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- Author or Editor: Stephan Fueglistaler x
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Abstract
This paper addresses issues of statistical misrepresentation of the a priori parameters (henceforth called ancillary parameters) used in geophysical data estimation. Parameterizations using ancillary data are frequently needed to derive geophysical data of interest from remote measurements. Empirical fits to the ancillary data that do not preserve the distribution of such data may induce substantial bias. A semianalytical averaging approach based on Taylor expansion is presented to improve estimated cirrus ice water content and sedimentation flux for a range of volume extinction coefficients retrieved from spaceborne lidar observations by CALIOP combined with the estimated distribution of ancillary data from in situ aircraft measurements of ice particle microphysical parameters and temperature. It is shown that, given an idealized distribution of input parameters, the approach performs well against Monte Carlo benchmark predictions. Using examples with idealized distributions at the mean temperature for the tropics at 15 km, it is estimated that the commonly neglected variance observed in in situ measurements of effective diameters may produce a worst-case estimation bias spanning up to a factor of 2. For ice sedimentation flux, a similar variance in particle size distributions and extinctions produces a worst-case estimation bias of a factor of 9. The value of the bias is found to be mostly set by the correlation coefficient between extinction and ice effective diameter, which in this test ranged between all possible values. Systematic reporting of variances and covariances in the ancillary data and between data and observed quantities would allow for more accurate observational estimates.
Abstract
This paper addresses issues of statistical misrepresentation of the a priori parameters (henceforth called ancillary parameters) used in geophysical data estimation. Parameterizations using ancillary data are frequently needed to derive geophysical data of interest from remote measurements. Empirical fits to the ancillary data that do not preserve the distribution of such data may induce substantial bias. A semianalytical averaging approach based on Taylor expansion is presented to improve estimated cirrus ice water content and sedimentation flux for a range of volume extinction coefficients retrieved from spaceborne lidar observations by CALIOP combined with the estimated distribution of ancillary data from in situ aircraft measurements of ice particle microphysical parameters and temperature. It is shown that, given an idealized distribution of input parameters, the approach performs well against Monte Carlo benchmark predictions. Using examples with idealized distributions at the mean temperature for the tropics at 15 km, it is estimated that the commonly neglected variance observed in in situ measurements of effective diameters may produce a worst-case estimation bias spanning up to a factor of 2. For ice sedimentation flux, a similar variance in particle size distributions and extinctions produces a worst-case estimation bias of a factor of 9. The value of the bias is found to be mostly set by the correlation coefficient between extinction and ice effective diameter, which in this test ranged between all possible values. Systematic reporting of variances and covariances in the ancillary data and between data and observed quantities would allow for more accurate observational estimates.
Abstract
Global warming projections of dynamics are less robust than projections of thermodynamics. However, robust aspects of the thermodynamics can be used to constrain some dynamical aspects. This paper argues that tropospheric expansion under global warming (a thermodynamical process) explains changes in the amplitude of the quasi-biennial oscillation (QBO) in the lower and middle stratosphere (a dynamical process). A theoretical scaling for tropospheric expansion of approximately 6 hPa K−1 is derived, which agrees well with global climate model (GCM) experiments. Using this theoretical scaling, the response of QBO amplitude to global warming is predicted by shifting the climatological QBO amplitude profile upward by 6 hPa per kelvin of global warming. In global warming simulations, QBO amplitude in the lower to middle stratosphere shifts upward as predicted by tropospheric expansion. Applied to observations, the tropospheric expansion framework suggests a historical weakening of QBO amplitude at 70 hPa of 3% decade−1 from 1953 to 2020. This expected weakening trend is half of the 6% decade−1 from 1953 to 2012 detected and attributed to global warming in a recent study. The previously reported trend was reinforced by record low QBO amplitudes during the mid-2000s, from which the QBO has since recovered. Given the modest weakening expected on physical grounds, past decadal modulations of QBO amplitude are reinterpreted as a hitherto unrecognized source of internal variability. This large internal variability dominates over the global warming signal such that, despite 65 years of observations, there is not yet a statistically significant weakening trend.
