A new tracer is presented to diagnose tropical cyclones （TCs） and their correspondent rainfall. It is defined as water vapour potential vorticity （WPV） by replacing potential temperature with specific humidity in ...A new tracer is presented to diagnose tropical cyclones （TCs） and their correspondent rainfall. It is defined as water vapour potential vorticity （WPV） by replacing potential temperature with specific humidity in the potential vorticity （PV）. The WPV is compared with PV and moist potential vorticity （MPV） in diagnosing three tropical cyclone cases occurred in North-West Pacific during 10 July to 21 July 2005 （Haitang）, 30 July to 9 August 2005 （Matsa） and 25 September to 3 October 2005 （Longwang） separately. The results show that in tracing the track of TCs, WPV is not nicer than PV but better than MPV. While diagnosing TCs＇ onshore rainfall, WPV is better than MPV in all the three cases. Moreover, the advection of WPV is a good indication of TC rainfall after its landing.展开更多
The effects of water and ice clouds on the cloud microphysical budget associated with rainfall are investigated through the analysis of grid-scale data from a series of two-dimensional cloud-resolving model equilibriu...The effects of water and ice clouds on the cloud microphysical budget associated with rainfall are investigated through the analysis of grid-scale data from a series of two-dimensional cloud-resolving model equilibrium sensitivity simulations. The model is imposed without large-scale vertical velocity. In the control experiment, the contribution from rainfall （cM） associated with net evaporation and hydrometeor loss/convergence is about 29% of that from the rainfall （Cm） associated with net condensation and hydrometeor gain/divergence and about 39% of that from the rainfall （CM） associated with net condensation and hydrometeor loss/convergence. The exclusion of ice clouds enhances rainfall contribution of CM, whereas it reduces rainfall contributions of Cm and cM. The removal of radiative effects of water clouds increases rainfall contribution of CM, barely changes rainfall contribution of Cm and reduces the rainfall contribution of cM in the presence of the radiative effects of ice clouds. Elimination of the radiative effects of water clouds reduces the rainfall contributions of CM and Cm, whereas it increases the rainfall contribution of cM in the absence of the radiative effects of ice clouds.展开更多
As a useful index, i.e. the Richardson number Ri, is modified in non-uniform saturated moist flow, based on the fact that liquid water is partially dropped out in parcel air. This is more realistic in real moist atmos...As a useful index, i.e. the Richardson number Ri, is modified in non-uniform saturated moist flow, based on the fact that liquid water is partially dropped out in parcel air. This is more realistic in real moist atmosphere, especially in the rainfall process. The modified Ri presents adequately the influence of numerator, i.e. Brunt- Vaisala frequency （BVF）, on instability. Compared to several former formulae generalized by Durran and Klemp, the modified Ri evidently decreases the stability in rainy regions. In theory, the modified BVF and Ri fix the discontinuity of latent heat release in the transition areas between saturated and unsaturated air by introducing the condensation probability function. Furthermore, the diagnostic analysis of the modified Ri validates the rationality of its application in the non-uniform saturated moist process.展开更多
The bimodal structure of the Meiyu front system is readdressed after Zhou et al.（2005）. The physical mechanism of the formation of the bimodal distribution is discussed. The bimodal structure of the Melyu front syst...The bimodal structure of the Meiyu front system is readdressed after Zhou et al.（2005）. The physical mechanism of the formation of the bimodal distribution is discussed. The bimodal structure of the Melyu front system considerably results from atmospheric moisture gradients, though atmospheric temperature gradients are also not negligible. According to the definition of equivalent potential temperature, and by scale analysis, we find that atmospheric equivalent potential temperature gradients, which could be regarded as an indicator of the Meiyu front system, could be mainly attributed to the variations of atmospheric potential temperature gradients with a scaling factor of 1 and moisture gradients multiplied by a scaling factor of an order of about 2.5 × 10^3, which means that small variations of atmospheric moisture gradients could lead to large variations of equivalent potential temperature gradients, and thus large variations of the Meiyu front system. Quantitative diagnostics with a mesoscale simulation data in the vicinity of the Meiyu front system show that moisture gradients contribute to equivalent potential temperature gradients more than potential temperature gradients.展开更多
