The influence of observations propagated by convectively coupled equatorial waves

Transcription

1 Quarterly Journal of the Royal Meteorological Society Q. J. R. Meteorol. Soc. 137: , April 2011 A The influence of observations propagated by convectively coupled equatorial waves Qoosaku Moteki, a * Kunio Yoneyama, a Ryuichi Shirooka, a Hisayuki Kubota, a Kazuaki Yasunaga, a Junko Suzuki, a Ayako Seiki, a Naoki Sato, b Takeshi Enomoto, c Takemasa Miyoshi d and Shozo Yamane e a Research Institute for Global Change (RIGC), Japan Agency for Marine Earth Science and Technology (JAMSTEC), Yokosuka, Japan b Tokyo Gakugei University, Koganei, Japan c Earth Simulator Center (ESC), JAMSTEC, Yokohama, Japan d University of Maryland, College Park, Maryland, USA e Doshisha University, Kyotanabe, Japan *Correspondenceto: Qoosaku Moteki, Research Institute for Global Change, Natsusima-cho 2-15, Yokosuka city, Kanagawa, ,Japan. moteki@jamstec.go.jp This paper describes the propagation of the influence of radiosonde observations made during MISMO (Mirai Indian Ocean cruise for the Study of the Madden Julian oscillation-convection Onset), which was conducted over the Indian Ocean in the boreal autumn of The impact of these observations was assessed using an experimental reanalysis called ALERA that was produced by the local ensemble transform Kalman filter with the atmospheric global circulation model for the Earth Simulator. The difference of the analysisensemble mean between the analysis cycles with and without the MISMO observations was used to quantify the influence of these observations on the analysis field, which we call impact signals. Since the impact signals were contaminated by noise, probably due to the model s truncated spectral basis, a significance test was performed using the analysis ensemble spread, and the numerical noise was then successfully eliminated. The results indicated that convectively coupled equatorial waves propagated the impact signals to the central Pacific to the east and to the African continent to the west. In particular, the analysis fields around typhoons Cimaron, Chebi, and Durian over the tropical Western Pacific were significantly modified by the propagation of the impact signals through the Kelvin waves. Here two factors played important roles: (1) the meridional positions of the typhoons; and (2) the duration of the observations. The equatorial Rossby waves also made a significant contribution to the propagation of the impact signals. Such influences through the waves resulted in the reduction of the analysis spread. The shape of the region of reduced spread resembled the Matsuno Gill pattern with an east-west width of more than km. Copyright c 2011 Royal Meteorological Society Key Words: observation impact; signal propagation;kelvin wave;typhoon;mismo; ALERA Received 4 February 2010; Revised 20 December 2010; Accepted 22 December 2010; Published online in Wiley Online Library 19 April 2011 Citation: Moteki Q, Yoneyama K, Shirooka R, Kubota H, Yasunaga K, Suzuki J, Seiki A, Sato N, Enomoto T, Miyoshi T, Yamane S The influence of observations propagated by convectively coupled equatorial waves. Q. J. R. Meteorol. Soc. 137: DOI: /qj.779 Copyright c 2011 Royal Meteorological Society

2 642 Q. Moteki et al. 1. Introduction The impact of additional observations on the analysis and forecast errors in downstream regions has been investigated by many researchers using observing system experiments (OSEs) in midlatitudes (Langland et al., 1999; Szunyogh et al., 2002; Langland, 2005; Fourrie et al., 2006; Sellwood et al., 2008). These studies have shown that additional observations (e.g. dropsondes) over sparsely observed regions reduce the errors in downstream regions. In such OSE studies, the effect of these additional observations, which we call impact signals, is quantified as the difference between analysed or predicted fields with and without the assimilation of these additional observations. For instance, Szunyogh et al. (2002) reported that the impact signals of dropsonde observations over the North Pacific propagated at a speed of per day due to the Rossby wave packet propagation and that they contributed to error reduction over North America. Many of these previous studies were conducted in midlatitudes, so it is important to investigate the impact