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1 NO.1 LIU Ying, LIU Chongjian, XU Hui and ZHAO Yongming 67 A Numerical Study of Sensitivity of the Physical Dissipative Technique to Precipitation Parameterization in a Mesoscale Model LIU Ying 1 ( ), LIU Chongjian 1 ( ), XU Hui 1 ( ), and ZHAO Yongming 2 ( ) 1 Chinese Academy of Meteorological Sciences, Beijing CMA (China Meteorological Administration) Training Center, Beijing (Received March 30, 2004; revised June 15, 2004) ABSTRACT In this paper the numerical comparative experiments on sensitivity of the physical dissipative technique to the precipitation parameterizations, especially the different combination of the explicit micro-physical schemes and cumulus convection parameterizations, in the PSU/NCAR mesoscale model MM5V3 with a triple-nested domain are conducted using the case of heavy rain occurring in the northern China in October The experiments have revealed some meaningful results, notably the dramatic improvement in the simulative accuracy and quality by the physical dissipative technique based on the second law of thermodynamics, meanwhile, the weak sensitivity of the technique to the schemes of parameterization resulting mainly from improving the field of rainfall by the physical dissipative technique has been reached via improving the outputs of the model variables such as wind field determining the divergence field that is one of the most important factors in the case of designing the schemes of precipitation parameterization. Key words: numerical simulation, mesoscale, dissipation, precipitation parameterization 1. Introduction Recently, the improvement of accuracy in the outputs of a numerical mesoscale model by the physical dissipative technique is reached (Liu et al., 2002; Liu and Liu, 2003). The effect of improvement of this technique differs not only from model to model, but from scheme to scheme of parameterization employed in the same model. The rapid development of the computer technology makes possible the complicated numerical experiments by a model with high resolution and multiple domains nested and explicit schemes of precipitation included and, thus various schemes of parameterization of high resolution and explicit formulation have drawn more and more attention (Chen et al., 1992; Zhang, 1998; Wang et al., 2001; Chen et al., 2003). For example, Betts- Miller, Kain-Fritsch, Anthes-Kuo, Arakawa-Schubert and Grell schemes (Anthes, 1977; Grell, 1993; Kain and Fritsch, 1990; Fritsch and Chappell, 1980; Betts, 1986; Betts and Miller, 1986) are the schemes of cumulus convection parameterizations employed currently frequently in the PSU/NCAR mesoscale model MM5, which simulate the convective precipitation through a set of parameters describing the triggering mechanism of convection under a certain assumption. In view of that different thermodynamic effects on the formation of precipitation are involved with every scheme via the parameters, there exist surely the differences in improving margins caused by the physical dissipative technique, especially the new one (Liu et al.,2002) which is based on the second law of thermodynamics. Therefore, the investigation on the sensitivity of various schemes of precipitation, including the implicit and explicit schemes and their combinations, to the physical dissipative technique via comparative experiments is very meaningful to the future design and/or choice of the schemes of parameterization when different weather cases are simulated using the mesoscale model. This work is supported by the Project of the Special Funds of Social Public Good for Scientific Research Institutions (in China) under Contract 2002DIA20013.

