Terrain and cloud height heavily impact ozone information despite ozone being concentrated in the stratosphere. The ozone weighting function (OWF) provides important information towards understanding the capabilities and limitations of a given channel. The factors that impact the OWF can be analyzed using radiative transfer theory and modeling. At the 9.6-μm infrared spectral region, both the OWF values and peaks are related to the surface temperature, terrain altitude, and cloud height. Warmer surface temperatures, lower terrain altitude, or lower cloud levels will give larger weighting function values, and the peak of the weighting function slightly increases with the increase in surface temperature, terrain altitude, or cloud height. For longer UV bands such as 306 and 318 nm, OWF shows smaller values for higher terrains, while showing larger values when clouds are present. However, in the shorter UV bands such as 274 and 288 nm, OWF has almost no relationship with the surface and clouds. Therefore, with satellite-based infrared ozone remote sensing, high terrain and cloud presence will reduce ozone sensitivity and information content. In addition, for UV bands, the effect is spectrally dependent: lower terrain altitude and the presence of clouds will increase the zone information content in the longer UV band, but they have no effect in the short UV band. A simulation of an ozone retrieval in the infrared band shows that higher terrain results in lower precision for colder emitting surface temperatures and less ozone absorption signal.
Ozone is one of the most important trace gases in the atmosphere. The highest level of ozone in the lower portion of the stratosphere, through absorption of the solar ultraviolet radiation, protects all biological systems on Earth (Hofmann and Montzka 2009). Tropospheric ozone, which forms by the reaction of sunlight to air containing hydrocarbons and nitrogen oxides, is an atmosphere pollutant and a constituent of smog (Finlayson-Pitts and Pitts 1997; Pierce et al. 2009). Ozone present in the upper troposphere also acts as a greenhouse gas, absorbing some of the infrared energy emitted by the earth, which has an effect on climate change. In contrast to the stratospheric ozone, which shields the earth from harmful UV rays, tropospheric ozone poses a health problem. The long-tem, high-density ozone information should be of significant value to the atmospheric chemistry community and for global climate change (McPeters et al. 1997).
Satellite-based remote sensing can be used to measure the atmospheric ozone all over the globe because of the inherently good spatial and temporal coverage of spaceborne observations (Finlayson-Pitts and Pitts 1997; Fishman and Larsen 1987). Both the UV and infrared bands could be used to obtain ozone concentration information because of the ozone absorption in these spectral regions. The backscattered ultraviolet (BUV)-type instruments, such as the Nimbus Total Ozone Mapping Spectrometer (TOMS), the Feng-Yun-3 (FY-3) Total Ozone Unit (TOU) and Solar Backscatter Ultraviolet Sounder (SBUS), the Aura Ozone Monitoring Instrument (OMI), and the European Remote Sensing Satellite-2 (ERS-2) Global Ozone Monitoring Experiment (GOME), measure the solar ultraviolet radiances backscattered by the earth and its atmosphere, which could be used to derive accurate total ozone amounts and vertical profiles in the stratosphere (Wang et al. 2010; Li and Lu 1997; Mijling et al. 2010; Bhartia et al. 1996). However, these bands show little sensitivity to the changing tropospheric ozone, especially in the shortwave ozone absorption regions. The radiance spectra observed by the high-spectral-resolution infrared (IR) sounders, such as the Aqua Atmospheric Infrared Sounder (AIRS), the Aura Tropospheric Emission Spectrometer (TES), the Meteorological Operation (MetOp) Infrared Atmospheric Sounding Interferometer (IASI), and the National Polar-orbiting Operational Environmental Satellite System (NPOESS) Preparatory Project (NPP) Cross-Track Infrared Sounder (CrIS), which cover the 9.6-um ozone absorption band, have been used to retrieve upper-tropospheric ozone profiles because of the good sensitivity in this area (Seemann et al. 2003; Clerbaux et al. 2007; Wei et al. 2010; Qu et al. 2001). In addition, agreement between IR-retrieved ozone amounts near the tropopause and aircraft ozone measurements was found (Pittman et al. 2009).
