Associate Editor: Alex Guenther; University of California, Irvine, California, United States
Tropospheric ozone (O3) has increased substantially since the preindustrial era due to anthropogenic emissions (Lamarque et al., 2010). In contrast to long-lived greenhouse gases (GHG) such as carbon dioxide, the lifetime of tropospheric O3 ranges from hours to weeks leading to a significantly more variable spatial distribution. In the latest Intergovernmental Panel for Climate Change (IPCC) assessment (AR5) (Myhre et al., 2013), the estimated radiative forcing (RF) of tropospheric O3 computed using chemistry-climate models ranged widely from +0.2 to +0.6 W m–2 but the cause of this large inter-model spread remains unexplained. Most of the longwave O3 RF is in the 9.6-µm O3 band, which accounts for more than 97% of total longwave O3 absorption (Rothman et al., 1987). Shortwave forcing, which accounts for ~1/4 of total tropospheric O3 RF (Myhre et al., 2013), is not considered here, and we therefore restrict our analysis and conclusions to longwave GHG effects. Spectrally resolved satellite measurements of this O3 band allow evaluation of the sensitivity of top-of-atmosphere (TOA) flux to tropospheric O3 change by means of instantaneous Radiative Kernels (IRK) and longwave radiative effect (LWRE). The IRK represents the TOA flux sensitivity to the vertical distribution of O3 and LWRE is the net reduction in TOA flux due to the tropospheric O3 column, respectively (Worden et al., 2011). The tropospheric O3 GHG effect can be quantified with IRK or LWRE.
O3 LWRE estimates, inferred from the satellite observational based IRK, for example from Tropospheric Emission Spectrometer (TES) or Infrared Atmospheric Sounding Interferometer (IASI) data (Worden et al., 2011; Doniki et al., 2015), are useful for further diagnosing the inter-model spread of O3 RF in the IPCC AR5 assessment. For example, Bowman et al. (2013) used TES retrieved O3 and IRKs to reduce the inter-model uncertainty of the preindustrial-to-present O3 RF of the chemistry-climate models participating in the Atmospheric Chemistry and Climate Model Intercomparison Project (ACCMIP) (Lamarque et al., 2013) by 30%. Their study also suggested that the vertical TOA flux sensitivity to tropospheric O3 is highly variable but is structurally consistent with atmospheric opacity, which determines on the amount of upwelling longwave radiation available for O3 absorption (Lacis and Hansen, 1974; Berntsen et al., 1997; Worden et al., 2008; Worden et al., 2011). The atmospheric opacity is highly correlated with the three key variables in the hydrological cycle: water vapor, clouds and temperature. Water vapor has significant absorption over a wide spectral range in the longwave; as a result, the outgoing longwave radiation is strongly reduced over high water vapor regions and hence the TOA flux sensitivity to tropospheric O3 changes is low. Similarly, clouds (liquid or solid state of water vapor) absorb more OLR than water vapor and reduce atmospheric transparency by attenuating upwelling radiation below the cloud layer, also leading to a low TOA flux sensitivity to tropospheric O3 changes. Lastly, besides its control of the phase transition between water vapor and cloud through the Clausius-Clapeyron relation, air temperature also determines the amount of longwave emission: the warmer the troposphere is, the higher of the TOA flux sensitivity to tropospheric O3 changes will be.
In this paper, we will extend the work of Bowman et al. (2013) and further elucidate the influence of water vapor, clouds, temperature and tropospheric O3 column to the O3 LWRE. For consistency, we aim to be able to use data from a single instrument. Aura TES provides observations of water vapor, temperature, relative humidity (RH) and tropospheric O3. Aura TES does not provide direct cloud measurements but we shall assume that RH is a good proxy for cloud coverage. RH is also a good variable that represents simultaneously the coupled effects of water vapor, temperature and cloud in the O3 LWRE (Bowman et al., 2013). Following Doniki et al, (2015), we update the calculation of tropospheric O3 TOA flux sensitivity (IRK) using a more accurate, 5-angle Gaussian Quadrature approximation, which is described in section 2. In section 3, we examine the relationship of TES TOA flux sensitivity to tropospheric O3 with TES RH, water vapor, tropospheric O3 column, and surface temperature in January and July of 2006 in order to investigate the primary drivers that determine the variation of tropical and sub-tropical O3 GHG effect. Section 4 summarizes our main results. At the end, we discusses some implications from our study.
