1. Introduction
An important topic in the study of climate change is how the stratospheric temperatures respond to external forcings such as the increases of greenhouse gases, volcano eruptions, secular changes of ozone concentration, and solar cycles (Ramaswamy et al. 2006; Randel et al. 2009; Seidel et al. 2011). The long-term satellite data used in the study of stratospheric responses to external forcing are usually from the Microwave Sounding Unit (MSU) and the Stratospheric Sounding Unit (SSU) (Ramaswamy et al. 2001; Randel et al. 2009, 2016; Seidel et al. 2011, 2016; Thompson et al. 2012; Zou et al. 2014; Zou and Qian 2016). A large amount of effort has been invested in merging multidecadal time series for climate trend analysis and making these datasets into a climate-quality data record (Christy et al. 2003; Mears and Wentz 2009; Zou and Wang 2010; Zou et al. 2014). Succeeding MSU and SSU, the Advanced Microwave Sounding Unit A (AMSU-A) on board several NOAA polar-orbiting satellites since 1998 measures microwave radiances at 15 discrete frequency channels between 23 and 90 GHz (Mears and Wentz 2009; Kidwell et al. 2014; Wang and Zou 2014). Its measurement capability surpasses MSU with six channels sensitive to temperatures in the stratosphere. Although originally designed for weather observation, after homogenizing the data from different satellites the merged and recalibrated AMSU-A radiances can also play a vital role in stratospheric climate study. Another potential valuable dataset for stratospheric trend study is the Atmospheric Infrared Sounder (AIRS) on board the NASA Aqua satellite. The AIRS instrument has demonstrated stable and accurate performance (Pagano et al. 2003; Aumann et al. 2006; Chahine et al. 2006; Aumann and Pagano 2008) since its launch in September 2002. Using 10 years of measurements, statistically significant trends already can be seen from the radiances of AIRS channels sensitive to emission and absorption in the stratosphere [hereafter referred as stratospheric channels, in the CO2 15-μm (υ2) band; Pan et al. 2015]. The AIRS radiances of the stratospheric channels, in principle, have considerable information content on vertical temperature profiles because 1) in our study AIRS has 50 channels sensitive to emissions and absorptions in the stratosphere (Pan et al. 2015) and 2) the AIRS stratospheric channels usually have narrower weighting functions than the AMSU-A microwave channels, a common feature in the contrast of IR and microwave soundings. However, all the AIRS stratospheric channels are also sensitive to CO2 emission and absorption, which makes separation of secular changes of CO2 and stratospheric temperatures from such AIRS stratospheric channels a challenge task. The AMSU-A radiances are sensitive to oxygen emission and absorption but not sensitive to CO2 emission and absorption at all. Thus, a synergistic use of AIRS and AMSU observations, in principle, can help to better understand the global stratospheric temperature change at a higher vertical resolution than previous studies that employed MSU or SSU measurements. Such synergistic use of AIRS and AMSU can also make it possible to infer CO2 change in the stratosphere.
Optimal fingerprinting extracts maximum information from data on climate trends in the atmosphere against a background of natural variability. As a detection and attribution technique for climate change studies, optimal fingerprinting was pioneered by Bell (1986), Hasselmann (1993, 1997), and North et al. (1995) and has been applied onto a variety of observational datasets, such as tropopause height (Santer et al. 2003), tropospheric water vapor (Santer et al. 2007), and hydrological cycle in the western United States (Barnett et al. 2008). It has also been applied to synthetic infrared radiances based on climate model simulations (Leroy et al. 2008; Huang et al. 2010a,b) but never applied to observed infrared radiances. In this paper, we apply optimal detection directly to globally averaged AIRS infrared radiances and AMSU-A microwave radiances measured from 2003 to 2012 to detect the secular trend in the stratospheric temperature with the natural variability taken into account. The rest of this paper is arranged as follows. Section 2 describes the decadal radiance changes in the stratospheric channels observed by AIRS and AMSU-A. The optimal fingerprinting methods and details about how to apply this technique are also explained in section 2. The detection results of stratospheric changes are shown and discussed in section 3. Section 4 presents conclusions and further discussion.