Considering some simple topological properties of vorticity vector, the frozen-in property of vorticity herein is revis- ited. A vortex line, as is analogous to velocity vector along a streamline, is defined as such a...Considering some simple topological properties of vorticity vector, the frozen-in property of vorticity herein is revis- ited. A vortex line, as is analogous to velocity vector along a streamline, is defined as such a coincident material （curve） line that connects many material fluid elements, on which the local vorticity vector for each fluid element is also tangent to the vortex line. The vortex line evolves in the same manner as the material line that it is initially associated with. The vortex line and the material line are both oriented to the same directions, and evolve with the proportional magnitude, just like being ＇frozen＇ or ＇glued＇ to the material elements of the fluid under the barotropic assumption. To relax the limits of incompressible and barotropic atmosphere, the frozen-in property is further derived and proved in the baroclinic case. Then two effective usages are given as examples. One is the derivation of potential vorticity conservation from the frozen-in property in both barotropic and baroclinic atmospheres, as a theory application, and the other is used to illuminate the vorticity generation and growth in ideal cases and real severe weather process, e.g., in squall line, tornado, and other se- vere convection weather with vortex. There is no necessity to derive vorticity equation, and this method is very intuitive to explain vorticity development qualitatively, especially for fast analysis for forecasters. Certainly, by investigating the evolution of vortex line, it is possible to locate the associated line element vector and its development on the basis of the frozen-in property of vorticity. Because it is simple and visualized, it manifests broad application prospects.展开更多
The precipitation efficiency and its relationship to physical factors are examined by analyzing a two-dimensional cloud-resolving model simulation during TOGA COARE in this study. The basic physical factors include co...The precipitation efficiency and its relationship to physical factors are examined by analyzing a two-dimensional cloud-resolving model simulation during TOGA COARE in this study. The basic physical factors include convective avail- able potential energy, water-vapor convergence, vertical wind shear, cloud ratio, sea surface temperature, air temperature, and precipitable water. Precipitation efficiencies do not show a close relationship to air temperature nor to sea surface tem- perature nor to precipitable water. The precipitation efficiency increases as the water-vapor convergence rate increases and vertical wind shear weakens, whereas it decreases as the convective available potential energy dissipates and anvil clouds develop.展开更多
The effects of sea surface temperature（SST）,cloud radiative and microphysical processes,and diurnal variations on rainfall statistics are documented with grid data from the two-dimensional equilibrium cloud-resolvin...The effects of sea surface temperature（SST）,cloud radiative and microphysical processes,and diurnal variations on rainfall statistics are documented with grid data from the two-dimensional equilibrium cloud-resolving model simulations.For a rain rate of higher than 3 mm.h 1,water vapor convergence prevails.The rainfall amount decreases with the decrease of SST from 29℃ to 27℃,the inclusion of diurnal variation of SST,or the exclusion of microphysical effects of ice clouds and radiative effects of water clouds,which are primarily associated with the decreases in water vapor convergence.However,the amount of rainfall increases with the increase of SST from 29℃ to 31℃,the exclusion of diurnal variation of solar zenith angle,and the exclusion of the radiative effects of ice clouds,which are primarily related to increases in water vapor convergence.For a rain rate of less than 3 mm.h 1,water vapor divergence prevails.Unlike rainfall statistics for rain rates of higher than 3 mm.h 1,the decrease of SST from 29℃ to 27℃ and the exclusion of radiative effects of water clouds in the presence of radiative effects of ice clouds increase the rainfall amount,which corresponds to the suppression in water vapor divergence.The exclusion of microphysical effects of ice clouds decreases the amount of rainfall,which corresponds to the enhancement in water vapor divergence.The amount of rainfall is less sensitive to the increase of SST from 29℃ to 31℃ and to the radiative effects of water clouds in the absence of the radiative effects of ice clouds.展开更多
For the potential vorticity （PV） invariant, there is a PV-based complete-form vorticity equation, which we use heuris- tically in the present paper to answer the following question： for the Ertel-Rossby invariant ...For the potential vorticity （PV） invariant, there is a PV-based complete-form vorticity equation, which we use heuris- tically in the present paper to answer the following question： for the Ertel-Rossby invariant （ERI）, is there a corresponding vorticity tendency equation？ Such an ERI-based thermally-coupled vorticity equation is derived and discussed in detail in this study. From the obtained new vorticity equation, the vertical vorticity change is constrained by the vertical velocity term, the term associated with the slope of the generalized momentum surface, the term related to the horizontal vorticity change, and the baroclinic or solenoid term. It explicitly includes both the dynamical and thermodynamic factors＇ influence on the vorticity change. For the ERI itself, besides the traditional PV term, the ERI also includes the moisture factor, which is excluded in dry ERI, and the term related to the gradients of pressure, kinetic energy, and potential energy that reflects the fast-manifold property. Therefore, it is more complete to describe the fast motions off the slow manifold for severe weather than the PV term. These advantages are naturally handed on and inherited by the ERI-based thermally-coupled vorticity equation. Then the ERI-based thermally-coupled vorticity equation is further transformed and compared with the traditional vorticity equation. The main difference between the two equations is the term which describes the contribution of the solenoid term to the vertical vorticity development. In a barotropic flow, the solenoid term disappears, then the ERI-based thermally-coupled vorticity equation can regress to the traditional vorticity equation.展开更多
