Hurricanes Ivan, Jeanne, Karl (2004) and mid-latitude trough interactions

Summary Singular vectors (SVs) constructed from the adjoint model of the U.S. Naval Operational Global Atmosphere Prediction System (NOGAPS) for three Atlantic hurricanes in 2004, Ivan, Jeanne and Karl, are examined to understand interactions between them and a mid-latitude trough system. By optimizing the perturbation energy localized in a small region centered at the 48-hour projected position of a tropical cyclone, the initial time singular vector represents the sensitive region to the final state within the specified region for a specified optimization period. For hurricane Ivan, the SV analysis reveals the merging of a shortwave mid-latitude trough and Ivan to form a new trough system. This new trough system impacted the evolution of hurricane Jeanne in subsequent time through the upstream flow of the trough that moved toward Jeanne. This is consistent with previous studies on the sensitivity of tropical cyclone prediction using SV diagnostics. The SV associated with Jeanne at later stage shows that Jeanne influenced the third hurricane Karl through the trough system as Karl went through extratropical transition and became part of the trough. This effect is magnified when the SV is computed using the moist adjoint system containing large scale precipitation. Detailed diagnostics of the SVs for individual components at different levels show that the sensitivity associated with the trough is very similar for those optimized for Jeanne and Karl, respectively, thus providing evidence that the mid-latitude trough impacted Jeanne and Karl at the same time. This study demonstrates the capability of singular vector in diagnosing complicated interactions among a mid-latitude trough and three co-existing tropical cyclones.     

Application and Characteristic Analysis of the Moist Singular Vector in GRAPES-GEPS

The singular vector (SV) initial perturbation method can capture the fastest-growing initial perturbation in a tangent linear model (TLM). Based on the global tangent linear and adjoint model of GRAPES-GEPS (Global/Regional Assimilation and Prediction System—Global Ensemble Prediction System), some experiments were carried out to analyze the structure of the moist SVs from the perspectives of the energy norm, energy spectrum, and vertical structure. The conclusions are as follows: The evolution of the SVs is synchronous with that of the atmospheric circulation, which is flow-dependent. The moist and dry SVs are located in unstable regions at mid-to-high latitudes, but the moist SVs are wider, can contain more small- and medium-scale information, and have more energy than the dry SVs. From the energy spectrum analysis, the energy growth caused by the moist SVs is reflected in the relatively small-scale weather system. In addition, moist SVs can generate perturbations associated with large-scale condensation and precipitation, which is not true for dry SVs. For the ensemble forecasts, the average anomaly correlation coefficient of large-scale circulation is better for the forecast based on moist SVs in the Northern Hemisphere, and the low-level variables forecasted by the moist SVs are also improved, especially in the first 72 h. In addition, the moist SVs respond better to short-term precipitation according to statistical precipitation scores based on 10 cases. The inclusion of the large-scale condensation process in the calculation of SVs can improve the short-term weather prediction effectively.     

包含“开关”变量的MM5四维变分资料同化系统

数值模式中的湿物理过程对于模拟各种尺度的天气现象非常重要,但它会使得模式方程的状态变量不连续,这种不连续在模式程序中表现为“开关”变量。本文对包括Kuo降水参数化方案的非静力中尺度数值模式MM5的四维变分资料同化系统进行研究,利用对实际降水的模拟,比较详细地讨论了有关的“开关”变量以及切向线性化和伴随问题。结果表明：对于一个离散的数值模式,保持“开关”变量与基态一致,用伴随码方法构造的伴随模式计算的梯度值能够为最小化过程提供较好的下降方向;Kuo方案中对流每隔一个积分步的交替发生并不影响目标函数最小化的收敛速度;“开关”变量的存在也不影响将风、温度、气压和比湿结合起来同化对MM5降水预报准确性的提高。     