2. Data and methods
a. Observed trends of brightness temperatures on the AIRS and AMSU-A stratospheric channels
Procedures to obtain globally averaged radiances from the AIRS level 1b (L1b) dataset and then to estimate the trends Δd for AIRS radiances on 50 stratospheric channels between 662.5 and 674.9 cm−1 have been explained in Pan et al. (2015). They found a negative trend with a magnitude of no more than 0.23 K decade−1 for brightness temperatures of the AIRS lower-stratospheric channels, while a statistically significant cooling trend as large as 0.58 K decade−1 was found for brightness temperatures in the AIRS midstratospheric channels. In this paper, we further improve the estimates of the brightness temperature trends on the AIRS stratospheric channels by taking the secular shift of the center frequency of each AIRS channel into account (Strow et al. 2006). While AIRS frequency can be extremely stable and shift below 0.1% of a full-width half maximum for demanding applications like climate monitoring, the brightness temperature trends caused by frequency shift could be nonnegligible and need to be removed (Gaiser et al. 2003; Strow et al. 2006). AIRS spectral response functions (SRFs) on each channel are measured during prelaunch testing (available from http://asl.umbc.edu/pub/airs/srf). Here we assume the SRF shape fixed and only consider the contribution of SRF center frequency shift to brightness temperature bias ΔBT_shift(t, υ) over 2003–12. First, the monthly climatology of radiances with a spectral resolution of 0.001 cm−1 covering AIRS CO2 υ2 band was simulated by the Line-By-Line Radiative Transfer Model (LBLRTM) (Clough et al. 2005), into which monthly atmospheric profiles with the horizontal resolution of 1.5° × 1.5° in 2008 from the European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis (ERA-Interim; Dee et al. 2011; ECMWF 2014) are taken as input. After this, the monthly climatology of radiances was multiplied by AIRS SRF on each grid box and averaged into global-mean spectra BT(t, υ) on 50 AIRS stratospheric channels. Then we generated the spectra BT_shift(t, υ) considering the center frequency shift. The shift of the center frequency of each AIRS channel from 2003 to 2012 was determined using the method depicted in Strow et al. (2006). We add these frequency shifts onto SRFs and obtain time-varying AIRS SRFs. Again, we multiply the monthly climatology of radiances by the new AIRS SRFs to generate the BT_shift(t, υ). The differences between BT_shift(t, υ) and BT(t, υ) are just the brightness temperature biases ΔBT_shift(t, υ) due to the shift of the center frequency. Finally, we calculate the linear trends Δd_shift from ΔBT_shift(t, υ) and remove them from our previous estimate in Pan et al. (2015) to get a new Δd to be used in optimal fingerprinting. Both the previous and this new estimate of Δd on AIRS stratospheric channels are presented in Fig. 1.
The linear trends on 50 AIRS stratospheric channels when the biases due to channel center frequency shift are removed (red line) and not removed (black line).
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-17-0037.1
The global average of homogenized brightness temperatures for the AMSU-A channels 10–14 is directly obtained from version 3.3 of the Remote Sensing System (RSS) long-term intersatellite merging and intercalibrated radiance product (Mears and Wentz 2009; Mears et al. 2011). The RSS team showed improved agreement of time series on short time scales and long-term trends between the radiosonde data and the satellite data. The same method as in Pan et al. (2015) has been used to compute the linear trend of the homogenized AMSU-A radiances (hereafter, the homogenized AMSU-A radiances are referred to as AMSU-A radiance). Figure 2 summarizes the linear trends of global average brightness temperature of the AIRS and AMSU-A stratospheric channels.
The 10-yr linear trend of global-mean brightness temperature of the AIRS and AMSU-A stratospheric channels. Five AMSU-A channels are labeled with their channel numbers instead of actual frequencies.
