ISSN 1006-9895

CN 11-1768/O4

  • Volume 36,Issue 3,2012 Table of Contents
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    • Analyses of the Causes of Severe Drought Occurring in Southwest China from the Fall of 2009 to the Spring of 2010

      2012, 36(3):443-457. DOI: 10.3878/j.issn.1006-9895.2011.11101

      Abstract (10211) HTML (0) PDF 7.74 M (4833) Comment (0) Favorites

      Abstract:A severe drought occurred in Southwest China from the fall of 2009 to the spring of 2010. Either its persistent time and area or decreased amount of rainfall were less observed during the last 50 years. Thus, in this paper, the occurring causes of this drought are analyzed by using the NCEP/NCAR reanalysis data and SST data from the impacts of thermal anomalies in the tropical western Pacific (TWP) and the tropical Indian Ocean (TIO) on the atmospheric circulation over the TWP and South Asia. The results show that during the period from the fall of 2009 to the spring of 2010, both the TWP and the TIO were in a warming state. Under the common thermal effect of both oceans, a strong anticyclonic anomalous circulation appeared in the lower troposphere over the TWP and the South China Sea, which caused not only the strengthening of the southwest flow anomaly, but also the appearance of a low trough anomaly over South China and Central China. In this case, the northwest flow anomaly and descending flow anomaly behind the trough controlled the eastern part of the Tibetan Plateau, and water vapor was difficultly transported from the Bay of Bengal into the Yunnan-Guizhou Plateau (Yun-Gui Plateau in short). Thus, less rainfall for a long time was caused in this region. Moreover, the analysis results also show that the circulation anomaly over the mid- and high latitudes had an important impact on the severe drought. Since the polar wave guide of quasi-stationary planetary wave propagations over the high latitudes was stronger, but the low-latitude wave guide was weaker from the fall of 2009 to the spring of 2010, which led to convergence and divergence of the wave E-P fluxes for quasi-stationary planetary waves in the upper troposphere and the stratosphere over the region about 60°N and in the middle and upper troposphere over the region about 35°N, respectively. Thus, the zonal mean wind was weakened in the upper troposphere and the stratosphere over the region about 60°N, but it was strengthened in the upper troposphere over the region about 35°N. This caused an obviously negative phase of the AO (Arctic Oscillation) and brought strong winter monsoon and eastward tracks of cold waves into East Asia, which led to a weakening of cold air arriving in Southwest China. Thereby, the persistent severe drought occurred in Southwest China.

    • Impacts of Random Error on the Predictability of Chaotic Systems

      2012, 36(3):458-470. DOI: 10.3878/j.issn.1006-9895.2011.11072

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      Abstract:Based on the nonlinear local Lyapunov exponent (NLLE) approach, the influences of random error and initial error on the predictability of the Logistic map and the Lorenz system are studied. The influences of initial error and random error on the predictability mainly depend on their relative magnitudes. When the magnitude of initial error is much greater than that of random error, the predictability limit of two systems is mainly determined by the initial error. On the contrary, when the magnitude of random error is much greater than that of initial error, the predictability limit of two systems is mainly determined by the random error. When the magnitude of initial error is close to that of random error, both of them contribute to the predictability limit of two systems. In addition, the authors have investigated the influences of random error on the predictability by integrating the error growth equations. The results are similar to those obtained using experimental data. This finding indicates that due to the impacts of random error, only an approximation of the true predictability of chaotic systems can be obtained when the random error is sufficiently small. It is impossible to obtain the true predictability for large random errors. The present study also attempts to use the filtering method to reduce the impact of random error on the estimates of the predictability limit of chaotic systems. The results show that by using the high-pass Lanczos filter, both the high-frequency sequence and the noise sequence perform conformably either in intensity or in the evolution of trends. This method can effectively remove the random noise and then improve the estimate of the predictability limit of chaotic systems, which also gives some enlightenment to the removal of the noise contained in observational data.

