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Bjorn Stevens

Abstract

Analytic solutions to a planetary boundary layer (PBL) model with an eddy-diffusivity profile (i.e., a K profile) and nonlocal fluxes are presented for the quasi-steady regime. The solutions demonstrate how different processes contribute to the quasi-steady profiles of heat and/or other scalars in the convective boundary layer. It is shown that for a standard cubic form of the K profile, and flux scales based on the surface fluxes, the nondimensional nonlocal term should be less than six; larger values can cause scalar profiles of water vapor to increase with height in the upper portion of the PBL and can produce weakly superadiabatic layers in the upper PBL temperature profiles. Solutions are also shown to be sensitive to the choice of flux scale: fluxes scaled by their vertically averaged values imply that nondimensional profiles of top-down scalars will have a neutral point somewhere in the PBL, a result in conflict with previous work on the subject, and the predictions of the same model with fluxes scaled by their surface values. The analysis also shows that allowing K to go to zero with the square of the distance from the PBL top results in nonconvergent profiles; in general K should reduce to some positive value at the top of the PBL, or go to zero less rapidly. It is further shown that the class of models investigated here may be physically interpreted as relaxation models, that is, they tend to relax profiles of scalars in the PBL to implicitly defined similarity profiles on a convective timescale. Finally, analysis of a 1-yr integration of a climate model, interpreted in light of the author’s analytic results, suggests that a dynamically important aspect of the nonlocal term is its role in ventilating the surface layer, and thereby indirectly affecting the diagnoses of PBL depth in many models.

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Bjorn Stevens

Abstract

This reply addresses a comment questioning one of the lines of evidence I used in a 2015 study (S15) to argue for a less negative aerosol radiative forcing. The comment raises four points of criticism. Two of these have been raised and addressed elsewhere; here I additionally show that even if they have merit the S15 lower bound remains substantially (0.5 W m–2) less negative than that given in the AR5. Regarding the two other points of criticism, one appears to be based on a poor understanding of the nature of S15’s argument; the other rests on speculation as to the nature of the uncertainty in historical SO2 estimates. In the spirit of finding possible flaws with the top-down constraints from S15, I instead hypothesize that an interesting—albeit unlikely—way S15 could be wrong is by inappropriately discounting the contribution of biomass burning to radiative forcing through aerosol–cloud interactions. This hypothesis is interesting as it opens the door for a role for the anthropogenic (biomass) aerosol in causing the Little Ice Age and again raises the specter of greater warming from ongoing reductions in SO2 emissions.

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Bjorn Stevens

Abstract

A prototype problem of a nonprecipitating convective layer growing into a layer of uniform stratification and exponentially decreasing humidity is introduced to study the mechanism by which the cumulus-topped boundary layer grows. The problem naturally admits the surface buoyancy flux, outer layer stratification, and moisture scale as governing parameters. Large-eddy simulations show that many of the well-known properties of the cumulus-topped boundary layer (including a well-mixed subcloud layer, a cloud-base transition layer, a conditionally unstable cloud layer, and an inversion layer) emerge naturally in the simulations. The simulations also quantify the differences between nonprecipitating moist convection and its dry counterpart. Whereas dry penetrative convective layers grow proportionally to the square root of time (diffusively) the cumulus layers grow proportionally to time (ballistically). The associated downward transport of warm, dry air results in a significant decrease in the surface Bowen ratio. The linear-in-time growth of the cloud layer is shown to result from the transport and subsequent evaporation of liquid water into the inversion layer. This process acts as a sink of buoyancy, which acts to imbue the free troposphere with the properties of the cloud layer. A simple model, based on this mechanism, and formulated in terms of an effective dry buoyancy flux (which is constrained by the subcloud layer’s similarity to a dry convective layer), is shown to provide good predictions of the growth of the layer across a wide range of governing parameters.