2 68 ACTA METEOROLOGICA SINICA VOL.19 Much work of the comparative experiments about the effect of various diabatic physical processes and different schemes of convection parameterizations in a mesoscale model has been done and, the relevant results reveal in detail that different schemes would surely lead to the different accuracy and quality of outputs of the model. However, it is reached in the case keeping the horizontal diffusion schemes in the model unchanged, and, in fact, the problems to be solved are the sensitivity of various processes and schemes to the physical dissipative technique and the response of various schemes and their different combinations employed in the different domains of the model to the improvement of the outputs after incorporating the physical dissipative technique. As a result, several numerical experiments are designed in this paper to investigate it using the existing schemes of physical processes in the MM5V3 against the case of a severe disastrous weather event occurring in the northern China in October In the next section the basic principle of the physical dissipative technique and the substantial scheme of experiments are introduced, a number of the technological procedures of the parameterizations of precipitation taken as the option of experiments are illustrated, and some characteristics of the weather event and the model parameters are described. A number of the preliminary results of experiments are given in Section 3. At last in the section of the conclusive remarks some ways contributed to the reasonable choice and usage of the schemes of precipitation in a mesoscale model are provided, which is the main purpose of this paper as well. 2. Basic principle of the physical dissipative technique and schemes of experiments 2.1 Brief introduction to the physical dissipative technique The atmosphere is a system with forcing and dissipation whose governing equations consist usually of the terms of forcing and dissipation. If a system is driven only by the forcing without dissipation it will be continuously driven away from the equilibrium with the infinite growth of the energy of the system leading to instability. Generally the dissipation of a system is described in light of the terms of (horizontal) dissipation. For example, there is a dissipative scheme consisting of a second-order diffusion operator on the boundary and a fourth-order one in the inner area in the PSU/NCAR mesoscale model MM5. As stated in the references (Liu et al., 2002; Liu and Liu, 2003), the terms of (fourth-order) horizontal diffusion in the right-hand side of a governing equation in the original MM5 has generally the following form K A 4 A i = K A [4(A i±1 A i ) (A i±2 A i )], where for the sake of convenience, the format is expressed as one-dimensional formula of the central difference and, A is any independent variable with the corresponding A i denoting the value at the onedimensional grid-point i. It is easily seen that the physical diffusion is appropriately described by the quantity A i±1 of one-grid distance in the scheme since the normal contribution of diffusion from A i±1 to A i is gained based on the above formula while the terms of two-grid distance(a i±2 ) will lead to the inverse diffusion so that the new extremes that are larger than the maxima and/or smaller than the minima in the original system will be created, which will not only violate the principle of the second law of thermodynamics but also cause the computational instability. Therefore, the studies (Liu et al., 2002; Liu and Liu, 2003) made the corrections through changing the sign of the terms of two-grid distance to meet the direction of the physical dissipation with the result that the forecast/simulation accuracy of the model is improved dramatically. 2.2 Schemes of experiments Next one will specifically examine the sensitivity of the physical dissipative technique to the several different parameterization schemes of precipitation and their combinations in the mesoscale model MM5, including the schemes of convection parameterization and explicit microphysics, by means of the comparative experiments. The schemes of convection parameterization involved in this paper include Grell (named Scheme 3), Kain-Fritsch (6) and Betts-Miller (7) schemes, whose points of handling the cumulus can be stated as fol-

3 NO.1 LIU Ying, LIU Chongjian, XU Hui and ZHAO Yongming 69 lows: Grell scheme (3) (Anthes, 1977; Grell, 1993) is, in fact, a kind of a single-cloud scheme where a cloud is described as two stable circulations forming on the updraft and downdraft (among which the moist convection contains the cooling effect) with an assumption of the direct mixing between the cloud and its outward occurring only at the top and bottom of the cloud while without entrainment and detrainment at the edges of the cloud, and of the conservation of the vertical mass flux. In such a simplified model, the feedback of the large-scale heating and moistening into the cumulus is completely determined by the compensatory mass fluxes and detrainment at the top and bottom of the cloud and thus the precipitation rate becomes the function of the average wind shear of the lower levels of the model atmosphere. Kain-Fritsch scheme (6) (Kain and Fritsch, 1990; Fritsch and Chappell, 1980) is a cloud model scheme of the buoyancy-energy form with mass conservation, where the entrainment of the updraft and detrainment of the downdraft are taken into consideration and the convective activities will be regarded as the only factor exhausting the available buoyancy energy within a finite interval of time. The important feature of this scheme is to take into account the icing microphysics of the cloud-ice freezed from the liquid saturated