Spatial Propagation of Different Scale Errors in Meiyu Frontal Rainfall Systems

Transcription

1 NO.2 YANG Shunan and TAN Zhemin 129 Spatial Propagation of Different Scale Errors in Meiyu Frontal Rainfall Systems YANG Shunan (fló ) and TAN Zhemin (!ó ) Key Laboratory for Mesoscale Severe Weather/Ministry of Education, and School of Atmospheric Sciences, Nanjing University, Nanjing (Received August 3, 2011; in final form January 24, 2012) ABSTRACT The spatial propagation of meso- and small-scale errors in a Meiyu frontal heavy rainfall event, which occurred in eastern China during 4 6 July 2003, is investigated by using the mesoscale numerical model MM5. In general, the spatial propagation of simulated errors depends on their horizontal scales. Small-scale (L <100 km) initial error may spread rapidly as an isotropic circle through the sound wave. Then, many scattered convection-scale errors are triggered in moist convection zone that will spread abroad through the isotropic, round-shaped sound wave further more. Corresponding to the evolution of the rainfall system, several new convection-scale errors may be generated continuously by moist convection within the propagated round-shaped errors. Through the above circular process, the small-scale error increases in amplitude and grows in scale rapidly. Mesoscale (100 km <L<1000 km) initial error propagates up- and down-stream wavelike through the gravity wave, meanwhile migrating down-stream slowly along with the rainfall system by the mean flow. The up-stream propagation of the mesoscale error is very important to the error growth because it can accumulate error energy locally at a place where there is no moist convection and far upstream from the initial perturbation source. Although moist convection plays an important role in the rapid growth of errors, it has no impact on the propagation of meso- and small-scale errors. The diabatic heating could trigger, strengthen, and promote upscaling of small-scale errors successively, and provide error source to error growth and propagation. The rapid growth of simulated errors results from both intense moist convection and appropriate spatial propagation of the errors. Key words: initial error, spatial propagation, upscale growth, moist convection, Meiyu frontal rainfall Citation: Yang Shu nan and Tan Zhemin, 2012: Spatial propagation of different scale errors in Meiyu frontal rainfall systems. Acta Meteor. Sinica, 26(2), , doi: /s Introduction The concept of predictability was first introduced by Thompson (1957) to describe the sensitivity of numerical weather prediction models to model initial conditions, due to the chaotic nature of the atmosphere. Even small-scale and small-amplitude initial errors may grow upscale so rapidly by inverse cascading, which will contaminate the prediction skill of a model for weathers at the whole range of spatial scales (Lorenz, 1969). Corresponding to the improvement of computer technology and numerical models, especially the increase of model resolution, the atmospheric predictability research has experienced a transition from synoptic scale to meso- and small-scale. As indicated by Lorenz (1969), the timescale of skillful prediction showed distinct divergence for air motions of different scales. In general, for large or synoptic scale weather systems, the timescale of predictability is about two weeks, while for the motion with a wavelength of 20 km, the efficient prediction can only last tens of minutes (Lorenz, 1969; Lilly, 1990). Anthes et al. (1985) first studied the mesoscale predictability with a mesoscale limited regional model, and indicated some enhanced predictability at meso- Supported by the National Natural Science Foundation of China ( ), China Meteorological Administration Special Public Welfare Research Fund (GYHY ), and Specialized Research Fund for the Doctoral Program of Higher Education of China ( ). Corresponding author: zmtan@nju.edu.cn. The Chinese Meteorological Society and Springer-Verlag Berlin Heidelberg 2012

2 130 ACTA METEOROLOGICA SINICA VOL.26 scale than synoptic scale. But Errico and Baumhefner (1987) and Vukicevic and Errico (1990) further demonstrated that the slow error growth in Anthes et al. (1985) arose from the combined effects of fixed lateral boundary conditions, unbalanced initial errors, and relatively strong numerical dissipation. Zhang et al. (2002, 2003) investigated the growth of initial error in a surprise snowstorm of January 2000 and found that the initial small-scale and small-amplitude error may grow rapidly at scales below 200 km due to moist convection. In a general framework, Tan et al. (2004) investigated the limitation of mesoscale predictability on an idealized baroclinic wave, and showed that the rapid growth of initial error is related to moist convection. The diabatic heating associated with moist convection plays an important role in the growth of initial error. By conducting high-resolution numerical experiments on storm- and convection-scale systems, Walser et al. (2004) and Walser and Schär (2004) investigated the possible influence of initial error on the prediction of intense convective systems. They found that diabatic heating associated with moist convection acted as a prime source of rapid growth of error, which led to a significant loss of predictability, as shown in Tan et al. (2004). Although increasing in model resolution could resolve many physical and dynamical processes more precisely, some small-scale instabilities not resolved before may be introduced into the simulation, and smaller-scale errors often possess more intensive, nonlinear and rapid growth. Therefore, exploring the error growth and error propagation mechanisms with high-resolution models is significant in expanding our knowledge about the atmospheric predictability. It has been accepted extensively that the stronger the moist convection is, the faster the error growth will be (Ehrendorfer et al., 1999; Tan et al., 2004; Zhang et al., 2006). Nevertheless, employing limitedarea ensemble experiments on the real cases, Walser et al. (2004) found that there existed a case which possessed violent moist convection as well as a high prediction skill surprisingly. This is discrepant to traditional awareness about predictability at meso- or convection-scale and presents a predictability mystery about the ambiguous behavior of moist convection, i.e., whether or not it reduces the mesoscale predictability. Hohenegger et al. (2006) presented a possible explanation that the different predictability levels cannot be simply judged by the intensity of moist convection but may need absolute instability, meaning that errors could propagate up-stream against the mean flow. When there is no up-stream propagation of errors, even though intense moist convection exists, the errors may be quickly blew out of the moist convection area and not contaminate the prediction skill. The evolution of initial error is described by both error growth, which depends on moist convection, and its spatial propagation. The latter is defined as the spreading of error energy from one point or region to its surrounding space (i.e., expansion of error spatial range), which is distinguished from the scale growth of error that just concerns about the scale change. Hohenegger and Schär (2007) demonstrated that the errors amplified within active moist convection could propagate throughout the domain by sound and gravity waves together in a few hours. Sound waves could amplify perturbation to far remote locations but with smaller amplitude, while gravity waves can propagate larger amplitude perturbation and accelerate the error growth. However, the mechanism of spatial propagation of errors at different scales is still an open question. What are the differences in the spatial propagation of errors at different scales? How would the differences in the error spatial propagation impact the error growth? Meiyu front and associated heavy rainfall are typical mid- and low-latitude multi-scale weather systems in East Asia. There is still a great challenge on the forecasting of precipitation in Meiyu season in China. Recently, predictability of Meiyu precipitation systems at mesoscale was studied based on some cases (Bei and Zhang, 2007; Liu and Tan, 2009; Zhai and Lin, 2009). Liu and Tan (2009) proposed a multi-stage model of error growth in the Meiyu precipitation system. Zhai and Lin (2009) also showed that the scale and amplitude of initial error play a significant role in the error growth. However, the propagation of initial errors in Meiyu precipitation systems has not been studied so

