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    Map and cross section for AIRS v5 ozone on 15 May 2004. (top) 1° × 1° binned ozone data at 250 hPa for the Northern Hemisphere and FNL PV (2 and 4 PVU, black). (bottom) Ozone cross section along 160°E. Also shown are 2- and 4-PVU contours (orange lines), thermal tropopause (black dots), selected potential temperature (K) surfaces (yellow dash), and zonal wind (m s−1) (white contours).

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    AIRS ozone weighting functions in the 1041.7 cm−1 (9.6 μm) region for a midlatitude atmospheric state.

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    Locations of ozonesonde stations (open circle with cross inside) collected from WOUDC, SHADOZ, and NOAA/ESRL/GMD for the compilation of the ozone climatology.

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    An example of monthly mean ozone profiles in the latitudinal bin between 60°N ∼ 70°N for May in (left) SLB altitude and (right) TB altitude. Original ozone profiles are shown as gray dots and the monthly mean and 1σ standard deviation are shown as black line and error bars. Also shown as the black dashed line is the mean tropopause height, which is the average computed from individual thermal tropopause.

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    January mean Northern Hemisphere ozone profiles (standard deviations given by error bars) according to latitudinal bin (every 10°, shown are selected bins between 0° and 5°N, 30° and 40°N, 60° and 70°N, and 80° and 90°N) using SLB (blue line), TB (red line), and the LLM climatologies (gray line). The red dashed line is the mean tropopause height, which is the average tropopause height computed from the individual thermal tropopause for each profile in each temporal and spatial bin.

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    SLB ozone (a) mean and (b) coefficient of variation (standard deviation divided by the mean) and TB ozone (c) mean and (d) coefficient of variation in January. Also plotted are the 300-, 350-, 380-, and 400-K isentropes (white dashed lines), the thermal tropopause (red dots pointed out by the arrow), and the zonal wind (m s−1) (black contours) from the NCEP FNL Jan 2004 monthly mean data.

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    (top to bottom) The four leading eigenvectors of the covariance matrix for (a) SLB and (b) TB from the composite ozonesonde dataset. The total percentages of ozone variance from these four eigenvectors are 99.7% for SLB case and 99.49% for TB case.

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    Example of smoothed averaging kernels using SLB ozone climatology at the location of 52.2°N, 5.90°E derived from (left) the AST algorithm and (right) the OE algorithm. The calculated DOF for AST is 1.69, and DOF for OE is 1.56.

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    Relationship between tropopause height (km) and total ozone (Dobson unit) from a composite ozonesonde dataset (black dots) and four retrieval experiments (red dots): (a) AST algorithm with SLB ozone climatology, (b) AST algorithm with TB ozone climatology, (c) OE algorithm with SLB ozone climatology, and (d) OE algorithm with TB ozone climatology. Linear regression lines are plotted with slopes (b) and y axis intercepts (m). Correlation coefficient is r. There are around 1120 profiles in each comparison.

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    Example of a single-profile retrieval using ozonesonde profile (black solid line) from station Uccle (50.51°N, 4.04°E). (a) Results from the four retrieval experiments (solid line) and their first guess (first guess in SLB for case 1 and 3 is red dashed line; first guess in TB for case 2 and 4 is light-blue dashed line) are given. The thermal tropopause is plotted in black dashed line. (b) Vertical profiles of ozone from ozonesonde (black solid line) and a priori (red solid line) with variance (red dashed line) for SLB and a priori (light blue solid line) with variance (light blue dashed line) for TB. Variance is defined as diag(𝗦a).

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    PDF of ozone differences (retrieval − truth is red histogram) in ppbv showing the distribution of retrieval error for the 1-day ensemble using ECMWF data as the true atmosphere. Several statistical values are shown for the 150–200-hPa layer from case (left) 3 and (right) 4: 1) the modal values (in red solid line), 2) the median values (in green solid line), and 3) the mean values (in blue solid line). The shaded gray histogram is the ozone differences between a priori state and the true state for the same ensemble. Recall that both panels use the OE retrieval algorithm with the left panel using SLB ozone climatology and the right panel using TB ozone climatology.

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    Ozone relative errors using the ECMWF ozone as the truth ensemble for the four experimental cases from 100 to 300 hPa. Relative differences are defined as (retrieval − truth)/(truth) × 100%. Values shown are the median in a solid line with triangle symbols and first quartile (25%) and third quartile (75%) in dashed lines. The red color is the relative differences between the retrievals, and the truth and the gray color is the relative differences between the a priori state and the truth.

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    A horizontal view of AIRS v5 ozone (color contours) at 275 mb on 28 Apr 2008 during the START08 campaign. Also shown are the PV dynamical structure with the 2-PVU contour (orange) from GFS analysis and the GV ground track in dark red.

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    (a) Percent differences between GV and four retrieval experiments as a function of three retrieval layers for the START08 campaign. Values shown are median and 1σ variability. Percent difference is defined as (satellite − aircraft)/(aircraft) × 100%. (b) Vertical profiles of ozone from GV and four retrieval experiments during the START08 campaign constructed using relative height to the GFS thermal tropopause. Values shown are median and 1σ variability. Variability bars are offset in the vertical for better visualization of the ranges.

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Ozone Profile Retrieval from an Advanced Infrared Sounder: Experiments with Tropopause-Based Climatology and Optimal Estimation Approach

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  • * Perot Systems Government Services, Fairfax, Virginia
  • | + National Center for Atmospheric Research, Boulder, Colorado
  • | # IM Systems Group, Inc., Rockville, Maryland
  • | @ NOAA/NESDIS/Center for Satellite Application and Research, Camp Springs, Maryland
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Abstract

Motivated by a significant potential for retrieving atmospheric ozone profile information from advanced satellite infrared sounders, this study investigates various methods to optimize ozone retrievals. A set of retrieval experiments has been performed to assess the impact of different background states (or the a priori states) and retrieval algorithms on the retrieved ozone profiles in the upper troposphere and lower stratosphere (UTLS) using Atmospheric Infrared Sounder (AIRS) measurements. A new tropopause-based ozone climatology, using publicly available global ozonesonde data to construct the a priori state, is described. Comparisons are made with the AIRS version 5 (v5) ozone climatology. The authors also present the result of a newly implemented optimal estimation (OE) algorithm and compare it to the current AIRS science team (AST) algorithm used in version 5. The ozone climatology using tropopause-referenced coordinates better preserves the shape and the magnitude of the ozone gradient across the tropopause, especially in the extratropical region. The results of the retrieval experiments indicate that the tropopause-referenced climatology not only helps to optimize the use of instrument sensitivity in the UTLS region, but it also provides better constraints to the OE algorithm.