of additional observations over the ocean in the Tropics. Because the operational observations are sparser in the Tropics than in midlatitudes and because convection is highly active in this region throughout the year, the analysis and forecast fields have larger uncertainties. This suggests that additional observations in the Tropics could significantly contribute to the reduction of the analysis and forecast errors. However, the large uncertainty in the Tropics makes it difficult to assess OSEs objectively. The impact signals of the observations estimated in the OSEs might become contaminated by dynamically meaningless noise due to the model s truncated spectral basis and the assimilation schemes (e.g. an assumption of linearity, the interpolation error). Although previous studies evaluated the impact of additional observations on the assumption that such noise was small, Hodyss and Majumdar (2007) pointed out that the level of undesirable noise grew over regions with high uncertainty, as in the Tropics. They also speculated that a contaminating signal may occur through the processes of assimilation, interpolation, etc., even when grid point-based models are used. Moteki et al.(2007) attempted to eliminate such numerical noise in ALERA (AFES-LETKF Experimental ReAnalysis; Miyoshi et al., 2007) with significant tests. ALERA is an experimental ensemble reanalysis dataset produced by the 4D-LETKF (four-dimensional Local Ensemble Transform Kalman Filter; Hunt et al., 2007; Miyoshi and Yamane, 2007) with AFES (Atmospheric General Circulation Model for the Earth Simulator; Ohfuchi et al., 2004). This study assessed the impact of the dropsondes released over the tropical Western Pacific during the Pacific Area Longterm Atmospheric observation for Understanding of climate change 2005 (PALAU2005; Moteki et al., 2008). They showed that the undesirable noise was successfully eliminated by a significance test using the analysis ensemble spread as a reference of the analysis error, and the extracted impact signals prevailed at a realistic propagation speed. Their approach indicated the possibility of assessing the influence of observations of various field campaigns in the Tropics. This paper aims to assess the influence of the additional radiosonde observations during a field campaign called MISMO (Mirai Indian Ocean cruise for the Study of the Madden Julian oscillation convection Onset; Yoneyama et al., 2008). During MISMO, the additional radiosonde observations were conducted from the research vessel (RV) Mirai and from the Maldives Islands for about 40 days (Figure 1). Several convectively coupled equatorial waves and the onset of large-scale convection were successfully captured by the MISMO observations. Katsumata et al. (2009) have reported synoptic-scale variability of heat and moisture sources as well as sinks associated with the waves during MISMO. Because the uncertainty in the analysis and forecast generally becomes larger in a convectively active phase, convectively coupled equatorial waves could be strong candidates for dispersing the impact signals. Yasunaga et al. (2010)have shown that the propagation of equatorial waves observed during MISMO is partially represented in the distribution of the analysis ensemble spread in ALERA. The first objective of the present study was to investigate the contribution of convectively coupled equatorial waves to the propagation of the influence of the MISMO observations. In addition, the relationship between the equatorial waves and the typhoons Cimaron (TY0619), Chebi (TY0620), and Durian (TY0621) was considered by investigating the variation of the impact signal field as the second objective. These typhoons formed over the tropical Western Pacific and moved westward with similar routes between 10 and 20 N (Figure 1). Several previous studies using a statistical composite analysis showed the role of tropical waves in tropical cyclone activities and tropical cyclogenesis (Hall et al., 2001; Bessafi and Wheeler, 2006; Frank and Roundy, 2006). Further, the added observations are expected to enhance the accuracy of analysis over the tracks of waves and the fields around typhoons. The third objective was to discuss a potential use of the analysis ensemble spread in the assessment of the analysis improvement. This paper is organized as follows. Section 2 provides an outline of the MISMO campaign and the design of OSEs with ALERA. Section 3 describes the definition of the impact signal and its propagation through the tropical waves. The impact of the MISMO observations on the analysis fields around the three typhoons is shown in section 4. In section 5, the reduction in ensemble spread due to the MISMO observations is examined. In section 6, the advantage and remaining problems on the proposed indices using the spread is discussed. Section 7 provides conclusions derived from analyses of the previous sections. 