    • Simulation of Physical Characteristics Evolution in Cloud Merger

      2012, 36(3):471-486. DOI: 10.3878/j.issn.1006-9895.2011.10223

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      Abstract:Physical characteristics evolution in cloud merger is critical to the evolution of cloud precipitation, which is also important for short-term forecasting and study of precipitation. So, in this paper, using WMF (Weather Research and Forecasting) model, the authors simulated a merging process in Guiyang on 5 May 2005, combined radar observations and MICAPS (Meteorological Information Comprehensive Analysis and Processing System) data, and analyzed the processes of precipitation convection merger and the evolution of associated physical characteristics. The cumulus merger processes are of diversification, experience the process from neighbouring isolated cells merging to cell-cloud cluster merging, and neighbouring cloud clusters merging into widespread precipitation system. In the merging processes of several stages, the change of temperature stratification structure curve all shows that unstable energy releases during the merging, and unstable stratification before merging tends to more stable stratification after merging, especially at middle levels, tends to neutral one, which is advantageous for the dominant development scale becoming longer. The physical characteristics alter significantly, which shows that before and after the first merging and complete merging, the maximum precipitation at the convective center all increases strongly. However, the changing of the maximum upward flow velocity is contrary to the changing of the maximum precipitation. The maximum upward flow velocity generally decreases after the merging. While, the average upward flow velocity all decreases before and after the first merging and complete merging. The average precipitation in the whole cloud region mostly tends to increase.

    • The Quantitative Research on Cold Vortex in Summer over Northeast China

      2012, 36(3):487-494. DOI: 10.3878/j.issn.1006-9895.2011.11071

      Abstract (3813) HTML (0) PDF 3.92 M (3350) Comment (0) Favorites

      Abstract:Using daily reanalysis data, released by NCEP/NCAR, about geopotential height from 1981 to 2010 (30 years in total) to retrieve and analyze the cold vortex over Northeast China (CVONC), to extract and analyze the average state of CVONC, the authors define a deviation index on CVONC and discuss its rationality to depict the intensity of CVONC. It shows that: (1) the probability distribution of CVONC's geopotential height of occlusive center at 500 hPa is similar to the Gaussian normal distribution, and the average state of CVONC extracted by the expected value of Gaussian normal distribution hold general characters of CVONC; (2) the definition of deviation index on CVONC based on its average state could represent not only the deflected degree from the average state of CVONC, but also some information about the areas of low pressure, which means that it could indicate the intensity characteristics of CVONC directly.

    • Attenuation Correction of Reflectivity for X-Band Dual-Polarization Radar

      2012, 36(3):495-506. DOI: 10.3878/j.issn.1006-9895.2011.11075

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      Abstract:Strong attenuation in rain affects the detection accuracy and application of the X-band radar. This paper aims to seek a method of attenuation correction for X-band dual-polarization radar in precipitation. Before correction, the radar data are pre-processed with quality control; after analyzing all the methods from the past works, an attenuation correction algorithm is developed which is based on the self-consistent method with constraints; finally some validation methods are studied. Some comparisons are made between the corrected composite reflectivity of the X-band radar and a nearby S-band radar observed at the same time; moreover, the corrected relationships between KDP vs. ZH and AH vs. ZH are also similar to the theoretical values predicted by scattering simulation. In addition, the authors also compare the corrected reflectivity with the surface rain-gauge observations. The analysis results indicate that the corrected reflectivity is more significant than the uncorrected one; specially for the larger area of rainfall (including convective rainfall) using the above attenuation correction algorithm for X-band radar, rainfall amounts can be estimated with higher accuracy.

    • Characteristics of Stratification Structure and Cloud Physics of the Freezing Rain over Southern China in January 2008