含有开关参数化物理过程的模式变分资料同化的非光滑优化方法:几个理论问题

时间、空间上离散的模式如果含有带开关的参数化物理过程，某些对应的变分同化问题可以看成为非光滑优化问题。本系统地讨论了与此相关的几个理论问题。首先，利用次梯度这个非光滑优化中的基本概念可以对通常的伴随方程的解进行清楚的解释和定义。利用一个带对流调整的多层扩散模式，演示了通常的伴随方程的解在奇异点处不是由代价函数的Gateaux导数构成，而是代价函数的一个次梯度。其次，在非光滑优化的框架下对现有的解决这类问题的方法进行了评述。这些方法包括：（1）利用光滑优化方法和通常的伴随模式，并且讨论了这个方法的收敛条件；（2）正则化方法。这个方法是把模式中不光滑的项用光滑的项近似，以把问题变为光滑优化问题。（3）次梯度方法。这个方法利用通常的伴随模式来计算一个次梯度，是收敛的算法，不过收敛速度很慢。（4）非光滑优化中的Bundle方法。这个方法比次梯度方法收敛得快，不过需要利用所有的次梯度信息。由于计算所有的次梯度十分困难，现有的Bundle方法大都进行了一些改变，仅需要用户能够计算出一个次梯度。不过这个改变是无奈的，多个次梯度的信息可以提高Bundle方法的效率。本最主要的工作是提出了集值伴随方程的概念。集值伴随模式可以在奇异点处计算出所有支撑次梯度，因此利用集值伴随方程有可能提出基于Bundle方法的更好算法。     

Adjoint sensitivity study on idealized explosive cyclogenesis

The adjoint sensitivity related to explosive cyclogenesis in a conditionally unstable atmosphere is investigated in this study.The PSU/NCAR limited-area,nonhydrostatic primitive equation numerical model MM5 and its adjoint system are employed for numerical simulation and adjoint computation,respectively.To ensure the explosive development of a baroclinic wave,the forecast model is initialized with an idealized condition including an idealized two-dimensional baroclinic jet with a balanced three-dimensional moderateamplitude disturbance,derived from a potential vorticity inversion technique.Firstly,the validity period of the tangent linear model for this idealized baroclinic wave case is discussed,considering different initial moisture distributions and a dry condition.Secondly,the 48-h forecast surface pressure center and the vertical component of the relative vorticity of the cyclone are selected as the response functions for adjoint computation in a dry and moist environment,respectively.The preliminary results show that the validity of the tangent linear assumption for this idealized baroclinic wave case can extend to 48 h with intense moist convection,and the validity period can last even longer in the dry adjoint integration.Adjoint sensitivity analysis indicates that the rapid development of the idealized baroclinic wave is sensitive to the initial wind and temperature perturbations around the steering level in the upstream.Moreover,the moist adjoint sensitivity can capture a secondary high sensitivity center in the upper troposphere,which cannot be depicted in the dry adjoint run.     

Adjoint-based Sensitivity Analysis of a Mesoscale Low on the Mei-yu Front and Its Implicationsfor Adaptive Observation

An adjoint sensitivity analysis of one mesoscale low on the mei-yu Front is presented in this paper.The sensitivity gradient of simulation error dry energy with respect to initial analysis is calculated. And after verifying the ability of a tangent linear and adjoint model to describe small perturbations in the nonlinear model, the sensitivity gradient analysis is implemented in detail. The sensitivity gradient with respect to different physical fields are not uniform in intensity, simulation error is most sensitive to the vapor mixed ratio. The localization and consistency are obvious characters of horizontal distribution of the sensitivity gradient, which is useful for the practical implementation of adaptive observation. The sensitivity region tilts to the northwest with height increasing; the singular vector calculation proves that this tilting characterizes a quick-growing structure, which denotes that using the leading singular vectors to decide the adaptive observation region is proper. When connected with simulation of a mesoscale low on the mei-yu Front, the sensitivity gradient has the following physical characters: the obvious sensitive region is mesoscale, concentrated in the middle-upper troposphere, and locates around the key system; and the sensitivity gradient of different physical fields correlates dynamically.     

Adjoint-based Sensitivity Analysis of a Mesoscale Low on the Mei-yu Front and Its Implications for Adaptive Observation

An adjoint sensitivity analysis of one mesoscale low on the mei-yu Front is presented in this paper. The sensitivity gradient of simulation error dry energy with respect to initial analysis is calculated. And after verifying the ability of a tangent linear and adjoint model to describe small perturbations in the nonlinear model, the sensitivity gradient analysis is implemented in detail. The sensitivity gradient with respect to different physical fields are not uniform in intensity, simulation error is most sensitive to the vapor mixed ratio. The localization and consistency are obvious characters of horizontal distribution of the sensitivity gradient, which is useful for the practical implementation of adaptive observation. The sensitivity region tilts to the northwest with height increasing; the singular vector calculation proves that this tilting characterizes a quick-growing structure, which denotes that using the leading singular vectors to decide the adaptive observation region is proper. When connected with simulation of a mesoscale low on the mei-yu Front, the sensitivity gradient has the following physical characters： the obvious sensitive region is mesoscale, concentrated in the middle-upper troposphere, and locates around the key system; and the sensitivity gradient of different physical fields correlates dynamically.     