3 NO.2 YANG Shunan and TAN Zhemin 131 far. In the present study, spatial propagation features of initial errors at different scales, and associated impact on the error growth will be examined and discussed for a Meiyu frontal heavy rainfall case. The structure of this paper is as follows. An overview of the Meiyu frontal rainfall event and a brief introduction to experimental design are provided in Section 2. Section 3 discusses the overall spatial propagation process of the initial errors and the related characteristics. The spatial propagation mechanisms for different scale errors and their sensitivity to moist convection are investigated in Sections 4 and 5. Section 6 contains a brief summary. 2. Experimental design Meiyu frontal rainfalls resulting from quasistationary, east-west orientated frontal zones often cause severe, abrupt, and sustained flooding during the warm season in East Asia. A Meiyu frontal heavy rainfall event occurred along the Yangtze and Huaihe basin in China during 4 6 July This rainfall event happened under the typical Meiyu frontal environment favorable for the development of mesoscale convective systems (MCSs). There existed a largescale upper-level trough and a subtropical anticyclone at 500 hpa. The mesoscale upper- and low-level jets were coupled with the east-west orientated quasistationary shear-line of horizontal wind at 700 hpa, along which several MCSs were generated successively, moved downstream, and joined together (Liao and Tan, 2005). Due to these favorable atmospheric circulation patterns, heavy precipitation occurred in Hubei, Anhui, and Jiangsu provinces continuously. Figure 1a shows the observed 6-h accumulated precipitation from 1200 to 1800 UTC 4 July. Along the east-west orientated quasi-stationary Meiyu front, precipitation took on a belt shape with two obvious heavy rainfall centers. Detailed description of this rainfall event and the interaction of different scale weather systems can be found in Liao and Tan (2005) and Chu et al. (2007). In this study, the fifth-generation National Center for Atmospheric Research-Pennsylvania State University (NCAR-PSU) nonhydrostatic Mesoscale Model (MM5 Version 3) ( Dudhia, 1993) is used. We employ here four model domains (D1, D2, D3, and D4; see Fig. 2) with 36-, 12-, 4-, and 1.33-km horizontal grid Fig h accumulated precipitation (mm) from 1200 to 1800 UTC 4 July from (a) observation, (b) CNTL L, and (c) CNTL H.

4 132 ACTA METEOROLOGICA SINICA VOL.26 Fig. 2. (a) Configuration of the four nested domains, and (b) the detailed innermost domain. Shadings represent terrain height. resolutions, respectively. The outer 36-km resolution coarse domain contains horizontal grid points covering most of China, the 12-km resolution domain has horizontal grid points for simulating the mesoscale structure of the Meiyu frontal rainfall system, the nested domain D3 has horizontal grid points with a resolution of 4 km which could resolve moist convection explicitly, and the innermost domain D4 contains horizontal grid points covering the heavy rainfall centers (Figs. 1 and 2) with a high resolution of 1.33 km. The high-resolution control simulation (hereafter referred to as CNTL H) is conducted over all the four nesting domains and the results of its D4 domain are analyzed for small-scale error propagation, while the low-resolution control simulation (hereafter referred to as CNTL L) only employs D1 and D2. The initial and boundary conditions for unperturbed control simulations (CNTL H and CNTL L) are derived from the 1 1 NCEP final analysis data with time intervals of 6 h. The outer domain D1 is initialized at 0000 UTC 4 July, while the nested domain D2 is initialized 3 h latter (0300 UTC 4 July) by using the forecasting results from D1, and D1 and D2 are one-way nested. In CNTL H, the initial and boundary conditions for D3 and D4 are constructed like in D2, and the model is integrated for 36 h by two-way nesting. The simple ice-phase microphysics scheme and the Blackadar planetary boundary layer parameterization (Blackadar, 1979) are used for D3 and D4. The Bettes-Miller cumulus convective parameterization scheme (Betts and Miller, 1986) is used in D1 and D2, while for D3 and D4 in CNTL H, no convective parameterization is used since the explicit microphyics is at play. In the previous predictability studies, small amplitude random errors are often added to initial conditions (e.g., Tan et al., 2004; Liu and Tan, 2009). But after being projected to spectral space, this kind of random initial errors may exist in the whole spatial scales, and correspondingly, initial errors at different scales will all grow during the entire simulation. Therefore, in order to highlight the growth and propagation mechanism of small-scale initial error, two different types of errors, namely, small-scale and smallamplitude initial errors are employed in this study (Table 1). Specifically, one is small-scale monochromatic temperature error (which only contains grid-scale errors), and the other is the local Gaussian temperature error, which is similar to that in Hohenegger and Schär (2007). In order to investigate the propagation features of initial errors, a small-scale monochromatic temperature error is added to initial temperature field over D2 in CNTL L, i.e., the perturbation experiment MONO. The initial temperature in D2 of MONO is given as T mono (i, j, k) =T cntl l(i, j, k)+t 0 sin[(i + j)π/2], (1) where T mono and T cntl l are the initial temperatures in D2 of MONO and CNTL L, respectively. Subscripts i, j, and k run over x, y, and σ grid points