The ozone spatial and temporal distributions over the Tibet Plateau and polar regions play an important role in climate change and chemical processes (Bian et al. 2006). It is also very important to get the ozone information above the clouds to help understand the chemical and dynamical processes in the upper troposphere and lower stratosphere (Pittman et al. 2009). Ozone weighting function (OWF), which reflects the sensitivity of the radiance measurement to the ozone in the atmosphere at a given pressure level, is used for ozone profile retrieval and ozone information content analyses (Wei et al. 2010; Hasekamp and Landgraf 2001, 2002; Wassmann et al. 2011; Cheng et al. 1990). The ozone data in cloudy regions can be retrieved considering the fact that the OWF peak is above all but the highest clouds; how does cloud height impact the ozone information content? In the case of high terrain like the Tibet Plateau region, how do surface conditions (surface temperature, emissivity, and height) impact the ozone information content? The impacts of terrain and cloud height on ozone retrieval need to be investigated and quantified. Thus, the main objective of this work is to use satellite radiance measurements to examine how terrain and cloud height affect ozone retrieval. The sensitivity of OWF to the terrain and cloud height provides a quality flag of the ozone product as well as a better understanding of the capabilities and limitations of the satellite measurements for ozone retrieval. It also provides the Earth Observing System (EOS) science team more information on improving the ozone retrieval algorithms.
Theoretical analysis on the influence of terrain and cloud height on OWF is described in section 2. Simulations under different terrain and cloud heights are detailed in section 3. Simulation of ozone retrievals in the infrared band is described in section 4, followed by the summary and conclusions in section 5.
2. Theoretical analyses of the ozone weighting functions
a. OWF in the infrared ozone absorption band
In the infrared band, neglecting the scattering part in the atmospheric transfer equation, the true clear radiance exiting from the earth–atmosphere system is approximated by
where is the spectral radiance, is the total transmittance from the top of the atmosphere (TOA) at pressure level , is the surface emissivity, is the Planck radiance—a function of atmospheric temperature. The subscript denotes the surface, is the surface-reflected downwelling transmittance, and stands for the reflected solar radiation, which is considered negligible for bands with wavelengths longer than 4.0 μm during the day. Hereafter, we will omit the spectral symbol in the equation.
OWF is the measure of radiance sensitivity in relation to the perturbation of fraction change of the ozone profile. Following Li and Lu (1997) and Li et al. (2000), the analyzed OWF can be shown as in Eq. (2). It can be calculated efficiently from a given atmospheric state as shown,
where ; , are the surface skin and air temperatures, respectively, and is the ozone transmittance function. The term is the ozone mixing ratio profile in the atmosphere. In Eq. (2), OWF has a close relationship with the differences between surface skin temperature and surface air temperature. Under the same atmospheric state, larger differences result in larger values of the ozone weighting function, which means a higher sensitivity to ozone concentration. In addition, OWF is also correlated with the atmosphere state, total transmittance, and radiance optical path in the atmosphere. In regions of high terrain, the second part of the OWF in Eq. (2) has a shorter integrating path, which will theoretically give a smaller weighting function value. At the same time, the total transmittance in the first part of Eq. (2) is a little larger than that from the low-surface terrain situation. If the reflecting part of the radiance by the surface is neglected, then the difference in OWF between the two ground heights can be expressed as
Here we assume the same atmospheric state with different surface characteristics for the two surface terrain height situations. Subscripts and stand for high and low terrain surface, respectively. From Eq. (3), we can see that contributions to the difference of two OWFs divide into two parts: the first part comes from the surface skin and surface air temperature gradient, and the total transmittance difference; the second part comes from optical path integration between the two surface heights. When clouds are in the atmosphere, the equation will become more complicated because of the scattering of radiances in the cloud. However, for the 9.6-μm ozone absorption band, clouds usually can be treated as a “blackbody” surface. Under this situation, cloud heights will have similar effects on the OWFs as terrain heights do. Actual calculated results will be shown in section 3.
b. OWFs in the UV band
For BUV instruments, ozone profiles are usually retrieved by using wavelengths between 250 and 310 nm, where absorption limits the penetration in the stratosphere; total ozone products are derived using the UV wavelengths between 310 and 331 nm, where the radiance is sensitive to total ozone in the atmosphere. Considering only Rayleigh scattering and ozone absorption, the single-scattering (ss) UV radiance measured by satellites is given by
where is the solar flux; is the surface reflectivity; is the ozone effective Rayleigh scattering coefficient per unit pressure; is the Rayleigh scattering phase function for a scattering angle ; is the effective ozone absorption coefficient per unit ozone amount; and stand for solar zenith angle and instrument view angle, respectively; and is the column ozone above the pressure . In addition, a plane-parallel atmosphere is assumed.