Due to the importance of the mass forcing induced by precipitation and condensation in moist processes, the La- grangian continuity equation without a source/sink term utilized to prove the Ertel-Rossby invariant （ER...Due to the importance of the mass forcing induced by precipitation and condensation in moist processes, the La- grangian continuity equation without a source/sink term utilized to prove the Ertel-Rossby invariant （ERI） and its con- servation property is re-derived considering the mass forcing. By introducing moist enthalpy and moisture entropy, the baroclinic ERI could be adapted to moist flow. After another look at the moist ERI, it is deployed as the dot product be- tween the generalized velocity and the generalized vorticity in moist flow, which constitutes a kind of generalized helicity. Thus, the baroclinic ERI is further extended to the moist case. Moreover, the derived moist ERI forumla remains formally consistent with the dry version, no matter whether mass forcing is present. By using the Weber transformation and the Lagrangian continuity equation with a source/sink effect, the conservation property of the baroclinic ERI in moist flow is revisited. The presence or absence of mass forcing in the Lagrangian continuity equation determines whether or not the baroclinic ERI in moist flow is materially conserved. In other words, it would be qualified as a quasi-invariant but only being dependent on the circumstances. By another look at the moist baroclinic ERI, it is surely a neat formalism with a simple physical explanation, and the usefulness of its anomaly in diagnosing atmospheric flow is demonstrated by case study.展开更多
The moist atmosphere with occurring precipitation is considered to be a multiphase fluid composed of dry air, water vapor and hydrometeors. These compositions move with different velocities： they take a macroscopic m...The moist atmosphere with occurring precipitation is considered to be a multiphase fluid composed of dry air, water vapor and hydrometeors. These compositions move with different velocities： they take a macroscopic motion with a reference velocity and a relative motion with a velocity deviated from the reference velocity. The reference velocity can be chosen as the velocities of dry air, a gas mixture and the total air mixture. The budget equations of continuity and momentum are formulated in the three reference-velocity frames. It is shown that the resulting equations are dependent on the chosen reference velocity. The diffusive flux due to compositions moving with velocities deviated from the reference velocity and the internal sources due to the phase transitions of water substances result in additional source terms in continuity and momentum equations. A continuity equation of the total mass is conserved and free of diffusive flux divergence if the reference velocity is referred to the velocity of the total air mixture. However, continuity equations in the dry-air and gas- mixture frames are not conserved due to the mass diffusive flux divergence. The diffusive flux introduces additional source terms in the momentum equation. In the dry-air frame, the diffusive flux of water substances and the phase transitions of water substances contribute to the change of the total momentum. The additional sources of total momentum in the frame of a gas mixture are associated with the diffusive flux of hydrometeors, the phase transitions of hydrometeors and the gas- mixture diffusive flux. In the frame of total air mixture, the contribution to the total momentum comes from the diffusive flux of all atmospheric compositions instead of the phase transitions. The continuity and momentum equations derived here are more complicated than the traditional model equations. With increasing computing power, it becomes possible to simulate atmospheric processes with these sophisticated equations. It is helpful to the improvement of precipitation forecast.展开更多
文摘A new tracer is presented to diagnose tropical cyclones （TCs） and their correspondent rainfall. It is defined as water vapour potential vorticity （WPV） by replacing potential temperature with specific humidity in the potential vorticity （PV）. The WPV is compared with PV and moist potential vorticity （MPV） in diagnosing three tropical cyclone cases occurred in North-West Pacific during 10 July to 21 July 2005 （Haitang）, 30 July to 9 August 2005 （Matsa） and 25 September to 3 October 2005 （Longwang） separately. The results show that in tracing the track of TCs, WPV is not nicer than PV but better than MPV. While diagnosing TCs＇ onshore rainfall, WPV is better than MPV in all the three cases. Moreover, the advection of WPV is a good indication of TC rainfall after its landing.