5 NO.2 YANG Shunan and TAN Zhemin 133 Table 1. Numerical experimental design Experiment Simple description CNTL H High-resolution control experiment with all the four domains D1 D4 CNTL L Low-resolution control experiment with only D1 and D2 MONO Perturbation experiment with initial monochromatic temperature error added to CNTL L PERT Perturbation experiment with initial Gaussian temperature error added to CNTL H, A 0 =1.0K PERT A5 As PERT, but the initial perturbation amplitude is A 0 =5.0K PERT A02 As PERT, but the initial perturbation amplitude is A 0 =0.2K FD Sensitivity experiment turning off the diabatic heating of PERT and CNTL Hatt =0h FD2 Sensitivity experiment turning off the diabatic heating of PERT and CNTL Hatt =6h over D2, and T 0 = 0.2 K is the initial perturbation amplitude. The total wavelength of this initial temperature perturbation is roughly 34 km (2 2 times the horizontal grid spacing). On the other hand, the initial error in MONO is prescribed everywhere in the model space, which makes it indistinguishable whether the local error growth is induced by error propagation or just the result of initial error growth itself. Therefore, in order to investigate the spatial propagation for different scale errors in detail, based on the high resolution experiment CNTL H, the second perturbation experiment PERT is designed, in which a local Gaussian temperature error is introduced into the initial temperature field. The initial temperature in D4 of PERT is given as T pert (x, y, z) =T cntl (x, y, z)+a 0 ( exp (x x 0) 2 2σ 2 (y y 0) 2 2σ 2 (z z 0) 4 ) 4d 4, (2) where T cntl and T pert are the initial temperatures in CNTL H and PERT, respectively; x, y, and z run over the three-dimensional gird points of the D4 domain. A 0 is the amplitude of initial error set to be 1, 5, and 0.2 K in PERT, PERT A5, and PERT A02, respectively. σ = 13 km (equivalent of 10 horizontal grid points) and d 2 km (equivalent of one vertical layer) are the radius of initial error in horizontal and vertical direction, respectively. The location of the error center is denoted by (x 0, y 0, z 0 ). Moreover, in order to detect the influence of moist convection on different scale errors spatial propagation, two additional experiments are conducted based on the high resolution simulation, in which the diabatic heating of D2, D3, and D4 is turned off at the beginning and after 6 h of integration, respectively, both in CNTL H and PERT. The two runs are referred to as Fake Dry (FD for short) and Fake Dry2 (FD2 for short) hereafter (see Table 1). 3. The overall propagation of initial errors There are two control experiments at the low and high resolutions. Figures 1b and 1c show the 6-h accumulated precipitation valid at 1800 UTC 4 July (with 15-h lead time) in CNTL L and CNTL H, respectively. The two control simulations produced the observed east-west precipitation belt (Fig. 1a) along the quasi-stationary Meiyu front very well in terms of both in the rainfall intensity and location, although the simulated precipitation in CNTL L was slightly weaker, while that in CNTL H was a bit heavier compared with observation. In addition, these two simulations have reasonably simulated the weather systems in this Meiyu frontal rainfall event, such as the 850-hPa lowlevel jet and humidity distribution, the 500-hPa subtropical anticyclone, and the 300-hPa upper-level jet (figure omitted). The differences between MONO and CTNL L show the growth and propagation of initial errors. At the beginning of the integration, initial errors decay extensively except for the areas within the moist convection zone, which is similar to that in Tan et al. (2004). After a longtime integration, complex and nonlinear interactions among different scale errors occur (Tribbia and Baumhefner, 2004). Moreover, the extension of different scale errors has enlarged and they overlapped with each other, making them indistinguishable. This confuses the analysis of spatial propagation of errors. Therefore, we will only discuss the error evolution during the first 6 h of simulation, during which a qualitative analysis of error evolution

6 134 ACTA METEOROLOGICA SINICA VOL.26 and spatial propagation may not be impacted although the error s amplitude is a little small. Figure 3 shows the 500-hPa zonal wind differences between MONO and CNTL L. During the first 6 h of simulation, three small-scale errors developed in the active moist convective zone along the Meiyu front. Fig. 3. Differences of 500-hPa zonal wind between MONO and CNTL L (contours with interval of 0.02 m s 1 ; negative values are dashed) together with vertical motion (> 0; shaded; m s 1 ) and horizontal wind (vectors) of CNTL L, valid at (a) 50, (b) 70, (c) 90, (d) 110, (e) 150, (f) 180, (g) 210, and (h) 340 min. The thick solid line in (b), (e), and (g) indicates location of the vertical cross-section in Fig. 4 for errors A, B, and C, respectively.