Abstract
Global warming projections of dynamics are less robust than projections of thermodynamics. However, robust aspects of the thermodynamics can be used to constrain some dynamical aspects. This paper argues that tropospheric expansion under global warming (a thermodynamical process) explains changes in the amplitude of the quasi-biennial oscillation (QBO) in the lower and middle stratosphere (a dynamical process). A theoretical scaling for tropospheric expansion of approximately 6 hPa K−1 is derived, which agrees well with global climate model (GCM) experiments. Using this theoretical scaling, the response of QBO amplitude to global warming is predicted by shifting the climatological QBO amplitude profile upward by 6 hPa per kelvin of global warming. In global warming simulations, QBO amplitude in the lower to middle stratosphere shifts upward as predicted by tropospheric expansion. Applied to observations, the tropospheric expansion framework suggests a historical weakening of QBO amplitude at 70 hPa of 3% decade−1 from 1953 to 2020. This expected weakening trend is half of the 6% decade−1 from 1953 to 2012 detected and attributed to global warming in a recent study. The previously reported trend was reinforced by record low QBO amplitudes during the mid-2000s, from which the QBO has since recovered. Given the modest weakening expected on physical grounds, past decadal modulations of QBO amplitude are reinterpreted as a hitherto unrecognized source of internal variability. This large internal variability dominates over the global warming signal such that, despite 65 years of observations, there is not yet a statistically significant weakening trend.
Abstract
The impact of cloud radiative heating on transport time scales from the tropical upper troposphere to the stratosphere is studied in two-dimensional numerical simulations. Clouds are idealized as sources of radiative heating and are stochastically distributed in space and time. A spatial probability function constrains clouds to occur in only part of the domain to depict heterogeneously distributed clouds in the atmosphere.
The transport time from the lower to upper boundaries (age of air) is evaluated with trajectories. The spectra of age of air obtained in the simulations are bimodal, with the first mode composed of trajectories that remain in the cloudy part of the domain during their passages from the lower to upper boundaries, and the second mode composed of the remaining trajectories that visit the cloud-free regions. For the first group of trajectories only, the mean age scales inversely with the time-mean radiative heating in cloudy air, and the one-dimensional advection–diffusion equation provides an adequate model for transport.
However, the exchange between the cloudy and cloud-free regions renders the mean age over all trajectories (including those that visit the cloud-free region) much longer than the time expected if all air parcels remain in cloudy air. In addition, the overall mean age is not inversely proportional to the time-mean heating rate in cloudy air. Sensitivity calculations further show that the sizes, durations, and amplitudes of the individual clouds are also important to the transport time.
The results show that the frequently used decomposition of radiative heating into clear-sky and cloud radiative heating may give incorrect interpretations regarding the time scale of transport into the stratosphere.
Abstract
The impact of cloud radiative heating on transport time scales from the tropical upper troposphere to the stratosphere is studied in two-dimensional numerical simulations. Clouds are idealized as sources of radiative heating and are stochastically distributed in space and time. A spatial probability function constrains clouds to occur in only part of the domain to depict heterogeneously distributed clouds in the atmosphere.
The transport time from the lower to upper boundaries (age of air) is evaluated with trajectories. The spectra of age of air obtained in the simulations are bimodal, with the first mode composed of trajectories that remain in the cloudy part of the domain during their passages from the lower to upper boundaries, and the second mode composed of the remaining trajectories that visit the cloud-free regions. For the first group of trajectories only, the mean age scales inversely with the time-mean radiative heating in cloudy air, and the one-dimensional advection–diffusion equation provides an adequate model for transport.
However, the exchange between the cloudy and cloud-free regions renders the mean age over all trajectories (including those that visit the cloud-free region) much longer than the time expected if all air parcels remain in cloudy air. In addition, the overall mean age is not inversely proportional to the time-mean heating rate in cloudy air. Sensitivity calculations further show that the sizes, durations, and amplitudes of the individual clouds are also important to the transport time.
The results show that the frequently used decomposition of radiative heating into clear-sky and cloud radiative heating may give incorrect interpretations regarding the time scale of transport into the stratosphere.