Corresponding author address: Jennifer C. Wei, Perot Systems Government Services, Camp Springs, MD 20746. Email: jennifer.wei@noaa.gov

Abstract

Motivated by a significant potential for retrieving atmospheric ozone profile information from advanced satellite infrared sounders, this study investigates various methods to optimize ozone retrievals. A set of retrieval experiments has been performed to assess the impact of different background states (or the a priori states) and retrieval algorithms on the retrieved ozone profiles in the upper troposphere and lower stratosphere (UTLS) using Atmospheric Infrared Sounder (AIRS) measurements. A new tropopause-based ozone climatology, using publicly available global ozonesonde data to construct the a priori state, is described. Comparisons are made with the AIRS version 5 (v5) ozone climatology. The authors also present the result of a newly implemented optimal estimation (OE) algorithm and compare it to the current AIRS science team (AST) algorithm used in version 5. The ozone climatology using tropopause-referenced coordinates better preserves the shape and the magnitude of the ozone gradient across the tropopause, especially in the extratropical region. The results of the retrieval experiments indicate that the tropopause-referenced climatology not only helps to optimize the use of instrument sensitivity in the UTLS region, but it also provides better constraints to the OE algorithm.

Corresponding author address: Jennifer C. Wei, Perot Systems Government Services, Camp Springs, MD 20746. Email: jennifer.wei@noaa.gov

1. Introduction

Hyperspectral infrared (IR) sounding instruments, such as the Atmospheric Infrared Sounder (AIRS), Infrared Atmospheric Sounding Interferometer (IASI), and the future Cross-Track Infrared Sounder, (CrIS), are designed to retrieve temperature and water vapor profiles with high spatial and temporal coverage for improving numerical weather forecasts. The spectral coverage ∼(650–2700 cm−1) and resolution (0.25 to 2.5 cm−1) of these sounders also enable retrievals of ozone profiles and other trace gases such as O3, CO, CH4, CO2, HNO3, and N2O. Trace gas retrievals for nadir-viewing IR instruments are essential for the retrieval accuracy of the primary products: the temperature and moisture profiles (Duda and Barth 2005). Given that these satellite instruments are scheduled to provide soundings for multiple decades, the potential of long-term, high-density ozone and other trace gas information should also be of significant value to the atmospheric chemistry community.

AIRS-retrieved ozone has been evaluated against several datasets. Initial validation studies have shown that IR-retrieved ozone profiles using AIRS measurements capture the variability in the extratropical upper troposphere and lower stratosphere (ExUTLS) region observed in the ozonesonde data (Bian et al. 2007; Monahan et al. 2007). Seasonal trends and patterns from AIRS total ozone column compared well with the Ozone Monitoring Instrument (OMI) and the Solar Backscatter Ultraviolet (SUBV/2) instrument (Divarkarla et al. 2008). While providing the near-real-time AIRS-retrieved ozone at several pressure levels in the upper troposphere and lower stratosphere (UTLS) during the 2005 and 2008 Stratosphere–Troposphere Analyses of Regional Transport Experiments (START05 and START08), significant agreement between the AIRS-retrieved ozone near the tropopause and aircraft ozone measurements was also found (Pan et al. 2007a; Pittman et al. 2009). All these results provided motivation for further investigations of ozone information content near the tropopause from IR thermal sounders.

Figure 1 shows a hemispherical view [map at 250 hPa and cross section of the Northern Hemisphere (NH) at 160°E] of AIRS version 5 (v5) ozone data together with dynamical variables of potential vorticity (PV), potential temperature θ, and the thermal tropopause [based on the National Centers for Environmental Prediction (NCEP) final (FNL) operational global analysis data] on 15 April 2004. This example provides a perspective of the large dynamical variability of ozone in the extratropical tropopause region and the consistency between the AIRS retrievals and the PV field. This chemical–dynamical consistency illustrates how AIRS has significant potential for providing information on ozone variability in this region. Because the ozone variability in the UTLS region is largely controlled by the synoptic-scale meteorological features of the tropopause (Pan et al. 2004, 2007b), the high-density horizontal coverage of the AIRS instrument captures the realistic dynamical variability observed in the data.

The objective of this paper is to present results of a set of retrieval experiments, which evaluate the use of a tropopause-referenced ozone climatology as the retrieval a priori, or first guess, and the use of an optimal estimation (OE, or maximum a posteriori) retrieval algorithm (Rodgers 2000). This work is part of a continued effort to improve the ozone profile retrieval in the UTLS region and to explore the best use of the instrument’s vertical sensitivity for quantifying ozone variability.

AIRS primarily retrieves ozone from channels around 1042 cm−1 (9.6 μm). In general, the radiances R of the reference state X are computed in the radiative transfer equation as
i1520-0426-27-7-1123-e1
Equation (1) can be linearized as
i1520-0426-27-7-1123-e2
where K is defined as the weighting function:
i1520-0426-27-7-1123-e3
Bν[T(p)] is the brightness temperature, and τν is the surface-to-space transmittance. The weighting function is a measure of the forward model radiance sensitivity to the full atmospheric radiance to a perturbation in the geophysical state X. Shown in Fig. 2 are the weighting functions for the ozone channels. This figure illustrates the AIRS instrument sensitivity to the full atmospheric radiances when a 1% perturbation in ozone in each of the 100 radiative transfer algorithm (RTA) layers is applied. The AIRS measurements possess approximately 1.64 pieces of information [or degrees of freedom (DOF)] for ozone in the extratropical region, which are elucidated by the averaging kernels (Maddy and Barnet 2008). This information indicates that the AIRS instrument has a strong sensitivity to ozone in the stratosphere and a weaker sensitivity in the troposphere. The retrieval of ozone gradients across the tropopause is therefore a result of the radiance sensitivity in these two layers in the atmosphere.