7 NO.2 YANG Shunan and TAN Zhemin 135 They are denoted as errors A, B, and C hereafter. It is shown in Fig. 3 that error A (hereafter ERA) generates near 115 E at about 50 min of simulation, and then both its amplitude and extent increase rapidly. The spatial propagation of ERA reveals a round-in-shape spreading with its center almost unmoved. Till 90 min, the continuous spreading of ERA leads to a fast amplitude decrease, and then it dissipates gradually. From the vertical distribution of ERA in Figs. 4a and 4b, it is shown that there exists a small terrain near the genesis location of ERA, which may trigger local instability. Thus, ERA first develops at low levels over the terrain, and then spreads upward to higher levels with one wavelength distribution nearly perpendicular to the surface. After that, due to the vanishing of low-level vertical motion (figure omitted), ERA disappears. Error B (hereafter ERB) develops from the residual perturbations of dissipated ERA near 116 E. Similar to the earlier evolution of ERA, ERB also grows under the local instability condition triggered by the terrain, and then spreads upward to form a wave shape distribution (Fig. 4c). In the horizontal direction, ERB grows rapidly in amplitude, and spreads roundin-shape uniformly with an almost unmoved center (Figs. 3d and 3g). After that, there also exists amplitude decaying of ERB. However, because of the long lasting low-level vertical motion over the terrain (figure omitted), ERB keeps its evolution. After being enlarged in horizontal range, the center of ERB moves downstream along with the mean flow, and its spatial propagation at that time shows an alternative up- and down-stream propagation, which is distinct from that in the earlier stage (Fig. 3g). Fig. 4. Vertical distributions of upward motion (thick solid lines with interval of 0.04 m s 1 ) and downward motion (thick dashed lines with interval of 0.04 m s 1 ) of MONO, and zonal wind difference (thin black lines with interval of 0.02 m s 1 ; negative values are dashed) between MONO and CNTL L along the cross-section line in Fig. 3 of ERA at 50 (a) and 70 min (b), respectively; ERB at 140 min (c); and ERC at 220 min (d).

8 136 ACTA METEOROLOGICA SINICA VOL.26 By 3 h, an organized intensive convection system has formed near E (Figs. 3e and 4d), in which error C (hereafter ERC) generates and grows rapidly (Figs. 3f 3h). ERC also experiences a round-in-shape spreading stage with its center unmoved. Because the intensive diabatic heating is mostly located in the mid troposphere, ERC propagates from the mid troposphere to upper and lower levels in the vertical (figure omitted). After the up-scale evolution of ERC, its vertical distribution shows a somewhat westward leaning feature (Fig. 4d), while the horizontal propagation of ERC shows up- and down-stream fluctuation propagation (Fig. 3h), similar to that of ERB. In addition, there appears obvious error growth between 115 and 116 E without active moist convection (Fig. 3h). The above discussion demonstrates that the wave-shaped propagation of initial errors, especially its up-stream propagation, is not only important to local growth of errors within moist convection but can also accumulate error energy at regions without moist convective instability, indicating the significance of error spatial propagation to the predictability. To quantify the evolution of the three errors mentioned above, temporal variations of the location, maximum amplitude, and horizontal spatial extent of 500-hPa zonal wind differences between MONO and CNTL L are calculated every 10 min. In the calculation of locations of error centers, the start point is set at the genesis location of each error, and the relative grid points are counted to measure the moving speed of each error. The maximum amplitude of each error is computed to quantify growth of errors with unitofcms 1. In the error propagation analysis, the horizontal extent is calculated by measuring diameters of the grid points with absolute value of error larger than 0.02 m s 1 supposing that the errors spatial distribution are round in shape in their early stage. This calculation can reasonably represent the horizontal extent of errors due to their round-shape spreading in the earlier evolution stage, but when the error distribution turns into ellipse with an obvious zonal feature, this method may be incorrect. Therefore, the spatial extent of errors will not be calculated any more when the anisotropy appears in the distribution of simulated errors. Figure 5 shows the movement, amplification, and propagation of errors A, B, and C. The three errors all increase in both amplitude and spatial extent in the initial stage. When these errors spread abroad continuously, their amplitude decreases sharply because of the extensive propagation of error energy. At this stage, even ERC that develops within the active moist Fig. 5. The center (line with squares; unit: grid point), amplitude (line with triangles; cm s 1 ), and horizontal spread (line with dots; unit: grid point) of errors in MONO at the initial 6 h of simulation. (a) ERA, (b) ERB, and (c) ERC.

9 NO.2 YANG Shunan and TAN Zhemin 137 convection cannot gain enough perturbation energy from the surrounding environment, but as the evolution of moist convection intensifies, the amplitudes of ERB and ERC increase again. The centers of these three errors all maintain locally while being confined within the small-scale and round-in-shape spreading. Therefore, the growth of small-scale error is local. When the scale of the errors is enlarged, their centers transform downstream slowly by mean flow, which brings errors into a wider range. Although the genesis location, lasting time, and growth of the three errors are different, their evolution and propagation are very similar. Along with the enlarging of errors spatial scale, these three errors all show a similar propagation, i.e., transforming from spreading round-in-shape with local rapid growth in amplitude to propagating up- and down-stream wavelike with their centers moving downstream slowly. The spatial propagation of error can accumulate perturbation energy even at places without active moist convection. The propagation depends on the error s horizontal scale. With the increasing of error s scale, its spatial propagation has a distinct change. What are the detailed spatial propagation features for different scale errors? This question will be investigated in the next section. 4. Propagation of different scale errors To further investigate the spatial propagation of different scale errors, this section employs a highresolution perturbation experiment PERT, which adds a local, small amplitude, Gaussian temperature error to the initial condition of CNTL H over the D4 domain. This small-scale initial error is located to the northwest of the active moist convection zone of the Meiyu front (Fig. 6). There is a strong westerly to the southwest of the mean flow, so the initial error will be blew out of D4 soon after the integration is started, and cannot move into the Meiyu frontal convective zone in a short period of time. As a result, the error growth in the early stage in this intensive moist convection zone will be realized only by the error spatial propagation, and then the propagated error may grow Fig. 6. Initial temperature difference at 600 hpa between PERT and CNTL H (contours with interval of 0.1 K), and 6-h accumulated precipitation of CNTL H (shaded; mm). rapidly. Although the initial error in PERT has a small amplitude, small extent, and is located far from the active moist convection zone, it can also lead to very large differences in precipitation. The simulated 6- h accumulative precipitation differences at 12 h have grown up to about mm (figure omitted). In the next two subsections, the horizontal propagation of small-scale (L <100 km) and mesoscale (100 km <L<1000 km) errors is discussed in detail, respectively. 4.1 Propagation of small-scale errors After the initial intensive decaying for about 10 min, the initial error in PERT starts to propagate abroad in the isotropic round shape, and quickly spreads all over the simulation area in 20 min. At 30 min, the simulated 600-hPa temperature differences larger than K have already appeared near N (Fig. 7), and much lower amplitude errors can also be seen all over the domain of D4 (figure omitted). The simulated errors have spread nearly 3.3 latitude degrees within 20 min, indicating fast sound wave spreading with a speed of about 303 m s 1. As shown in Figs. 7a and 7b, the initial smallscale error firstly spreads with isotropic round shape in horizontal, and then extends into the active moist convection areas. By 120 min, there have been many isolated small-scale errors in belt-shape, well matching the Meiyu frontal rainfall zone (Fig. 7c). After being