moisture. Betts-Miller scheme (Betts, 1986; Betts and Miller, 1986) is a scheme of the convective adjustment form, which maintains that the existing of the cumulus convection enables the thermodynamic characteristics of a model to adjust from the equilibrium into a quasiequilibrium thermodynamic profile of reference that is determined based on a great number of observations. Therefore, the Betts-Miller scheme (7) can provide a better vertical distribution of the convective heating and moistening. As for the explicit schemes of microphysics the following types are taken into consideration (Lou, 2002). Mix Phase scheme (5): supercooled water involved, melting slowly snow, including the ice crystal and snow as the predictive variables. Goddard scheme (6): the predictive equation of the graupel added based on Scheme 5. Reisner scheme (7): the predictive equations of the number concentration and graupel added based on Scheme 5. The six sets of experiments are designed according to different schemes of precipitation with the triplenested domains used see Table 1 for details where the numerical code 1 for IC in Scheme 5 means no scheme of convective parameterization employed. Table 1. Schemes for experiments Domain Scheme 1 Scheme 2 Scheme 3 Scheme 4 Scheme 5 Scheme 6 IM IC IM IC IM IC IM IC IM IC IM IC Note that IM denotes the scheme of microphysics and IC the scheme of convective parameterization. The main objectives of Schemes 1 and 2 are to investigate the impact of the physical dissipative technique on the difference in precipitation resulting from the different schemes of convective parameterization employed; Schemes 3 and 4 will mainly investigate the impact of the different schemes of microphysics on the difference in precipitation; and Scheme 5 and 6 will investigate the impact of the schemes with /without Table 2. The model simulation parameters Domain Grid size (km) Dimensions (x, y) Time step (s) Starting time Integration hours h 48

4 70 ACTA METEOROLOGICA SINICA VOL.19 convective parameterization involved on the difference in precipitation. The simulative ranges and grid numbers are listed in Table Brief introduction to the case The weather event simulated in this paper is the heavy rain process occurring in the northern China during October 2003 beyond the flood season. Under the interaction between the warm-moist currents from the southern China and broad East China Sea and the stronger cold air from the north, the torrential rain covers extensively the area of the northern China during the late autumn. As an example, the Jinghai County of Tianjin located at the heavy rain center area experienced the rainfall of mm within the period of 48 h from 00Z 10 October to 00Z 12 October, which is the strongest rainfall occurring at this county in 2003 and the strongest one for this period in the past 50 years as well. Under the influence of the strong cold air, the great part of Tianjin experienced the high winds with an instant maximum speed of 18 m s 1 reached, the northeastlies of forces 9-10 occurred over the Bohai Sea with the gust of force 12, and the storm surge occurred near the coast east of Tianjin in the small hours on 11 till 02Z 12 October with the maximum tide of 5.54 m at 20:15Z 10 October which exceeds the warning level by 0.64 m. 3. Results 3.1 Precipitation The integration of 60 h from 12Z 9 October till 00Z 12 October 2003 is conducted with the triplenested domains among which the 3rd domain is integrated for 48 h from 00Z 10 October till 00Z 12 October. The focus will be put on the field of precipitation in this paper. Firstly, it is seen from Figs.1 to 7 that the trend of the 48 h accumulative rainfall area larger than 50 mm is improved by the physical dissipative technique with all the 6 schemes of the comparative experiments in that the trend of the rainfall area after improving is closer to the observations than that by the corresponding control run. On the other hand, the 48 h accumulative rainfall as a whole is closer to the observations as well, which results from the slant of the heavy rain area simulated by control runs by south compared with the observations while the improved heavy rain area by north compared with the one by the control run. For example, in the southern half part of Tianjin it experienced the rainfall larger than 100 mm during the period between 00Z 10 October and 00Z 12 October. However the results of the control runs (e.g. with the Scheme 1) show almost no records larger than 100 mm in the southern part of Tianjin while the results improved show that the rainfall area of 100 mm is well simulated. In addition, the similar improvement is reached as well in the southern-half area of Beijing: e.g., compared with the observational area of rainfall larger than 50 mm in the south by east of Beijing, the simulative results by the original model show no rainfall larger than 50 mm in the whole Beijing with an isohyet of 25 mm through the middle part of Beijing while the improved results show an isohyet of 50 mm through the middle part of Beijing, which is very close to the observations (Fig.2). The similar results on the trend of the rainfall area and on the amplitude of maximum rainfall are met with the other schemes (Schemes 2 to 6), among which Scheme 3 is especially prominent (Fig.4). The results by this scheme of experiment show that not only the trend of the rainfall areas larger than 50 mm is improved so as to generally coincide with the observations, but the heavy rainfall area larger than 100 mm is dramatically improved also. By the way, Scheme 3 is the only scheme by which the heavy rainfall area larger than 100 mm simulated is Fig.1. The observational 48 h accumulative rainfall (cm) from 00Z 10 October to 00Z 12 October 2003.