2. Method and data
2.1. O3 IRK
The TOA flux in 9.6-µm O3 band (FTOA) can be computed as
where Lv(θ, O3(z),q(z)) is the TOA spectral radiance in units of W m–2 sr–1 cm–1. θ is the zenith angle from 0 to, ϕ is the azimuthal angle from 0 to 2π, and v is the spectral frequency from v1 = 980cm–1 to v2 = 1080cm–1 (or, equivalently, from 10.20 µm to 9.26 µm). Lv depends on the vertical distribution of O3 as well as other atmospheric states, such as water vapor, temperature, cloud optical depth and emissivity; these atmospheric states are collectively denoted by q.
The O3 instantaneous radiative kernel (IRK; in the unit of W m–2 ppb–1) is defined as the sensitivity of the TOA radiative flux to increase in the vertical distribution of O3 (see Worden et al., 2011):
where O3(zl) is O3 concentration at level zl.is the spectral radiance Jacobians, which is analytically calculated in the TES retrieval algorithm. Note that O3 IRK also depends on geophysical quantities q(z) other than O3 itself. In this study, we are particularly interested in understanding how the key players in the hydrological cycle, including water vapor, temperature, and clouds, impact the O3 IRK variation; therefore, this is to study the second derivatives .
The zenith integral in Eq. (2) can be rewritten as the first moment ofusing the change of variable x = cosθ:
In general, the first moment of any function can be a Gaussian quadrature (GQ): Abramowitz and Stegun, 1964). wk and xk can be obtained using the methods discussed in the Appendix of Li (2000). For the application to Eq. (3), Doniki et al. (2015) show that a 5-point (N = 5) GQ is more accurate than the previous single-angle anisotropy estimate (Worden et al., 2011). With this quadrature, Eq. (2) can be evaluated as, where wk are the weights at selected abscissas xk, which are the roots of the Jacobi polynomial (
where θk= cos–1Xk. The values of wk and θk are shown in Table 1.
|Weight, wi||TOA Nadir Angle, θi (°)||Surface Zenith Angle (°)|
For convenience, we also define a logarithmic instantaneous radiative kernel (LIRK) with respect to ln O3 (zl) to represent the change in TOA flux due to fractional change of O3 abundance at each level:
LIRK is in units of W m–2.
2.2 Long wave radiative effect (LWRE)
The instantaneous radiative kernel, at a given location i and sampling time j, can be used to calculate the TOA longwave radiative effect (LWRE; in W m–2), defined as the reduction in TOA longwave flux due to increase of O3 abundance:
which can also be obtained in terms of fractional changes using LIRK:
We then define a tropospheric LWRE,, as the net change of TOA flux due to the total tropospheric column absorption or 100% change of the species in the entire troposphere. can be obtained by integrating IRK vertically from surface to the tropopause (TP) and letting to be the change from O3 abundance (e.g. measured by TES) to zero in that layer:
Following Bowman et al. (2013) to avoid different results due to different tropopause definitions [Stevenson et al., 2004], we define a chemical tropopause as the 150 ppb ozone isopleth, also used by Young et al., (2013) and Rap et al., (2015). Therefore, ZTP in Eq. (8) corresponds to the altitude of the 150 ppb isopleth over a particular location.
The new version of monthly averaged O3 IRK, LIRK and LWRE for 2006 has been run using about 16 global surveys (GS) TES data in each month. Each GS takes approximately every two days (~26 hours) to finish 16 orbits. One GS has about 3000 soundings to make the global coverage. Therefore, there are about 48000 soundings to grid bin to a 2° by 2.5° monthly mean map.
Note that the LWRE data we have processed (January, April, July, and October of 2006) with the new 5-point GQ is only 10% of the complete 5-year record. But the spatial patterns and the climatology of the LWRE obtained from these data are consistent with the previous 5-year record using the 1-point GQ LWRE (Figure 1 of Bowman et al., 2013). All the figures in Bowman et al. (2013) are well replicated with the 5-point GQ data.