10 138 ACTA METEOROLOGICA SINICA VOL.26 Fig. 7. Temperature difference (shaded) at 600 hpa between PERT and CNTL H valid at (a) 30, (b) 60 (> K; K is contoured by the bold dashed line), (c) 120, and (d) 210 min (> 0.01 K). amplified, these small-scale errors in the moist convection will spread abroad again with the same propagation way as initial errors (Fig. 7d), but their amplitude (about K) is very small. A little while after the isotropic spreading, several new intensive convection-scale errors are generated continuously within the round-shape due to the development of new moist convection (Fig. 7d). These newly generated small-scale errors will then spread rapidly by sound wave once more, which accumulates error energy successively. Obviously, both the initial local errors and associated new errors in the moist convection show a circular evolution and propagation with sound wave isotropic spreading, and new convection-scale errors developing, and sound wave spreading again. To further quantify the error propagation in PERT, the difference total energy (DTE) is employed as in Zhang et al. (2003) and Tan et al. (2004): DTE = 1 2 (U 2 ijk + V 2 ijk + κt 2 ijk), (3) where U, V,andT are the wind components and temperature differences between CNTL H and PERT, κ = C P /T r, T r is the reference temperature, and i, j, and k run over x, y, andσ grid points over the analysis domain (D4 exclusive of boundary points). Figure 8 shows the power spectrum of domainintegrated DTE between CNTL H and PERT during the first 6 h of simulation. At the beginning of integration, the power spectrum shows an extensive distribution from 60 to 300 km, which is contradictive to the horizontal extent of about km intuitively given in Fig. 6. This inconsistency arises from the limitations of Fourier decomposition in which the base functions possess global features that may cause local small-scale fields to be projected onto extensive areas (van Tuyl and Errico, 1989). Along with the spreading of initial error, this kind of limitations disappears soon. During the first hour of simulation, due to the fast isotropic spreading of initial error, there exists rapid growth of DTE at most horizontal scales (Fig. 8a). About 1 h latter, several convection-scale errors are

11 NO.2 YANG Shunan and TAN Zhemin 139 Fig. 8. Power spectrum of DTE (m 2 s 2 ) between PERT and CNTL H plotted every 10 min from (a) 0 to 60 min, (b) 70 to 120 min, (c) 130 to 180 min, (d) 190 to 240 min, (e) 250 to 300 min, and (f) 310 to 360 min. generated in the moist convection zone. Correspondingly, the power spectrum of DTE increases evidently, with wavelength from 10 to 20 km (Fig. 8b). By 2 h, these small-scale errors in the rainfall zone have developed and began to spread abroad extensively by round-shape isotropic sound wave (Fig. 7d). With the enlarging of the error s extent, the power spectrum of DTE at mesoscale grows rapidly during this stage (Fig. 8c). Later on, many new convection-scale differences are generated within the moist convection zone, so in this period, the power spectrum of DTE shows an increase at small scale and a decrease at mesoscale (Fig. 8d). Between 4 and 6 h of simulation, the DTE power spectrum maintains a very similar shape, suggesting that the error distribution has been adjusted iteratively by error spreading governed by the background instability (Figs. 8e and 8f). After 6 h of simulation, the power spectrum of DTE begins to immigrate to larger scale gradually due to the upscale growth of errors in the moist convection zone (figure omitted). The above analyses demonstrate that although the initial error is local with small amplitude and small scale and far away from the moist convection zone, it can also spread all over the simulation domain rapidly