基金Project supported by the National Key Basic Research and Development Project of China (Grant No.2012CB417201)the National Natural Sciences Foundation of China (Grant Nos.40930950 41075043,41275065,and 41075044)the 985 Program of Zhejiang University (Grant No.188020+193432602/215)
文摘The effects of water and ice clouds on the cloud microphysical budget associated with rainfall are investigated through the analysis of grid-scale data from a series of two-dimensional cloud-resolving model equilibrium sensitivity simulations. The model is imposed without large-scale vertical velocity. In the control experiment, the contribution from rainfall （cM） associated with net evaporation and hydrometeor loss/convergence is about 29% of that from the rainfall （Cm） associated with net condensation and hydrometeor gain/divergence and about 39% of that from the rainfall （CM） associated with net condensation and hydrometeor loss/convergence. The exclusion of ice clouds enhances rainfall contribution of CM, whereas it reduces rainfall contributions of Cm and cM. The removal of radiative effects of water clouds increases rainfall contribution of CM, barely changes rainfall contribution of Cm and reduces the rainfall contribution of cM in the presence of the radiative effects of ice clouds. Elimination of the radiative effects of water clouds reduces the rainfall contributions of CM and Cm, whereas it increases the rainfall contribution of cM in the absence of the radiative effects of ice clouds.
基金Supported by the National Natural Science Foundation of China under Grant No 40433007, and the Fund for 0utstanding 0versea Scholars of Chinese Academy of Sciences under Grant No 2004-2-7.
文摘As a useful index, i.e. the Richardson number Ri, is modified in non-uniform saturated moist flow, based on the fact that liquid water is partially dropped out in parcel air. This is more realistic in real moist atmosphere, especially in the rainfall process. The modified Ri presents adequately the influence of numerator, i.e. Brunt- Vaisala frequency （BVF）, on instability. Compared to several former formulae generalized by Durran and Klemp, the modified Ri evidently decreases the stability in rainy regions. In theory, the modified BVF and Ri fix the discontinuity of latent heat release in the transition areas between saturated and unsaturated air by introducing the condensation probability function. Furthermore, the diagnostic analysis of the modified Ri validates the rationality of its application in the non-uniform saturated moist process.
文摘The bimodal structure of the Meiyu front system is readdressed after Zhou et al.（2005）. The physical mechanism of the formation of the bimodal distribution is discussed. The bimodal structure of the Melyu front system considerably results from atmospheric moisture gradients, though atmospheric temperature gradients are also not negligible. According to the definition of equivalent potential temperature, and by scale analysis, we find that atmospheric equivalent potential temperature gradients, which could be regarded as an indicator of the Meiyu front system, could be mainly attributed to the variations of atmospheric potential temperature gradients with a scaling factor of 1 and moisture gradients multiplied by a scaling factor of an order of about 2.5 × 10^3, which means that small variations of atmospheric moisture gradients could lead to large variations of equivalent potential temperature gradients, and thus large variations of the Meiyu front system. Quantitative diagnostics with a mesoscale simulation data in the vicinity of the Meiyu front system show that moisture gradients contribute to equivalent potential temperature gradients more than potential temperature gradients.