2. Description of MISMO and ALERA 2.1. Additional radiosonde observations during MISMO The Japan Agency for Marine Earth Science and Technology (JAMSTEC) conducted a field experiment named MISMO in October December 2006, focusing on the initiation of convection in the Madden Julian Oscillation (Madden and Julian, 1994) in the central equatorial Indian Ocean. The radiosonde observations for our OSEs were performed from RV Mirai around a fixed location (0, 80.5 E) and from the Maldives Islands (Gan: 0.7 S, 73.2 E; and Hulhule: 4.2 N, 73.5 E). The GPS Vaisala RS92 sondes were launched during 1200 UTC 22 October 1200 UTC 9 December at RV Mirai (4 8 per day), 0000 UTC 31 October 1200 UTC 26 December at Gan (2 4 per day), and 1200 UTC 18 October 0000 UTC 26 November at Hulhule (2 4 per day). In this study, the period of

3 Propagation of Observation Impact through Tropical 643 Hulhule Gan R/V Mirai TY0619 CIMARON TY0620 CHEBI TY0621 DURIAN Figure 1. Best tracks of typhoons Cimaron, Chebi, and Durian. The open circles indicate the locations of the additional observations at RV Mirai, Gan, and Hulhule UTC 22 October 1200 UTC 2 December was selected for our OSEs because the radiosonde observations were reliably performed. Figure 2 depicts the longitude time cross-section of OLR (outgoing long-wave radiation) from 0000 UTC 22 October to 1200 UTC 2 December The daily estimates of OLR with a 2.5 resolution from polar-orbiting satellites (Gruber and Krueger, 1984) are provided by the National Oceanic and Atmospheric Administration (NOAA). Each equatorial wave mode filter (TD-MRG: tropical depression, also referred to as an easterly wave or an African wave, and mixed Rossby gravity; ER: equatorial Rossby; Kelvin; and MJO) is based on the method of Wheeler and Weickmann (2001). To distinguish each mode more clearly, frequencies of days and days as well as zonal wave numbers of 1 14 and 0 5 are adopted following Straub and Kiladis (2002) for the Kelvin wave and MJO modes, respectively. Equivalent depths in the range of 8 90 m are used for the Kelvin wave mode filter. For the TD-MRG wave and ER wave modes, respectively, frequencies of days and days and zonal wave numbers of 0 14 and 1 10 are adopted following Frank and Roundy (2006). The bold solid lines indicate the subjectively extracted propagation on the basis of the negative anomalies of the filtered OLR. Although the negative anomaly less than 7to 15 W m 2 is typically used to detect each wave mode in a statistical composite analysis, we extracted all successive wave features, including larger anomalies more than 3 Wm 2, as candidates to explain the propagation of the impact signals for descriptive purposes. The features of the TD-MRG, ER, Kelvin, and MJO modes (indicated by the bold solid lines) passing over the MISMO observation region (indicated by the bold dashed lines) were extracted 7, 2, 9, and 2 times, respectively. In addition, focusing on the variation of the raw OLR over the MISMO region in Figure 2, the MISMO period was roughly divided into four phases: October (moderate convection), 1 5 November (convectively suppressed), 6 15 November (moderate convection), and 16 November 2 December (active convection after the onset of intraseasonal oscillation like MJO); these periods are called P1, P2, P3, and P4, respectively. The variation of convection was confirmed by the humidity and radar echo data (Yoneyama et al., 2008; Katsumata et al., 2009). These periods were used as a basis for designing the sensitivity experiments of OSEs Design of ALERA and OSEs The ALERA dataset was produced by analysis/forecast cycles using a system composed of a 40-member ensemble forecast with AFES 2.2 (Enomoto et al., 2008) at a T159/L48 resolution and 4D-LETKF for the period