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Bjorn Stevens

Abstract

Based on research showing that in the case of a strong aerosol forcing, this forcing establishes itself early in the historical record, a simple model is constructed to explore the implications of a strongly negative aerosol forcing on the early (pre-1950) part of the instrumental record. This model, which contains terms representing both aerosol–radiation and aerosol–cloud interactions, well represents the known time history of aerosol radiative forcing as well as the effect of the natural state on the strength of aerosol forcing. Model parameters, randomly drawn to represent uncertainty in understanding, demonstrate that a forcing more negative than −1.0 W m−2 is implausible, as it implies that none of the approximately 0.3-K temperature rise between 1850 and 1950 can be attributed to Northern Hemisphere forcing. The individual terms of the model are interpreted in light of comprehensive modeling, constraints from observations, and physical understanding to provide further support for the less negative (−1.0 W m−2) lower bound. These findings suggest that aerosol radiative forcing is less negative and more certain than is commonly believed.

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Cathy Hohenegger and Bjorn Stevens

Abstract

In his comment, D. M. Schultz asked for clarification concerning (i) the validity of the results of C. Hohenegger and B. Stevens for the development of convection over the midlatitudes and (ii) the exact meaning and computation of the term “moisture convergence.” This reply aims at clarifying these two aspects.

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Gilles Bellon and Bjorn Stevens

Abstract

The adjustment of the trade wind atmospheric boundary layer to an abrupt sea surface warming is investigated using a large-eddy simulation (LES) and two simple bulk models: a mixed-layer model (MLM), and a model based on the mixing-line hypothesis (XLM). The near-surface temperature adjusts in a few hours, faster than can be expected from the characteristic time scales associated with the physical processes at play. The near-surface humidity adjusts more slowly, with a time scale of about a day, and it exhibits an initial decrease before increasing to its equilibrium value. An analysis of the MLM suggests that the initial tendency of humidity and temperature results from the difference in Bowen ratios between the equilibrium and the perturbation. An analysis of the three linear modes of the XLM shows that the fastest-decaying mode adjusts the subcloud-layer buoyancy, with a constructive interaction of all of the physical processes. The second-fastest-decaying mode is an adjustment of the boundary layer thermodynamical structure and the slowest mode adjusts the boundary layer depth. Approximate analytical expressions of the time scales characterizing these linear modes are derived both for the MLM and the XLM. The MLM exhibits no scale separation between the fastest and second-fastest time scales and a scale separation between these and the slowest time scale only in the case of a shallow well-mixed boundary layer. The XLM exhibits a scale separation between the buoyancy adjustment of the subcloud layer and the overall thermodynamic adjustment, while conserving the scale separation with the slower adjustment of the boundary layer depth.

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Louise Nuijens and Bjorn Stevens

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The role of wind speed on shallow marine cumulus convection is explored using large-eddy simulations and concepts from bulk theory. Focusing on cases characteristic of the trades, the equilibrium trade wind layer is found to be deeper at stronger winds, with larger surface moisture fluxes and smaller surface heat fluxes. The opposing behavior of the surface fluxes is caused by more warm and dry air being mixed to the surface as the cloud layer deepens. This leads to little difference in equilibrium surface buoyancy fluxes and cloud-base mass fluxes. Shallow cumuli are deeper, but not more numerous or more energetic. The deepening response is necessary to resolve an inconsistency in the subcloud layer. This argument follows from bulk concepts and assumes that the lapse rate and flux divergence of moist-conserved variables do not change, based on simulation results. With that assumption, stronger winds and a fixed inversion height imply larger surface moisture and buoyancy fluxes (heat fluxes are small initially). The consequent moistening tends to decrease cloud-base height, which is inconsistent with a larger surface buoyancy flux that tends to increase cloud-base height, in order to maintain the buoyancy flux at cloud base at a fixed fraction of its surface value (entrainment closure). Deepening the cloud layer by increasing the inversion height resolves this inconsistency by allowing the surface buoyancy flux to remain constant without further moistening the subcloud layer. Because this explanation follows from simple bulk concepts, it is suggested that the internal dynamics (mixing) of clouds is only secondary to the deepening response.