      2012, 36(3):507-522. DOI: 10.3878/j.issn.1006-9895.2011.11082

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      Abstract:Southern China suffered four severe freezing rain and snow storm processes during January 2008. In this paper, a classical freezing rain process during 25-29 January 2008 was selected as a research case. Characteristics of stratification structure and cloud physics of the freezing rain were analyzed. Combining with observation, the freezing rain process during 28-29 January 2008 was simulated by the CAMS (Chinese Academy of Meteorological Sciences) mesoscale cloud model. The authors studied characteristics of micro-macroscale structure of cloud system over the freezing rain area and initially analyzed the microphysical process in the cloud and the mechanism of freezing rain formation. The results show that, the stable and thicker melting layer and cold layer at low levels was direct cause that the wide range of freezing rain appeared. Two different types of clouds existed over different freezing rain areas in this freezing rain process. Two types of clouds have different characteristics of stratification structure and cloud physics and mechanism of freezing rain formation. Clouds over the Hunan Province freezing rain area belonged to mixed-phase cloud: the cloud thickness was deeper, the cloud top temperature was lower, and in the clouds there were large amount of ice-phase particles. Under the consideration of stratification ("cold-warm-cold" layer), the freezing rain over Hunan Province was formed by ice-crystal mechanisms (the melting process). That is, the freezing rain developed as the falling snow encounters a layer of warm air, and then the snow completely melted and became rain. As the rain continued to fall, it passed through a thin layer of cold air just above the surface, cooled to a temperature below freezing, and formed supercooled drops. When the supercooled raindrop dropped and struck the ground, or anything else below 0℃, they instantly freeze, forming the freezing rain. However, clouds over the Guizhou Province freezing rain area belonged to warm clouds: the cloud thickness was thinner, the cloud top temperature was higher, and in the clouds there were little ice-phase particles. Under the consideration of stratification ("warm-cold" layer), the freezing rain over Guizhou Province was formed by supercooled warm-rain processes (collision-coalescence process). Supercooled raindrops developed by microscopic cloud droplets collecting one another as they fall. Ice processes were not involved in the formation of these raindrops.

    • An Integrated East Asian Winter Monsoon Index and Its Interannual Variability

      2012, 36(3):523-538. DOI: 10.3878/j.issn.1006-9895.2011.11083

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      Abstract:The collaborative relationship among members of the East Asian winter monsoon (EAWM) system is first examined through the multivariate EOF (MV-EOF). Univariate EOF is then used to define the intensity index of each single system. Based on the above analyses, an integrated index of the East Asian winter monsoon (EAWMII) is defined. The new index exhibits distinct interannual variability and takes into account variations of Siberian high, East Asian trough, and meridional shear of upper-tropospheric zonal wind. Results show that the EAWMII can capture well the continuous weakening of the EAWM since the mid-1980s. It is also statistically significantly correlated with variations of both atmospheric circulation fields and surface temperature during winter. In addition, the EAWMII is closely related to the Arctic Oscillation (AO) index, the Nio3.4 sea surface temperature index, and the North Pacific Oscillation (NPO) index. The impact of AO on the East Asian surface temperature primarily occurs in the middle and high latitudes of Eurasia, Northeast China, and North Japan, etc. The influence of NPO is mainly registered in South China, East China, North Korea, South Korea, and South Japan. It is very likely that the AO affects the EAWM via the NPO.

    • The Preliminary Analysis of the Procedures of Extracting Predicable Components in Numerical Model of Lorenz System

      2012, 36(3):539-550. DOI: 10.3878/j.issn.1006-9895.2011.11094

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      Abstract:The authors have proposed to extract the predictable components to make prediction in the numerical model which has nonlinear chaos. The method of extracting predicable components was introduced in a simple numerical model, and the numerical experiments were done based on Lorenz system. In the experiment, the authors found that the velocity of initial error increase is different for different components in the phase space, and there are some particular directions with slow error increase. That is to say, there exist predictable components which are relatively stable and insensitive to initial perturbation. The numerical model of the predictable components was established by extracting predicable components based on the evolution of the eigenvalues of the tangent operator error, and projecting the model variables onto the substrates. On the basis of these, the impacts of chaotic states, the errors of model parameters, and the external random noise on extracting the predicable components were studied. And the authors found that the numerical model of the predicable components has a better forecasting skill.

    • Analysis of the Characteristics of Mesoscale Disturbance for Landfalling Typhoon Matsa

