Application of the two different salinity parameterization schemes in the sea ice model

In this study, we mainly introduce two salinity parameterization schemes used in Sea Ice Simulator （SIS）, that is, isosaline scheme and salinity profile scheme. Comparing the equation of isosaline scheme with that of salinity profile scheme, we found that there was one different term between the two schemes named the salinity different term. The thermodynamic effect of the salinity difference term on sea ice thickness and sea ice concentration showed that： in the freezing processes from November to next May, the sea ice temperature could rise on the influence of the salinity difference term and restrain sea ice freezing; at the first melting phase from June to August, the upper ice melting rate was faster than the lower ice melting rate. Then sea ice temperature could rise and accelerate the sea ice melting; at the second melting phase from September to October, the upper ice melting rate was slower than the lower ice melting rate, then sea ice temperature could decrease and restrain sea ice melting. However, the effect of the salinity difference term on the sea ice thickness and sea ice concentration was weak. To analyze the impacts of the salinity different term on Arctic sea ice thickness and sea ice concentration, we also designed several experiments by introducing the two salinity parameterizations to the ice-ocean coupled model, Modular Ocean Model （MOM4）, respectively. The simulated results confirmed the previous results of formula derivation.

Improving the CoLM in Taklimakan Desert Hinterland with Accurate Key Parameters and an Appropriate Parameterization Scheme

Improving and validating land surface models based on integrated observations in deserts is one of the challenges in land modeling. Particularly, key parameters and parameterization schemes in desert regions need to be evaluated in-situ to improve the models. In this study, we calibrated the land-surface key parameters and evaluated several formulations or schemes for thermal roughness length （z 0h ） in the common land model （CoLM）. Our parameter calibration and scheme evaluation were based on the observed data during a torrid summer （29 July to 11 September 2009） over the Taklimakan Desert hinterland. First, the importance of the key parameters in the experiment was evaluated based on their physics principles and the significance of these key parameters were further validated using sensitivity test. Second, difference schemes （or physics-based formulas） of z 0h were adopted to simulate the variations of energy-related variables （e.g., sensible heat flux and surface skin temperature） and the simulated variations were then compared with the observed data. Third, the z 0h scheme that performed best （i.e., Y07） was then selected to replace the defaulted one （i.e., Z98）; the revised scheme and the superiority of Y07 over Z98 was further demonstrated by comparing the simulated results with the observed data. Admittedly, the revised model did a relatively poor job of simulating the diurnal variations of surface soil heat flux, and nighttime soil temperature was also underestimated, calling for further improvement of the model for desert regions.

NUMERICAL STUDIES OF PLANETARY BOUNDARY LAYER PARAMETERIZATION SCHEMES ON SUPER TYPHOON SANBA(2012)DURING ITS INITIAL STAGE

The formation and development of typhoons are closely related to the disturbed low vortexes at the planetary boundary layer(PBL). The effects of five PBL parameterization schemes(PBL schemes hereinafter) on the trajectory,intensity, and distribution of physical quantities are studied using the mesoscale WRF model on Super Typhoon Sanba(2012) during its initial stage. Results show that the five PBL schemes exhibit significant different effects on the simulated intensity and path. The results simulated by QNSE and ACM2 without the Bogus method are close to the best track data in the numerical experiments. When the Bogus method is adopted, the simulated trajectories improve significantly because the initial field is close to the true data. Among the five PBL schemes, QNSE and ACM2 with the Bogus method present improved simulated path and intensity compared with the three other schemes. This finding indicates that the two schemes deal with the initial PBL process satisfactorily, especially in the formation and development of disturbed low vortexes. The differences in the treatment methods of the five PBL schemes affect the surface layer physical quantities and the middle and upper atmospheres during the middle to late periods of the typhoon.Although QNSE and ACM2 present better simulation results than other schemes, they exhibit a few differences in the internal structure of the typhoon. The results simulated by MYJ are worse, and this method may be unsuitable for studying the formation and development of typhoons.