Abstract
The quasi-biennial oscillation (QBO) is an alternating, descending pattern of zonal winds in the tropical stratosphere with a period averaging 28 months. The QBO was disrupted in 2016, and arguably again in 2020, by the formation of an anomalous easterly shear zone, and unprecedented stagnation and ascent of shear zones aloft. Several mechanisms have been implicated in causing the 2016 disruption, most notably triggering by horizontal eddy momentum flux divergence, but also anomalous upwelling and wave stress. In this paper, the 1D theory of the QBO is used to show how seemingly disparate features of disruptions follow directly from the dynamics of the QBO response to triggering. The perturbed QBO is interpreted using a heuristic version of the 1D model, which establishes that 1) stagnation of shear zones aloft resulted from wave dissipation in the shear zone formed by the triggering, and 2) ascent of shear zones aloft resulted from climatological upwelling advecting the stagnant shear zones. Obstacles remain in the theory of triggering. In the 1D theory, the phasing of the triggering is key to determining the response, but the dependence on magnitude is less steep. Yet in MERRA-2, there are triggering events only 20% weaker than the 2016 triggering and equal to the 2020 triggering that did not lead to disruptions. Complicating matters further, MERRA-2 has record-large analysis tendencies during the 2016 disruption, reducing confidence in the resolved momentum budget.
Abstract
The quasi-biennial oscillation (QBO) is an alternating, descending pattern of zonal winds in the tropical stratosphere with a period averaging 28 months. The QBO was disrupted in 2016, and arguably again in 2020, by the formation of an anomalous easterly shear zone, and unprecedented stagnation and ascent of shear zones aloft. Several mechanisms have been implicated in causing the 2016 disruption, most notably triggering by horizontal eddy momentum flux divergence, but also anomalous upwelling and wave stress. In this paper, the 1D theory of the QBO is used to show how seemingly disparate features of disruptions follow directly from the dynamics of the QBO response to triggering. The perturbed QBO is interpreted using a heuristic version of the 1D model, which establishes that 1) stagnation of shear zones aloft resulted from wave dissipation in the shear zone formed by the triggering, and 2) ascent of shear zones aloft resulted from climatological upwelling advecting the stagnant shear zones. Obstacles remain in the theory of triggering. In the 1D theory, the phasing of the triggering is key to determining the response, but the dependence on magnitude is less steep. Yet in MERRA-2, there are triggering events only 20% weaker than the 2016 triggering and equal to the 2020 triggering that did not lead to disruptions. Complicating matters further, MERRA-2 has record-large analysis tendencies during the 2016 disruption, reducing confidence in the resolved momentum budget.
Abstract
The quasi-biennial oscillation (QBO) is a descending pattern of alternating easterly and westerly winds in the tropical stratosphere. Upwelling is generally understood to counteract the descent of the QBO. The upwelling hypothesis holds that where upwelling exceeds the intrinsic descent rate of the QBO, the QBO cannot descend and a buffer zone forms. Descent-rate models of the QBO, which represent a highly simplified evolution of a QBO wind contour, support the upwelling hypothesis. Here, we show that the upwelling hypothesis and descent-rate models only correctly describe buffer zone formation in the absence of wave dissipation below critical levels. When there is wave dissipation below critical levels, the 1D QBO response to upwelling can be either to 1) reform below the upwelling, 2) undergo period-lengthening collapse, or 3) expand a preexisting buffer zone. The response depends on the location of the upwelling and the lower boundary condition. Mean-flow damping always forms a buffer zone. A previous study of reanalyses showed that there is mean-flow damping in the buffer zone due to horizontal momentum flux divergence. Therefore, the 1D model implicates lateral terms in buffer zone formation that it cannot self-consistently include.