2.3 Relative humidity
The relative humidity (RH) represents the amount of water vapor in air in a percentage of the amount of water vapor needed for saturation at the same temperature. RH is estimated as the ratio of the partial pressure ew of water vapor to the equilibrium water vapor pressure ew* at a given temperature
where P is pressure. Regions with RH close to 100% typically have clouds; consequently, RH is often used as a proxy for the presence of clouds. In contrast, RH much less than 100% means water vapor is far from saturation at the given temperature and therefore is indicative of clear sky.
Since individual variations of temperature, water vapor, and clouds may change the O3 GHG effect in different directions, RH, as a function of H2O(z) and T(z), and as a proxy of cloud coverage, may be a better variable to describe the aggregated effect of the hydrological cycle on the O3 GHG effect.
3.1 Signatures of temperature, water vapor, clouds, and tropospheric O3 on O3 LWRE
Figure 1 shows the global distribution of the TOA flux in 9.6-µm O3 band, tropospheric O3 LWRE, RH data at 500 hPa, water vapor total column amount, tropospheric column O3, and surface temperature in January and July 2006 all observed by TES. Since the averaging kernels of the TES retrievals peak at 500 hPa, we choose RH at 500 hPa. The spatial pattern of O3 LWRE is quite similar to that of TOA flux, which is denoted as outgoing longwave radiation (OLR) (top two panels). At high latitudes, tropospheric O3 LWRE is generally weak (< 0.3 W m–2 poleward of 45°) and decreases rapidly with latitude as a consequence of the negative gradient in surface temperature and O3 variation (Doniki et al., 2015). The lower temperature results in less OLR and consequently less sensitivity to O3. The processes controlled O3 variation include ozone hole in the Polar regions and stratospheric intrusion into the troposphere.
The spatial pattern of O3 LWRE is high (> 0.8 W m–2) for values of RH less than 20%. Conversely, low LWRE regions (< 0.3 W m–2) occur when RH is greater than 80%. Low RH generally occurs in subtropical dry regions (near 30°) such as the Sahara and Middle East in July, and subtropical Atlantic in both January and July. The zonal average of O3 LWRE at subtropics is about 0.6 W m–2. In contrast, the zonal average O3 LWRE is 0.4 W m–2 in the ITCZ, especially at the convective continental regions, e.g. tropical rainforests, where RH is usually high.
In the tropics, LWRE values < 0.3 W m–2 are associated with RH greater than 80% and low TOA flux less than 15 W m–2. The lower values of tropical O3 LWRE also follow the meridional transitions of ITCZ between January and July. For example, in January, four deep convection zones, with tropical maxima in RH close to 100% and low TOA flux, ~13 W m–2, for the 9.6-µm O3 band are found in the central Pacific and tropical continents (Amazon basin, Congo basin, and Indonesia). These regions of maximum RH all correspond to minima in LWRE (< 0.3 W m–2) and are mostly south of the equator. When the ITCZ moves to north of the equator in July, the convection zones with RH > 80% and low TOA flux near 13 W m–2 shift to the East Tropical Pacific near the coast of Mexico, Africa Savanna, extending east across India and Southeast Asia to the north of Indonesia, as shown in Figure 1. The LWRE are consistently low over high RH regions in the tropical deep convection zones, where cloud layer shields the OLR flux originating from the troposphere and the OLR flux observed at TOA is mostly from O3 above the cloud. This cloud effect has been demonstrated in Figure 3 of Worden et al. (2011), suggesting that a strong sensitive layer in the mid-troposphere for clear-sky cases becomes a thinner layer that is shifted upwards in the all-sky cases in O3 IRK data. In contrast, Figure 1 also shows that the areas between these deep convection zones at the same latitude are dominated by downwelling and are drier and cloud free with values of LWRE values that are higher due to less atmospheric attenuation.
The seasonal differences shown in the right column of Figure 1 also suggest the opposing temporal changes in LWRE and RH. For example, when ITCZ moves to north in July, the four deep convection zones (Central Tropical Pacific, Amazon basin, Congo basin, and Indonesia) in January become dryer with low RH resulting in enhanced LWRE. The same relationship holds for most of the other regions except Australia, where effects other than water and cloud coverage, such as surface temperature dominate, described below.
Over Australia, the high LWRE values in January (> 0.7 W m–2) are mainly due to high surface temperature and larger thermal contrast over the desert. A larger thermal contrast will amplify the sensitivity of the TOA flux to the tropospheric O3 (Bowman et. al., 2013). In July, the lower RH and higher tropospheric O3 column comparing with those in January, both of which should have led to a larger LWRE, however is compensated by the reduction of surface thermal contrast during the austral winter. Therefore, despite the Australian O3 enhancement in July, the LWRE did not increase.