基金supported by the Special Scientific Research Fund of the Meteorological Public Welfare of the Ministry of Sciences and Technology,China(Grant No.GYHY201406003)the Open Research Fund Program of Plateau Atmosphere and Environment Key Laboratory of Sichuan Province,China(Grant No.PAEKL-2015-K3)the National Natural Science Foundation of China(Grant Nos.41375054,41575064,91437215,41405055 and 41375052)
文摘Considering some simple topological properties of vorticity vector, the frozen-in property of vorticity herein is revis- ited. A vortex line, as is analogous to velocity vector along a streamline, is defined as such a coincident material （curve） line that connects many material fluid elements, on which the local vorticity vector for each fluid element is also tangent to the vortex line. The vortex line evolves in the same manner as the material line that it is initially associated with. The vortex line and the material line are both oriented to the same directions, and evolve with the proportional magnitude, just like being ＇frozen＇ or ＇glued＇ to the material elements of the fluid under the barotropic assumption. To relax the limits of incompressible and barotropic atmosphere, the frozen-in property is further derived and proved in the baroclinic case. Then two effective usages are given as examples. One is the derivation of potential vorticity conservation from the frozen-in property in both barotropic and baroclinic atmospheres, as a theory application, and the other is used to illuminate the vorticity generation and growth in ideal cases and real severe weather process, e.g., in squall line, tornado, and other se- vere convection weather with vortex. There is no necessity to derive vorticity equation, and this method is very intuitive to explain vorticity development qualitatively, especially for fast analysis for forecasters. Certainly, by investigating the evolution of vortex line, it is possible to locate the associated line element vector and its development on the basis of the frozen-in property of vorticity. Because it is simple and visualized, it manifests broad application prospects.
基金supported by the National Basic Research Program of China(Grant No.2014CB441402)the National Natural Science Foundation of China(Grant Nos.41275065,41075044,and 41075043)the 985 Program of Zhejiang University
文摘The precipitation efficiency and its relationship to physical factors are examined by analyzing a two-dimensional cloud-resolving model simulation during TOGA COARE in this study. The basic physical factors include convective avail- able potential energy, water-vapor convergence, vertical wind shear, cloud ratio, sea surface temperature, air temperature, and precipitable water. Precipitation efficiencies do not show a close relationship to air temperature nor to sea surface tem- perature nor to precipitable water. The precipitation efficiency increases as the water-vapor convergence rate increases and vertical wind shear weakens, whereas it decreases as the convective available potential energy dissipates and anvil clouds develop.
基金Project supported by the National Basic Research Program of China (Grant No. 2012CB417201)the National Natural Science Foundation of China (Grant Nos. 41075034,40930950,40975034,and 41075044)
文摘The effects of sea surface temperature（SST）,cloud radiative and microphysical processes,and diurnal variations on rainfall statistics are documented with grid data from the two-dimensional equilibrium cloud-resolving model simulations.For a rain rate of higher than 3 mm.h 1,water vapor convergence prevails.The rainfall amount decreases with the decrease of SST from 29℃ to 27℃,the inclusion of diurnal variation of SST,or the exclusion of microphysical effects of ice clouds and radiative effects of water clouds,which are primarily associated with the decreases in water vapor convergence.However,the amount of rainfall increases with the increase of SST from 29℃ to 31℃,the exclusion of diurnal variation of solar zenith angle,and the exclusion of the radiative effects of ice clouds,which are primarily related to increases in water vapor convergence.For a rain rate of less than 3 mm.h 1,water vapor divergence prevails.Unlike rainfall statistics for rain rates of higher than 3 mm.h 1,the decrease of SST from 29℃ to 27℃ and the exclusion of radiative effects of water clouds in the presence of radiative effects of ice clouds increase the rainfall amount,which corresponds to the suppression in water vapor divergence.The exclusion of microphysical effects of ice clouds decreases the amount of rainfall,which corresponds to the enhancement in water vapor divergence.The amount of rainfall is less sensitive to the increase of SST from 29℃ to 31℃ and to the radiative effects of water clouds in the absence of the radiative effects of ice clouds.