Abstract
The quasi-biennial oscillation (QBO) is a descending pattern of alternating easterly and westerly winds in the tropical stratosphere. Upwelling is generally understood to counteract the descent of the QBO. The upwelling hypothesis holds that where upwelling exceeds the intrinsic descent rate of the QBO, the QBO cannot descend and a buffer zone forms. Descent-rate models of the QBO, which represent a highly simplified evolution of a QBO wind contour, support the upwelling hypothesis. Here, we show that the upwelling hypothesis and descent-rate models only correctly describe buffer zone formation in the absence of wave dissipation below critical levels. When there is wave dissipation below critical levels, the 1D QBO response to upwelling can be either to 1) reform below the upwelling, 2) undergo period-lengthening collapse, or 3) expand a preexisting buffer zone. The response depends on the location of the upwelling and the lower boundary condition. Mean-flow damping always forms a buffer zone. A previous study of reanalyses showed that there is mean-flow damping in the buffer zone due to horizontal momentum flux divergence. Therefore, the 1D model implicates lateral terms in buffer zone formation that it cannot self-consistently include.
Abstract
The quasi-biennial oscillation (QBO) is a descending pattern of winds in the stratosphere that vanishes near the top of the tropical tropopause layer, even though the vertically propagating waves that drive the QBO are thought to originate in the troposphere several kilometers below. The region where there is low QBO power despite sufficient vertically propagating wave activity to drive a QBO is known as the buffer zone. Classical one-dimensional models of the QBO are ill suited to represent buffer zone dynamics because they enforce the attenuation of the QBO via a zero-wind lower boundary condition. The formation of the buffer zone is investigated by analyzing momentum budgets in the reanalyses MERRA-2 and ERA-Interim. The buffer zone must be formed by weak wave-driven acceleration and/or cancellation of the wave-driven acceleration. This paper shows that in MERRA-2 weak wave-driven acceleration is insufficient to form the buffer zone, so cancellation of the wave-driven acceleration must play a role. The cancellation results from damping of angular momentum anomalies, primarily due to horizontal mean and horizontal eddy momentum flux divergence, with secondary contributions from the Coriolis torque and vertical mean momentum flux divergence. The importance of the damping terms highlights the role of the buffer zone as the mediator of angular momentum exchange between the QBO domain and the far field. Some far-field angular momentum anomalies reach the solid Earth, leading to the well-documented lagged correlation between the QBO and the length of day.
Abstract
The quasi-biennial oscillation (QBO) is a descending pattern of winds in the stratosphere that vanishes near the top of the tropical tropopause layer, even though the vertically propagating waves that drive the QBO are thought to originate in the troposphere several kilometers below. The region where there is low QBO power despite sufficient vertically propagating wave activity to drive a QBO is known as the buffer zone. Classical one-dimensional models of the QBO are ill suited to represent buffer zone dynamics because they enforce the attenuation of the QBO via a zero-wind lower boundary condition. The formation of the buffer zone is investigated by analyzing momentum budgets in the reanalyses MERRA-2 and ERA-Interim. The buffer zone must be formed by weak wave-driven acceleration and/or cancellation of the wave-driven acceleration. This paper shows that in MERRA-2 weak wave-driven acceleration is insufficient to form the buffer zone, so cancellation of the wave-driven acceleration must play a role. The cancellation results from damping of angular momentum anomalies, primarily due to horizontal mean and horizontal eddy momentum flux divergence, with secondary contributions from the Coriolis torque and vertical mean momentum flux divergence. The importance of the damping terms highlights the role of the buffer zone as the mediator of angular momentum exchange between the QBO domain and the far field. Some far-field angular momentum anomalies reach the solid Earth, leading to the well-documented lagged correlation between the QBO and the length of day.
Abstract
The cooling-to-space (CTS) approximation says that the radiative cooling of an atmospheric layer is dominated by that layer’s emission to space, while radiative exchange with layers above and below largely cancel. Though the CTS approximation has been demonstrated empirically and is thus fairly well accepted, a theoretical justification is lacking. Furthermore, the intuition behind the CTS approximation cannot be universally valid, as the CTS approximation fails in the case of pure radiative equilibrium. Motivated by this, we investigate the CTS approximation in detail. We frame the CTS approximation in terms of a novel decomposition of radiative flux divergence, which better captures the cancellation of exchange terms. We also derive validity criteria for the CTS approximation, using simple analytical theory. We apply these criteria in the context of both gray gas pure radiative equilibrium (PRE) and radiative–convective equilibrium (RCE) to understand how the CTS approximation arises and why it fails in PRE. When applied to realistic gases in RCE, these criteria predict that the CTS approximation should hold well for H2O but less so for CO2, a conclusion we verify with line-by-line radiative transfer calculations. Along the way we also discuss the well-known “τ = 1 law,” and its dependence on the choice of vertical coordinate.