      2012, 36(3):551-563. DOI: 10.3878/j.issn.1006-9895.2011.11085

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      Abstract:Doppler radar reflectivity and the surface automatic weather stations (AWS) wind observations demonstrate that the mesoscale cyclonic eddies at the low level are active in the spiral-cloud bands of landfalling typhoon Matsa. Numerical simulation has been carried out to investigate the evolution characteristics of typhoon Matsa in 2005 after its landfalling by using the new-generation mesoscale weather research and forecasting (WRF) model, and the four-dimensional variational Dopple radar analysis system (4D-VDRAS) is used to retrieve single-Doppler velocity. Then a preliminary study has been made on the mesoscale features of typhoon Matsa after landfalling in parallel with diagnostic analyses of the conversion of kinetic energy and vorticity between typhoon Matsa and mesoscale systems on the area mean basis. Results show that: (1) The results of numerical simulation and Doppler radial velocity retrieval indicate that the mesoscale cyclonic eddies at the low level are active in the spiral-cloud bands of landfalling typhoon Matsa, and there is severe mesoscale upward movement accompanying the mesoscale cyclonic eddies. The stronger the mesoscale upward movement is, the larger Doppler radar reflectivity is.(2) The diagnostic results of the kinetic energy conversion between Matsa and mesoscale systems demonstrate that the mesoscale cyclonic eddies at the low level obtain kinetic energy from landfalling typhoon Matsa to develop, whilst Matsa obtains kinetic energy from the mesoscale disturbances in the upper layers to be sustained after landfalling.(3) The diagnostic results of the vorticity conversion between Matsa and mesoscale systems show that Matsa obtains positive vorticity from the mesoscale cyclonic eddies at the low levels by means of the mesoscale upward movement, but in the upper layers, both the mesoscale horizontal and vertical movements play important roles. Therefore, the positive cyclonic vorticity is transported continuously to Matsa, and Matsa could be sustained for a long time after landfalling.

    • The Relationship between the Onset Date of Preceding Winter and Following Summer Rainfall in Eastern China

      2012, 36(3):564-578. DOI: 10.3878/j.issn.1006-9895.2011.11106

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      Abstract:By using NCEP/NCAR reanalysis datasets, the starting dates of preceding winters in eastern China have been divided from 1961 to 2010, the authors investigate the relationship between the onset date of preceding winter and the following summer precipitation in eastern China. Results indicate that there are two positive correlation bands and two negative correlation bands. The four bands are corresponding with the main rainbelts in eastern China in summer. The positive ones are located in South China, Southwest China, the region north of the Yellow River with latitudes between 39°N and 42°N, and central and southern Northeast China. The negative ones are in Huanghuai, Jianghuai, the middle and lower reaches of the Yangtze River, and most regions north of latitude 42°N. The statistical results show that the frequency of rainfall pattern II is larger than that of the climate state, those for both rainfall patterns I and III are less than that of the climate state when earlier preceding winters come. While for later winters, that for pattern I is larger than that of the climate state, those for both rainfall patterns II and III are much smaller than that of the climate state. The rainbelt outcomes from the statistics and composition analysis in the typical years are consistent with each other. The statistical results show that the later preceding winters are prime when it is pattern I, earlier winters for pattern II, and there is not significant relationship between the winter starting dates and pattern III. In a word, the patterns of precipitation are closely related to the starting dates of the seasons. The different starting dates of winters are corresponding to different air-sea interactions which result in different patterns of precipitation.

    • Climatological Characteristics of Overshooting Convective Precipitation in Summer and Winter over the Tropical and Subtropical Regions

      2012, 36(3):579-589. DOI: 10.3878/j.issn.1006-9895.2011.11109

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      Abstract:The climatological characteristics of overshooting convective precipitation including frequency, conditional rain rate, and precipitation profiles are investigated based on the measurements of Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR) during 1998-2007 over the tropical and subtropical areas. Results indicate that both deep and overshooting convections are mainly distributed over the intertropical convergence zone, the South Pacific convergence zone, the Asia monsoon region, Africa south of 20°N, and America. The distributions of deep and overshooting convections show remarkable regionality and seasonal variations. Meanwhile, deep convections over land penetrate into TTL (Tropical Tropopause Layer) more easily than those over ocean. And totally, the overshooting convection frequencies are under 0.2% over most of the tropical and subtropical areas. Conditional rain rates of the overshooting convections over most regions exceed 10mm/h, and those over ocean are higher than that over land. But the contribution of the overshooting convections to total rain is small due to the low frequency. The shapes of deep and overshooting convective precipitation profiles are similar, but rain rates of overshooting convections are larger than that of deep convections, and the differences also show remarkable regionality. Moreover, seasonal variations of deep and overshooting convective precipitation profiles over the tropical areas (15°S-15°N) are minimal.