12 140 ACTA METEOROLOGICA SINICA VOL.26 by the sound wave. Then, these propagated errors may trigger many scattered convection-scale errors in the moist convective area, which will spread abroad by the isotropic, round shape sound wave further more. Through the above circular propagation, the smallscale and small-amplitude error may accumulate successively. To study the sensitivity of small-scale error s spatial propagation to the amplitude of initial error, two more perturbation experiments are carried out with the initial error amplitude (A 0 ) being 5 K in PERT A5 and 0.2 K in PERT A02, respectively. Figures 9a and 9b show the 600-hPa temperature differences valid at 30 min between CNTL Hand PERT A5, PERT A02, respectively. Comparing Fig. 9 with Fig. 7, it is seen that the isotropic spreading of errors during the first 1 h of simulation possesses strong linear character, with the outline circles of K in PERT, K in PERT A5, and K in PERT A02 almost superposing one another (see the bold dashed line in Figs. 7a, 9a, and 9b). This indicates that the isotropic spreading of small-scale error may not be impacted by its initial amplitude. Correspondingly, the DTE growth rates with different initial amplitudes are nearly the same within the first 60 min of simulation (figure omitted). Although the initial amplitude of error has no impact on the propagation of initial error and the DTE growth rate in the early stage, the evolution of the errors distribution will be different. Comparison of Figs. 9a and 9b with Fig. 7a shows that the newly developed scattered small-scale errors in the moist convection region (i.e., the southwest quadrant of D4) in PERT are much more than those of PERT A5, but fewer than those of PERT A02. Moreover, the spreading of these newly generated small-scale errors will impact the following error growth. By 120 min, the extension of simulated errors in PERT is much larger than that in PERT A5 (figure omitted). Therefore, the initial difference with smaller amplitude may much easier and more vibrantly trigger following isolated small-scale errors in moist convection areas, and may then induce a more rapid DTE growth after 1 h of integration (figure omitted). 4.2 Propagation of mesoscale errors When the initial small-scale and small-amplitude error grows upscale rapidly in the early stage, more and more mesoscale errors (100 km <L<1000 km) will appear in the moist convective area, and then their propagation will also change gradually. In this subsection, mesoscale errors are constructed by removing the differences between PERT and CNTL H with horizontal wavelength smaller than 100 km and larger than 1000 km using the Fourier filtering. Figure 10 shows the horizontal distribution of 500-hPa zonal wind differences at mesoscale between PERT and CNTL H. As shown in Fig. 10a, the mesoscale error is evident as early as 1 h of simulation, but its amplitude is so small (only about ms 1 ) for horizontal zone wind. After that, such local mesoscale errors begin to propagate rapidly up- Fig. 9. Temperature difference (shaded) at 600 hpa between CNTL H and (a) PERT A5 (> K; with K outlined by the bold dashed line), and (b) PERT A02 (> K; with K outlined by the bold dashed line), valid at 30 min.

13 NO.2 YANG Shunan and TAN Zhemin 141 Fig hPa zonal wind difference at mesoscale (100 km <L<1000 km) between PERT and CNTL H (negative values are dashed) valid at (a) 1 h, (b) 4 h, (c) 6 h (interval is 0.01 m s 1 ), and (d) 16 h (interval is 0.1 m s 1 ). and down-stream in the horizontal. After 3 h, the mesoscale error has extended nearly 14 longitude degrees with an obvious wavelike distribution (Fig. 10b). As shown in Fig. 10, there is a distinct zonal distribution for the mesoscale error; therefore, the meridional mean error is applied here for the discussion of mesoscale errors propagation. Figure 11 shows the meridional mean difference (averaged between 28 and 36 N) of 500-hPa zonal wind at mesoscale. Across the whole longitude range, the mesoscale error contains number 5 6 waves within E with the wavelength of about 3.7 to 4.4 latitude degrees ( km). Remarkably, there is also wavelike evolution of error at the upstream location of initial error without active moist convection, which results from the up-stream propagation of maximum amplitude error. Therefore, the up-stream propagation of mesoscale error plays a significant role in the local error growth, similar to that for small-scale error. Along with the evolution of the precipitation system, many mesoscale errors could be generated within the active moist convection zone, and then propagate up- and down-stream wavelike rapidly. Figure 12 shows the longitude-time (Hovmöller) diagram of mean 500-hPa zonal wind differences at mesoscale, mean zonal wind, and 1-h accumulated precipitation averaged between 28 and 36 N. It is shown that the spatial propagation of such mesoscale errors can be categorized into three types: slowly moving down-stream (black bold solid line), propagating up-stream (black bold dashed line), and propagating down-stream (black bold dotted line). For instance, at about 8 h of simulation, a weak negative-value error center formed near 117 E, which then propagated fast up- and down-stream (AA and AB in Fig. 12). From 8 to 15 h of simulation, the down-stream spreading errors propagated from 117 to 126 E at a speed of 39.3 ms 1, and the up-stream spreading errors propagated from 117 to Eataspeedofabout11ms 1. Assuming a two-dimensional (x-z) inviscid

14 142 ACTA METEOROLOGICA SINICA VOL.26 Fig. 11. The meridional (28 36 N) average of 500-hPa zonal wind difference (cm s 1 ) at mesoscale between PERT and CNTL H, valid at (a) 2 h, (b) 3 h, (c) 4 h, (d) 6 h, (e) 7 h, and (f) 8 h. Boussinesq flow without Coriolis force, the horizontal component of the group velocity of gravity wave (c gx ) is (see Eq. (7.45a) of Holton (2004)) c gx = U 0 ± U g, (4) Nm 2 U g = (m 2 + k 2 ) m 2 + k, 2 (5) where U 0 is the horizontal mean wind speed, U g is the relative group velocity of gravity wave, and k and m denote the horizontal and vertical wave number, respectively. The horizontal wavelength of zonal wind difference at mesoscale is about km (Fig. 11), while the vertical wavelength is about 16 km (figure omitted). Assuming constant (dry) Brunt-Vaisala frequency N 2 (N = 0.01 s 1 ), the relative group velocity of gravity wave based on Eq. (5) for such mesoscale errors is about 25.5 m s 1. It is shown that from 7 to 15 h of simulation, the mean wind speed is about 12.9 m s 1 in the upstream regions, and about 14.8 m s 1 in the downstream regions (Fig. 12). With Eq. (4), the group velocity of gravity wave for up- and down-stream propagations is about 12.6 and 40.3 m s 1, respectively. It is evident that the calculated group velocity of gravity wave in the up- and down-stream (12.6 and 40.3 m s 1 )is approximately equal to the directly estimated propagation speed (11.0 and 39.3 m s 1 ) of mesoscale error from Fig. 12. Alexander et al. (1995) reported that the local heat source originated from moist convection could trigger gravity wave in the atmosphere. The above analyses demonstrate that the up-stream and down-stream wavelike propagations of mesoscale error are carried out by gravity wave. The gravity wave can spread errors all over the west-east Meiyu frontal rainfall zone rapidly (Figs. 10c and 10d). Besides the above two wavelike propagations, there is another slow down-stream transferring of mesoscale errors along the line CC (Fig. 12), which is just similar to the movement of the rainfall system (gray shaded in Fig. 12). The error growth results from the moist convection instability. This error moves down-stream slowly along with the precipitation system by mean wind speed. Above all, after its formation, the mesoscale error may transfer down-stream slowly along with the rainfall system, as well as propagate up- and down-steam rapidly by gravity wave. The up-stream propagation of mesoscale error can accumulate error even at places