基于总能量模的GRAPES全球模式奇异向量扰动研究

以发展基于奇异向量技术为初值扰动的GRAPES全球集合预报系统为目的,在GRAPES模式及其干动力框架下的切线性、伴随模式基础上开展了以总能量模为权重算子的奇异向量计算技术研究,建立奇异向量的计算求解模块,并通过奇异向量检验方法和切线性近似方法验证了奇异向量求解的正确性.通过对中高纬度的GRAPES奇异向量水平结构的线性演变分析,证实了在最优时间间隔内GRAPES奇异向量能够快速增长,并能描述中高纬度大气的斜压不稳定特征.分析在初始时刻和最优化时间间隔时刻的GRAPES奇异向量总能量及其分量(动能和势能)的垂直分布特征,发现在中高纬度区域,GRAPES奇异向量能够描述对流层不同层次的斜压不稳定增长特征.     

Characteristics of adjoint sensitivity to potential vorticity

Structures of adjoint sensitivities to potential vorticity for specific initial and final norm are investigated for a short-range cyclone forecast in a three-dimensional quasigeostrophic (QG) model. Moreover, adjoint sensitivities to potential vorticity are compared with nonlinear sensitivities calculated for the same cyclogenesis case in the QG model. The adjoint sensitivities using different initial and final norms (e.g., total QG disturbance energy and potential enstrophy) show approximately similar characteristics for the horizontal and vertical structures and evolutions. Consistent with previous studies, the horizontal structure of the adjoint sensitivity is smaller for the energy norm than for the potential enstrophy norm. The dynamical mechanism of cyclone development by adjoint sensitivity coincides with that of nonlinear sensitivity, with slight differences in the region of sensitivity maxima over the upstream (nascent) low for the adjoint (nonlinear) sensitivity. The adjoint sensitivities show different vertical distributions from the nonlinear sensitivities. Consistent with the sensitive regions denoted by singular vectors and error evolution in the QG model, maxima of the adjoint sensitivities are located at both the upper and lower boundaries, with prominent secondary peaks in the lower to mid-troposphere of the domain. The level of the secondary maxima changes depending on the initial and final norm used. The secondary peak is located in the lower to mid- (mid-) troposphere for the total QG disturbance energy (potential enstrophy) as the initial and final norm. Based on the correspondence in the level of the sensitivity maxima in the interior of the domain between the adjoint and nonlinear sensitivities, adjoint sensitivities may serve as an alternative to nonlinear sensitivities given the enormous computing expenses in nonlinear sensitivity calculation.     

基于奇异矢量的优化短期集合预报

在1-2 d的短期预报中,由奇异矢量构建的初始扰动主要是线性发展,为了防止在积分终止时刻,由同一奇异矢量导出的正负初始扰动的积分在集合平均时互相抵消,文中首先通过理论推导和实际计算证明了对集合成员进行优化的必要性,以及从不同奇异矢量导出的集合成员中,表现好于控制预报的一组成员相对于控制预报的离差恒大于或恒小于表现劣于控制预报的另一组成员,利用这个特征,在做集合预报时,把奇异矢量导出的正负两组预报分成离差相对大一组、离差相对小一组,就可以避免求集合平均时成员相互抵消,从而提出了一种优化基于奇异矢量的短期集合预报的方法.文中使用NCAR/PSU(美国国家大气研究中心/宾夕法尼亚大学)中尺度有限区域模式MM5第1版,及其对应切线性、伴随模式,对1999年夏季发生的两个梅雨锋低涡个例作了分析,在计算奇异矢量时采用了干能量模,分析结果表明:相对于正负两个初始扰动都入选的集合,严格按照这种方法挑选出来的优化集合可以有效地提高集合平均的精确度.在生成初始扰动的方法上,文中的计算表明,相对于用单个奇异矢量生成初始扰动,把正交的多个奇异矢量累加起来导出的初始扰动具有更大的增长率,能有效地增大集合成员间的离差,提高集合成员的预报精度.     