    • Ocean-to-Atmosphere Forcing in the Vicinity of the Sea Surface Temperature Front in the East China Sea—Seasonal Variations

      2012, 36(3):590-606. DOI: 10.3878/j.issn.1006-9895.2011.11113

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      Abstract:A suite of high-resolution satellite measurements are used to investigate local atmospheric response to a sea surface temperature (SST) front over the East China Sea and its seasonal variation. The analyses reveal a significant in-phase relationship between SST and 10-m neutral wind velocity, accompanied by convergence (divergence) on the warmer (colder) flank of the front during spring time when the oceanic front is intensified, indicative of ocean-to-atmosphere influences. The extent of the influence on near surface wind field by SST is proportional to the strength of the SST front with its maximum in spring and minimum in summer and autumn. The satellite observations detect direct responses of total, convective, and stratiform precipitation to the Kuroshio front. Especially in spring and early summer, enhanced rainfall and the frequent occurrence of convective precipitation are collocated on the warmer flank of the SST front. Furthermore, considerable increase in the cloud top height is observed across the front from cold to warm water. The distribution and structure of precipitation suggest that the influence of warm ocean current in the East China Sea penetrates above the MABL (Marine Atmospheric Boundary Layer) to reach the entire troposphere. The results also show that convective precipitation is more sensitive to SST variation than stratiform precipitation. High and low clouds over the Kuroshio Current exhibit opposite annual cycle, low clouds ranging from 0.5-2 km prevail in winter, while high clouds with the cloud base above 10 km dominate in summer. The area with cloud amount larger than 30% is elevated by nearly 8 km from winter to early summer. Deep convective clouds mainly concentrate during March to June, indicating that deep convection frequently occurs on the warmer flank of the SST front in spring and early summer.

    • The Impacts of Westerly Upper-Level Trough on the Extratropical Transition of Tropical Cyclones Landing over China and its Possible Mechanisms

      2012, 36(3):607-618. DOI: 10.3878/j.issn.1006-9895.2011.11076

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      Abstract:Based on the Tropical Cyclone (TC) data and Japanese 25-year reanalysis data of Japan Meteorological Agency from 1979 to 2008, compositing and comparative analysis was firstly performed to study the intensifying and weakening TC during the Extratropical Transition (ET) over China.The analyses reveal a nice corresponding relationship between the variation of TC's intensity after ET and initial strength of the westerly upper-level trough. Then TC Haima which made landfall on China in 2004 was taken as an example, the evolution of its transition process was reproduced by the mesoscale atmospheric model. The authors modified the intensity of upper-level trough in the initial fields using the method of piecewise potential vorticity (PV) inversion and investigated the impacts of different troughs on Haima's re-intensification process during ET. The results indicate that Haima moved quickly (slowly) when the trough enhanced (weakened), furthermore, the deeper (shallower) the upper trough is, the stronger (weaker) the Haima re-intensifies; the deeper trough shows wide and strong upper-level jet and enhanced divergence, which is favorable for Haima's redevelopment; besides, the deeper upper trough was accompanied by stronger positive belt of PV, the upper-level positive PV propagated downward to lower levels to result in the growth of Haima's positive PV and the intense development of low-level baroclinic frontal zone, finally, the low-level cyclone was reinforced obviously.

    • Long-Term Climate Simulation of CCSM4.0 and Evaluation of Its Performance over East Asia and China

      2012, 36(3):619-632. DOI: 10.3878/j.issn.1006-9895.2011.11092

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      Abstract:A 700-year long-term climate simulation is performed by the Community Climate System Model version 4.0 (CCSM4.0) with a low atmospheric horizontal resolution (T31, an equivalent grid spacing of about 3.75°). To systematically evaluate the capability of the model over East Asia and China, the last 100-year results of surface air temperature and precipitation in China, sea level pressure, geopotential height at 500 hPa and 100 hPa, and wind field at 850 hPa over East Asia are qualitatively compared to observation and reanalysis data, and a few statistical variables of the former three climatic elements are quantitatively examined. Results show that the model can reasonably reproduce the basic spatial patterns of the above climatic fields, though the magnitudes are somewhat different from observations. The best (worst) performance is found for surface air temperature (precipitation) as a whole. Specifically, the simulated geographical distribution of surface air temperature agrees with observations. However, it is overestimated on the Qinghai-Tibetan Plateau, and the warm center on the Tarim Basin is missed by the model throughout the year. The spatial distribution of precipitation is poorly simulated. A fake precipitation center, which is the strongest in summer, occurs over central southern China all year around except in winter. The simulation of sea level pressure is generally better in winter than in summer, though the simulated thermal contrast between the East Asian continent and adjacent oceans is larger than observations. The model can well capture the East Asia major trough and subtropical high over the western North Pacific at 500 hPa during winter and summer, though the values are larger than observations. The simulated intensity of the South Asia high at 100 hPa in summer is consistent with observations, whereas the extent and center location exhibit some deviations. The East Asian winter and summer monsoon circulations at 850 hPa are well simulated. However, the northwesterly flow is overestimated in winter. In summer, the Somalia cross-equatorial flow is underestimated, while the southwesterly flow over eastern China is overestimated. Collectively, CCSM4.0 has a reliable capability to simulate the large-scale climate features over East Asia and China, though some deficiencies still exist in a quantitative manner.