Study on the Influences of GWDO Parameterization Scheme and Terrain on a Rainstorm in Dabie Mountain

[Objective] The research aimed to study the influences of GWDO parameterization scheme and terrain on a rainstorm in Dabie Mountain.[Method] By using NCEP/NCAR 1°×1° analytical data,the conventional and unconventional ground observation data,WRFV3.1.1 version of non-hydrostatic balance meso-scale mode,a meso-scale shear line rainstorm process which happened in Dabie Mountain zone during 05:00-14:00 on June 21,2008 was carried out the diagnostic analysis and numerical test.In the control experiment,the gravity wave drag by orography(GWDO) parameterization scheme was added.The influences of GWDO parameterization scheme and terrain on the rainstorm process were discussed respectively by the sensitivity test.[Result] The orography dragging coefficient had the good improvement role on the rainstorm intensity or falling zone.The result had the very big difference when considering or non-considering the orography dragging coefficient.After the parameterization scheme was added,the rainstorm intensity or falling zone was better than that of non-addition.When there was no dragging coefficient,the shear line disturbance was strong,and the gravity wave activity was obvious.The precipitation was stronger in the zone where the gravity wave was obvious.The terrain in Dabie Mountain and the surrounding place also had the important effect on the shear line precipitation.When the terrain in Dabie Mountain was removed,the precipitation intensity on the shear line increased significantly,and the strengthening of rain belt in the west was the most obvious.When the terrain in the southeast of Dabie Mountain was removed,the precipitation in the east had the obvious increasing effect.The terrain wasn’t favorable for the rainstorm strengthening.The intensity variation of rain belt not only related to the terrain,but also related to the disturbance variation on the shear line.[Conclusion] The research provided the theory basis for the prediction and forecast of rainstorm.

Performance of Convective Parameterization Schemes in Asia Using RegCM:Simulations in Three Typical Regions for the Period 1998–2002

This study discusses the sensitivity of convective parameterization schemes（CPSs） in the Regional Climate Model（version 4.3）（Reg CM4.3） over East/South Asia. The simulations using different CPSs in Reg CM are compared to discover a suitable scheme for this region, as the performance of different schemes is greatly influenced by region and seasonality. Over Southeast China and the Bay of Bengal, the Grell scheme exhibits the lowest RMSEs of summer precipitation compared to observed data. Moreover, the Emanuel over land and Grell over ocean（ELGO） scheme enhances the simulation, in comparison with any single CPS（Grell/Emanuel） over Western Ghats, Sri Lanka, and Southeast India. Over the Huang–Huai–Hai Plain（3H） and Tibetan Plateau（TP） regions of China, the Tiedtke scheme simulates the more reasonable summer precipitation with high correlation coefficient and comparable amplitude. Especially, it reproduces a minimum convective precipitation bias of 8 mm d^-1and the lowest RMSEs throughout the year over East/South Asia. Furthermore, for seasonal variation of precipitation, the Tiedtke scheme results are closer to the observed data over the 3H and TP regions. However, none of the CPSs is able to simulate the seasonal variation over North Pakistan（NP）. In comparison with previous research, the results of this study support the Grell scheme over South Asia. However, the Tiedtke scheme shows superiority for the 3H, TP and NP regions. The thicker PBL, less surface latent heat flux, the unique ability of deep convection and the entrainment process in the Tiedtke scheme are responsible for reducing the wet bias.

An Improvement of the Mass Flux Convection Parameterization Scheme and its Sensitivity Tests for Seasonal Prediction over China

A modified cumulus parameterization scheme, suitable for use in a seasonal forecast model, is presented. This parameterization scheme is an improvement of the mass flux convection scheme developed by Gregory and Rowntree (1989; 1990). This convection scheme uses a 'bulk' cloud model to present an ensemble of convective clouds, and aims to represent shallow, deep, and mid-level convection. At present, this convection scheme is employed in the NCC T63L20 model (National Climate Center, China Meteorological Administration). Simulation results with this scheme have revealed some deficiencies in the scheme, although to some extent, it improves the accuracy of the simulation. In order to alleviate the deficiencies and reflect the effect of cumulus convection in the actual atmosphere, the scheme is modified and improved. The improvements include (i) the full estimation of the effects of the large-scale convergence in the lower layer upon cumulus convection, (ii) the revision of the initial convective mass flux, and (iii) the regulation of convective-scale downdrafts. A comparison of the results obtained by using the original model and the modified one shows that the improvement and modification of the original convection scheme is successful in simulating the precipitation and general circulation field, because the modified scheme provides a good simulation of the main features of seasonal precipitation in China, and an analysis of the anomaly correlation coefficient between the simulation and the observations confirms the improved results.