It is well known that ozone has a strong gradient in the tropopause region (e.g., Logan 1999). The ozone gradient, coupled with the large dynamical variability of the extratropical tropopause, presents a challenge for accurate ozone retrieval near the tropopause, especially for a relatively low vertical resolution nadir-viewing IR instrument such as AIRS. The current operational ozone retrieval algorithm was designed primarily with total column amounts in mind, and it has not been optimized for resolving vertical structures across the tropopause. In an effort to optimize profile retrieval, this work examines two algorithms: the AIRS science team algorithm (AST) and the OE algorithm. The AST algorithm relies exclusively on the signal-to-noise of the measurements and does not require an a priori assumed covariance matrix to minimize the observed minus calculated radiances (Susskind et al. 2003). The OE technique is a widely used retrieval methodology that follows a Bayesian approach and characterizes the solution by combining information from the measurement and the a priori (Rodgers 1976, 2000).

The AST algorithm in version 5 uses a zonally and monthly averaged ozone climatology on a fixed pressure grid (abbreviated as LLM climatology; McPeters et al. 2007) as first guess. The LLM climatology was compiled using ozone data from the Stratospheric Aerosol and Gas Experiment II (SAGE II; 1988–2001), the Upper-Atmosphere Research Satellite Microwave Limb Sounder (MLS; 1991–99), and ozonesondes (1988–2002). In this work, we construct a tropopause-referenced ozone climatology as an alternative representation of ozone variability, and we examine the effect of using this climatology as a constraint for the inverse problem.

To investigate the ozone retrieval performance using the new a priori climatology and OE algorithm, we designed a set of four retrieval experiments, detailed in section 4. Two independent ozone datasets are used to represent the true atmosphere: one is from a selected day of the European Centre for Medium Range Weather Forecasts (ECMWF) analyses ozone profiles on a global scale and the other is from in situ measurements of ozone collected on board the National Science Foundation–National Center for Atmospheric Research (NSF–NCAR) Gulfstream V (GV) aircraft during the START08 experiment (Pan et al. 2010). The results of the retrieval experiments indicate that the use of the tropopause-referenced climatology and the OE algorithm reduces the retrieval uncertainty.

The layout of this paper is as follows. A description of the new “tropopause-based” (TB) ozone climatology is given in section 2. A description of the AIRS Science Team retrieval algorithm and the implementation of the optimal estimation method are given in section 3. Results of the retrieval experiments using different a priori and retrieval algorithms are given in section 4, followed by the summary and conclusions in section 5.

2. A tropopause-referenced ozone climatology

The use of tropopause-referenced coordinates is an established method in UTLS ozone analyses, with the demonstrated advantage of separating the ozone variability from the tropopause height variability (Logan 1999; Pan et al. 2004, 2007b; Considine et al. 2008). As indicated by a number of previous studies, the ensemble statistical behavior of ozone profiles using the tropopause-referenced coordinates are expected to better preserve the gradient across the tropopause and to minimize ozone variance due to day-to-day meteorological variability in the UTLS region. The characteristics of the new climatology will be examined in comparison with the climatology using regular altitude/pressure coordinates. The effect of using this new climatology in ozone retrieval will be discussed.

The tropopause-referenced ozone climatology is constructed using altitude regarding the thermal tropopause for each individual profile. The a priori covariance matrix of ozone is also computed in these coordinates for the purpose of the optimal estimation implementation. In this case, ozonesonde data are chosen because each sonde usually contains in situ temperature measurements. The temperature profile associated with each ozone profile provides information needed for identifying the thermal tropopause, which is determined from the temperature lapse rate (World Meteorlogical Organization 1957). The relevant ozonesonde stations are shown in Fig. 3. The ozonesonde data are from the collection of the World Ozone and Ultraviolet Data Center (WOUDC; available online at available at http://www.woudc.org/), the Southern Hemisphere Additional Ozonesondes (SHADOZ) network, with supplemental data from the National Oceanic and Atmospheric Administration (NOAA)/Earth System Research Laboratory (ESRL), Global Monitoring Division [(GMD), formerly known as the Climate Monitoring and Diagnostics Laboratory (CMDL), available online at ftp://ftp.cmdl.noaa.gov/ozwv/ozone/].

Ozone profiles are selected from 1983 to 2008 following the criteria from Logan (1999, and J. Logan 2008, personal communication) for screening bad data according to the types of ozone sounding instruments. Given that ozonesonde profiles end at different altitudes, the profiles are completed by applying a smooth transition to existing ozone climatology (i.e., LLM ozone climatology) above the balloon-bursting height using the corresponding climatological profile of the latitudinal bin and the month. Average balloon-bursting heights are around 50 hPa. Each “complete” ozonesonde profile is then downgraded from its original vertical resolution to the 100 RTA layers used by the AIRS science team (Strow et al. 2006), with considerations of total ozone molecule conservation in the observed vertical range (Ziemke et al. 2001). This 100-layer pressure grid with 0.5-km resolution in the UTLS region and spanning the range of 1100 ∼ 0.005 hPa is also provided in the AIRS level 2 “support” products. Similar to the LLM climatology (McPeters et al. 2007), ozone profiles on the fixed 100 RTA pressure layers are then averaged in 10° latitudinal resolution for each month. These newly created profiles become our “sea level–based” (SLB) ozone climatology, adopting the terminology used in Birner 2006. For the TB ozone climatology, exactly the same ozone profiles within the same latitudinal and monthly bin are averaged relative to the thermal tropopause grids with 2-km resolution in geometric altitude and extending from 6 km below the tropopause to 25 km above it. The corresponding thermal tropopause, based on the World Meteorological Organization (WMO) definition (World Meteorlogical Organization 1957), is calculated from the temperature lapse rate. We use the Reichler et al. (2003) algorithm in deriving the thermal tropopause. All the aforementioned steps are necessary for the forward model calculation.