The satellite-observed backscattered solar radiance depends on the absorption and scattering of the atmospheric ozone, the scattering and absorption of atmospheric aerosols and clouds, and the reflectivity of the surface. From Eq. (4), considering only Rayleigh scattering and ozone absorption, the OWF under single-scattering situations can be expressed as
where is the ozone mixing ratio profile in the atmosphere. From Eq. (5), we can see that OWF could be affected by the radiance transfer path in the atmosphere, which has a relationship with surface height. In most cases under the same atmospheric and surface conditions, the longer the radiative transfer path, the bigger the weighting function value in the same layer above the surface.
In UV bands, the effects of terrain and cloud on OWF are spectrally dependent. Ozone absorption cross sections reach a maximum near 250 nm and then decrease rapidly at longer wavelengths. In the atmosphere, ozone is mainly present in the high stratosphere and most of the absorption, about 90%, occurs there. The backscattering UV radiance contribution functions, which are the fractional contribution to the backscattered radiance, show that only a little radiation reaches the troposphere at wavelengths shorter than 298 nm, where strong ozone absorption sharply cuts off the penetration of radiances below 30 km (Bhartia et al. 1996). Hence, radiation emanating from Earth at these wavelengths is unaffected by clouds and the surface (Torres and Bhartia 1995). However, at longer wavelengths backscattering radiances go deep into the troposphere, where they are not only affected by multiple scattering in the optically thick atmosphere but also by terrestrial surfaces and clouds. So from Eq. (5), we can see that in longer wavelengths clouds and surface characteristics will affect OWF.
For longer UV wavelengths, OWF values depend on the surface reflectivity and surface height under the same atmospheric conditions. Higher surface reflectivity will give bigger OWF values for all layers. However, Earth’s surface reflectivity in UV is quite small over most of the world (Herman and Celarier 1997). Even over deserts UV reflectivity remains below 10%. So, Earth’s surface type has little effect on OWFs. The effect of surface height on OWFs is more complicated. High altitude means large surface reflective radiances, which help to increase the sensitivity to ozone concentration. But it will also reduce the radiative transfer path in the second part of Eq. (5), which has a negative effect on OWF values. The calculated OWFs for different surface altitudes will be shown in section 3.
Clouds in the atmosphere alter the absorption of BUV radiation by ozone. Absorption below the cloud layer is reduced, while the absorption inside and above the cloud is enhanced. These effects are complex but have little influence on OWFs, since there is little ozone in the troposphere. However, compared with the low reflectivity of land surfaces in the UV band (typically ranging from 2% to 7%), research has shown that the average reflectivity of cloud-filled fields of view of TOMS for the region from 60°N to 60°S for one week was about 56.1% (Eck et al. 1995). So, when there are clouds in the atmosphere, the OWF value in the longer UV band above the cloud will be very large because of the high reflectivity over clouds. Multiple-scattering and reflection OWF calculations in cloudy conditions will be given in section 3.
3. Ozone weighting function calculations
As discussed above, in the infrared and longer UV bands, Earth surface and cloud altitudes produce important radiative transfer effects in the earth–atmosphere system. First, they alter the reflected radiance between the surface and atmosphere. The second effect is that they alter the radiative transfer path, which changes the optical path by ozone absorption and scattering in the atmosphere. These two effects contribute to the radiance’s sensitivity to the ozone profile, and affect the retrieval accuracy. Weighting function values will be larger with higher surface reflectivity (or surface emission) or longer radiance transfer paths. Furthermore, the OWF depends on the instrument spectrum band and the real atmosphere states, such as the ozone, temperature, and water vapor profiles. The OWFs based on fast and accurate radiance transfer models are calculated to quantify the influence of different surface and cloud height situations.
The Community Radiative Transfer Model (CRTM), which was developed by National Oceanic and Atmospheric Administration (NOAA)’s Joint Center for Satellite Data Assimilation (JCSDA), is a fast and accurate radiance transfer model. It is vital software to simulate radiances and radiance gradients at the top of the atmosphere for satellite data assimilation in numerical weather prediction models (Han et al. 2006). In this paper, CRTM is used to calculate the OWFs for IASI channel 1054.75 cm−1 (in the ozone 9.6-μm absorption band). To compare the different typical ozone climate profile effects, both the U.S. Standard Atmosphere and subarctic summer atmosphere profiles are used to drive the OWFs. Considering that the impact of surface and clouds on the OWFs under different geometry situations is almost the same, only one case with a 30° view angle is shown in this study. Figure 1 gives the calculated results for different surface skin temperatures. The solid and dotted lines stand for U.S. Standard Atmosphere and subarctic summer atmosphere profiles, respectively. The peak positions of the OWF are located in the troposphere (from 500 to 400 hPa), which shows the potential to derive the tropospheric ozone information from this spectral region. However, OWF values for the subarctic summer atmosphere profile are always smaller than the U.S. Standard Atmosphere profile for the same surface type. From Fig. 1, we find that the higher surface skin temperature results in more sensitivity of the measured radiance to the ozone profile, since higher surface skin temperature “likely results in” a larger difference between the surface skin and surface air. This is consistent with the theoretical analysis in section 2. There is a little lift of the peak position with increasing surface temperature. Figure 2 shows the OWFs for different surface altitudes. Consistent with the theoretical analysis, high surface altitude gives low OWF values due to the shorter integrated radiative transfer path. Also, the peak positions have shifted upward slightly with the increase in surface altitudes. Figure 3 gives the OWFs for different cloud heights. The effects of the cloud height on the ozone weighing function are almost identical to the effects of varying surface altitudes—the higher the cloud heights, the lower OWF values; the peak position shifts upward with increasing cloud height.