A modified moist ageostrophic <Emphasis Type="Italic">Q</Emphasis> vector

The quasi-geostrophic Q vector is an important rainfall associated with large-scale weather systems diagnostic tool for studying development of surface and is calculated using data at single vertical level. When ageostrophic Q vector was introduced, it required data at two vertical levels. In this study, moist ageostrophic Q vector is modified so that it can be calculated using data at a single vertical level. The comparison study between the original and modified moist ageostrophic Q vectors is conducted using the data from 5 to 6 July 1991 during the torrential rainfall event associated with the Changjiang-Huaihe mei-yu front in China. The results reveal that divergences of original and modified moist ageostrophic Q vectors have similar horizontal distributions and their centers are almost located in the precipitation centers. This indicates that modified moist ageostrophic Q vector can be used to diagnose convective development with reasonable accuracy.     

集合预报多尺度奇异向量初值扰动方法研究

目前国际上采用的奇异向量集合预报初值扰动法对于初值不确定性的描述存在一定的不足,为了更有效地反映初始误差的时空多尺度特性,基于GRAPES全球奇异向量计算技术,计算了不同空间分辨率及不同最优时间间隔的多个尺度的奇异向量,并采用基于高斯分布的线性组合法来构造多尺度奇异向量的扰动初值,以代表在相空间中增长最快的多尺度初值误差模态。通过2019年1月19日的初值扰动集合预报试验,对比分析了单一尺度奇异向量初值扰动法与多尺度初值扰动法的扰动特征及集合预报效果。结果表明,多尺度奇异向量初值扰动法为区域集合预报提供的初始扰动场是合理的,扰动的大小随时间增长,且在空间分布上较好地反映了当前大气的斜压不稳定特征。此外,多尺度奇异向量扰动可以描述一定的大尺度以及中小尺度运动误差特征,较单一尺度奇异向量扰动能反映出更多初始场的不确定性信息。检验分析表明,GRAPES多尺度奇异向量集合预报在集合一致性、连续等级概率评分、离群值等方面有一定的优势,相比于单一尺度奇异向量法有较好的预报技巧。因此,基于GRAPES的多尺度奇异向量初值扰动法对于集合预报的预报效果有一定的提高,能为构建一套完善的GRAPES区域奇异向量集合预报系统提供一定的科学依据和应用基础。      

The impact of atmospheric nonlinearities on the fastest growth of ENSO prediction error

In this paper we explore the impact of atmospheric nonlinearities on the optimal growth of initial condition error of El Niño and the Southern Oscillation (ENSO) prediction using singular vector (SV) analysis. This is performed by comparing and analyzing SVs of two hybrid coupled models (HCMs), one composed of an intermediate complexity dynamical ocean model coupled with a linear statistical atmospheric model, and the other one with the same ocean model coupled with a nonlinear statistical atmosphere. Tangent linear and adjoint models for both HCMs are developed. SVs are computed under the initial conditions of seasonal background and actual ENSO cycle simulated by the ocean model forced with the real wind data of 1980–1999. The optimization periods of 3, 6 and 9 months are individually considered. The results show that the first SVs in both HCMs are very similar to each other, characterized by a central east-west dipole pattern spanning over the entire tropical Pacific. The spatial patterns of the leading SV in both HCMs are not sensitive to optimization periods and initial time. However, the first singular value, indicating the optimal growth rate of prediction error, displays considerable differences between the two HCMs, indicating a significant impact of atmospheric nonlinearities on the optimal growth of ENSO prediction error. These differences are greater with increasing optimization time, suggesting that the impact of atmospheric nonlinearities on the optimal growth of prediction error becomes larger for a longer period of prediction.     