Sensitivity Study of the South China Sea Summer Monsoon in 1998 to Different Cumulus Parameterization Schemes

In this study, the improved high-resolution regional climate model of the China National Climate Center （RegCM_NCC） is used to examine the sensitivity of the simulated circulation and rainfall during the South China Sea summer monsoon （SCSSM） period during 1998 in an effort to compare to other cumulus param- eterization schemes. The investigation has indicated that the model is capable of simulating the seasonal march of the SCSSM and that the results were very sensitive to the choice of cumulus parameterization schemes. It seems that the Kuo cumulus parameterization scheme simulates the process of the SCSSM onset reasonably well, which can reproduce the onset timing and dramatic changes before and after the onset, especially the upper- and lower-level wind-fields. However, there are still some discrepancies between the simulations and observations. For example, the model can not completely simulate the intensity of the rainfall or the location of the western Pacific subtropical high as well as the feature of the rapid northward propagation of seasonal rain belt.

A Sensitivity Study on Parameterization Scheme of Snow Internal and Interfacial Processes in Snow Model

In order to develop a seasonal snow model of land surface process as accurately as possible for climatic study. it is necessary to fully understand the effects of important snow internal processes and interaction with air and to get an insight into influence of several relevant parameterization schemes with parameters' uncertainty to some degree. Using the snow model (SAST) developed by first author and other one and some useful field observation data, this paper has conducted a series of sensitivity studies on the parameterization schemes. They are relative to compaction process, snow thermal conduction, methodology of layering snow pack and to key parameters such as snow albedo, water holding capacity. Then, based on the results from the sensitivity studies, some useful conclusions for snow cover model improvement are obtained from the analysis of the results.

Impact of Horizontal Resolution and Cumulus Parameterization Scheme on the Simulation of Heavy Rainfall Events over the Korean Peninsula

In this paper, we present the results from high-resolution numerical simulations of three heavy rainfall events over the Korean Peninsula. The numerical results show that the prediction accuracy for heavy rainfall events improved as horizontal resolution increased. The fine-grid precipitation fields were much closer to the real precipitation fields in the case of large synoptic forcing over the Korean Peninsula. In the case of large convective available potential energy and weak synoptic forcing, it seems that even when using a high resolution, the models still showed poor performance in reproducing the observed high precipitation amounts. However, activation of the cumulus parameterization scheme in the intermediate resolution of 9 km, even at a grid spacing of 3 km, had a positive impact on the simulation of the heavy rainfall event.

A STUDY ON THE IMPACTS OF LATENT HEAT PARAMETERIZATION SCHEME ON PREDICTION SKILL OF ENSO WITH A SIMPLE OCEAN-ATMOSPHERE COUPLED MODEL

This study revises Weare＇s latent heat parameterization scheme and conducts an associated theoretic analysis. The revised Weare＇s scheme is found to present potentially better results than Zebiak＇s scheme. The Zebiak-Cane coupled ocean-atmosphere model, initialized by the National Centers for Environmental Prediction and the National Center for Atmospheric Research （NCEP/NCAR） reanalysis of wind stress anomaly at 925 hPa, is referred to as the ZCW coupled model. The atmosphere models of the ZCW coupled model that use Zebiak＇s scheme and the revised Weare＇s scheme are referred to as the ZCW0 and ZCWN atmosphere models, respectively. The coupled ocean-atmosphere models that use Zebiak＇s scheme and the revised Weare＇s scheme are referred to as the ZCWoand ZCWN coupled models, respectively. The simulations between the ZCW0 and ZCWN atmosphere models and between the ZCW0 and ZCWN coupled models are analyzed. The results include： （1） The evolution of heat, meridional wind and divergence anomalies simulated by similar ZCW0 and ZCWN atmosphere models, although the magnitudes of the former are larger than those of the latter; （2） The prediction skill of the Nino3 index from 1982 to 1999 by the ZCWN coupled model shows improvement compared with those by the ZCW0 coupled model; （3） The analysis of E1 Nino events in 1982/1983, 1986/1987, and 1997/1998 and La Nifia events in 1984/1985, 1988/1989, and 1998/2000 suggests that the ZCWN coupled model is better than the ZCW0 coupled model in predicting warm event evolution and cold event generation. The results also show the disadvantage of the ZCWN coupled model for predicting E1 Nino.