To demonstrate the distinction between the SLB and TB climatologies, an example is shown in Fig. 4 using ozonesonde data in the latitudinal bin between 60° and 70°N for the month of May. The ozone profiles and the mean in TB coordinates are first calculated in altitude relative to the corresponding individual tropopause (i.e., the altitude at the tropopause is 0 km), but they are only displayed with a vertical adjustment using the mean tropopause height (marked as the black dashed line). The mean tropopause height is calculated from all the sonde data within the same latitudinal range from the same month. This approach is similar to the one used in temperature profile analyses (Birner 2006).

Figure 4 shows that the TB average profile has a much stronger gradient across the tropopause compared to the SLB average. It also shows the contrast in ozone variability between these two climatologies near the tropopause. The SLB profiles (left panel) show a larger variability near the tropopause because they include both the natural ozone variability and the variability of tropopause height. The TB profiles (right panel), however, are much more compact in the same region. This comparison is consistent with previous analyses where the thermal tropopause not only marks the sharp change in the temperature structure but it also identifies discontinuity in the chemical composition of the region (Pan et al. 2004).

The results of the mean and variability of ozone from the newly constructed SLB and TB climatologies are in general similar to the ones shown in previous studies (e.g., Logan 1999; Lamsal et al. 2004; Considine et al. 2008). Figure 5 shows statistical comparisons of mean and 1σ standard deviation for SLB, TB, and LLM climatologies in selected NH latitudinal bins during the month of January. As shown in the figure, the mean profiles from SLB, TB, and LLM profiles are closely aligned in the troposphere over the region of weak tropopause height variations (tropics and polar latitudes). However, significant differences exist among the ozone profiles in the UTLS region over midlatitudes because of the substantial variability related to daily changes in tropopause height. The shape of the TB profile is similar to the SLB and LLM profiles up to about 8 km, but it exhibits stronger gradients around the tropopause and smaller standard deviation when compared to the SLB and LLM profiles. In the region of the ozone peak, at around 20 km, we find that the LLM ozone profile is the largest of all. One possible explanation for the observed differences is that the LLM ozone climatology incorporates satellite measurements, which have better sensitivity in the stratosphere; whereas the SLB and TB ozone climatologies are only from ozonesonde, which have greater accuracy in the troposphere and often do not contain data above the balloon-bursting altitude of around 50 hPa. Another possible explanation may have to do with the different time frames used in the construction of the LLM climatology compared to the SLB/TB climatologies.

Figure 6 compares the global-scale ozone distribution and variability for January between the TB and SLB ozone climatologies constructed from the same dataset. The general characteristics of the mean ozone distribution are the following: 1) a decrease in the height of ozone maximum with an increase in latitude and 2) sharp ozone gradients between the vertically stratified lower stratosphere and well-mixed troposphere are clearly elucidated in this figure. These features in global ozone distribution are in good agreement with other reports, such as Logan (1999) and Hassler et al. (2008). If the ozone variability is taken to be (standard deviation)/(mean) (as a measure of the coefficient of variation), then this variability generally falls below 40%, except in the subtropical UTLS where the variability is typically up to 60% as shown in Fig. 6. This value can increase to greater than 80% in the vicinity of the subtropical jet, right below thermal tropopause. However, the large variability is significantly reduced in TB climatology. Together, Figs. 5 and 6 show that the use of TB climatology will help preserve the ozone gradient across the tropopause and minimize the variability introduced by daily changes of the tropopause height.

3. Algorithm implementation issues

The NOAA/National Environmental Satellite, Data, and Information Service (NESDIS)/Center for Satellite Applications and Research (STAR) near-real-time processing system for IR hyperspectral thermal sounder instruments is designed to extract as much information as possible from the hyperspectal radiances, including vertical temperature and humidity profiles, cloud products, surface products, and trace gas concentrations. The trace gas products are necessary for optimizing the quality of the primary products (i.e., temperature and water vapor) because of the sensitivity of ozone in the 15-μm band used in the temperature sounding.

The details of the AST and OE retrieval algorithms are described elsewhere (Susskind et al. 2003; Barnet et al. 2005; Warner et al. 2007; Maddy and Barnet 2008; Maddy et al. 2008; Xiong et al. 2008; Maddy et al. 2009) and are not the focus of this paper. Nevertheless, we can briefly investigate the similarities and differences between these two algorithms using the retrieval equations.

The AST algorithm solves the geophysical state 𝗫 equation as follows:
i1520-0426-27-7-1123-e4
where 𝗥obs ∈ 𝗥n is the observed instrument radiances; 𝗥calc ∈ 𝗥n is the calculated radiances for the current estimate of the retrieved state; i ∈ 𝗥L is the retrieved profile for iteration i; 𝗞i ∈ 𝗥n×L is the channel n by level/layer L derivatives of the radiative transfer with respect to 𝗫 for iteration i; 𝗪 ∈ 𝗥n×n is the channel-by-channel noise covariance matrix, including both systematic and instrument error terms; 𝗛 is the constraint matrix from empirical orthogonal functions (EOFs) of 𝗞iT𝗪𝗞i; and Ψi is the background term of the weighted radiance residuals (see Susskind et al. 2003 for details).
The OE algorithm solves the geophysical state 𝗫 equation as follows:
i1520-0426-27-7-1123-e5
where 𝗫a ∈ 𝗥L is the a priori profile, 𝗦a ∈ 𝗥L×L is the a priori error covariance matrix, and the rest of the terms are explained in the AST formula above. The details for this OE algorithm can be found in Maddy et al. (2009).