    • An Extended-Range Forecast Method for the Persistent Heavy Rainfall over the YangtzeHuaihe River Valley in Summer Based on the Low-frequency Oscillation Characteristics

      2012, 36(3):633-644. DOI: 10.3878/j.issn.1006-9895.2011.11111

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      Abstract:Based on the daily precipitation datasets at 200 stations in the south of China and the corresponding NCEP/NCAR daily reanalysis data from 1981 to 2008, Analysis By Synthesis (ABS) and Butterworth band-pass filter are adopted to diagnose the Low-Frequency Oscillation (LFO) characteristics of the summer rainfall over the Yangtze-Huaihe River Valley (YHRV). And then an experiment for the Extended-Range Forecast (ERF) of persistent heavy rainfall over YHRV is made. The major conclusions are as follows: summer precipitation over YHRV has an obvious characteristic of LFO with 20-50 days period, and for climate average, the 20-50-day low-frequency components account for nearly 20%, and there are significant annual variations for the intensity of LFO signal. There is a good relationship between the 20-50-day components and actual precipitation, especially the phase changes in peak values correspond to alternation of precipitation concentrated period and break period. Therefore the 20-50-day low-frequency components of precipitation which is taken as the predictand for the ERF experiment and the persistent heavy rainfall process over YHRV are closely linked. Meanwhile based on the links between LFO of large scale circulation in East Asia and summer persistent heavy rainfall over YHRV, 10 indexes of circulation critical systems are built, which can correctly reflect the intensity and tendency of the 20-50-day low-frequency components of precipitation, and are used as predictors for the ERF experiment. Combining with the NCEP Climate Forecast System (NCEP/CFS) output the forecast model based on the LFO signal has some reference value for ERF of persistent heavy rainfall over YHRV.

    • A Multilevel Perturbation Method—Hydrostatic Deduction and Its Applicability to Designing the Nonhydrostatic Model

      2012, 36(3):645-656. DOI: 10.3878/j.issn.1006-9895.2011.11080

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      Abstract:Based upon the results from the scale analysis of the vertical equation of motion for the atmosphere and forecast experience, especially numerical weather forecast experience, the multilevel perturbation method has been proposed. It can be proved that in the vertical perturbation equation the magnitude of the perturbation decreases with n, n=1, 2, …. But, on the other hand, since the magnitude of truncation error is proportional to that of the discretized term, in the vertical equation of motion or the perturbation equation the truncation error of the discretized vertical pressure gradient force (VPGF) is the largest vertical truncation error, which can represent the total vertical truncation error in the equation. Hence the decrease in the magnitude of VPGF with n is favorable for reduction of the total vertical truncation error and use of the method can limit such an error within a permissible range, to make computation of VPGF more correct and describe convective activity better than ever. Therefore the impact of the largest truncation error on the tendency of w would be unable to distort or cover up the contribution of vertical Coriolis force term and that of curvature term to the tendency. Further, it can be proved that the solution of level n perturbation balance equation is a hydrostatic perturbation. The method is, substantially, a tool to be used to deduct the hydrostatic part from level n perturbation, in order to reduce the level n+1 perturbation in magnitude. In this way a high level perturbation VPGF may easily come closer to the other terms without perturbation in magnitude. Furthermore, because the sum of VPGF and gravity does not vary with n, the physical properties of the vertical equation of motion would not change. Therefore, the method may be named the multilevel perturbation hydrostatic deduction method. It can diminish the difference between the improved basic state vertical profile and the actual atmospheric vertical profile quite small, and under hydrostatic equilibrium in the vast majority of the model atmosphere there would be almost no vertical sound waves.