Comparative Studies of Different Mesoscale Convection Parameterization Schemes in the Simulation of Mei-Yu Front Heavy Rain

The mei-yu front heavy rainstorms occurred over Nanjing on 3 5 and 8 9 July 2003 and were simulated in this paper using the Weather Research and Forecasting Model (WRFv3.1) with various mesoscale convection parameterization schemes (MCPSs). The simulations show that the temporal and spatial evolution and distribution of rainstorms can be modeled; however, there was incongruity between the comparative simulations of four different MCPSs and the observed data. These disparities were exhibited in the simulations of both the 24-hour surface rainfall total and the hourly precipitation rate. Further analysis revealed that the discrepancies of vertical velocity and the convective vorticity vector (CVV) between the four simulations were attributed to the deviation of rainfall values. In addition, the simulations show that the mid-scale convection, particularly the mesoscale convection system (MCS) formation, can be well simulated with the proper mesoscale convection parameterization schemes and may be a crucial factor of the mei-yu front heavy rainstorm. These results suggest that, in an effort to enhance simulation and prediction of heavy rainfall and rainstorms, subsequent studies should focus on the development and improvement of MCPS.

CWRF-based ensemble simulation of tropical cyclone activity near China and its sensitivity to the model physical parameterization schemes

To evaluate the downscaling ability with respect to tropical cyclones(TCs)near China and its sensitivity to the model physics representation,the authors performed a multi-physics ensemble simulation with the regional Climate-Weather Research and Forecasting(CWRF)model at a 30 km resolution driven by ERA-Interim reanalysis data.The ensemble consisted of 28 integrations during 1979-2016 with varying CWRF physics configurations.Both CWRF and ERA-Interim can generally capture the seasonal cycle and interannual variation of the TC number near China,but evidently underestimate them.The CWRF downscaling and its multi-physics ensemble can notably reduce the underestimation and significantly improve the simulation of the TC occurrences.The skill enhancement is especially large in terms of the interannual variation,which is most sensitive to the cumulus scheme,followed by the boundary layer,surface and radiation schemes,but weakly sensitive to the cloud and microphysics schemes.Generally,the Noah surface scheme,CAML(CAM radiation scheme as implemented by Liang together with the diagnostic cloud cover scheme of Xu and Randall(1996))radiation scheme,prognostic cloud scheme,and Thompson microphysics scheme stand out for their better performance in simulating the interannual variation of TC number.However,the Emanuel cumulus and MYNN boundary layer schemes produce severe interannual biases.Our study provides a valuable reference for CWRF application to improve the understanding and prediction of TC activity.

Sensitivity of Numerical Simulations of the East Asian Summer Monsoon Rainfall and Circulation to Different Cumulus Parameterization Schemes

A 5-level spectral AGCM (ImPKU-SLAGCM) is used to examine the sensitivity of the simulated results of the summer monsoon rainfall and circulation in East Asia to different cumulus parameterization schemes in the climatological-mean case and in the cases of weak and strong Asian summer monsoons, respectively. The results simulated with the Arakawa-Schubert's(hereafter A-S's), Kuo's and Manabe's cumulus parameterization schemes show that these simulated distributions of the summer monsoon rainfall and circulation in East Asia depend strongly on the cumulus parameterization schemes either in the climatological-mean case or in the cases of weak and strong Asian summer monsoons. From the simulated results, it might be shown that the Kuo scheme appears to be more suitable for the simulation of the summer monsoon rainfall and circulation in East Asia than the A-S scheme or the Manabe scheme, although the A-S scheme is somewhat better in the simulations of the tropical rainfall. This might be due to that the Kuo's cumulus parameterization scheme is able to reflect well the characteristics of rainfall cloud system in the East Asian summer monsoon region, where the rainfall system used to be a mixing of cumulus and stratus.

Numerical Experiments of Three Boundary Layer Parameterization Schemes on Simulation Results of Low-vortex Rainstorm Weather in Langfang Region

Using mesoscale numerical model WRFV3.7,simulation tests of a low-vortex rainstorm were carried out in Langfang area,and simulation results of three boundary layer parameterization schemes(MYJ,YSU,ACM2)were contrasted.The results showed that the rainstorm in Langfang area had better dynamic condition.By the influence of northeast cold vortex,cold vortex at high altitude cooperated with the surface wind speed convergence,which provided better dynamic condition for strong convective rainfall.Three boundary layer parameterization schemes all simulated surface wind speed convergence of rainstorm center.Simulation results of 24-h rainfall distribution showed that the simulation of YSU scheme was better than ACM2 and MYJ.The simulation results of flow field and temperature field also verified that YSU scheme was better than other schemes.

