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Intensification of tropical storms measured as the central pressure tendency represents a subtle imbalance, of the order of $10^{-3}$, between the inflow and outflow of air in the storm core. Factors driving this imbalance, especially in cases of rapid intensification, remain elusive. Here, using an analysis of intensification rates and precipitation in North Atlantic cyclones, it is shown that the storms on average deepen at a rate with which maximum local precipitation removes mass from the atmospheric column. Means for lifetime maximum intensification rate and maximum concurrent precipitation (multiplied by the acceleration of gravity) are, respectively, $23$ and $17$ hPa day$^{-1}$. This equivalence is not limited to average values: both intensification rates and precipitation have the same dependence on the inverse radius of maximum wind. It is further shown using a numerical model that with the mass sink switched off, storms driven by sensible and latent heat alone either do not develop at all or develop significantly more slowly reaching lower maximum intensities. It is discussed that the conclusions of previous studies about the relative insignificance of the mass sink arose from a long-standing misinterpretation of mass nonconservation assessments for assesments of the actual impact of the mass sink on storm dynamics. Condensation mass sink provides for a fundamental positive feedback between surface pressure and vertical velocity that was earlier shown to be instrumental in analytical descriptions of storm intensification. This feedback allows the storm circulation to get more compact during intensification in contrast to modeled heat-driven storms that increase their radius of maximum wind as they intensify. These findings indicate that the condensation mass sink is a dominant process governing the dynamics of tropical storms., Comment: 34 pages, 11 figures, 2 tables

Along with the accumulation of atmospheric carbon dioxide, the loss of primary forests and other natural ecosystems is a major disruption of the Earth system causing global concern. Quantifying planetary warming from carbon emissions, global climate models highlight natural forests' high carbon storage potential supporting conservation policies. However, some model outcomes effectively deprioritize conservation of boreal and temperate forests suggesting that increased albedo upon deforestation could cool the planet. Potential conflict of global cooling versus regional forest conservation could harm environmental policies. Here we present theoretical and observational evidence to demonstrate that, compared to the carbon-related warming, the model skills for assessing climatic impacts of deforestation is low. We argue that deforestation-induced global cooling results from the models' limited capacity to account for the global effect of cooling from evapotranspiration of intact forests. Transpiration of trees can change the greenhouse effect via small modifications of the vertical temperature profile. Due to their convective parameterization (which postulates a certain critical temperature profile), global climate models do not properly capture this effect. This parameterization may lead to underestimation of warming from the loss of evapotranspiration in both high and low latitidues, and therefore, conclusions about deforestation-induced global cooling are not robust. To avoid deepening the environmental crisis, these conclusions should not inform policies of vegetation cover management. Studies are mounting quantifying the stabilizing impact of natural ecosystems evolved to maintain environmental homeostasis. Given the critical state and our limited understanding of both climate and ecosystems, an optimal policy would be a global moratorium on the exploitation of all natural forests., Comment: 17 pages, 5 figures, 1 table

Emanuel's concept of maximum potential intensity (E-PI) estimates the maximum velocity of tropical cyclones from environmental parameters assuming thermal wind (gradient-wind and hydrostatic balances) and slantwise neutrality in the free troposphere. E-PI's key equation relates proportionally the radial gradients of saturated moist entropy and angular momentum. Here the E-PI derivation is reconsidered to show that the thermal wind and slantwise neutrality imply zero radial gradients of saturation entropy and angular momentum at an altitude where, for a given radius, the tangential wind has a maximum. It is further shown that, while E-PI's key equation requires that, at the point of maximum tangential wind, the air temperature must increase towards the storm center, the thermal wind equation dictates the opposite. From the analysis of the equations of motion at the altitude of maximum tangential wind in the free troposphere, it is concluded that here the air flow must be supergradient. This implies that the supergradiency factor (a measure of the gradient-wind imbalance) must change in the free troposphere as the air flow tends to restore the balance. It is shown that such a change modifies the derivative of saturation entropy over angular momentum, which cannot therefore remain constant in the free troposphere as E-PI requires. The implications of these findings for the internal coherence of E-PI, including its boundary layer closure, are discussed., Comment: Minor Revision for JAS. Reply to reviewers can be found in appendix C. 20 pages, 1 figure