However, there are many regions where LWRE variations correspond to changes in tropospheric O3 column. For example, a strong O3 LWRE in the Africa savanna in January and Congo basin in July is related to O3 enhancement due to biomass burning during their respective winters (Bowman et al., 2013). Since the ITCZ migrates from the Congo to the African savanna from January to July, the enhanced LWRE in both regions is also associated with lower RH.
In July, there is a large olive-shaped area with the global highest O3 LWRE (> 1 W m–2) over Sahara deserts and the Middle East, which is a result of multiple effects. The surface temperature is highest (> 310 K), which causes the highest values of TOA flux (> 18 W m–2). The local minimum of RH (< 20%) suggests clear sky. Cloud formation is less likely since tropopause descent and a dominant sinking flow of the Hadley circulation further prohibit upward movement of upper tropospheric air and adiabatic cooling. The Hadley cell is a tropical atmospheric circulation in vertical and meridional directions and is characterized as a rising motion near the equator up to the tropopause, where the air separates into northward and southward branches reaching across to the subtropics (Holton and Hakim, 2012). The air parcel then descends and both branches return to the equator near the surface where subsequent convection closes the circulation.
Therefore, the atmosphere in the subtropical region is more transparent during boreal summer. In addition, an O3 enhancement (tropospheric column > 45 DU) that is partly produced locally as well as transported both westward from an extended Asian monsoon anticyclone system and eastward by an Arabian anticyclone (Li et al., 2001; Liu et al., 2009) contributes to this O3 LWRE maximum. Consequently, the maximum Middle East LWRE in July is a result of high surface temperatures and O3 combined with low water vapor and cloud-free conditions.
In summary, we found that the combined impact of water vapor, cloud and temperature on LWRE is mostly explained by RH, especially in tropics and subtropics. Tropospheric O3 variation may control the LWRE when the local atmosphere is transparent and TOA flux sensitivity is non-zero.
3.2 Vertical distribution of O3 LIRK
Figure 2 shows the zonal pattern of RH and O3 LIRK averaged from 0° to 25°S in January and from 0° to 5°N in July to account for the seasonal shift in the ITCZ belt. The ITCZ belt in July is much narrower so we chose 0° to 5°N instead of 0° to 25°N. An anti-correlation between RH and O3 LIRK is found in both S. Tropics and N. Tropics in the free troposphere (300–900 hPa) with the magnitude of correlation coefficients (R) 0.71 and 0.52, respectively and with similar slopes of –0.32 and –0.31 mW m–2 per % RH. Convection zones (e.g. tropical rainforests) characterized by high RH greater than 80% in the free troposphere between 300 and 900 hPa are associated with O3 LIRK magnitudes less than 14 mW m–2. The opposite holds for dry regions between the convection zones. The regions where RH is less than 40% correspond to LIRK magnitude greater than 20 mW m–2. In July, the correlation plot suggests when RH is below 50%, LIRK tend to be high. Further increase of LIRK are found due to O3 enhancement (red points in Figure 2 for July, > 60 ppb). These O3 enhancement are found at N. tropical Atlantic (see Figure 1).
The Walker circulation characterized by high RH in January is a primary driver for the Central Pacific deep convection zones, near 170°W (Lau and Yang, 2003). The Walker circulation describes the motion of airflow in the zonal and vertical direction in the tropical troposphere and explains the formation of monsoons in the Indian and Central Pacific Ocean (Walker and Bliss, 1932; Lau and Yang, 2003). These effects dominate the tropospheric features in the LIRK in the Central Pacific, where the peak values are reduced significantly.
In addition to the Central Pacific, other deep convection zones near 60°W, 20°E, and 130°E respectively in Figure 2 coincide with the local maxima in 500 hPa RH over the Amazon basin, Congo basin, and Indonesia, south of equator in Figure 1. All these regions also correspond to LWRE minima due to the reduction of mid tropospheric sensitivity. Areas between the convection zones are affected by the downward flow in the circulation resulting in regions that stay cool, dry, and cloud free. Consequently, the atmosphere is more transparent leading to higher TOA flux sensitivity to mid tropospheric O3 and higher values of LIRK.