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Axel Seifert and Bjorn Stevens

Abstract

The rain formation in shallow cumulus clouds by condensational growth and collision–coalescence of liquid drops is revisited with the aim of understanding the controls on precipitation efficiency for idealized cloud drafts. For the purposes of this analysis, a one-dimensional kinematic cloud model is introduced, which permits the efficient exploration of many microphysical aspects of liquid shallow clouds with both spectral and two-moment bulk microphysical formulations. Based on the one-dimensional model and the insights gained from both microphysical approaches, scaling relations are derived that provide a link between microphysical and macroscopic cloud properties. By introducing the concept of a macroscopic autoconversion time scale, the rain formation can be traced back to quantities such as cloud depth, average vertical velocity, lapse rate, and cloud lifetime. The one-dimensional model also suggests that the precipitation efficiency can be expressed as a function of the ratio of the macroscopic autoconversion time scale and cloud lifetime and that it exhibits threshold-like behavior.

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Bjorn Stevens and Stephanie Fiedler

Abstract

Kretzschmar et al., in a comment in 2017, use the spread in the output of aerosol–climate models to argue that the models refute the hypothesis (presented in a paper by Stevens in 2015) that for the mid-twentieth-century warming to be consistent with observations, then the present-day aerosol forcing, must be less negative than −1 W m−2. The main point of contention is the nature of the relationship between global SO2 emissions and In contrast to the concave (log-linear) relationship used by Stevens and in earlier studies, whereby becomes progressively less sensitive to SO2 emissions, some models suggest a convex relationship, which would imply a less negative lower bound. The model that best exemplifies this difference, and that is most clearly in conflict with the hypothesis of Stevens, does so because of an implausible aerosol response to the initial rise in anthropogenic aerosol precursor emissions in East and South Asia—already in 1975 this model’s clear-sky reflectance from anthropogenic aerosol over the North Pacific exceeds present-day estimates of the clear-sky reflectance by the total aerosol. The authors perform experiments using a new (observationally constrained) climatology of anthropogenic aerosols to further show that the effects of changing patterns of aerosol and aerosol precursor emissions during the late twentieth century have, for the same global emissions, relatively little effect on These findings suggest that the behavior Kretzschmar et al. identify as being in conflict with the lower bound in Stevens arises from an implausible relationship between SO2 emissions and and thus provides little basis for revising this lower bound.

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Gilles Bellon and Bjorn Stevens

Abstract

A simple framework to study the sensitivity of atmospheric boundary layer (ABL) models to the large-scale conditions and forcings is introduced. This framework minimizes the number of parameters necessary to describe the large-scale conditions, subsidence, and radiation. Using this framework, the sensitivity of the stationary ABL to the large-scale boundary conditions [underlying sea surface temperature (SST) and overlying humidity and temperature in the free troposphere] is investigated in large-eddy simulations (LESs). For increasing SST or decreasing free-tropospheric temperature, the LES exhibits a transition from a cloud-free, well-mixed ABL stationary state, through a cloudy, well-mixed stationary state and a stable shallow cumulus stationary state, to an unstable regime with a deepening shallow cumulus layer. For a warm SST, when increasing free-tropospheric humidity, the LES exhibits a transition from a stable shallow cumulus stationary state, through a stable cumulus-under-stratus stationary state, to an unstable regime with a deepening, cumulus-under-stratus layer. For a cool SST, when increasing the free-tropospheric humidity, the LES stationary state exhibits a transition from a cloud-free, well-mixed ABL regime, through a well-mixed cumulus-capped regime, to a stratus-capped regime with a decoupling between the subcloud and cloud layers.

This dataset can be used to evaluate other ABL models. As an example, the sensitivity of a bulk model based on the mixing-line model is presented. This bulk model reproduces the LES sensitivity to SST and free-tropospheric temperature for the stable and unstable shallow cumulus regimes, but it is less successful at reproducing the LES sensitivity to free-tropospheric humidity for both shallow cumulus and well-mixed regimes.

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