From the weighting functions calculated with the infrared channel above, we find that surface characteristics (surface temperature, altitude, and cloud height) have two important effects on the OWFs. First, they change the absolute OWF values, which may affect the retrieval accuracy for tropospheric ozone. Second, the ozone optimal information level has a shift for different surface characteristics, which is important to understand, as the ozone product is derived from satellite infrared radiance measurements under different surface height situations.
Figure 4 shows the OWFs calculated in UV bands for the U.S. Standard Atmosphere. Different lines stand for different surface altitudes or cloud situations. The SCIATRAN (Rozanov et al. 2002) code is used here to do the simulation. This code was developed at the Institute of Remote Sensing at the University of Bremen and has been used for modeling radiative processes in the atmosphere for retrieval of trace gases from Scanning Imaging Absorption Spectrometer for Atmospheric Cartography (SCIAMACHY) measurements (Rozanov et al. 2002; Rozanov et al. 2005). A very efficient forward-adjoint radiative perturbation theory is implemented in SCIATRAN to derive the OWF under multiple-scattering conditions (Rozanov 2006; Rozanov et al. 1997; Box et al. 1988). In this paper, OWFs for ozone absorption bands 274, 288, 298, 306, and 318 nm with a spectral resolution of 1 nm are calculated. The first three bands have been used to derive the ozone profile in the stratosphere and the last two bands for retrieving the total ozone level. The peak positions are all located at high altitudes (above 20 km), which limits the retrieval of ozone profiles in the troposphere. From Fig. 4, we can see that surface altitudes and cloud heights have no effect on the OWFs for the 274- and 288-nm bands. This is consistent with our theoretical analysis in section 2. However, in longer ozone absorption bands, OWF values for high surface altitudes are smaller because of the shorter radiative path integration and the relatively small surface reflectivity (which we set to 5% during the calculation) in the UV band. This is different from the cloudy situation, which gives a larger weighting function values due to the high reflectivity over clouds. Compared with the infrared band, the surface altitudes and cloud location only change the OWF value, but have almost no impact on the peak altitude.
4. Simulation for ozone retrieval
The analyses given above have shown the effects of terrain altitude on the peak position and the magnitude of weighting functions in the IR band. But how could it affect the performance of retrieving ozone profiles? To answer this question, two experiments under clear-sky conditions were conducted. These two experiments shared the same atmospheric profiles (about 2394 profiles) but with different surface properties. The profiles used are a subset of the SeeBor database (Borbas et al. 2005), which contains information on atmospheric temperature, water vapor, ozone, and surface properties, such as temperature, pressure, etc. In the first experiment (EXP CNTL), taken as a benchmark, the surface pressure was assumed to be 1000 hPa, while in the second experiment (EXP SEN), the surface pressure was assumed to be 600 hPa. The surface air temperature in both experiments was interpolated from the air temperature profile based on the surface pressure, and the surface skin temperature was 1 K warmer than the surface air temperature. For simplicity, surface emissivity was assumed to be 0.98 for both experiments. The brightness temperatures within the IR band from 950 to 1100 cm−1 with an interval about 0.8 cm−1 were calculated based on CRTM for both experiments. To minimize the impact of instrumentation, a noise equivalent differential radiance (NEDR) of 0.05 W (m2 μm sr)−1 was specified, and the noise equivalent differential temperature (NEDT) was calculated based on NEDR, wavenumber, and brightness temperature at a given channel. Generally, the NEDT of EXP SEN was larger than that of EXP CNTL, since the brightness temperatures of EXP SEN are lower than that of EXP CNTL. An iterative-based one-dimensional variational data assimilation (1DVAR) physical algorithm (Li et al. 2000) was used for the ozone profile retrieval; the atmospheric temperature as well as the water vapor profiles used in the brightness temperature calculation were fed into the algorithm and kept fixed during iterations. The natural logarithm of ozone amount is used in the physical algorithm, since the infrared radiance received by satellite is more linear to the nature logarithm of absorbing gas amount than to that of normal amount (Ma et al. 1999; Li et al. 2000). The average profile of ozone was taken as the first guess in all 2394 retrievals, and the standard deviation of departures between profiles and the average was taken as the background error covariance. A maximum of five iterations were specified, which guarantees the convergence of both experiments.