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-17-0037.1
b. Optimal fingerprinting technique
1) Introduction
2) Construction of spectral fingerprints
Eight spectral fingerprints [Si in Eq. (1)] are defined in our study, each corresponding to a Δαi: one for the uniform change of CO2 in the atmosphere and the remaining for temperature changes in seven vertical layers from 300 to 0.009 hPa (Fig. 3). Five of the seven layers are in the stratosphere with pressure centered at 2.7, 8.8, 19.8, 41.2, and 86.3 hPa, respectively. The spectral fingerprints S are constructed by perturbing the temperature in different stratospheric layers and CO2 in the calculation of synthetic radiances mentioned in the previous section. Technically this is done by the spectral radiative kernel technique (Huang et al. 2014; Pan et al. 2015). First the monthly output from the 500-yr preindustrial control run by GFDL CM3 (Donner et al. 2011) and 240-yr preindustrial control run by HadGEM2-CC (Martin et al. 2011) models, both available from phase 5 of the Coupled Model Intercomparison Project (CMIP5) archive, are fed into the Principal Component–Based Radiative Transfer Model (PCRTM; Liu et al. 2006) to generate synthetic AIRS radiances and into the Community Radiative Transfer Model (CRTM; Weng et al. 2005) to produce synthetic AMSU-A radiances. The CO2 spectral fingerprint is then defined as the changes of radiances in response to a 1-ppmv increase of CO2 while other geophysical parameters remain unchanged. The spectral fingerprints for temperature in a given layer are defined as the changes of radiances in response to a 1-K increase of temperature in that layer. The monthly spectral fingerprint is computed on each model grid box and then weighted by the cosines of their latitudes to obtain a set of global-mean spectral fingerprint. Spectral fingerprints are derived using every 10 years of simulations from the GFDL CM3 and HadGEM2-CC control runs. Thus, we have 74 sets of estimated fingerprints Si. The mean of the 74 sets of Si is used as S in Eq. (3) and shown in Fig. 4. Then, δSi = Si − S is used to construct the fingerprint uncertainty covariance matrix Σs in Eq. (6).
The seven layers used in this study for constructing spectral fingerprints for temperature change. The pressure boundary of each layer is labeled on the right and layer-averaged pressure is shown in the center (hPa).
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-17-0037.1
The spectral fingerprints for CO2 and temperature changes in seven different layers. The layer-mean pressure is labeled in each panel. The spectral radiance change is expressed in terms of brightness temperature change with respect to 1-ppmv change of CO2 mixing ratio or 1-K change of temperature.
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-17-0037.1
3) Estimation of natural variability
The 500-yr GFDL CM3 and 240-yr HadGEM2-CC control runs are used to construct natural variability of infrared and microwave brightness temperatures. There are several reasons for qualifying climate model output for studies of stratospheric variability, among them the lack of a solar cycle in the forcing of the models and poor reproduction of the quasi-biennial oscillation and polar sudden stratospheric warming events. For these reasons, we compare the two climate models’ simulations of stratospheric temperature with 29 years of detrended radiosonde observations (1979–2007) from 47 stations compiled in the Radiosonde Atmospheric Temperature Products for Assessing Climate (RATPAC)-lite dataset, a subset of RATPAC recommended for climate trend studies (Randel and Wu 2006; Randel et al. 2009). Figure 5 shows the probability density functions (PDFs) of modeled and observed temperature anomalies for four different pressure levels in the stratosphere at six RATPAC-lite stations ranging from south to north. The PDFs for the temperature anomalies by the models’ control runs are estimated by computing PDFs for multiple nonoverlapping 29-yr intervals of control run output and then averaging those PDFs together for each model separately. Overall, the models’ PDFs of stratospheric temperature variability correspond well to observed variability in all pressure levels, though both models tend to overestimate the PDF spread in the polar regions and underestimate it in the tropics. The PDFs for other RATPAC-lite stations are similar to those shown in Fig. 5.
The PDFs of stratospheric temperature anomalies as simulated by the GFDL CM3 (green curves) and HadGEM2-CC control runs (red curves). The PDFs of detrended and deseasonalized monthly mean temperature anomalies from RATPAC-lite observations are shown in blue. The PDFs are shown (top)–(bottom) for six stations from the Antarctic region to Arctic region and (left)–(right) for four different levels in the stratosphere. The PDFs are estimated using the kernel density estimation method (Jones et al. 1996).