Impacts of boundary layer parameterization schemes and air-sea coupling on WRF simulation of the East Asian summer monsoon

The planetary boundary layer （PBL） scheme in the regional climate model （RCM） has a significant impact on the interactions and exchanges of moisture, momentum, and energy between land, ocean, and atmosphere; however, its uncertainty will cause large systematic biases of RCM. Based on the four different PBL schemes （YSU, ACM2, Boulac, and MYJ） in Weather Research and Forecasting （WRF） model, the impacts of these schemes on the simulation of circulation and precipitation during the East Asian summer monsoon （EASM） are investigated. The simulated results of the two local turbulent kinetic energy （TKE） schemes, Boulac and MYJ, are more consistent with the observations than those in the two nonlocal closure schemes, YSU and ACM2. The former simulate more reasonable low-level southwesterly flow over East China and west pacific subtropical high （WPSH） than the latter. As to the modeling of summer monsoon precipitation, both the spatial distributions and temporal evolutions from Boulac and MTT are also better than those in YSU and ACM2 schemes. In addition, through the comparison between YSU and Boulac experiments, the differences from the results of EASM simulation are more obvious over the oceanic area. In the experiments with the nonlocal schemes YSU and ACM2, the boundary layer mixing processes are much stronger, which lead to produce more sea surface latent heat flux and enhanced convection, and finally induce the overestimated precipitation and corresponding deviation of monsoon circulation. With the further study, it is found that the absence of air-sea interaction in WRF may amplify the biases caused by PBL scheme over the ocean. Consequently, there is a reduced latent heat flux over the sea surface and even more reasonable EASM simulation, if an ocean model coupled into WRF.

Sensitivity of Precipitation over China to Different Cumulus Parameterization Schemes in RegCM4

The effect of different cumulus parameterization schemes（CPSs） on precipitation over China is investigated by using the International Centre for Theoretical Physics（ICTP） Regional Climate Model version 4.3（Reg CM-4.3） coupled with the land surface model BATS1e（Biosphere-Atmosphere Transfer Scheme version1e）. The ERA-interim data are utilized to drive a group of simulations over a 31-yr period from September1982 to December 2012. Two typically sensitive regions, i.e., the eastern Tibetan Plateau（TP; 29°–38°N,90°–100°E） and eastern China（EC; 26°–32°N, 110°–120°E）, are focused on. The results show that all the CPSs have well reproduced the spatial distribution of annual precipitation in China. The simulation with the Emanuel scheme shows an overall overestimation of precipitation in China, different from the other three CPSs which only overestimate over northern and northwestern China but underestimate over southern China. Seasonally, the Tiedtke scheme shows the smallest overestimation in winter and summer, and the best simulation of the annual variance of precipitation. Interannual variations of precipitation among the four CPSs are generally simulated better in summer than in winter, and better for entire China than in the subregions of TP and EC. The precipitation trend is simulated better over EC than over TP, and better in summer than in winter. An overestimate（underestimate） of the East Asian summer monsoon index（EASMI） exists in the simulations with the Grell and the Emanuel（the Kuo and the Tiedtke） schemes.The smallest EASMI bias in the Tiedtke simulation could explain its small precipitation bias. A negative correlation between the EASMI and summer precipitation over the middle and lower reaches of Yangtze River is found in the Grell and the Emanuel simulations, but was missed by the simulations using the Kuo and the Tiedtke schemes.

A data assimilation-based method for optimizing parameterization schemes in a land surface process model