15 NO.2 YANG Shunan and TAN Zhemin 143 Fig. 12. Hovmöller diagrams of 500-hPa zonal wind difference (color shaded) at mesoscale between PERT and CNTL H, zonal wind speed (black line with interval of 1 ms 1 ), and 1-h accumulated precipitation (gray shaded) of CNTL H, averaged between 28 and 36 N. The black bold solid, dashed, and dotted lines indicate three kinds of propagation of mesoscale errors. without active moist convection, so it is a significant factor impacting local error growth. It is indicated by previous studies that moist convection plays a significant role in small-scale and mesoscale error growth (Tan et al., 2004; Liu and Tan, 2009). How does moist convection impact on the spatial propagation of errors? To address this question, sensitivity experiments without diabatic heating are carried out. The sensitivity experiment FD is constructed by turning off diabatic heating of CNTL H and PERT at the beginning of simulation so as to investigate the impact of moist convection on the spatial propagation of errors. In spite of the shut-off of diabatic heating, evolution of 600-hPa temperature difference (figure omitted) reveals that the isotropic sound wave spreading mechanism of small-scale errors still exists. But after the propagation of initial error, the generation of new convection-scale error disappears due to the lack of active moist convection in FD. Therefore, the circular growth of initial error at small-scale shown in Section 4 is not observed. To investigate the impacts of diabatic heating on mesoscale errors spatial propagation, experiment FD2 is conducted here. In FD2, the diabatic heating is turned off in CNTL H and PERT after the numerical model has been firstly integrated for 6 h. Figures 10c and 13 display the 500-hPa zone wind difference at mesoscale valid at 6 and 9 h of simulation in FD2, respectively. Comparison of Fig. 10c with Fig. 13 shows that the wavelike propagation of mesoscale error still maintains even though no diabatic heating is released in FD2. Moreover, the propagation speed of mesoscale error in FD2 is close to the gravity wave group velocity in PERT (figure omitted). The above results are now analyzed from the perspective of wave dynamics. Sound wave is formed through alternate adiabatic compression and expansion of air, whose propagation feature is related to the compressible characteristic of fluid and not impacted by diabatic heating. The propagation speed of pure 5. Impacts of moist convection on spatial propagation of errors Fig hPa zonal wind difference at mesoscale in FD2 valid at 9 h (negative values are dashed; interval is m s 1 ).

16 144 ACTA METEOROLOGICA SINICA VOL.26 sound wave is: cp c s = ± RT, (6) c v where c p, c v, R, andt are specific heat at constant pressure, specific heat at constant volume, the atmospheric gas constant, and the air temperature. From Eq. (6), it is known that the propagation speed of sound wave will not be influenced by diabatic heating, and sound wave is non-dispersive; therefore, it will spread error energy steadily. On the other side, gravity wave is triggered in stratified atmosphere by buoyancy. Its propagation is decided only by atmospheric stratification and not influenced by diabatic heating (for the definition of wave and calculation of wave speed, see Chapter 7 of Holton (2004)). However, because of the dispersive characteristic of gravity wave, its propagation amplitude will be smaller and smaller with time. Simultaneously, the simulated mesoscale error will move down-stream slowly by advection wind. Therefore, the amplitude of error in FD2 is much smaller than that in PERT. Especially, the error amplitude of the former is about one order smaller than that of the latter after 21 h of simulation (figure omitted). The above discussion suggests that diabatic heating may not impact the spatial propagation of simulated errors, but it is very important to the growth of error. Diabatic heating can trigger intensive smallscale errors successively in active moist convection areas. In the meantime, it may also promote the upscale growth of small-scale errors by providing error source continuously for the spatial propagation of mesoscale errors, and this will distribute error energy in space rapidly. Therefore, the error growth depends on both moist convection and the spatial propagation of errors. If there is no moist convection, simulated error will not grow, while if no up-stream propagation exists, the rapid growing errors in moist convection areas may be carried off very soon. Therefore, the rapid growth of errors may need combined actions of intensive moist convection and favorable up-stream spatial propagation of errors. 6. Summary The present study explores the spatial propagation of different scale errors in a Meiyu frontal heavy rainfall event by using the mesoscale numerical model MM5 through both low- and high-resolution twin simulations. Analyses on the overall spatial propagation of initial errors demonstrate that along with the enlarging of errors extent, errors generated under different environment conditions all show a transformational propagation from the spreading round-in-shape with a local rapid growth to propagating up- and down-stream wavelike with their centers moving downstream slowly by mean flow. The spatial propagation characteristics of error depend on its scale. The initial local small-scale error far away from active moist convection zone could spread all over the simulation domain rapidly by sound wave. Then, many scattered convection-scale errors are triggered in the moist convection region and they spread abroad by isotropic, round shaped sound wave further more. Corresponding to the evolution of rainfall, several new convection-scale errors may generate continuously due to moist convection within the propagated round shaped error region. Through the above circular propagations, small-scale errors may accumulate successively. The isotropic sound wave spreading of small-scale errors in the early stage possesses a linear characteristic and is independent of the error amplitude. However, with the integration time increasing, initial errors with smaller amplitude may trigger isolated small-scale errors in the moist convection region much easilier and more vibrantly after being spread abroad by the sound wave. Therefore, DTE grows much more rapidly for errors with smaller initial amplitude after 1 h of integration. For the mesoscale error, there are three forms of spatial propagation: the slow downstream transferring by the mean flow, the fast up-stream and down-stream gravity wave propagations. Among them, the up-stream gravity wave propagation can trigger new wavelike mesoscale errors even at the upstream regions far away from the initial error source with/without the presence of moist convection. The sound wave spreading of small-scale errors and wavelike gravity wave propagation of mesoscale errors are both independent of diabatic heating associated with moist convection. In absence of diabatic heating, the simulated error can also grow fast through the spatial propagation at the initial stage. But after