The terrestrial water cycle links the soil and atmosphere moisture reservoirs through four fluxes: precipitation, evaporation, runoff, and atmospheric moisture convergence (net import of water vapor to balance runoff). Each of these processes is essential for human and ecosystem well-being. Predicting how the water cycle responds to changes in vegetation cover remains a challenge. Recently, changes in plant transpiration across the Amazon basin were shown to be associated disproportionately with changes in rainfall, suggesting that even small declines in transpiration (e.g., from deforestation) would lead to much larger declines in rainfall. Here, constraining these results by the law of mass conservation, we show that in a sufficiently wet atmosphere, forest transpiration can control atmospheric moisture convergence such that increased transpiration enhances atmospheric moisture import and resulting water yield. Conversely, in a sufficiently dry atmosphere increased transpiration reduces atmospheric moisture convergence and water yield. This previously unrecognized dichotomy can explain the otherwise mixed observations of how water yield responds to re-greening, as we illustrate with examples from China's Loess Plateau. Our analysis indicates that any additional precipitation recycling by additional vegetation increases precipitation but decreases local water yield and steady-state runoff. Therefore, in the drier regions and early stages of ecological restoration, the role of vegetation can be confined to precipitation recycling, while once a wetter stage is achieved, additional vegetation enhances atmospheric moisture convergence and water yield. Evaluating the transition between regimes, and recognizing the potential of vegetation for enhancing moisture convergence, are crucial for characterizing the consequences of deforestation and for motivating and guiding ecological restoration., Comment: 39 pages, 12 figures, 5 tables

The terrestrial water cycle links the soil and atmosphere moisture reservoirs through four fluxes: precipitation, evaporation, runoff and atmospheric moisture convergence. Each of these fluxes is essential for human and ecosystem well-being. However, predicting how the water cycle responds to changes in vegetation cover, remains a challenge (Lawrence and Vandecar, 2015; Ellison et al., 2017; te Wierik et al., 2021). Recently, rainfall was shown to decrease disproportionally with reduced forest transpiration following deforestation (Baudena et al., 2021). Here, combining these findings with the law of matter conservation, we show that in a sufficiently wet atmosphere forest transpiration can control atmospheric moisture convergence such that increased transpiration enhances atmospheric moisture import. Conversely, in a drier atmosphere increased transpiration reduces atmospheric moisture convergence and runoff. This previously unrecognized dichotomy can explain the seemingly random observations of runoff and soil moisture sometimes increasing and sometimes reducing in response to re-greening (e.g., Zheng et al., 2021). Evaluating the transition between the two regimes is crucial both for characterizing the risk posed by deforestation as well as for motivating and guiding global ecosystem restoration., Comment: 8 pages, 1 figure

Destabilization of the water cycle threatens human lives and livelihoods. Meanwhile our understanding of whether and how changes in vegetation cover could trigger abrupt transitions in moisture regimes remains incomplete. This challenge calls for better evidence as well as for the theoretical concepts to describe it. Here we briefly summarise the theoretical questions surrounding the role of vegetation cover in the dynamics of a moist atmosphere. We discuss the previously unrecognized sensitivity of local wind power to condensation rate as revealed by our analysis of the continuity equation for a gas mixture. Using the framework of condensation-induced atmospheric dynamics, we then show that with the temperature contrast between land and ocean increasing up to a critical threshold, ocean-to-land moisture transport reaches a tipping point where it can stop or even reverse. Land-ocean temperature contrasts are affected by both global and regional processes, in particular, by the surface fluxes of sensible and latent heat that are strongly influenced by vegetation. Our results clarify how a disturbance of natural vegetation cover, e.g., by deforestation, can disrupt large-scale atmospheric circulation and moisture transport. In view of the increasing pressure on natural ecosystems, successful strategies of mitigating climate change require taking into account the impact of vegetation on moist atmospheric dynamics. Our analysis provides a theoretical framework to assess this impact. The available data for Eurasia indicate that the observed climatological land-ocean temperature contrasts are close to the threshold. This can explain the increasing fluctuations in the continental water cycle including droughts and floods and signifies a yet greater potential importance for large-scale forest conservation., Comment: 25 pages, 5 figures, and 1 table