Conjugate Gradient Algorithm in the Four-Dimensional Variational Data Assimilation System in GRAPES

Minimization algorithms are singular components in four-dimensional variational data assimilation (4DVar). In this paper, the convergence and application of the conjugate gradient algorithm (CGA), which is based on the Lanczos iterative algorithm and the Hessian matrix derived from tangent linear and adjoint models using a non-hydrostatic framework, are investigated in the 4DVar minimization. First, the influence of the Gram-Schmidt orthogonalization of the Lanczos vector on the convergence of the Lanczos algorithm is studied. The results show that the Lanczos algorithm without orthogonalization fails to converge after the ninth iteration in the 4DVar minimization, while the orthogonalized Lanczos algorithm converges stably. Second, the convergence and computational efficiency of the CGA and quasi-Newton method in batch cycling assimilation experiments are compared on the 4DVar platform of the Global/Regional Assimilation and Prediction System (GRAPES). The CGA is 40% more computationally efficient than the quasi-Newton method, although the equivalent analysis results can be obtained by using either the CGA or the quasi-Newton method. Thus, the CGA based on Lanczos iterations is better for solving the optimization problems in the GRAPES 4DVar system.     

Mesoscale Moist Adjoint Sensitivity Study of a Mei-yu Heavy Rainfall Event

The mesoscale moist adjoint sensitivities related to the initiation of mesoscale convective systems (MCSs) are evaluated for a mei-yu heavy rainfall event. The sensitivities were calculated on a realistic background gained from a four-dimensional variational data assimilation of precipitation experiment to make the sensitivity computation possible and reasonable within a strong moist convective event at the mesoscale. The results show that the computed sensitivities at the mesoscale were capable of capturing the factors affecting MCS initiation. The sensitivities to the initial temperature and moisture are enhanced greatly by diabatic processes, especially at lower levels, and these sensitivities are much larger than those stemming from the horizontal winds, which implies that initiation of MCSs is more sensitive to low-level temperature and moisture perturbations rather than the horizontal winds. Moreover, concentration of sensitivities at low levels reflects the characteristics of the mei-yu front. The results provide some hints about how to improve quantitative precipitation forecasts of mei-yu heavy rainfall, such as by conducting mesoscale targetted observations via the adjoint-based method to reduce the low-level errors in the initial temperature and moisture.     

Adaptive observations in the context of 4D-Var data assimilation

Summary The design of adaptive observations strategies must account for the particular properties of the data assimilation method. A new adjoint sensitivity approach to the targeted observations problem is proposed in the context of four-dimensional variational data assimilation (4D-Var). The method is based on a periodic update of the adjoint sensitivity field that takes into account the interaction between time distributed adaptive and routine observations. Information provided by all previously located observations is used to identify best locations for new targeted observations. Adaptive observations at distinct instants in time are selected in a sequential manner such that the method is only suboptimal. The selection algorithm proceeds backward in time and requires only one additional adjoint model integration in the assimilation window. Therefore, the method is very efficient and is suitable for practical applications. A comparative performance analysis is presented using the traditional adjoint sensitivity method as well as the total energy singular vectors technique as alternative adaptive strategies. Numerical experiments are performed in the twin experiments framework using a two-dimensional global shallow water model in spherical coordinates and an explicit Turkel-Zwas discretization scheme. Data from a NASA 500mb analysis valid for 00Z 16 Mar 2001 6h obtained with the GEOS-3 model was used to specify the geopotential height at the initial time and the initial velocities were obtained from a geostrophic balance. Numerical results show that the new adaptive observations approach is a promising method for targeted observations and its implementation is feasible for large scale atmospheric models.     

Diagnostic analyses and application of the moist ageostrophic vector<Emphasis Type="Italic">Q</Emphasis>

Considering the main thermal forcing factor, which is critical for the development of synoptic systems,the concept of the moist ageostrophic vector Q is introduced. A formula of the moist ageostrophic Q and the ageostrophic diabatic equation, in which the divergence of the moist ageostrophic Q is taken as a single forcing term, is derived. Meanwhile, the moist ageostrophic Q is applied to diagnose a torrential rain process in North China. The results suggest that the moist ageostrophic Q can clearly reveal the system development during the torrential rain process; the corresponding relationship between the divergence of the moist ageostrophic Q and the rainfall area is better than that of the vertical velocity (ω) and the divergence of the dry Q; the 6-h rainfall region can be correctly drawn according to the negative area of the divergence of the moist ageostrophic Q, and its precipitation is positively correlated to the magnitude of the divergence of the moist ageostrophic Q. The research provides valuable information for improving short-term weather forecast.     