Abstract
The cooling-to-space (CTS) approximation says that the radiative cooling of an atmospheric layer is dominated by that layer’s emission to space, while radiative exchange with layers above and below largely cancel. Though the CTS approximation has been demonstrated empirically and is thus fairly well accepted, a theoretical justification is lacking. Furthermore, the intuition behind the CTS approximation cannot be universally valid, as the CTS approximation fails in the case of pure radiative equilibrium. Motivated by this, we investigate the CTS approximation in detail. We frame the CTS approximation in terms of a novel decomposition of radiative flux divergence, which better captures the cancellation of exchange terms. We also derive validity criteria for the CTS approximation, using simple analytical theory. We apply these criteria in the context of both gray gas pure radiative equilibrium (PRE) and radiative–convective equilibrium (RCE) to understand how the CTS approximation arises and why it fails in PRE. When applied to realistic gases in RCE, these criteria predict that the CTS approximation should hold well for H2O but less so for CO2, a conclusion we verify with line-by-line radiative transfer calculations. Along the way we also discuss the well-known “τ = 1 law,” and its dependence on the choice of vertical coordinate.
Abstract
Vertical mixing may lead to significant momentum and heat fluxes in the tropical tropopause layer (TTL) and these momentum and heat fluxes can force large climatological temperature and zonal wind changes in the TTL. The climatology of vertical mixing and associated momentum and heat fluxes as parameterized in the Interim ECMWF Re-Analysis (ERA-Interim) and as parameterized by the mixing scheme currently used in the ECMWF operational analyses are presented. Each scheme produces a very different climatology showing that the momentum and heat fluxes arising from vertical mixing are highly dependent on the scheme used. A dry GCM is then forced with momentum and heat fluxes similar to those seen in ERA-Interim to assess the potential impact of such momentum and heat fluxes. A significant response in the TTL is found, leading to a temperature perturbation of approximately 4 K and a zonal wind perturbation of approximately 12 m s−1. These temperature and zonal wind perturbations are approximately zonally symmetric, are approximately linear perturbations to the unforced climatology, and are confined to the TTL between approximately 10°N and 10°S. There is also a smaller-amplitude tropospheric component to the response. The results presented herein indicate that vertical mixing can have a large but uncertain effect on the TTL and that the choice and impact of the vertical mixing scheme should be an important consideration when modeling the TTL.
Abstract
Vertical mixing may lead to significant momentum and heat fluxes in the tropical tropopause layer (TTL) and these momentum and heat fluxes can force large climatological temperature and zonal wind changes in the TTL. The climatology of vertical mixing and associated momentum and heat fluxes as parameterized in the Interim ECMWF Re-Analysis (ERA-Interim) and as parameterized by the mixing scheme currently used in the ECMWF operational analyses are presented. Each scheme produces a very different climatology showing that the momentum and heat fluxes arising from vertical mixing are highly dependent on the scheme used. A dry GCM is then forced with momentum and heat fluxes similar to those seen in ERA-Interim to assess the potential impact of such momentum and heat fluxes. A significant response in the TTL is found, leading to a temperature perturbation of approximately 4 K and a zonal wind perturbation of approximately 12 m s−1. These temperature and zonal wind perturbations are approximately zonally symmetric, are approximately linear perturbations to the unforced climatology, and are confined to the TTL between approximately 10°N and 10°S. There is also a smaller-amplitude tropospheric component to the response. The results presented herein indicate that vertical mixing can have a large but uncertain effect on the TTL and that the choice and impact of the vertical mixing scheme should be an important consideration when modeling the TTL.