There are three terms underlined in Eq. (5) where the AST and OE algorithms differ: in the first underlined term, the OE algorithm is pivoting off the a priori state, whereas the AST algorithm is pivoting off the previous iteration; in the second, the OE algorithm constraints rely on the statistics of the a priori terms, whereas the AST algorithm does not use the a priori statistics; and in the third, the OE algorithm uses a priori state in the weighted radiance residuals, whereas the AST algorithm uses the geophysical state X from the previous iteration in the weighted radiance residuals.

To evaluate the impact of OE retrieval on the ozone product, we retain all the AST retrieval steps used in the NOAA processing system of the AIRS radiances, with the exception of the ozone retrieval step. A regularized nonlinear least squares solution (Susskind et al. 2003) is used in the AST algorithm, which minimizes the differences in radiances between the observed cloud-cleared radiances (Chahine 1982) and the forward RTA calculation. For the ozone retrieval step, we substitute the OE technique in place of the AST approach.

One of the algorithm implementation challenges is to make the OE algorithm as computationally efficient as the AST algorithm. The traditional OE algorithm, or maximum a posteriori, usually requires a huge amount of CPU time to calculate forward model derivatives. However, IR sounder measurements have limited vertical information and cannot “see” all of the vertical correlations within the a priori information. The new computationally efficient OE approach, developed at NOAA/NESDIS, does not necessarily require more iteration of the forward model derivation. With the OE algorithm, we follow the same approach as the AST algorithm, using the leading eigenvectors of the a priori covariance matrix as basis functions for the inversion solution and calculation of derivatives. We selected 12 of the leading eigenvectors to ensure that most of the variability in the covariance matrix was captured. Figure 7 shows the four leading eigenvectors for the SLB and TB case, which already represent 99.7% for SLB and 99.49% for TB of the ozone variance. With these steps, the execution time of the OE algorithm is as fast as the AST algorithm. For example, for each profile, the AST algorithm would take 3.4% in the inverse model and 96.6% in the forward model, whereas the OE algorithm would take 2.2% in the inverse model and 97.8% in the forward model. Details and analyses of the differences in AST and OE methodologies using CO as a target retrieval parameter are described in Maddy et al. (2009).

Averaging kernels or vertical resolution functions are usually employed to characterize the vertical resolution of the retrieval. These averaging kernels relate the amount of information in the retrieval derived directly from the measurements to the information coming from the first guess (i.e., the a priori state) on a case-by-case basis. As an example, Fig. 8 shows the smoothed averaging kernels, applying three data point boxcar average functions from the AST algorithm (left panel) and the OE algorithm (right panel) for an ozonesonde station from the midlatitudes (around 52°N). The averaging kernels are broader in the AST algorithm compared to the OE algorithm with the peaks centered at 253 and 414 hPa.

The DOF referred to in this work are different from DOF for signal and are given by the fractional number of the significant eigenfunctions of the averaging kernels. For this case shown in Fig. 8, DOF for the AST algorithm is 1.69 and DOF for the OE algorithm is 1.56. The DOF from the OE algorithm is slightly smaller than the DOF from the AST algorithm. This difference reflects the fact that the OE algorithm includes more constraints from the a priori state describing the expected vertical correlation in the retrieved products.

Another algorithm implementation challenge is to properly redistribute the TB ozone climatology from a relative to a tropopause coordinate to the fixed RTA pressure coordinate for the forward model calculation. In our case, we rely on the retrieved temperature profile to derive the thermal tropopause, and then we redistribute the a priori ozone to the preferred pressure grids. We note this procedure will propagate the errors introduced by the temperature retrievals. Furthermore, the implementation of OE with the TB climatology presents a challenge in the mapping of the eigenvectors of the a priori covariance matrix from the relative coordinate to a fixed pressure coordinate for the forward model calculation.

4. Results and discussion

A set of four retrieval experiments is performed to evaluate the impact of a different a priori and retrieval algorithm on AIRS ozone. They are as follows:

  • (i) case 1: AST algorithm with SLB ozone climatology;

  • (ii) case 2: AST algorithm with TB ozone climatology;

  • (iii) case 3: OE algorithm with SLB ozone climatology; and

  • (iv) case 4: OE algorithm with TB ozone climatology.

The results of the retrieval experiments are then evaluated against three groups of data. The first group is a subset of the ozonesonde data that are used to construct the new SLB and TB climatologies. The second group is the ozone field from a 1-day global ECMWF simulation. The third group is from aircraft in situ measurements.

a. Relationship between ozone column and tropopause height

A strong correlation between total ozone and tropopause height mostly based on spaceborne UV instruments is well documented in the literature (e.g., Zhao et al. 1994; Hoinka et al. 1996; Evtushevsky et al. 2008). A higher tropopause reduces total column ozone because of a shallower lower stratosphere where most of the ozone is concentrated. The height of the tropopause is largely influenced by synoptic-scale tropospheric weather systems. Evaluation of the relationship between the total retrieved ozone and the thermal tropopause from spaceborne IR instruments can serve as a qualitative diagnostic. We examine how well the total ozone–tropopause height relationship is reproduced using collocated ozonesonde and AIRS ozone profile dataset for the two retrieval algorithms in combination with the two different ozone climatologies. The ozonesonde profiles used are shown in Divarkarla et al. (2008). This dataset, a subset of ozonesonde data, contains 3 yr (2002–05) of matched AIRS data within a radius of 100 km and ±3 h of time coincidence with ozonesonde profiles from WOUDC. With the uncertainties in the estimation of total ozone for the levels above the sonde’s balloon-bursting altitude, the computed total ozone from ozonesonde uses an estimate of the column above this bursting altitude.