Further analysis of singular vector and ENSO predictability in the Lamont model—Part I: singular vector and the control factors

In this study, singular vector analysis was performed for the period from 1856 to 2003 using the latest Zebiak–Cane model version LDEO5. The singular vector, representing the optimal growth pattern of initial perturbations/errors, was obtained by perturbing the constructed tangent linear model of the Zebiak–Cane model. Variations in the singular vector and singular value, as a function of initial time, season, ENSO states, and optimal period, were investigated. Emphasis was placed on exploring relative roles of linear and nonlinear processes in the optimal perturbation growth of ENSO, and deriving statistically robust conclusions using long-term singular vector analysis. It was found that the first singular vector is dominated by a west–east dipole spanning most of the equatorial Pacific, with one center located in the east and the other in the central Pacific. Singular vectors are less sensitive to initial conditions, i.e., independence of seasons and decades; while singular values exhibit a strong sensitivity to initial conditions. The dynamical diagnosis shows that the total linear and nonlinear heating terms play opposite roles in controlling the optimal perturbation growth, and that the linear optimal perturbation is more than twice as large as the nonlinear one. The total linear heating causes a warming effect and controls two positive perturbation growth regions: one in the central Pacific and the other in the eastern Pacific; whereas the total linearized nonlinear advection brings a cooling effect controlling the negative perturbation growth in the central Pacific.     

结合“海棠”台风（2005）定量分析非绝热加热对湿 Q 矢量诊断能力的影响

湿Q矢量最大特点就是考虑了非绝热加热作用,各种湿Q矢量差异也主要表现在对非绝热加热计算处理方案的不同.因此,通过比较分析非绝热加热作用,可揭示出不同湿Q矢量之间诊断能力的差异.2005年第5号登陆台风"海棠"在7月19日08时20 H 08时,给福建省东北部及浙江省造成大范围暴雨.WRF模式成功模拟出此次台风暴雨过程.文章将结合"海棠"台风(2005)登陆台风暴雨过程,利用 WRF模式模拟输出的气象要素,通过计算降水场,定量分析了非绝热加热作用及其对湿Q矢量诊断能力的影响.结果表明:(1)对于公包括大尺度凝结加热的非绝热加热作用H1及包括了潜热加热(大尺度凝结加热和对流凝结加热)、感热加热和辐射加热的非绝热加热作用H2来讲,局地变化项的强迫作用较垂直平流项、水平平流项的强迫作用约小1-2个量级,可以忽略不计,垂直平流项的强迫作用是主要成分,对于水平平流项来讲,尽管其强迫作用明显小于垂直平流项的强迫作用,但也明显大于局地变化项的强迫作用,考虑其将更有利于充分反映H1、H2的强迫作用.对于包括非均匀饱和大气中潜热加热的H3来讲,水平平流项与垂直平流项的强迫作用相当,均为主要成分,而局地变化项的强迫作用为次要成分且不容忽视,对其考虑将有助于全面描述H2的强迫作用.(2)非绝热加热作用H1、H2以及H3强迫产生的24 h累积降水场具有相似的水平分佰特征,三者强迫产生的逐时雨量随时间演变特征也非常相似,这表明水汽凝结潜热是非绝热加热作用的主要成分.(3)进一步结合模拟降水场分析表明,相对于H1强迫产生的降水场来讲,H2与H3强迫产生的降水场更接近模拟结果,这揭示出包含H2的湿Q矢量与包含H2的湿Q矢量诊断能力相近,且对降水反映能力较包含H1的湿Q矢量诊断能力强.(4)不同湿Q矢量各自有其自身诊断特点,根据不同研究目的的需要,可有针对性的选取相应的湿Q矢量来作为研究工具.如需要具体、细敛分析水汽潜热的强迫作用,可以选朋包含H1、H3的湿Q矢量,如仅需考虑总的湿Q矢量强迫作用,则可以直接选用包含H2的湿矢量.     

On the Significance and Use of the Generalized Moist Potential Vorticity Equation

In this paper,the continuity and thermodynamic equations including moisture forcings were derived.Using these two equations and the basic momentum equation of local Cartesian coordinates,the budget equation of generalized moist potential vorticity(GMPV) was derived.The GMPV equation is a good generalization of the Ertel potential vorticity(PV) and moist potential vorticity(MPV) equations.The GMPV equation is conserved under adiabatic,frictionless,barotropic,or saturated atmospheric conditions,and it is closely associated with the horizontal frontogenesis and stability of the real atmosphere.A real case study indicates that term diabatic heating could be a useful diagnostic tool for heavy rainfall events.