基金supported by the National Basic Research Program of China(Grant No.2013CB430105)the Key Research Program of the Chinese Academy of Sciences(Grant No.KZZD-EW-05-01)+2 种基金the National Natural Science Foundation of China(Grant Nos.41375054 and 41375052)the Special Scientific Research Fund of the Meteorological Public Welfare of the Ministry of Sciences and Technology,China(Grant No.GYHY201406003)the Opening Foundation of the State Key Laboratory of Severe Weather,Chinese Academy of Meteorological Sciences(Grant No.2012LASW-B02)
文摘For the potential vorticity （PV） invariant, there is a PV-based complete-form vorticity equation, which we use heuris- tically in the present paper to answer the following question： for the Ertel-Rossby invariant （ERI）, is there a corresponding vorticity tendency equation？ Such an ERI-based thermally-coupled vorticity equation is derived and discussed in detail in this study. From the obtained new vorticity equation, the vertical vorticity change is constrained by the vertical velocity term, the term associated with the slope of the generalized momentum surface, the term related to the horizontal vorticity change, and the baroclinic or solenoid term. It explicitly includes both the dynamical and thermodynamic factors＇ influence on the vorticity change. For the ERI itself, besides the traditional PV term, the ERI also includes the moisture factor, which is excluded in dry ERI, and the term related to the gradients of pressure, kinetic energy, and potential energy that reflects the fast-manifold property. Therefore, it is more complete to describe the fast motions off the slow manifold for severe weather than the PV term. These advantages are naturally handed on and inherited by the ERI-based thermally-coupled vorticity equation. Then the ERI-based thermally-coupled vorticity equation is further transformed and compared with the traditional vorticity equation. The main difference between the two equations is the term which describes the contribution of the solenoid term to the vertical vorticity development. In a barotropic flow, the solenoid term disappears, then the ERI-based thermally-coupled vorticity equation can regress to the traditional vorticity equation.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.41375054,41575064,and 91437215)the Opening Foundation of the State Key Laboratory of Severe Weather,Chinese Academy of Meteorological Sciences(Grant Nos.2015LASW-B01 and 2015LASW-A02)
文摘Due to the importance of the mass forcing induced by precipitation and condensation in moist processes, the La- grangian continuity equation without a source/sink term utilized to prove the Ertel-Rossby invariant （ERI） and its con- servation property is re-derived considering the mass forcing. By introducing moist enthalpy and moisture entropy, the baroclinic ERI could be adapted to moist flow. After another look at the moist ERI, it is deployed as the dot product be- tween the generalized velocity and the generalized vorticity in moist flow, which constitutes a kind of generalized helicity. Thus, the baroclinic ERI is further extended to the moist case. Moreover, the derived moist ERI forumla remains formally consistent with the dry version, no matter whether mass forcing is present. By using the Weber transformation and the Lagrangian continuity equation with a source/sink effect, the conservation property of the baroclinic ERI in moist flow is revisited. The presence or absence of mass forcing in the Lagrangian continuity equation determines whether or not the baroclinic ERI in moist flow is materially conserved. In other words, it would be qualified as a quasi-invariant but only being dependent on the circumstances. By another look at the moist baroclinic ERI, it is surely a neat formalism with a simple physical explanation, and the usefulness of its anomaly in diagnosing atmospheric flow is demonstrated by case study.
基金Project supported by the National Basic Research Program of China(Grant No.2009CB421505)the Key Program of the Chinese Academy of Sciences(Grant No.KZZD-EW-05)+2 种基金the National Natural Sciences Foundation of China(Grant Nos.41175060,40930950,and 41005005)the Project of CAMS,China(Grant No.2011LASW-B15)the Spectial Scientific Research Fund of Meteorological Public Welfare of Ministry of Sciences and Technology,China(Grant No.GYHY200906004)
文摘The moist atmosphere with occurring precipitation is considered to be a multiphase fluid composed of dry air, water vapor and hydrometeors. These compositions move with different velocities： they take a macroscopic motion with a reference velocity and a relative motion with a velocity deviated from the reference velocity. The reference velocity can be chosen as the velocities of dry air, a gas mixture and the total air mixture. The budget equations of continuity and momentum are formulated in the three reference-velocity frames. It is shown that the resulting equations are dependent on the chosen reference velocity. The diffusive flux due to compositions moving with velocities deviated from the reference velocity and the internal sources due to the phase transitions of water substances result in additional source terms in continuity and momentum equations. A continuity equation of the total mass is conserved and free of diffusive flux divergence if the reference velocity is referred to the velocity of the total air mixture. However, continuity equations in the dry-air and gas- mixture frames are not conserved due to the mass diffusive flux divergence. The diffusive flux introduces additional source terms in the momentum equation. In the dry-air frame, the diffusive flux of water substances and the phase transitions of water substances contribute to the change of the total momentum. The additional sources of total momentum in the frame of a gas mixture are associated with the diffusive flux of hydrometeors, the phase transitions of hydrometeors and the gas- mixture diffusive flux. In the frame of total air mixture, the contribution to the total momentum comes from the diffusive flux of all atmospheric compositions instead of the phase transitions. The continuity and momentum equations derived here are more complicated than the traditional model equations. With increasing computing power, it becomes possible to simulate atmospheric processes with these sophisticated equations. It is helpful to the improvement of precipitation forecast.