from May 2005 to January As for the LETKF setting, the tuning parameters of LETKF are chosen to be the same as Miyoshi et al. (2007). That is, 10% multiplicative spread inflation and a local patch of model grid points for Gaussian localization are adopted. The assimilated observations were adapted from those used in the operational numerical weather prediction system of the Japan Meteorological Agency (JMA). The hourly observations are assimilated with seven hourly time slots at each analysis in 4D-LETKF as the same treatment as the JMA 4D variational assimilation system. It should be noted that satellite observations were not assimilated, with the exception of satellite-based wind data, because of technical problems. Miyoshi et al. (2007) confirmed that the accuracy of ALERA is comparable to the accuracies of the JMA operational analysis and the reanalysis by the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) (Kalnay et al., 1996) except in the upper atmosphere (above 30 hpa) and in high latitudes of the Southern Hemisphere. Also, the wave dispersion relationship for zonal wind at 200 hpa in ALERA was confirmed to be reasonably similar to that in NCEP reanalysis (not shown). Note that, in an AFES free-running simulation as well as the other global models (Lin et al., 2006), signals for mixed Rossby gravity waves tended to be generally weaker and signals for Kelvin waves had too large phase speeds and tended to be stronger than those from reanalysis datasets. The analysis ensemble mean and the spread of wind, temperature, humidity, and geopotential height were calculated from the 40-member analysis. The dataset used in this study was interpolated from the T159/L48 model s coordinate system to a longitude/latitudecoordinate system with a 1.25 resolution and a vertical pressure coordinate system with 17 levels from 10 to 1000 hpa, a commonly used system in deterministic reanalysis products. Temporal and spatial distributions of the spread qualitatively represent those of the errors and are dynamically consistent with actual phenomena (Miyoshi and Yamane, 2007; Moteki et al., 2007; Nishii and Nakamura, 2010), though the spread does not strictly match with the errors in space and time. The analysis ensemble spread provides valuable information for extracting significant impact signals, as described in the next section. In this study, OSEs are conducted with the observational datasets used in the ALERA and MISMO radiosonde data. As described before, we found that there were four different phases of convective activity. We then conducted five sensitivity experiments (EX1 EX5) for the period 22 October 2 December 2006, as summarized in Table I. 3. Propagation of the impact signal through convectively coupled equatorial waves 3.1. Definition of impact signal The impact signal is defined as the difference between analyses with and without assimilation of the MISMO data. Similarly to the analyses conducted by Hodyss and Majumdar (2007), this paper only considers horizontal velocity and temperature at each grid point of 1.25 by 1.25 resolution in the troposphere. To eliminate undesired noise and to extract dynamically related signals, a significance test is performed using the analysis ensemble spread (S). The test

4 644 Q. Moteki et al. (a) (c) (b) (d) P1 P2 P3 P4 Figure 2. Longitude time cross section of OLR from 0000 UTC 22 October to 1200 UTC 2 December Filtered-OLR negative anomalies of (a) TD-MRG wave, (b) ER wave, (c) Kelvin wave, and (d) MJO are contoured with an interval of 3 W m 2. Shading is for the raw OLR. Averaging was performed over 5 10 N for (a) and (b) and over 0 5 N for (c) and (d). Dashed lines indicate locations of the Maldives Islands and RV Mirai. Bold solid lines represent propagation of the convectively coupled equatorial waves extracted from the negative anomalies of filtered OLR. The four phasesof convective activities P1 P4 are shown in (d). Experiment Table I. Summary of OSEs. Description Experiment 1 (EX1) Without assimilation of all MISMO radiosonde data Experiment 2 (EX2) With assimilation of all MISMO radiosonde data Experiment 3 (EX3) With assimilation of MISMO radiosonde data during 1 5 November Experiment 4 (EX4) With assimilation of MISMO radiosonde data during6 15November Experiment 5 (EX5) With assimilation of MISMO radiosonde data during 