Figure 9 shows a good qualitative agreement between the retrieved total ozone and observed total ozone with respect to tropopause height in the extratropical region. The distribution of tropopause height is inversely proportional to that of total ozone column content. The correlation coefficient r represents the day-to-day variations in total ozone due to changes in the tropopause height. This correlation coefficient suggests that the variations of the tropopause height explain ∼(55%–60%) of the variations in ozone. All four retrievals are in good agreement with the observations, with the OE algorithm cases (cases 3 and 4) in better agreement than the cases using the AST algorithm. In this large sample, the linear fitting line qualitatively indicates the relationship between total ozone and tropopause height.

b. Ensemble retrieval experiments using ECMWF data

In this section, we examine the performance of the four retrieval experiments compared to ECMWF data. Before presenting ensemble statistics, an example using a single profile is given in Fig. 10 to show the results of four retrieval operations, relative to the initial guess and the truth (ozonesonde profile). In this case, the ozone profile has a sharp gradient from the upper troposphere to the lower stratosphere, which is better captured by using the TB ozone climatology. The result also shows that two algorithms (AST and OE) provide different constraints. Case 4 (OE algorithm with TB climatology) provided the best retrieval in the UTLS region.

To quantify the performance of the four experiments, a statistical analysis using a large ensemble of global profiles from 1 day of ECMWF data is performed. The analysis is focused on the UTLS region, between 100 and 300 hPa. The day selected is one of the so-called IASI “focus days”: 19 October 2007. The ensemble consists of 238 full-resolution granules from the AIRS, including both ascending and descending orbits, for a total of ∼320 000 profiles. In this ensemble experiment, the ECMWF atmospheric state is assumed to be the “true atmosphere.” To focus on the ozone profile retrieval performance, synthetic clear-sky radiances for the AIRS spectral resolution are generated from ECMWF temperature, water vapor, and ozone. The radiative effects of other important species such as CO, CH4, and HNO3, as well as surface parameters, are taken as known quantities. The strength of this approach is that the a priori ensemble and the true-state ensemble are somewhat independent of each other, with the latter having much larger ozone variability, thus providing statistically significant results.

Several issues using ECMWF data are worth mentioning. First, the ozone field from the ECMWF simulation has a known positive bias in the range of 20%∼40% in the UTLS region compared to the ozonesonde network (Dethof and Holm 2004), and the bias is largest in the wintertime. The retrieval experiments, therefore, start from a statistically biased a priori state. Second, the synthetic radiances produced using the ECMWF data are noise free. In real measurements, the noise in AIRS radiances is from both the instrument noise and the cloud field. The instrument noise is estimated to be considerably smaller than the atmospheric variability in ozone. Based on AIRS instrument calibration and sensitivity, we can calculate the instrument response to be about 0.1 K for 1% perturbation in ozone, and the noise equivalent differential temperature (NEDT) is about 0.2 ∼ 0.4 K at ozone band. These two parts give us approximate 2% ∼ 4% ozone perturbations from the instrumental noise. Compared with the ozone variance, which is greater than 20% in the UTLS region based on climatology, the results of our experiments would not be affected significantly by omitting the instrumental noise in the simulated radiances. The instrument noise, however, is used in the retrieval as requested by each algorithm. The cloud field dominates the noise in radiances, yet it is difficult to reproduce realistically when deriving synthetic radiances from ECMWF data. Because our goal is to examine relative, instead of absolute, retrieval performances using clear-sky spectra, the exclusion of these noises should not compromise the results from this analysis.

For each retrieval, from both algorithms, we utilize the fitting parameters (e.g., χ2 fitting) and error estimate to compute a number of useful parameters for quality assurance (QA). When the QA indicators exceed a threshold, the radiances are assumed to be bad, and thus the profile is rejected. For example, for all the accepted profiles, we found the χ2 fitting (result now shown) for the four ensemble experiments to be very similar.

Statistical results of the four retrieval experiments are given in four layers that are consistent with the AIRS standard ozone profile product: 100–150, 150–200, 200–250, and 250–300 hPa. The distribution of the differences between the retrieval and the ECMWF true state, and between the a priori and the ECMWF true state, are found to be non-Gaussian. Figure 11 shows the Probability Distribution Function (PDF) of the ozone differences in the 150–200-hPa layer between retrievals and truth (ECMWF) and the differences between a priori state and true state. These histograms illustrate the non-Gaussian characteristic of the data. This characteristic is common to all four UTLS layers between 100 and 300 hPa. When using SLB ozone climatology, we find a bimodal distribution from both retrievals and a priori state likely due to the presence of double tropopauses in this region. This bimodal distribution, however, is not seen when using TB ozone climatology. This case study also shows that the statistical values of mode, median, and mean for the distribution have significant differences due to the skewness of the distribution. The non-Gaussian behavior of the results suggests the use of the median, instead of the mean, as a more appropriate statistic.

The retrieval results using median values for the UTLS region are shown in Fig. 12. The results are presented as relative differences, defined as (retrieval − truth)/(truth) × 100%. The averages of the four layers, both the median value and the range between the 25% and 75% values (defined as the width of the distribution), are summarized in Table 1. Based on the median values, OE with TB ozone climatology (case 4) shows the best performance in the UTLS region, with an average difference with respect to ECMWF in all four layers of about 1.7%. Both AST and OE algorithms with TB ozone climatology (case 2 and case 4) have smaller median bias compared to those with the SLB ozone climatology (case 1 and case 3) (6.9% and 1.7% versus 13.2% and 7.5%, respectively). The TB ozone climatology reduces retrieval bias by 6% as compared to the SLB a priori. In general, all retrievals reduce more than 10% of the bias and 20% of the width from the a priori state in the UTLS region. Furthermore, we found that the OE algorithm shows a better ozone constraint in this region than the AST algorithm.

c. Retrieval experiments compared with in situ measurements

In this section, we compare the four retrieval experiments with aircraft in situ measurements. The in situ ozone data are from the START08 experiment (Pan et al. 2010). This experiment was conducted using the NSF–NCAR GV research aircraft during April–June 2008. START08 was designed to study the chemical transport characteristics of the ExUTLS region. A total of 18 research flights covered a large region of North America (25°–65°N in latitudes and up to 14.3 km vertical range). This dataset is useful for satellite validation because the flights targeted the region of large ozone variability. Figure 13 gives an example of the large UTLS ozone gradient in the central United States on 28 April 2008 targeted by the START08 research flight 4 (RF04). The figure displays AIRS v5 ozone at 275 hPa along with the PV field derived using the NCEP Global Forecast System (GFS) analysis. The 2-PVU contour, often considered to be the dynamical tropopause, is used as an indicator of stratospheric and tropospheric airmass boundary. The ozone distribution at 275 hPa from AIRS v5 data illustrates again how the variability and gradient of ozone obtained from AIRS retrieval are consistent with the dynamical feature (see Fig. 1).