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-17-0037.1
Using the output from 500-yr GFDL CM3 and 240-yr HadGEM2-CC preindustrial control runs, the synthetic brightness temperatures of the 50 AIRS stratospheric channels in CO2 υ2 band and of the AMSU-A channels 10–14 are simulated as follows: Monthly mean profiles of temperature, humidity, ozone, and cloud on each grid box are fed into the radiative transfer models to generate the brightness temperatures over the stratospheric channels used in this study. Then global averages of simulated synthetic brightness temperature are calculated and are used to form 74 segments of 10-yr time series. We use each segment to compute its own 10-yr linear trend, in a way similar to how the observed climate change Δd is computed. The 74 realizations of such linear trend from GCM control runs form δε in our study. They pass the one-sample Kolmogorov–Smirnov test and thus can be presumed observing Gaussian distribution, an important assumption in the optimal fingerprinting for the natural variability term. Thus we can proceed to calculate the covariance matrix Σn using Eq. (5).
To obtain the inverse matrix in Eq. (3) requires empirical orthogonal function (EOF; aka principal component) decomposition in order to maintain numeric stability in the inversion. Figure 6 shows the first four eigenvectors of the natural variability covariance matrix Σn. The first four eigenvectors explain 67.2%, 22.3%, 8.6%, and 1.0% of the total variance, respectively. In practice, 34 leading EOFs are used for inverting the matrix in Eq. (3).
The four leading EOFs of the covariance matrix of the natural variability, which are plotted with respect to the AIRS channel frequencies and AMSU-A channel number.
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-17-0037.1
3. Results and discussion
a. Retrieved stratospheric temperature and CO2 change
Red lines in Fig. 7 are decadal stratospheric temperature trends inferred from the AIRS and homogenized AMSU-A data using the optimal fingerprinting detection. Taking natural variability as inferred from the climate models [section 2b(3)] into account, the stratosphere still exhibits cooling trends within 10 years at the 95% significance level in all the layers except the lowest layer near 100 hPa. The magnitudes of such cooling trends increase with height. The globally averaged cooling rate in the lower stratosphere (30–59 hPa) is 0.39 ± 0.32 (2σ) K decade−1 and for the two midstratospheric layers (14–30 and 6–14 hPa) it is 0.46 K decade−1, respectively, all with a 2σ uncertainty around 0.23 K decade−1. The cooling rate in the upper stratosphere above 6 hPa is 0.65 ± 0.11 K decade−1.
The temperature changes of five stratospheric layers due to external forcing as estimated using the optimal fingerprinting technique. Red lines are the results using both the AIRS and AMSU-A observations and black lines are the results using only the AIRS data. Blue lines are the results for the layer-mean temperatures in TMS, TUS, and TTS by homogenized SSU data record. Horizontal ticked lines indicate the 2σ uncertainty.
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-17-0037.1
Our results for stratospheric temperature trends are consistent with those determined using other datasets. Linear temperature trends in the stratosphere from 1979 to 2007 have been examined using SSU, MSU, and radiosonde data (Randel et al. 2009), and it is found that the upper stratosphere has a larger cooling trend than the lower stratosphere. A recent study (Zou and Qian 2016) homogenized SSU observations from 1978 to 2016 for layer-mean temperatures of the midstratosphere (TMS; centered at ~15 hPa), of the upper stratosphere (TUS; ~5 hPa), and of the top stratosphere (TTS; ~1.5 hPa). The global-mean temperature trends over the period of 2003 to 2012 from the homogenized SSU data record are −0.50 ± 0.17 K decade−1 for the TMS, −0.61 ± 0.20 K decade−1 for the TUS, and −0.62 ± 0.21 K decade−1 for the TTS. These trend estimates (blue asterisks in Fig. 7) are consistent with our results. Note our inference of stratospheric cooling is an optimal determination of the presence of a long-term climate trend distinct from natural variability but is not an attribution to a specific cause such as the solar cycle or increasing stratospheric carbon dioxide.
Error covariances between the estimated temperature changes and between estimated temperature and CO2 changes are shown as red ellipses in Fig. 8. Each ellipse shows the 1σ error with respect to the optimal estimate of Δαi in Eq. (1). The first four columns of Fig. 8 show that errors in estimated temperature change in different layers are largely uncorrelated. Among 10 panels of error covariance between estimated temperatures change in different layers, weak correlations only exist between estimated changes in three layers that are centered at 20, 41, and 86 hPa. Anticorrelation of errors between adjacent layers is a signature of overrepresentation of vertical resolution: a positive error in one layer and a negative error in an adjacent layer roughly cancel each other in order to explain the data, and no information exists to distinguish between the adjacent layers. Figure 8, right, shows that error in estimated CO2 rising rate has little correlation with errors in estimated stratospheric temperature changes in all five layers, which suggests that, if a bias exists in the estimated CO2 rising rate, it does not affect the estimated temperature changes in all five stratospheric layers.