In July, the region with RH greater than 80% and O3 LIRK less than 14 mW m–2 is over the Southeast Asia (90°E–150°E) as a consequence of the Asian monsoon, which transports water vapor from the Pacific and brings more precipitation to the southeast coast of Asia. Other low LIRK regions such as the eastern tropical Pacific near the coast of Mexico (~110°E) and African Savanna (~10°E) are also characterized by relatively high RH between 60–70%. In contrast, the regions with RH less than 40% and O3 LIRK greater than 30 mW m–2 are found over the tropical Atlantic (–60°E to 0°) and Indian Ocean (50°E to 70°E). The LIRK in the eastern tropical Pacific, (–180°E to –120°E), where RH is also less than 40%, has a moderately high LIRK at ~25 mW m–2. Figure 1 suggests that tropospheric O3 columns are much higher in the tropical Atlantic (more than 30 DU) than in the tropical Pacific (less than 20 DU). When RH and cloud optical depth are both low, attenuation by water vapor absorption or clouds on the TOA flux sensitivity to tropospheric O3 is negligible resulting in higher tropospheric O3 LWRE that can vary with O3 amount. Under these conditions, more tropospheric O3 over the tropical Atlantic than tropical Pacific will further strengthen the greenhouse gas effect. Table 2 summarizes what are discussed above based on Figure 2.
|RH||O3 LIRK (mW m–2)||Regions|
|Jan.||>70%||< 14||Central Pacific deep convection zones (–170°E)
Amazon basin near (–60°E)
|Southern tropics||Congo basin near (20°E)
Indonesia near (130°E)
|Jul.||>70%||< 14||Southeast Asia (90°E–150°E)
Tropical Pacific near the coast of Mexico (–110°E)
African Savanna (10°E)
|Northern tropics||<40%||> 25||the tropical Atlantic (–50°E to 0°)
Indian Ocean (50°E to 70°E)
the eastern tropical Pacific, (–180°E to –120°E)
Figure 3 shows the meridional distribution of RH and O3 LIRK globally zonal averaged profiles. The correlation coefficients between RH and O3 LIRK between 300 and 900 hPa at tropics and subtropics (±30°) are approximately –0.6. O3 LIRK is characterized by a strong tropical stratospheric component (not the focus of this paper), with two legs extending into subtropical mid-troposphere, coinciding with subtropical low RH at the descending branches of the Hadley cell. The subtropical high O3 LIRK in middle and upper troposphere is also partly due to free tropospheric O3 enhancements in the upper troposphere from stratosphere-troposphere exchange (especially in the northern hemisphere). In these area, O3 (shown in Figure 3, the 3rd row) is greater than 50 ppb due to stratosphere-troposphere exchange (Hitchman and Rogal, 2010; Rogal et al., 2010; Tilmes et al., 2010; Neu et al., 2014), lightning (Christian et al., 2003; Sauvage et al., 2007; Murray et al., 2012), or biomass burning (Bowman et al., 2009; van der Werf et al., 2010). The correlation scatter plot between RH and LIRK for July again show some of the cases, RH about 40%, the O3 enhancement at Middle East further increase the LIRK, the same as in Figure 2 correlation plot for July. The effect of O3 enhancement in July under hot dry condition also explains why the correlation coefficient is always slightly lower in July than in January.
The tropical low O3 LIRK is associated with the tower of high RH, which is partly due to the upwelling motion in Hadley cell causing deep convection in the ITCZ. Figure 3 also show the O3 LIRK tropical minimum shifts around the equator seasonally following the ITCZ.
The large-scale atmospheric circulation has a strong influence on the hydrological cycle, which impacts the ozone GHG effect. From a latitudinal perspective, the Hadley cell leads to high amounts of water vapor and clouds in the tropics and low water vapor and clear sky in the subtropics. From a meridional perspective, the Walker circulation drives the formation of the deep convection for upwelling and clear sky over subsidence regions at tropical Pacific and tropical Indian Ocean. These in turn modulate the large-scale pattern of the ozone GHG effect.
In the tropics, the low O3 GHG effect, represented by LWRE and LIRK, is primarily driven by high concentration of water vapor and more clouds, both of which have the effect to attenuate the LWRE and LIRK (e.g. in the central tropical Pacific, Amazon basin, Congo basin, and Indonesia in January; the west tropical Pacific, Africa Savanna, and Southeast Asia in July).