17 NO.2 YANG Shunan and TAN Zhemin 145 the isotropic sound wave spreading, new convectionscale errors could not be generated due to the lack of moist convection as well as the circular growth of small-scale errors. Moreover, the mesoscale errors spatial propagation amplitude may become smaller and smaller as the integration proceeds because of the dispersion property of gravity wave. The impact of moist convection on error growth is reflected in its triggering and strengthening of small-scale errors successively, affording extra energy to error growth, promoting the upscaling of small-scale errors. Moist convection actually provides error source to the spatial propagation of errors. Therefore, the rapid growth of initial errors depends on the combined actions of moist convection and the favorable spatial propagation of errors. The above conclusions are derived from analysis of one Meiyu frontal rainfall event. Because characteristics of the background field are case dependent, more and further case studies are needed. In addition, the evolution of initial errors in high-resolution numerical experiments may possess certain non-linear features. This should also be investigated in detail in future studies. REFERENCES Alexander, M. J., J. Holton, and D. Durran, 1995: The gravity wave response above convection in a squall line simulation. J. Atmos. Sci., 52, Anthes, R. A., Y. H. Kuo, D. P. Baumhefner, R. M. Errico, and T. W. Bettge, 1985: Predictability of mesoscale atmospheric motions. Adv. Geophys., 28B, Basdevant, C. B., L. R. Sadoumy, and M. Béland, 1981: A study of barotropic model flows: Intermittency, waves and predictability. J. Atmos. Sci., 38, Bei, N., and F. Zhang, 2007: Impacts of initial condition errors on mesoscale predictability of heavy precipitation along the Mei-Yu front of China. Quart. J. Roy. Meteor. Soc., 133, Betts, A. K., and M. J. Miller, 1986: A new convective adjustment scheme. Part II: Single column tests using GATE wave, BOMEX, ATEX arctic air-mass data sets. Quart. J. Roy. Meteor. Soc., 112, Blackadar, A. K., 1979: High resolution models of the planetary boundary layer. Advances in Environmental Science and Engineering. Pfaffin, J. R., and E. N. Ziegler, Eds., Gordon and Breach, Newark, N. J., Chu, K., Z. -M. Tan, and M. Xue, 2007: Impact of 4DVAR assimilation of rainfall data on the simulation of mesoscale precipitation systems in a Mei-Yu heavy rainfall event. Adv. Atmos. Sci., 24, Dudhia, J., 1993: A nonhydrostatic version of the Penn State-NCAR mesoscale model: Validation tests and simulation of an Atlantic cyclone and cold front. Mon. Wea. Rev., 121, Ehrendorfer, M., R. M. Errico, and K. D. Reader, 1999: Singular-vector perturbation growth in a primitive equation model with moist physics. J. Atmos. Sci., 56, Errico, R. M., and D. P. Baumhefner, 1987: Predictability experiments using a high-resolution limited-area model. Mon. Wea. Rev., 115, Hohenegger, C., D. Lüthi, and C. Schär, 2006: Predictability mysteries in cloud-resolving models. Mon. Wea. Rev., 134, , and C. Schär, 2007: Predictability and error growth dynamics in cloud-resolving models. J. Atmos. Sci., 64, Holton, J. R., 2004: An Introduction to Dynamic Meteorology. Academic Press, 535 pp. Liao Jie and Tan Zhemin, 2005: Numerical simulation of a heavy rainfall event along the Meiyu front: influences of different scale weather systems. Acta Meteor. Sinica, 63, (in Chinese) Lilly, D. K., 1990: Numerical prediction of thunderstorms Has its time come? Quart. J. Roy. Meteor. Soc., 116, Liu, J. -Y., and Z. -M. Tan, 2009: Mesoscale predictability of Mei-Yu heavy rainfall. Adv. Atmos. Sci., 26, Lorenz, E. N., 1969: Predictability of a flow which possesses many scales of motion. Tellus, 21, Spyksma, K., and P. Bartello, 2008: Predictability in wet and dry convective turbulence. J. Atmos. Sci., 65, Tan, Z. -M., F. Zhang, R. Rotunno, and C. Snyder, 2004: Mesoscale predictability of moist baroclinic waves: Experiments with parameterized convection. J. Atmos. Sci., 61, Thompson, P. D., 1957: Uncertainty of the initial state as a factor in the predictability of large scale atmospheric flow patterns. Tellus, 9, Tribbia, J. J., and D. P. Baumhefner, 2004: Scale interactions and atmospheric predictability: An updated perspective. Mon. Wea. Rev., 132,