The influence of terrain altitude on retrieval performance was significant. Figure 5 shows the root-mean-square error (RMSE) of retrieved profiles to “the truth” for both experiments in normal and logarithmic form of the ozone mixing ratio; also shown is the diagonal of the background error covariance matrix (blue line). The background error covariance was minimized in both experiments in normal and logarithmic forms. In the normal form, the RMSE decreased from 200 to 20 hPa as well as from 10 to 5 hPa in both experiments. The decrease from 10 to 5 hPa is comparable between the two experiments. But EXP CNTL casts improvement over EXP SEN on the precision between 200 and 20 hPa, especially around 100–50 hPa. In EXP CNTL, the RMSE around 100–50 hPa is about 0.3 ppmv, while that of EXP SEN degrades to about 0.5 ppmv. The RMSE of the logarithmic form gives us another view of the precision, which shows the relative values. Different from that in the normal form, the improvement caused by iteration was mainly located over a vast altitude from 500 to 20 hPa in both experiments. The remarkable improvement of EXP CNTL over EXP SEN occurred around 200–50 hPa. The RMSE of the logarithmic form of the ozone mixing ratio in EXP CTNL around 200–50 hPa is about 35%, while that of EXP SEN is about 50%. In general, the precision of the ozone retrieval in EXP CNTL is about 30% better than that in EXP SEN. Comparing the retrieved total column ozone amount to the truth illustrates that the RMSE between the retrieved and the true total amount is less than 20 Dobson units (DU), and the retrievals deviate from the truth more significantly when the amount is large. A comparison between EXP CNTL and EXP SEN shows that the precision of the total ozone amount in EXP CNTL (with an RMSE of about 15.0 DU) is a little bit better than that in EXP SEN (with an RMSE of about 18.2 DU). The influences of terrain altitude and cloud height on the retrieval of the ozone profile and total column ozone amount are consistent. The different precision of the retrievals in the two experiments is a result of the difference in NEDT (although NEDR is the same) and the magnitude of the OWFs.
Satellite ozone products have significant value for accurately deriving ozone space–time distribution information all over the world, which is helpful in understanding the chemical and dynamical processes in the atmosphere. However, ozone retrieval results from satellite strongly depend on the surface characteristics and cloud altitudes. Knowledge of these influences on the ozone retrieval will provide data users a better understanding of the capabilities and limitations of the ozone products. In this study, we analyzed the influences of surface characteristics and cloud heights on the OWF from radiative transfer theory and model-calculated results. Our investigations indicate the following. 1) In the 9.6-um infrared band, OWF has a close relationship with surface skin temperature, air temperature, altitude, and cloud height in the atmosphere. Higher surface temperature and lower altitude will give larger OWF values. The maximum position of the OWF will shift upward slightly with the increase in surface temperature and surface altitude. The effects of the cloud height on the OWF are almost the same as that of surface altitude. 2) In the shorter ozone absorption UV bands like 274 and 288 nm, OWF has almost no relationship with the ground surface characteristics or cloud height in the atmosphere because of strong absorption in higher atmospheric levels. 3) For the longer ozone absorption bands such as 306 and 318 nm, OWF will decrease with the ground surface uplift (increases in surface altitude), but it will give larger values under cloudy conditions. Different from the infrared band, there is no peak position shifting for different surface characteristics. 4) Because of the enhanced instrument noise and decreased magnitude of OWFs, the precision of the ozone profile retrieved from IR observations over high terrain altitudes is degraded by about 30% compared to that over low terrain altitudes; significant differences in the two configurations are observed around 100–50 hPa in the normal form of the ozone mixing ratio and around 200–100 hPa in the logarithmic form. Also, the terrain altitude has the same impact on the total column ozone amount as on the ozone profile.
This study is partly supported by NOAA Grant NA10NES4400013.