Conversely, the subtropical high O3 GHG effect is dominated by high surface temperature and elevated tropospheric O3 amount, especially over desert regions where the effect by water vapor and clouds are much smaller than the tropics as a result of the downwelling branch of Hadley cell. Consequently, the high surface temperature and large thermal contrast amplifies the TOA flux sensitivity to tropospheric O3. The mid and upper tropospheric O3 enhancement further increases the O3 GHG effect over the region with the transparent atmosphere. The confluence of low RH, high tropospheric O3, and high surface temperature lead to a global maximum of the O3 GHG effect over the Middle East in summer.
The TES observations of O3 and RH are used to identify the primary large-scale circulation that determines the typical climate condition in the tropical and subtropical regions. TES RH observations link water vapor, temperature, and clouds and allow us to assess the primary drivers to the variations of O3 GHG effect in the tropics and subtropics. Although the dependence on O3 amount is not controlled exclusively by RH, we showed that the O3 GHG effect is only large when water vapor and cloud attenuation is reduced significantly and thermal contrast is large enough for the sensitivity of O3 GHG effect to tropospheric O3 to become significant.
Exploration how the hydrological cycles controls the patterns and magnitude of O3 TOA flux and flux sensitivity variation can help improve chemistry-climate model simulations and contribute to better estimates of present-day and future radiative forcing. For example, the downwelling of the Hadley circulation is the primary driver for the subtropical maximum of O3 GHG effect. The width of the Hadley cell has been expanding (Seidel and Randel, 2007) and is expected to continue expanding under current climate change scenarios, with increases in global mean temperature and pole-to-equator temperature gradient (Frierson et al., 2007). The poleward shift of the downward branch of the Hadley cell means a poleward expansion of subtropical dry zones, which have the strongest O3 GHG effect. The causes of this poleward shift include the increase of static stability in subtropics, tropopause height increase near the subtropics, and a shift in the ITCZ farther away from the equator due to the response to CO2 forcing (Held, 2000; Lu et al., 2007; Kang and Lu, 2012). These changes would all affect the global distribution of O3 GHG effect, especially for the subtropical maximum, and would have a positive feedback on global warming.
Furthermore, Pal et al. (2016) find that under business-as-usual emissions scenarios, climate extremes in some region like the Middle East, may hit wet-bulb temperatures (a combined measure of temperature and humidity) of 35°C before the end of this century. This wet-bulb temperature is at the limit of the human habitability where humidity prevents sweat from effectively cooling down the human body. People can survive in such heat, but only for a few hours. Their study shows that such heat waves will likely occur in places like Dubai or other Arabian Gulf regions. We show here that the Middle East currently has the global maximum O3 GHG effect due to high surface temperatures, high tropospheric O3 abundance and low RH. Without changes to the earth’s energy budget, increasing surface temperatures and widening of the Hadley circulation will add additional O3 radiative forcing to this region.
Finally, the Asian monsoon also tends to be strengthened by global warming (Li et al., 2010; Singh et al., 2014). The O3 transport from Southeast Asia is an important driver for summer-time O3 enhancements in the Middle East, which add another positive feedback to the Middle East O3 GHG effect. These feedbacks would combine to accelerate the increase in surface temperature and subsequent climate extremes in the Middle East.
List of abbreviations
|ACCMIP||Atmospheric Chemistry and Climate Model Intercomparison Project|
|GHG||Green House Gas|
|IRK||Instantaneous Radiative Kernel (mW/m2/ppb); Eq. (2) or (4)|
|LIRK||Logarithm Instantaneous Radiative Kernel (mW/m2); Eq. (5)|
|LWRE||Long Wave Radiative Effect (W/m2); Eq. (8)|
|OLR||Outgoing Longwave Radiation|
|RF||Radiative Forcing (W/m2)|
|RH||Relative Humidity (%); Eq. (9)|
|TOA||Top of atmosphere|
|FTOA||The TOA flux in 9.6-µm O3 band (W/m2); Eq. (1)|
|Lv||The TOA spectral radiance (W m–2 sr–1 cm–1)|
The data specifically used in this paper are archived at Jet Propulsion Laboratory (JPL) and are available from the authors upon request (email@example.com).