5 NO.1 LIU Ying, LIU Chongjian, XU Hui and ZHAO Yongming 71 Fig.2. Comparison of the 48 h accumulative rainfall (mm) from 00Z 10 October to 00Z 12 October 2003 (Scheme 1): (a) control run; (b) improved run. Fig.3. As in Fig.2 but for Scheme 2. Fig.4. As in Fig.2 but for Scheme 3.

6 72 ACTA METEOROLOGICA SINICA VOL.19 even bigger than that simulated by the corresponding original model (see Section 3 below in this paper for details), which demonstrates the prominent difference in the response of various explicit schemes of microphysics and convection to improving by the physical dissipative technique. In Sections 2 to 4 below it will be analyzed concretely. 3.2 Comparative experiments: schemes of convection parameterization In this section one will emphatically discuss the different response of the different schemes of convection parameterization to the physical dissipative technique (see Schemes 1 and 2 in Table 1) with also stress on Domain 3, the most inner domain. Schemes 1 and 2 both employ the explicit scheme of microphysics of Mix Phase (5) for Domain 1, Reisner (7) for both Domains 2 and 3, and the scheme of convection parameterization of Kain-Frisch for both Domains 1 and 2. The only difference between Schemes 1 and 2 is that Kain-Fritsch (6) is employed in Scheme 1 while Betts-Miller (7) in Scheme 2 for Domain 3. It is easily seen in comparison of Fig.2 with Fig.3 that the rainfall strength simulated by Schemes 1 and 2 is weaker than the observational one as a whole and even weaker with Scheme 1. One noticed that the difference between these two schemes lies in that Betts-Miller (7), in Domain 3, is used by Scheme 2 and Kain-Fritsch (6) by Scheme 1 that takes into account the irreversible entropy-increasing process of icing in a cloud. The physical nature of such a process should be in accordance with the principle of the second law of thermodynamics on which the physical dissipative technique is based. As a result, it is expected that Kain-Fritsch (6) will well respond to the physical dissipative technique compared with the other schemes. In fact, so far as this weather case discussed in this paper is concerned, the simulation of rainfall strength by Kain-Fritsch (6) is worse than that by Betts-Miller (7) originally, but the results after improving via the physical dissipative technique show a dramatic enhancement in the strength of precipitation by both the schemes with the closer patterns of precipitation to each other. 3.3 Comparative experiments: schemes of explicit microphysics In this section the response of different schemes of explicit microphysics that are employed in Schemes 3 and 4, respectively, to the physical dissipation technique will be discussed via the comparative experiments. These two schemes both employ Grell (3) in Domain 1 and Kain-Fritsch (6) in both Domains 2 and 3, and at the same time both employ the microphysics scheme of Mix-Phase (5) in domain 1 and Goddard (6) in Domain 2, respectively. The only difference between the two schemes lies in the microphysics scheme of Reisner (7) employed, in Domain 3, by Scheme 3 and Goddard (6) by Scheme 4. In principle, Reisner (7) is finer than Goddard (6) because the former contains one more predictive variable of the number concentration than the latter. However, the results by the control run show that not only the trend of the 48 h accumulative rainfall area simulated by both schemes is out of accord with the observations, but the strength of precipitation by Scheme 3 is so weak that it is even worse than the simulation by Scheme 4 (Fig. 5). On the other hand, the results after incorporating the physical dissipative technique show that the simulative outputs by Scheme 3 are improved dramatically for either the strength or range of precipitation (see Fig.4 as well as Section 3.1). Firstly, the strength of the heavy rain center after improving is more reasonable than that by the control run, and, secondly, the areas sketched with the isohyets of 200 mm and 100 mm (of the 48 h accumulative rainfall) are both closer to the observations than ones by the control run. Especially, after improving the area of maximum precipitation simulated by Scheme 4 is very different from the observations (the area sketched with isokyet of 200 mm is almost twice as much as the observations). As a result, it can be seen from the results mentioned above that the physical dissipative technique seems to have a function to promote exploiting the advantages of the finer scheme, say, Reisner (7), to the full, which is understandable from the point of view of the second law of thermodynamics because Reisner (7) incorporates the variable of the number concentration or density of