16 November 2 December statistics (TS) with 39 degrees of freedom are defined by uw/o u w TS u =, ((S u w/o )2 + (S u w )2 )/(N 1) vw/o v w TS v =, ((S v w/o )2 + (S v w )2 )/(N 1) TS T = Tw/o T w ((S T w/o )2 + (S T w )2 )/(N 1), (1) where N = 40 is the number of ensemble members in ALERA, and u, v,andt represent the zonal and meridional winds and temperature, respectively. The subscripts w and w/o indicate the analyses with and without assimilation of the MISMO observations, respectively. For the impact signal, we used a difference total energy (DTE) metric, which is defined as (cf. Hodyss and Majumdar, 2007) DTE = (u w/o u w ) 2 + (v w/o v w ) 2 + c p (T w/o T w ) 2, T r (2) where c p = 1004 J kg 1 K 1 is the specific heat capacity at constant pressure and T r = 300 K is a reference temperature. Figure 3 shows the horizontal distribution of vertically integrated DTE between 1000 and 100 hpa calculated from the simple difference between EX1 and EX2 and calculated

5 Propagation of Observation Impact through Tropical 645 (a) (b) (c) distributions in Figure 3(a) and (c) are almost identical. At 1200 UTC on 22 October, the signals expand within the region, as can be explained by realistic atmospheric phenomena (Figure 3(d)). Hereafter, the DTE that is calculated only from the significant difference is called the impact signal in this study. The wavenumber-frequency filter used to extract the equatorial waves was applied to the DTE anomaly normalized by spread (NDTE anomaly) because the filter cannot be applied to the field that includes undefined values. NDTE anomaly is defined as follows: NDTE anomaly = NDTE NDTE σ NDTE, (3) where NDTE is defined as follows: 2 2 u w/o u w v w/o v w NDTE = + ((S u w/o )2 + (S u w )2 ) ((S v w/o )2 + (S v w )2 ) 2 + c p T w/o T w, (4) T r ((S T w/o )2 + (S T w )2 ) (d) Figure 3. Horizontal distribution of vertically integrated DTE (m 2 s 2 ) between 1000 and 100 hpa from the simple difference between EX1 and EX2 at (a) 0000 UTC and (b) 1200 UTC 22 October and the significant difference exceeding the 95% confidence level at (c) 0000 UTC and (d) 1200 UTC 22 October. from the significant difference exceeding the 95% confidence level (t-test with degrees of freedom N 1). At 0000 UTC on 22 October, when the first radiosonde data at Hulhule were assimilated in the analysis cycle of EX2, the difference only appeared in about a 1500 km square within the localpatchoftheletkfsystem(figure3(a)).sincethe localized difference in the initial time of the analysis cycle spreads out to the entire globe due to the truncated spectral basis at the next analysis cycle, non-zero values appear in distant regions (Figure 3(b)). As a caveat established by Hodyss and Majumdar (2007), the simple difference field is contaminated by the dynamically meaningless noise. Although the growth of such noise in the analysis cycle was smaller than that in the forecast experiment, it is difficult to distinguish between signal and noise by a certain threshold value alone. Thus it is necessary to perform hypothesis testing to identify statistically significant signals. The meaningless noises are successfully eliminated in the DTE field calculated from the significant difference (Figure 3(c) and (d)). At 0000 UTC on 22 October, the where NDTE and σ NDTE are the time average and standard deviation of the NDTE at each longitude for the period from 0000 UTC 22 October to 1200 UTC 2 December Thus the DTE normalized by spread is the NDTE and the NDTE normalized for the effect of the distance from the MISMO region is the NDTE anomaly. Although the NDTE fields include noise, it is relatively smaller than the significant difference. Thus the significant difference will be more strongly reflected in the anomaly field of the filtered NDTE. Note that the type II error (the error of failing to reject a null hypothesis when it is in fact not true) in a significance test caused by the underestimated analysis ensemble spread was confirmed at several grid points. Such grid points discontinuously appeared far from the MISMO region and seemed to be dynamically meaningless. Because most of such grid points appeared in the lower layers in high mountainous regions with steep slopes but not over the Indian Ocean and tropical Western Pacific, it is expected that the negative effects from such grid points