining the present DCC-based calibration method. DCCs are identified by applying the criteria discussed in section 2 to the MODIS measurements. The TOA radiances are simulated with fixed cloud properties (COT = 200 and re = 20 μm) for those selected DCC targets. Results are given in BRF, normalized by incoming solar irradiance (F0 cosθ0). The influences of variations in the direct beam with changes in SZA and Earth–sun distance are substantially reduced. Figure 5 shows the scatterplots of simulated reflectances versus the MODIS band 1 (0.646 μm) observations for each month. It is noted that the comparison of both the Terra and Aqua MODIS 0.646-μm-band simulations and measurements shows a near one-to-one corresponding pattern. Considering that fixed cloud optical parameters are used for the simulations, variations in simulated reflectances are mostly due to different solar and viewing geometries. Variations of observed reflectance for a given simulated reflectance should be largely due to deviations of the cloud optical thicknesses of selected DCC pixels from COT = 200.
It is noted that only a few points are beyond the 20% uncertainty range, particularly in March for Terra, and in April for Aqua, which may be associated with moderately thick clouds such as anvil-type cirrus clouds in the TTL or pixels associated with the cloud edge. It has been reported that anvil-type cirrus clouds may be developed in the decaying stage of the lifetime of a DCC when upward motion becomes weaker and the convective cloud spreads laterally. Development of anvil-type cirrus clouds can be associated with the decrease of COT while still maintaining cold cloud-top temperature in the TTL. In contrast, overestimation is less frequent because the features of TOA radiance are less sensitive to the COT values if COTs are larger than 200, as shown in Fig. 2.
The frequency histograms of the relative errors of simulated reflectance in comparison with the observed values are given in Fig. 6, in which each curve represents a frequency distribution for the given month. About 90% of the total pixels are within a ±5% uncertainty range of the relative error for both Terra and Aqua throughout the 6-month period although the maximum frequency location shows an apparent seasonal variation. The mode and mean of relative errors are in the range of −0.81 ∼ 2.21% and −3 ∼ 0% for Terra, and −1.86 ∼ 1.34% and −3 ∼ 0% for Aqua, respectively. Moreover, less than 10% of the total pixels appear to be located outside the ±5% uncertainty range in both head and tail sides. Note that no significant differences are found between the two MODIS sensors in this study, consistent with other studies on sensor intercomparison (e.g., Minnis et al. 2008).
For the absolute sensor calibration or calibration monitoring, it may not be necessary to use a pixel-based approach because of the random behavior of error characteristics. Instead we use the daily mean value for examining the feasibility of using the DCC method for the visible sensor calibration. Daily mean radiance (or reflectance) is estimated only if the number of daily DCC pixels is greater than 10. Resultant scatterplots of simulated and observed daily mean reflectances are presented in Fig. 7. For both the Terra and Aqua MODIS sensors, it is shown that most of the points fall within an uncertainty range of ±5% (enveloped by two dashed lines) while only a few points are located outside the ±5% uncertainty range. This suggests that the visible-channel calibration can be accomplished within a 5% error range when the DCC method is applied on a daily basis.
Time series of observed and simulated daily mean radiances are plotted in Fig. 8. In these plots, radiance is used instead of reflectance to better observe the presence of seasonal variations. It appears that simulated values are coherent with observed values within a ±5% uncertainty range except for a few cases located outside the 5% range. There is no apparent seasonal variation in the relative errors.
The radiance range of Terra is 380–480 W m−2 sr−1 μm−1 while a higher variation range of 400–500 W m−2 sr−1 μm−1 exists for Aqua. The differences are due to different solar/viewing geometries associated with satellite passing times (note that the equatorial crossing times for Terra and Aqua are 10:30 a.m. and 1:30 p.m., respectively). A larger number of selected targets and the more dominant seasonal variation found in Aqua may also be due to the different crossing time, but seems to be associated with the diurnal variation of cloud development. Nevertheless, relative errors for the two MODIS sensors seem to be comparable.
Overall, a good agreement between simulated and observed radiances implies that the present DCC method can be reliably used for visible-channel calibration within a ±5% uncertainty range.