7 NO.1 LIU Ying, LIU Chongjian, XU Hui and ZHAO Yongming 73 the particles whose direction of diffusion is controlled by the second law. The point is that the horizontal diffusion scheme of the original model would fail in describing correctly the effect of the physical dissipation (the purpose of the physical dissipative technique just corrects the original horizontal diffusion so as to meet the direction of diffusion as pointed out by the second law of thermodynamics) with the result that the finer description of the number concentration added in Scheme 3 will accompany an incorrect effect of dissipation introduced at the same time. Thus, the results by the control run using Scheme 3 is even worse than ones using Scheme 4 that is simpler. By contrast, the results by the control run using Scheme 4 are better than ones using Scheme 3 in either the strength or range of precipitation owing to the simplicity of Scheme 4 where there exist no problems of inappropriate description of particle diffusion. On the other hand, the case is completely different when incorporating the physical dissipative technique by which the prediction of the number concentration in Reisner (7) is improved and thus the finer description becomes the real finer scheme leading to the better results reached. Fig.5. As in Fig.2 but for Scheme Comparative experiments: with/without convection parameterization In this section one will compare the response of the scheme with convection parameterization (Scheme 5) with one of the schemes without it (Scheme 6) to the physical dissipative technique (see Table 1). Both Schemes 5 and 6 employ the scheme of Fig.6. As in Fig.2 but for Scheme 5.

8 74 ACTA METEOROLOGICA SINICA VOL.19 Fig.7. As in Fig.2 but for Scheme 6. explicit microphysics Goddard (6) and the scheme of cumulus convection parameterization Kain-Fritsch (6) in either Domain 1 or 2, and Reisner (7) in Domain 3, with the only difference between Schemes 5 and 6 lying in the scheme of convection parameterization Grell (3) used in Domain 3 by Scheme 6 while none by Scheme 5. Indeed, the 48 h accumulative rainfall magnitude for this event simulated by Scheme 6 is closer to the observations than one by Scheme 5 although the ranges of rainfall simulated by these two schemes are very close to each other. For example, the observational maximum rainfall for this case is over 210 mm. On the other hand, the heavy rain area sketched with isohyet of 200 mm has been simulated by the control run using Scheme 6 which is weaker than the observations while the rainfall area simulated using Scheme 5 is far weaker with a greater deviation from the observations. After improving by the physical dissipative technique, the heavy rain area sketched with isohyet of 210 mm has been simulated by both Schemes 5 and 6. Furthermore, the range of the 210 mm rainfall area simulated by Scheme 6 with convection parameterization is closer to the observations than one by Scheme 5 without any parameterization. 4. Conclusive remarks Three sets of comparative experiments to investigate the different response of different schemes of explicit microphysics, schemes of cumulus convection parameterization, and schemes with/without convection parameterization to the physical dissipative technique, respectively, are performed. The specific results can be drawn as follows: (1) The improvement in the simulation of the 48 h accumulative rainfall from 00Z 10 October to 00Z 12 October 2003 by incorporating the physical dissipative technique is evident in either the magnitude or range of precipitation but with different details for different schemes of precipitation. (2) The physical dissipative technique displays a better potential for improvement with regard to the schemes containing the microphysics and convection parameterizations that are able to reflect correctly the direction of irreversible evolution. (3) The degree of improving by the physical dissipative technique using the scheme with convection parameterizations is higher than one using the scheme without it. To sum up, the response of the different schemes of precipitation to the physical dissipative technique is different from each other with the better potential of improvement for the schemes containing the reasonable explicit microphysics and/or cumulus convection parameterization. As a result, the results in this paper will help the design and improvement of the schemes of microphysics and convection parameterization in a mesoscale model (especially when it is involved with the irreversible evolution) so as to more reasonably describe the irreversible processes occurring really in the atmosphere. Indeed, the weather case studied and the schemes of precipitation parameterization for

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