on the analyses of this study are quite limited. Sections 5 and 6 will discuss the estimation error of the spread and remaining problems on the spread Tropical wave components of the impact signal To verify the hypothesis that convectively coupled equatorial waves could be candidates for propagating the impact signals, Figure 4 shows the longitude time cross-sections of the raw DTE, NDTE anomaly, filtered OLR, and filtered NDTE at 200 hpa. The 200 hpa level was selected since the maximum amplitude in the dynamic field for the tropical waves appeared at this level (Kiladis et al., 2005, 2009). The DTE are less than 5 m 2 s 2 between Eand E, and they are 5 20 m 2 s 2 in the vicinity of the MISMO region between 60 and 90 E (Figure 4(a) and (b)). Such effect of the distance from the MISMO region on the magnitude of the signals is well normalized in NDTE anomaly fields (Figure 4(c) and (d)): several coherent features outside the MISMO region appear. From

6 646 Q. Moteki et al. filtered NDTE fields in Figure 4(e) (h), we find that the hypothesis, which the impact signals could propagate in association with convectively coupled equatorial waves, is basically correct. That is, the negative anomalies of filtered- OLR correspond to the positive anomalies of filtered NDTE except for the TD-MRG wave component, which seems to be out of phase. In particular, the Kelvin wave mode indicates continuous signals for the longest distance and the largest amplitude among the four modes. However, to understand and compare characteristics between the wave modes for signal propagation, OSEs must be conducted with longer periods because there are few samples for lower-frequency waves (ER and MJO) in this dataset. Those features of DTE/NDTE show a relationship that larger impact signals correspond well to a convectively active phase of waves with a larger uncertainty. Also, the consistency of the impact signals and OLR patterns corroborates that the analysis ensemble spread is very effective in normalizing the difference of the datasets with and without the MISMO data, and a significance test using the spread works successfully to eliminate the meaningless noise. 4. Impact on tropical cyclones through convectively coupled Kelvin waves The previous section shows that the Kelvin wave component makes a significant contribution to the propagation of the impact signals and that its continuous signals extend up to the equatorial central Pacific. There is a possibility that the analysis fields around the three typhoons (Cimaron, Chebi, and Durian) generated over the western tropical Pacific were significantly affected by the MISMO observations through the Kelvin waves. Frank and Roundy (2006) and Bessafi and Wheeler (2006) discussed the role of convectively coupled Kelvin waves on tropical cyclogenesis and cyclone activities using statistical composite analyses. However, Frank and Roundy (2006) showed that the statistical signals of the Kelvin mode, which contribute to tropical cyclogenesis, are relatively unclear compared to those of the MJO and ER modes. Although such signals are generally hard to find in statistical composite analyses, they described that several cases of tropical cyclones would likely be affected by Kelvin waves. Yanase et al. (2010) demonstrates that the rapid intensification of Typhoon Durian is affected by a Kelvin wave from sensitivity experiments using a global cloud system-resolving model (NICAM: Non-hydrostatic ICosahedral Atmospheric Model; Satoh et al., 2008). If the MISMO observations could influence the analysis fields to the east of the MISMO region through Kelvin waves, the effect of Kelvin waves on the fields around the typhoons could be discussed using the DTE. Figure 5 shows the longitude time cross-section of the DTE averaged between 10 and 20 N, where the typhoons were generated and moved westward. Here the DTE at 500 hpa is presented because differences between DTE features of EX2 EX5 are the most significant at this level. The typhoon tracks from the Joint Typhoon Warning Center (JTWC) are shown for Cimaron, Chebi, and Durian. The propagation of the Kelvin wave extracted in Figure 2 is shown by black dotted lines. First, Figure 5(a) shows that the stronger DTE signals appear at the timing of the passage of each Kelvin wave. Then, the stronger DTE signals are conveniently