Optimizing the parameters of a land surface process model(LSPM) through data assimilation(DA) can not only improve and perfect the parameterization schemes in the LSPM through the physical mechanism, but also increase its regional adaptability and simulation capability. This has practical importance for improving simulation results and the climate-prediction capability of general circulation models(GCMs) and regional climate models(RCMs). This paper presents a DA-based method for optimizing the parameterization schemes in LSPMs. We optimize the unsaturated-soil water flow(Un SWF) model as an example by developing a soil-moisture assimilation scheme based on the Un SWF model and the extended Kalman filter(EKF) algorithm, and then combining them with the Variable Infiltration Capacity(VIC) model. Using a month as the assimilation window, we used the Shuffled Complex Evolution–University of Arizona(SCE-UA) algorithm to minimize the objective function through simulated and assimilated soil moisture, achieved the best fit with the given objective function measurement, and optimized the parameters of the Un SWF model, including the saturated-soil hydraulic conductivity, moisture content, matrix potential, and the Clapp and Hornberger constant. The optimal values of the model parameters were obtained during the DA period(the year 1986), and then the optimized parameters were used to improve the Un SWF model. Finally, numerical simulation experiments were carried out from 1986 to 1993 to evaluate the simulation capability of the improved model and to explore and realize the DA-based method for optimizing the soil water parameterization scheme in LSPMs. The experimental results indicated that the optimized model parameters improved and perfected the model based on the physical mechanism, and increased its simulation capability; the optimized model parameters had good temporal portability and their adaptability was stronger, achieving the aim of improving the model. Therefore, this method is reasonable and feasible. This paper provides a good reference for DA-based optimization of the parameterization schemes in LSPMs.

The Sensitivity of Numerical Simulation of the East Asian Monsoon to Different Cumulus Parameterization Schemes

In this paper, a 5-level spectral AGCM is used to examine the sensitivity of simulated East Asian summer monsoon circulation and rainfall to cumulus parameterization schemes. From the simulated results of East Asian monsoon circulations and rainfalls during the summers of 1987 and 1995, it is shown that the Kuo′s convective parameterization scheme is more suitable for the numerical simulation of East Asian summer monsoon rainfall and circulation. This may be due to that the cumulus in the rainfall system is not strong in the East Asian monsoon region.

Development of an Integrated Vertical-Slantwise Convective Parameterization Scheme and Its Associated Numerical Experiments

An integrated vertical-slantwise convective parameterization scheme, based on the vertical Kuo-Anthes and the slantwise Nordeng convective parameterization schemes, is introduced into the MM5 model. By employing the MM5 model with the proposed scheme, numerical simulations of a snowstorm event that occurred over southern China on 28-29 January 2008 and of Typhoon Haitang （2005） are conducted. The results indicate that during the snowstorm event, the atmosphere was convectively stable in the vertical direction but with conditional symmetric instability （CSI） in the lower troposphere, and when the area of CSI developed and extended to upper levels, strong rising motion occurred and triggered the release of large amount of energy, producing enhanced convective precipitation with the total precipitation much closer to the observation. The development and strengthening of CSI corresponded to changes in the intensity of snowfall, convergence, and ascending motions of air, revealing that CSI was responsible for the initiation and growth of the snowstorm. The results from a 72-h explicit simulation of Typhoon Haitang indicate that CSI occurred mainly at lower levels with a well-defined spiral structure, and it tended to have a larger impact on the intensity of typhoon than on its track. The minimum pressure at the typhoon center for the 72-h runs with the integrated vertical-slantwise convective parameterization scheme was on average 3 hPa （maximum 8 hPa） lower than that from the runs with only the vertical cumulus parameterization scheme. Introducing the influence of CSI into the model has improved the warm core structure at the middle and upper levels of the typhoon, with stronger and persistent upward motions causing increased precipitation, and the latent heat released through convection in turn made the typhoon develop further.

Parameterization for the Depth of the Entrainment Zone above the Convectively Mixed Layer

It has been noted that when the convective Richardson number Ri* is used to characterize the depth of the entrainment zone, various parameterization schemes can be obtained. This situation is often attributed to the invalidity of parcel theory. However, evidence shows that the convective Richardson number Ri* might be an improper characteristic scaling parameter for the entrainment process. An attempt to use an innovative parameter to parameterize the entrainment-zone thickness has been made in this paper. Based on the examination of the data of water-tank experiments and atmospheric measurements, it is found that the total lapse rate of potential temperature across the entrainment zone is proportional to that of the capping inversion layer. Inserting this relationship into the so-called parcel theory, it thus gives a new parameterization scheme for the depth of the entrainment zone. This scheme includes the lapse rate of the capping inversion layer that plays an important role in the entrainment process. Its physical representation is reasonable. The new scheme gives a better ordering of the data measured in both water-tank and atmosphere as compared with the traditional method using Ri*. These indicate that the parcel theory can describe the entrainment process suitably and that the new parameter is better than Ri*.