The 1σ error covariance for estimated temperature changes (K decade−1) and (right) CO2 changes (ppmv decade−1) due to external forcing. The panels are arranged according to pressure for the columns and the rows; for example, (top left) the error covariance between estimated temperature changes at 2.7 and 8.8 hPa. The ordinate unit is K decade−1 for all panels (see depiction with units at bottom left). Red ellipses are the results using both AIRS and AMSU-A observations, whereas black ones are the results using only AIRS.
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-17-0037.1
Our results give an estimate of the stratospheric CO2 change at 1.57 ± 0.10 (2σ) ppmv yr−1. Transport of CO2 from the troposphere to the stratosphere suggests that the stratospheric CO2 change up to 35 km lags behind the surface CO2 change by 4–5 yr (Engel et al. 2009). Such time lag, usually termed as age of air, can be as large as 5–7 yr for the extratropics in the low-to-middle stratosphere and for the globe in the upper stratosphere [Table 1 in Waugh and Hall (2002), with considerable variation based on location and method of observations]. Using the surface observations of CO2 compiled by the National Oceanic and Atmospheric Administration/Earth System Research Laboratory (NOAA/ESRL; Conway et al. 1994; Dlugokencky and Tans 2013), a near 4-yr time lag would lead to a 1.9 ppmv yr−1 increase of the stratospheric CO2 for the 10-yr period examined here, which is larger than our estimate. This underestimate of CO2 change can be due to a few reasons: 1) the CO2 natural variability is assumed zero in our method as the climate models that we used do not simulate time-dependent CO2 concentration, but in reality the CO2 does have spatial and temporal variability; 2) the models are limited to represent the residual term δε, which is more than just natural variability so that the uncertainty of CO2 increase could be estimated lower; and 3) given the intrinsic spread in the full age of air spectrum and the transport nature in the stratosphere (Waugh and Hall 2002), it is possible that the CO2 increase rate in the upper stratosphere is smaller than that in the lower and middle stratosphere. For example, an 8-yr time lag would lead to a CO2 trend of 1.8 ppmv yr−1. There have been few in situ observations available for the age of air in the upper stratosphere (Martell 1973; Waugh and Hall 2002); thus it is difficult at this moment to quantify this possible cause further.
To understand the impact of this underestimated CO2 rising rate on stratospheric temperature changes detected in this study, we have carried out two sensitivity tests (Figs. 9a,b). In the first study, we artificially increase the amplitude of CO2 spectral fingerprint in Fig. 4 by a factor of 10 before applying the optimal fingerprinting study. The estimated temperature changes are then shown as green lines in Fig. 9a, which are essentially no difference from the estimated temperature changes in the result section (red lines in Fig. 9). In the second study, we assume a different CO2 vertical profile in the stratosphere from the default one in the PCRTM, the radiative transfer model used in this study. The default PCRTM CO2 mixing ratio decreases from 368.3 ppmv at 100 hPa to 364 ppmv at 1 hPa. We here assume a constant mixing ratio of 368.3 ppmv through the entire stratosphere. Then we obtain a new CO2 spectral fingerprint and derive the estimated temperature change accordingly. The results are shown in Fig. 9b as green lines, which are virtually indistinguishable from the red lines, which are the estimated temperatures as shown in Fig. 7. Both results are consistent with the inference based on error covariances between CO2 and temperature estimates (Fig. 8); that is, the error in the estimate of CO2 rising rate has little impact on the estimated stratospheric temperature change.
The stratospheric temperature changes in response to external forcing. Red lines are the results using AIRS and AMSU-A together shown in Fig. 7, in which the CO2 spectral fingerprint is derived assuming the default CO2 background profile in the PCRTM. (a) Green lines are the results when the amplitude of CO2 spectral fingerprint is artificially increased by a factor of 10. (b) Green lines are derived using a different background CO2 profile (constant mixing ratio in the stratosphere) in the calculation of CO2 spectral fingerprint.