While water lifting plays a recognized role in the global atmospheric power budget, estimates for this role in tropical cyclones vary from no effect to a major reduction in storm intensity. To better assess this impact, here we consider the work output of an infinitely narrow thermodynamic cycle with two streamlines connecting the top of the boundary layer in the vicinity of maximum wind (without assuming gradient-wind balance) to an arbitrary level in the inviscid free troposphere. The reduction of a storm's maximum wind speed due to water lifting is found to decline with increasing efficiency of the cycle and is about 5% for maximum observed Carnot efficiencies. In the steady-state cycle, there is an extra heat input associated with the warming of precipitating water. The corresponding positive extra work is of an opposite sign and several times smaller than that due to water lifting. We also estimate the gain of kinetic energy in the outflow region. Contrary to previous assessments, this term is found to be large when the outflow radius is small (comparable to the radius of maximum wind). Using our framework, we show that Emanuel's maximum potential intensity (E-PI) corresponds to a cycle where total work equals work performed at the top of the boundary layer (net work in the free troposphere is zero). This constrains a dependence between the outflow temperature and heat input at the point of maximum wind, but does not constrain the radial pressure gradient. We outline the implications of the established patterns for assessing real storms., Comment: Revised resubmission to the Journal of the Atmospheric Sciences. Reply to the first and third reviewers can be found in the Appendix. 35 pages, 3 figures, 2 tables

Emanuel's concept of maximum potential intensity (E-PI) estimates the maximum velocity of tropical cyclones from environmental parameters. At the point of maximum wind, E-PI's key equation relates proportionally the centrifugal acceleration (squared maximum velocity divided by radius) to the radial gradient of saturated moist entropy. The proportionality coefficient depends on the outflow temperature. Here it is shown that a different relationship between the same quantities derives straightforwardly from the gradient-wind balance and the definition of entropy, with the proportionality coefficient depending on the radial gradient of local air temperature. The robust alternative reveals a previously unexplored constraint: for E-PI to be valid, the outflow temperature should be a function of the radial temperature gradient at the point of maximum wind. When the air is horizontally isothermal (which, as we argue, is not an uncommon condition), this constraint cannot be satisfied, and E-PI's key equation underestimates the squared maximum velocity by approximately twofold. This explains "superintensity" (maximum wind speeds exceeding E-PI). The new formulation predicts less superintensity at higher temperatures, corroborating recent numerical simulations. Previous analyses are re-evaluated to reveal inconsistent support for the explanation of superintensity by supergradient winds alone. In Hurricane Isabel 2003, maximum superintensity is found to be associated with minimal gradient-wind imbalance. Modified to diagnostically account for supergradient winds, the new formulation shows that air temperature increasing towards the storm center can mask the effect of gradient-wind imbalance, thus reducing "superintensity" and formally bringing E-PI closer to observations. The implications of these findings for assessing real storms are discussed., Comment: Third revision for the Journal of the Atmospheric Sciences. Reply to the two reviewers can be found in Appendix E. 41 pages, 3 figures, 2 tables

Jaramillo et al. (2018) (hereafter JMR1) asserted that our theory, henceforth known as CIAD (condensation-induced atmospheric dynamics), modifies the equation of vertical motion in a manner that violates Newton's third law. Jaramillo et al. (2019) (hereafter JMR2) have subsequently conceded that this is not the case. This would have resolved the original misunderstanding, had it not been for new claims in JMR2 that necessitate further correction., Comment: 6 pp

In a recent paper Rousseau-Rizzi and Emanuel (2019) presented a derivation of an upper limit on maximum hurricane velocity at the surface. This derivation was based on a consideration of an infinitely narrow (differential) Carnot cycle with the warmer isotherm at the point of the maximum wind velocity. Here we show that this derivation neglected a significant term describing the kinetic energy change in the outflow. Additionally, we highlight the importance of a proper accounting for the power needed to lift liquid water. Finally, we provide a revision to the formula for surface fluxes of heat and momentum showing that, if we accept the assumptions adopted by Rousseau-Rizzi and Emanuel (2019), the resulting velocity estimate does not depend on the flux of sensible heat., Comment: Our comments on paper "An evaluation of hurricane superintensity in axisymmetric numerical models" by Rapha\"el Rousseau-Rizzi and Kerry Emanuel published in J. Atmos. Sci. 76, 1697 (2019)