5. Conclusions
We developed a calibration method based on deep convective clouds for visible sensors. DCCs are identified by applying a criterion of TB11 ≤ 190 K with homogeneity checks. It has been shown that more than 90% of selected 4249 MODIS DCC pixels for January 2006 have COT > 100, and 70% of the pixels have COT > 150, suggesting that DCCs are optically thick clouds. Considering that 70% of the selected 4249 pixels have COT > 150, and there exists a sharp peak around 20 μm of effective radius, we assumed COT = 200 and re = 20 μm to be the typical values for DCCs, and those values were used for MODIS visible-band (0.646 μm) radiance simulation. It is noted that the use of fixed optical properties for radiance simulation of DCCs seems to induce less than a 5% uncertainty range. Thus, a visible sensor can be calibrated with the same degree of accuracy when DCC targets are used.
Examining the possible use of the DCC method to calibrate a solar sensor, measured radiances of the selected DCC targets at the MODIS 0.646-μm band were compared with simulated radiances. The comparison of Terra and Aqua MODIS radiances for a 6-month period from January to June 2006 demonstrated that, on a daily basis, solar sensors can be calibrated within a ±5% uncertainty range. Considering that MODIS (Barbieri 1997) and the Spinning Enhanced Visible and Infrared Imager (SEVIRI; Schmetz et al. 2002) calibrations aimed for an order of 5% accuracy for short-term analysis of meteorological variables, the 5% of calibration uncertainty targeted in this study should be acceptable.
We also tested whether the proposed calibration method is applicable to other MODIS visible bands [i.e., bands 3 (0.466 μm) and 4 (0.554 μm)], and found that those bands also have similar uncertainty ranges and patterns (not shown). This is plausible since optical properties of DDCs are nearly invariable over the visible spectrum (i.e., white targets), while gas absorption over those spectrums is not significant in particular under the DCC conditions. Therefore, it is concluded that the developed calibration method can be applied to other visible channels with a similar accuracy once the strong gas absorption band is avoided. However, it is still needed to assess the performance of the developed calibration method using other well-calibrated satellite sensors since optical properties of DCCs were based on the MODIS measurements and then the method was tested only for MODIS visible bands.
The present DCC method can be readily used for the solar-channel calibration because it only needs a DCC identification based on infrared-channel measurements and DCCs are abundant over the tropics. Note that many meteorological satellites carry blackbody calibrators for thermal infrared channels while onboard calibration for solar channels is rarely available. Furthermore, calibration accuracy of the present method may be improved by determining DCCs in a more rigorous way, because major uncertainties are from the cases of COT < 100.
Acknowledgments
The authors thank three anonymous reviewers for their constructive and valuable comments that led to an improved version of the manuscript. The authors also thank Dr. Yves Govaerts at EUMETSAT for valuable discussion. This work was supported by the Korea Meteorological Administration Research and Development Program under Grant CATER 2006-2103, and by the BK21 Program of the Korean government.
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APPENDIX
Test of Uncertainty Range
Table A1 summarizes results of sensitivity tests showing uncertainty ranges in the simulation of 0.646-μm BRF, caused by different surface, atmosphere, aerosol, and cloud parameters. The uncertainty range is defined as the maximum value of BRF found within the input range minus BRF from a reference condition. Testing the uncertainties for one parameter, the other parameters are held fixed using their respective reference values. In this test, five solar geometries (i.e., SZA = 0°, 10°, 20°, 30°, and 40°) are considered, with 95 viewing geometries expressed by combinations of five VZAs (= 0°, 10°, 20°, 30°, and 40°) with 19 RAAs (from 0° to 180° with a 10° interval). For Table A1, the largest BRF change among 95 viewing geometries is taken for the given SZA and input parameter in interest. Therefore, in Table A1, each uncertainty range represents a possible maximum simulation difference from the reference value within the given input range.
Examining surface influences on the uncertainty, a Lambertian surface is assumed. It is noted that, within the range of 0–0.4 surface albedo, the use of the ocean surface model as a reference could induce a maximum uncertainty of TOA BRF up to 0.09% of the reference BRF. Such small difference seems to be negligible in these deep convective cases. It is probably because the surface influence on the TOA BRF is obscured by the much larger impact by deep convective cloud.
Uncertainties induced by incorrect atmospheric profiles in 0.646-μm BRF simulations are examined using the midlatitude summer (MLS) profile, and uncertainties are assessed as the deviation from those of the tropical atmosphere profile (TRO). About 1.3% of BRF changes are noted when the TRO profile was replaced by the MLS profile. However, considering that DCCs occurred mainly over low latitudes, the actual uncertainty range caused by an incorrect assignment of atmospheric profile should be much smaller than 1.3%. Aerosol effect in the given range of the aerosol optical thickness (AOT; i.e., 0–3) appears negligible as expected.