Citation: Journal of Climate 30, 15; 10.1175/JCLI-D-17-0037.1
b. Synergy of microwave and infrared radiances
Distinguishing between carbon dioxide change and stratospheric temperature changes becomes more difficult and posterior uncertainty in stratospheric temperature changes becomes greater when AMSU-A radiances are not included in the spectral fingerprints. The estimated stratospheric temperature trends are shown as black lines in Fig. 7 and the corresponding error covariance plots are shown as black ellipses in Fig. 8 when the AMSU-A channels are removed from the spectral fingerprints. There are three consequences of removing the AMSU-A data: 1) the estimated CO2 change becomes less certain (1.05 ± 0.60 ppmv yr−1), 2) the posterior uncertainty of estimated stratospheric temperature changes becomes worse, and 3) errors in stratospheric temperature changes become more strikingly anticorrelated between adjacent layers. The correlation of errors between carbon dioxide change and stratospheric temperature changes becomes stronger, all of which is a consequence of the loss of information on carbon dioxide change. Such differences confirm the merit of the AMSU-A radiances in the spectral fingerprinting study: its independence with respect to CO2 change can help successfully disentangle the similarity among the infrared spectral fingerprints as shown in Fig. 4. In practice, Figs. 7 and 8 demonstrate that the joint use of AIRS and AMSU-A brightness temperatures not only narrows the uncertainty of estimated changes but also increases the effective vertical resolution of retrieved stratospheric temperature trends.
4. Conclusions
We have demonstrated that optimal fingerprinting, when applied to 10 years of high-spectral-resolution infrared data and passive microwave data, can detect decadal changes in stratospheric temperature and carbon dioxide that is unexplained by natural variability within 2σ uncertainty. The joint use of infrared and microwave brightness temperature anomalies effectively reduces uncertainties of the estimated changes of stratospheric temperature and carbon dioxide. It also improves the vertical resolution of the profile of stratospheric temperature changes and the distinction between carbon dioxide and temperature in satellite data. The hyperspectral IR data such as that obtained by AIRS make it possible to estimate the temperature changes with higher vertical resolution than the previous generation of global satellite observations. Data from high-quality hyperspectral IR measurements from current and future instruments such as AIRS, the Infrared Atmospheric Sounding Interferometer (IASI), and the Cross-Track Infrared Sounder (CrIS) and the Climate Absolute Radiance and Refractivity Observatory (CLARREO) mission should provide information-rich constraints on long-term trends in the atmosphere, including the stratosphere. Like passive nadir microwave radiance, the GPS radio occultation is also insensitive to CO2 change but can offer accurate temperature retrievals in the lower and middle stratosphere. Therefore, similar synergistic use of GPS occultation and infrared radiance can be useful for studying climate change as well (Goody et al. 1998; Huang et al. 2010a).
While most climate change studies use the climatology of geophysical parameters retrieved from satellite observations (the so-called retrieve-then-average approach), this study for the first time shows that optimal fingerprinting can be applied directly to observed radiances to detect climate changes (the average-then-retrieve approach). This study also suggests that, in addition to MSU and SSU, which have been extensively used in stratospheric temperature change studies, a new generation of hyperspectral sounders such as AIRS can also start to contribute to the studies of stratospheric climate.
Acknowledgments
We wish to thank the anonymous reviewers for their insightful and thorough comments. The GFDL CM3 and HadGEM2-CC simulation outputs are obtained from CMIP5 archives (via https://pcmdi.llnl.gov/projects/esgf-llnl). The AIRS L1b data are obtained from NASA GSFC DAAC. The global-mean homogenized AMSU-A data are directly obtained from Remote Sensing System (via http://images.remss.com/msu/msu_time_series.html). This research is supported by NASA Grants NNX14AJ50G and NNX15AC25G awarded to the University of Michigan. It is also supported by NASA Grant NNX14AR33G awarded to Harvard University. The corresponding author X. L. Huang is thankful to NOAA/GFDL and Princeton University for hosting his sabbatical, which led to this study.
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