Emanuel's concept of Maximum Potential Intensity (E-PI) relates the maximum velocity $V_{\rm max}$ of tropical storms, assumed to be in gradient wind balance, to environmental parameters. Several studies suggested that the unbalanced flow is responsible for E-PI sometimes significantly underpredicting $V_{\rm max}$. Additionally, two major modifications generated a considerable range of E-PI predictions: the dissipative heating and the power expended to lift water were respectively suggested to increase and reduce E-PI $V_{\rm max}$ by about 20%. Here we re-derive the E-PI concept separating its dynamic and thermodynamic assumptions and lifting the gradient wind balance limitation. Our analysis reveals that E-PI formulations for a balanced and a radially unbalanced flow are similar, while the systematic underestimate of $V_{\rm max}$ reflects instead an incompatibility between several E-PI assumptions. We discuss how these assumptions can be modified. We further show that irrespective of whether dissipative heating occurs or not, E-PI uniquely relates $V_{\rm max}$ to the latent heat flux (not to the total oceanic heat flux as originally proposed). We clarify that, in contrast to previous suggestions, lifting water has little impact on E-PI. We demonstrate that in E-PI the negative work of the pressure gradient in the upper atmosphere consumes all the kinetic energy generated in the boundary layer. This key dynamic constraint is independent of other E-PI assumptions and thus can apply to diverse circulation patterns. Finally, we show that the E-PI maximum kinetic energy per unit volume equals the local partial pressure of water vapor and discuss the implications of this finding for predicting $V_{\rm max}$., Comment: 29 pages, 1 figure. Derivation is generalized to account for the radially unbalanced flow

Our comments on paper "Is Condensation-Induced Atmospheric Dynamics a New Theory of the Origin of the Winds?" by A. Jaramillo, O. J. Mesa, and D. J. Raymond published in J. Atmos. Sci. 75, 3305 (2018)., Comment: 12 pages, 1 figure

The concept of Maximum Potential Intensity (MPI) is widely used in tropical cyclone research to estimate the minimum central pressure and the maximum velocity of tropical storms from environmental parameters. The MPI pressure derives from consideration of an idealized thermodynamic cycle, while the MPI velocity additionally requires information about real-time power and heat flows within the storm. Recently MPI velocity was proposed to be a substantial overestimate (by 10-30 percent) presumably neglecting the power needed to lift precipitating water (the gravitational power of precipitation). This conclusion did not involve a theoretical analysis of the MPI concept but was based on observed hurricane rainfall to estimate gravitational power of precipitation. However, since the MPI pressure estimate does explicitly account for lifting water, and the MPI velocity derives from this pressure, the question arises whether a correction to MPI velocity is required. Here we represent and examine the MPI derivations in their most general form and show that although a correction to MPI velocity is justified, it is an order of magnitude or so smaller than originally proposed. We show that the neglect of gravitational power of precipitation in the MPI velocity estimate was caused by the incomplete formulation of the general relationship between pressure work and dissipation of kinetic energy, taken per unit time and integrated over the storm. We highlight the importance of an internally consistent framework to estimate both storm energy and power and provide some perspectives for further investigating the role of moisture., Comment: 15 pages, 3 figures

Despite the dangers associated with tropical cyclones and their rainfall, the origins of storm moisture remains unclear. Existing studies have focused on the region 40-400 km from the cyclone center. It is known that the rainfall within this area cannot be explained by local processes alone but requires imported moisture. Nonetheless, the dynamics of this imported moisture appears unknown. Here, considering a region up to three thousand kilometers from storm center, we analyze precipitation, atmospheric moisture and movement velocities for North Atlantic hurricanes. Our findings indicate that even over such large areas a hurricane's rainfall cannot be accounted for by concurrent evaporation. We propose instead that a hurricane consumes pre-existing atmospheric water vapor as it moves. The propagation velocity of the cyclone, i.e. the difference between its movement velocity and the mean velocity of the surrounding air (steering flow), determines the water vapor budget. Water vapor available to the hurricane through its movement makes the hurricane self-sufficient at about 700 km from the hurricane center obviating the need to concentrate moisture from greater distances. Such hurricanes leave a dry wake, whereby rainfall is suppressed by up to 40 per cent compared to its long-term mean. The inner radius of this dry footprint approximately coincides with the radius of hurricane self-sufficiency with respect to water vapor. We discuss how Carnot efficiency considerations do not constrain the power of such open systems that deplete the pre-existing moisture. Our findings emphasize the incompletely understood role and importance of atmospheric moisture supplies, condensation and precipitation in hurricane dynamics., Comment: 38 pages, 17 figures, 1 Table; extended analyses: available E/P ratios reviewed and explained (Table 1); rainfall and moisture distributions 3 days before and after hurricanes, propagation velocity and its relationship to radial velocity; efficiency for non-steady hurricanes; hurricane motion and rainfall asymmetries discussed