By contrast, cloud parameters such as COT and effective radius show relatively large impacts on the BRF simulation, as noted from Figs. 3 and 4. About 4.4%–4.8% of BRF changes are shown in the COT range (i.e., 100–400) when COT = 200 is used as a reference value. Also noted are 1.6%–3% of BRF changes within the 10–30-μm range of effective radius, compared to BRF from re = 20 μm. Cloud-top height (Zc) and cloud geometrical depth (ΔZc) appear to cause minor changes (<1%) in BRF.
Overall it can be concluded that COT and effective radius are dominant factors to determine the accuracy of simulated BRFs. Considering that the simulation errors caused by surface, atmospheric, and aerosol properties are relatively small and that they should not be correlated with each other, those errors seem to be reduced by spatial or temporal averaging. In conclusion, simulation errors should be mainly from the incorrect assignment of COT and effective radius, but maximum error appears to be within about 5% in the given input ranges.
Frequency distributions of (a) 0.646-μm reflectance (πR0.646/F0 cosθ0), (b) effective radius, (c) COT for selected deep convective cloud pixels, and (d) three COT classes (COT < 100, 100 ≤ COT < 150, and COT ≥ 150) obtained from 1 month of Aqua MODIS data (January 2006) over the tropics (30°N–30°S, 180°W–180°E).
Citation: Journal of Applied Meteorology and Climatology 48, 11; 10.1175/2009JAMC2197.1
Distributions of (a) flux reflectance (or albedo) with SZA = 30° and (b) BRF with SZA = 30°, VZA = 20°, and RAA = 30°, for ice clouds whose COTs range from 0 to 400. Cloud effective particle radius of 20 μm is assumed.
Citation: Journal of Applied Meteorology and Climatology 48, 11; 10.1175/2009JAMC2197.1
(top) Simulated TOA BRFs of ice cloud for three COTs (100, 200, and 400). (bottom) BRF changes made by COT changes from 100 to 200, and from 200 to 400. Cloud effective radius of 20 μm is assumed.
Citation: Journal of Applied Meteorology and Climatology 48, 11; 10.1175/2009JAMC2197.1
(top) Simulated TOA BRFs of ice cloud for three re values (10, 20, and 30 μm). (bottom) BRF changes made by effective radius changes from 10 to 20 μm, and from 20 to 30 μm. COT = 200 is assumed.
Citation: Journal of Applied Meteorology and Climatology 48, 11; 10.1175/2009JAMC2197.1
Comparison between simulated and observed MODIS 0.646-μm-band reflectance for 6 months of the MODIS data on (a) Terra and (b) Aqua platforms. Simulations of DCC pixels are done with assumed cloud properties (i.e., COT = 200 and re = 20 μm).
Citation: Journal of Applied Meteorology and Climatology 48, 11; 10.1175/2009JAMC2197.1
Histograms showing relative errors of simulated reflectance of MODIS 0.646-μm band to observed reflectance for the DCC pixels from (a) Terra and (b) Aqua. The 5% uncertainty ranges are presented as gray boxes.
Citation: Journal of Applied Meteorology and Climatology 48, 11; 10.1175/2009JAMC2197.1
Scatterplots of simulated vs observed MODIS 0.646-μm-band reflectances for (a) Terra and (b) Aqua on a daily basis. Daily mean value is calculated only if the total number of DCC pixels for the given day is larger than 10.
Citation: Journal of Applied Meteorology and Climatology 48, 11; 10.1175/2009JAMC2197.1
Time series of daily mean simulated and observed MODIS 0.646-μm-band radiances for (a) Terra and (b) Aqua. Daily mean value is calculated only if the total number of DCC pixels for the given day is greater than 10. (bottom) Relative errors of simulated radiances along with corresponding number of DCC pixels used for the daily average (vertical bars).
Citation: Journal of Applied Meteorology and Climatology 48, 11; 10.1175/2009JAMC2197.1
Table A1. Uncertainty ranges (%) in simulations of 0.646-μm-channel reflectance, caused by changes in surface reflectance, atmospheric profile, aerosol, and cloud parameters. For calculating the TOA BRF for a given value (within the given range) of one parameter in interest, other parameters are held fixed using their respective reference values. Uncertainty for one parameter is expressed in percent change from its reference value, within the input range.