Statistical comparisons using START08 in situ measurements have been made for AIRS, IASI and OMI ozone profile products (Pittman et al. 2009). Following the same methodology, we examine the performance of the four ozone retrieval experiments. The results are shown in Fig. 14. In this comparison, satellite and aircraft data for the entire campaign are grouped according to three equivalent retrieval layers (details can be found in Pittman et al. 2009), bordered by 103-, 142-, 212-, and 300-hPa pressure surfaces.

Figure 14a shows the relative differences between the four retrieval experiments and the aircraft for each of the three layers. The comparison is given as the median values and 1σ variability of the satellite–aircraft relative differences. The medians of both AST and OE algorithm with SLB ozone climatology show similar positive biases of 10%–40% in these three layers. The medians of both algorithms with TB ozone climatology, however, show much smaller biases in the bottom two layers, between 142 and 300 hPa. The variances for all four retrieval experiments are within ±50%.

To evaluate the transition of ozone from the UT to the LS, we regrouped the three equivalent retrieval layers into relative altitude layers: lower-stratosphere layer, tropopause layer, and upper-troposphere layer, with respect to the GFS thermal tropopause. Figure 14b shows the median and 1σ variability of absolute ozone mixing ratios for the aircraft and the four retrieval experiments in each of the three relative altitude layers. From a median’s perspective, the results from both algorithms with TB ozone climatology performed very well in the tropopause layer, whereas the results with SLB ozone climatology have a slight positive bias in this layer. It is worth noting that the slopes of ozone gradients are independent of the choice of climatology when using the AST method but dependent when using the OE method, with the TB climatology showing the best results.

5. Summary and conclusions

We have investigated the use of OE algorithm and TB climatology for improving ozone profile retrievals in the UTLS using AIRS observations. We expect that the use of a tropopause-referenced ozone climatology as the retrieval’s a priori state would keep the strong ozone gradient across the tropopause and thus optimize retrieval sensitivity of ozone in the UTLS region, especially in the extratropical region. Four ensemble retrieval experiments were performed with combinations of AST and OE retrieval algorithms and the SLB and TB ozone climatologies as the a priori constraints. These experiments were compared to ozonesonde, ECMWF, and aircraft data. The results of the comparisons show that the OE algorithm along with the tropopause-referenced ozone climatology has the best performance.

The comparisons of the four retrieval experiments with the ECMWF 1-day global simulation and with aircraft data from the START08 campaign are fundamentally different. When using the ECMWF data as the true atmosphere, the forward model error and cloud-clearing errors are excluded, which allows us to examine the relative performance of the four retrieval cases under clear-sky conditions. When using the START08 data, the situation is more complicated. There is a significant sampling issue (Pittman et al. 2009) and the effects of forward model error and cloud-clearing error on the retrieval are difficult to quantify.

In the ensemble experiment using ECMWF data as the true state, we found both distributions of the differences between the a priori and the truth and the distributions of the differences between the retrievals and the truth to be non-Gaussian in the region of 100–300 hPa, especially when using a traditional pressure grid ozone climatology. These errors, however, tend to be more Gaussian when the tropopause-referenced ozone climatology is used. We use the median value to represent the retrieval bias and the differences between the upper (75%) and lower (25%) percentiles to represent the spread in the retrieval error and for comparisons among the four cases. Overall, the case 4 (OE algorithm with TB ozone climatology) shows the best performance in the ensemble retrieval experiment using the ECMWF profiles as the true state. The retrieval bias is reduced by about 6% (differences between case 1 and case 3 or differences between case 2 and case 4) when using tropopause-referenced ozone climatology.

Finally, the four retrieval experiments are examined using airborne in situ observations from the START08 experiment. The four retrieval cases are compared in terms of statistics in three layers between 100 and 300 hPa. Both AST and OE algorithms with SLB ozone climatology (case 1 and 3) show positive biases of 10%–40% in these three layers, whereas both algorithms with TB ozone climatology (case 2 and 4) show minimal biases (0% and −5%) in the bottom two layers from 142 to 300 hPa. When separating layers into those relative to the location of the thermal tropopause, the results from both algorithms with TB ozone climatology (case 2 and 4) performed well in the tropopause layer, whereas the results with SLB ozone climatology (case 1 and 3) show larger positive bias [30–40 parts per billion by volume (ppbv)] in this layer.

In theory, the accurate prescription of the geophysical covariance of ozone should improve the information content of the retrievals and hence the performance of the retrievals themselves. In practice, the implementation of the retrieval using TB climatology requires mapping of the eigenvectors of the a priori covariance matrix from the relative coordinates to a fixed pressure coordinate for the forward model calculation, which often induces interpolation errors. However, the results of the experiments show that the TB ozone climatology improved retrieval performance in the UTLS region for both AST and OE algorithms. Although we have limited our data analyses to AIRS, the TB climatology may also improve performances in the UTLS region for the operational IASI and future CrIS data.

Acknowledgments

We thank all institutes and colleagues who provided us with ozonesonde data for the dataset: 1) Dr. Vitali Fioletove and Dr. Larry Flynn for WOUDC, 2) Dr. Anne Thompson for SHADOZ, and 3) Dr. Sam Oltmans for NOAA/ESRL ozonesonde sites. We thank the START08 science team for the campaign data, especially Dr. Ru-Shan Gao for the ozone measurements from NOAA instruments. The authors also would like to thank Dr. Jennifer Logan for her useful comments to the improvement of this manuscript. The views, opinions, and findings contained in this paper are those of the authors and should not be constructed as an official National Oceanic and Atmospheric Administration or U.S. government position, policy, or decision.

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Fig. 1.
Fig. 1.