The power of atmospheric circulation is a key measure of the Earth's climate system. The mismatch between predictions and observations under a warming climate calls for a reassessment of how atmospheric power $W$ is defined, estimated and constrained. Here we review published formulations for $W$ and show how they differ when applied to a moist atmosphere. Three factors, a non-zero source/sink in the continuity equation, the difference between velocities of gaseous air and condensate, and interaction between the gas and condensate modifying the equations of motion, affect the formulation of $W$. Starting from the thermodynamic definition of mechanical work, we derive an expression for $W$ from an explicit consideration of the equations of motion and continuity. Our analyses clarify how some past formulations are incomplete or invalid. Three caveats are identified. First, $W$ critically depends on the boundary condition for gaseous air velocity at the Earth's surface. Second, confusion between gaseous air velocity and mean velocity of air and condensate in the expression for $W$ results in gross errors despite the observed magnitudes of these velocities are very close. Third, $W$ expressed in terms of measurable atmospheric parameters, air pressure and velocity, is scale-specific; this must be taken into account when adding contributions to $W$ from different processes. We present a formulation of the atmospheric power budget, which distinguishes three components of $W$: the kinetic power associated with horizontal pressure gradients ($W_K$), the gravitational power of precipitation ($W_P$) and the condensate loading ($W_c$). We use MERRA and NCAR/NCEP re-analyses to evaluate the atmospheric power budget at different scales: $W_K$ increases with temporal resolution approaching our theoretical estimate for condensation-induced circulation when all convective motion is resolved., Comment: 55 pages, 14 figures; minor revisions after another discussion, see https://doi.org/10.5194/acp-2017-17-AC7 and www.bioticregulation.ru/ab.php?id=he

Starting from basic physical principles, we present a novel derivation linking the global wind power to measurable atmospheric parameters. The resulting expression distinguishes three components of the atmospheric power (the kinetic power associated with horizontal and vertical motion and the gravitational power of precipitation) and highlights problems with previous approaches. Focusing on Lalibert\'e et al. (2015), we show how inappropriate treatment of material derivatives in the presence of phase transitions leads to significant errors in wind power analyses. We discuss the physical constraints on global wind power and the opportunities provided by considering the dynamic effects of water vapor condensation., Comment: 10 pages

The kinetic energy budget of the atmosphere's meridional circulation cells is analytically assessed. In the upper atmosphere kinetic energy generation grows with increasing surface temperature difference \$\Delta T_s\$ between the cold and warm ends of a circulation cell; in the lower atmosphere it declines. A requirement that kinetic energy generation is positive in the lower atmosphere limits the poleward cell extension \$L\$ of Hadley cells via a relationship between \$\Delta T_s\$ and surface pressure difference \$\Delta p_s\$: an upper limit exists when \$\Delta p_s\$ does not grow with increasing \$\Delta T_s\$. This pattern is demonstrated here using monthly data from MERRA re-analysis. Kinetic energy generation along air streamlines in the boundary layer does not exceed \$40\$~J~mol\$^{-1}\$; it declines with growing \$L\$ and reaches zero for the largest observed \$L\$ at 2~km height. The limited meridional cell size necessitates the appearance of heat pumps -- circulation cells with negative work output where the low-level air moves towards colder areas. These cells consume the positive work output of the heat engines -- cells where the low-level air moves towards the warmer areas -- and can in theory drive the global efficiency of atmospheric circulation down to zero. Relative contributions of \$\Delta p_s\$ and \$\Delta T_s\$ to kinetic energy generation are evaluated: \$\Delta T_s\$ dominates in the upper atmosphere, while \$\Delta p_s\$ dominates in the lower. Analysis and empirical evidence indicate that the net kinetic power output on Earth is dominated by surface pressure gradients, with minor net kinetic energy generation in the upper atmosphere. The role of condensation in generating surface pressure gradients is discussed., Comment: 26 pages, 9 figures, 2 tables; re-organized presentation, more discussion and a new figure (Fig. 4) added; in Fig. 3 the previously invisible dots (observations) can now be seen