Map and cross section for AIRS v5 ozone on 15 May 2004. (top) 1° × 1° binned ozone data at 250 hPa for the Northern Hemisphere and FNL PV (2 and 4 PVU, black). (bottom) Ozone cross section along 160°E. Also shown are 2- and 4-PVU contours (orange lines), thermal tropopause (black dots), selected potential temperature (K) surfaces (yellow dash), and zonal wind (m s−1) (white contours).

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1384.1

Fig. 2.
Fig. 2.

AIRS ozone weighting functions in the 1041.7 cm−1 (9.6 μm) region for a midlatitude atmospheric state.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1384.1

Fig. 3.
Fig. 3.

Locations of ozonesonde stations (open circle with cross inside) collected from WOUDC, SHADOZ, and NOAA/ESRL/GMD for the compilation of the ozone climatology.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1384.1

Fig. 4.
Fig. 4.

An example of monthly mean ozone profiles in the latitudinal bin between 60°N ∼ 70°N for May in (left) SLB altitude and (right) TB altitude. Original ozone profiles are shown as gray dots and the monthly mean and 1σ standard deviation are shown as black line and error bars. Also shown as the black dashed line is the mean tropopause height, which is the average computed from individual thermal tropopause.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1384.1

Fig. 5.
Fig. 5.

January mean Northern Hemisphere ozone profiles (standard deviations given by error bars) according to latitudinal bin (every 10°, shown are selected bins between 0° and 5°N, 30° and 40°N, 60° and 70°N, and 80° and 90°N) using SLB (blue line), TB (red line), and the LLM climatologies (gray line). The red dashed line is the mean tropopause height, which is the average tropopause height computed from the individual thermal tropopause for each profile in each temporal and spatial bin.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1384.1

Fig. 6.
Fig. 6.

SLB ozone (a) mean and (b) coefficient of variation (standard deviation divided by the mean) and TB ozone (c) mean and (d) coefficient of variation in January. Also plotted are the 300-, 350-, 380-, and 400-K isentropes (white dashed lines), the thermal tropopause (red dots pointed out by the arrow), and the zonal wind (m s−1) (black contours) from the NCEP FNL Jan 2004 monthly mean data.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1384.1

Fig. 7.
Fig. 7.

(top to bottom) The four leading eigenvectors of the covariance matrix for (a) SLB and (b) TB from the composite ozonesonde dataset. The total percentages of ozone variance from these four eigenvectors are 99.7% for SLB case and 99.49% for TB case.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1384.1

Fig. 8.
Fig. 8.

Example of smoothed averaging kernels using SLB ozone climatology at the location of 52.2°N, 5.90°E derived from (left) the AST algorithm and (right) the OE algorithm. The calculated DOF for AST is 1.69, and DOF for OE is 1.56.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1384.1

Fig. 9.
Fig. 9.

Relationship between tropopause height (km) and total ozone (Dobson unit) from a composite ozonesonde dataset (black dots) and four retrieval experiments (red dots): (a) AST algorithm with SLB ozone climatology, (b) AST algorithm with TB ozone climatology, (c) OE algorithm with SLB ozone climatology, and (d) OE algorithm with TB ozone climatology. Linear regression lines are plotted with slopes (b) and y axis intercepts (m). Correlation coefficient is r. There are around 1120 profiles in each comparison.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1384.1

Fig. 10.
Fig. 10.

Example of a single-profile retrieval using ozonesonde profile (black solid line) from station Uccle (50.51°N, 4.04°E). (a) Results from the four retrieval experiments (solid line) and their first guess (first guess in SLB for case 1 and 3 is red dashed line; first guess in TB for case 2 and 4 is light-blue dashed line) are given. The thermal tropopause is plotted in black dashed line. (b) Vertical profiles of ozone from ozonesonde (black solid line) and a priori (red solid line) with variance (red dashed line) for SLB and a priori (light blue solid line) with variance (light blue dashed line) for TB. Variance is defined as diag(𝗦a).

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1384.1

Fig. 11.
Fig. 11.

PDF of ozone differences (retrieval − truth is red histogram) in ppbv showing the distribution of retrieval error for the 1-day ensemble using ECMWF data as the true atmosphere. Several statistical values are shown for the 150–200-hPa layer from case (left) 3 and (right) 4: 1) the modal values (in red solid line), 2) the median values (in green solid line), and 3) the mean values (in blue solid line). The shaded gray histogram is the ozone differences between a priori state and the true state for the same ensemble. Recall that both panels use the OE retrieval algorithm with the left panel using SLB ozone climatology and the right panel using TB ozone climatology.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1384.1

Fig. 12.
Fig. 12.

Ozone relative errors using the ECMWF ozone as the truth ensemble for the four experimental cases from 100 to 300 hPa. Relative differences are defined as (retrieval − truth)/(truth) × 100%. Values shown are the median in a solid line with triangle symbols and first quartile (25%) and third quartile (75%) in dashed lines. The red color is the relative differences between the retrievals, and the truth and the gray color is the relative differences between the a priori state and the truth.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1384.1

Fig. 13.
Fig. 13.

A horizontal view of AIRS v5 ozone (color contours) at 275 mb on 28 Apr 2008 during the START08 campaign. Also shown are the PV dynamical structure with the 2-PVU contour (orange) from GFS analysis and the GV ground track in dark red.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1384.1

Fig. 14.
Fig. 14.

(a) Percent differences between GV and four retrieval experiments as a function of three retrieval layers for the START08 campaign. Values shown are median and 1σ variability. Percent difference is defined as (satellite − aircraft)/(aircraft) × 100%. (b) Vertical profiles of ozone from GV and four retrieval experiments during the START08 campaign constructed using relative height to the GFS thermal tropopause. Values shown are median and 1σ variability. Variability bars are offset in the vertical for better visualization of the ranges.

Citation: Journal of Atmospheric and Oceanic Technology 27, 7; 10.1175/2010JTECHA1384.1

Table 1.

A summary of the ensemble experiment. The “width” is calculated using the difference between the 75% and 25% values.

Table 1.
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