marked as i1 i8, and the Kelvin waves corresponding to i1 i8 are called K1 K8. In EX3 without assimilation of the MISMO data during P1, signal i2 disappears (Figure 5(b)). In a similar way, signal i3 completely disappears in EX4 without assimilation of MISMO data during P2 (Figure 5(c)). Thus, in the cases that the Kelvin waves K2 and K3 do not receive additional information from the MISMO observations, the stronger signals i2 and i3 in the EX2 are found to disappear. If the stronger DTE signals around the typhoons were due to another phenomenon that had a faster propagation speed than the Kelvin waves (e.g. eastward inertio-gravity waves), signal i2 in EX3 and signal i3 in EX4 should appear. If the signals were due to a phenomenon that had a slower propagation speed than the Kelvin waves (e.g. MJO), i3 i8 in EX3, i4 i8 in EX4, and i6 i8 in EX5 should disappear or weaken significantly. In contrast, the impact signals i3 i8 in EX3, i4 i8 in EX4, and i6 i8 in EX5 clearly appear atthepassagesofthekelvinwaves(figure5(b),(c),and (d)). Therefore the differences between the DTE features in EX2 EX5 imply that the Kelvin waves affect the analysed dynamic fields of the typhoons. In order to investigate the characteristics of DTE fields when Kelvin waves and typhoons coincided, Figure 6 shows the horizontal distribution of vertically integrated DTE between 1000 and 100 hpa centred on each typhoon. Here signals i2, i4, and i7 were selected, as these were the most remarkable for each typhoon. The figure shows the DTE distributions at 1200 UTC 1 November, 1200 UTC 8 November, and 0600 UTC 27 November when Cimaron and K2, Chebi and K4, and Durian and K7, respectively, were at the same longitude. This confirms that the positions of the pressure minimum analysed in ALERA coincide well with those from the best track data and that the rotating air flows at 700 hpa are well represented in the vicinity of the typhoon centre. The significant characteristic that is commonly seen in each typhoon case is the large DTE region extending from the centre to the southwest. The first term of the zonal wind difference in Eq. (4) was larger than the other two terms (not shown), and it has been suggested that the zonal wind difference associated with the Kelvin waves to the south of the typhoons affects the horizontal shear (i.e. relative vorticity) against the environmental zonal flow to the north and/or the divergence. This characteristic is consistent with the results from Figure 7(d) of Frank and Roundy (2006) that show significant westerly wind anomalies of the Kelvin wave mode to the southwest of tropical cyclones. The large DTE region to the south of the typhoons tended to migrate eastward: the DTE values tended to increase as the Kelvin waves approached and decrease after the passage. The local maximum of the DTE at the typhoon centre appeared within 6 h of the passage of the convection centre of the Kelvin wave mode. Such features are seen especially clearly for Durian (Figure 7). The large DTE region to the south of Durian migrates eastward (Figure 7(a) (c)). As in Figure 7(d), its speed is roughly estimated in the range of m s 1, which is appropriate as the phase speed of convectively coupled Kelvin waves. These features also support the notion that the Kelvin waves affect fields around the typhoons at their passage. Also, these are quite consistent with the claim of Yanase et al. (2010) shown by the sensitivity experiments using NICAM: Durian is rapidly intensified due to the passage of the Kelvin wave (corresponding to K7 in this study) around 29 November.

7 Propagation of Observation Impact through Tropical 647 (a) (b) (c) (d) (e) (f) (g) (h) Figure 4. Longitude time cross-section of (a, b) raw DTE, (c, d) NDTE anomaly, filtered NDTE anomalies of (e) TD-MRG wave, (f) Kelvin wave, (g) ER wave, and (h) MJO at 200 hpa from 0000 UTC 22 October to 1200 UTC 2 December Contours with intervals of 0.05 represent the positive anomalies of filtered NDTE. Negative anomalies of filtered OLR are shaded in (e) (h). Averaging was performed over 5 10 N for (a), (c), (e), and (g) and over 0 5 N for (b), (d), (f), and (h).

8 648 Q. Moteki et al. (a) K1 (b) K1 K2 K3 i2 i1 i3 K2 K3 i2 i1 i3 K4 K4 K5 K5 i5 i4 i5 i4 K6 i6 K6 i6 K7 K8 K7 K8 i8 i7 i8 i7 (c) K1 (d) K1 K2 K3 i2 i1 i3 K2 K3 i2 i1 i3 K4 K4 K5 K5 i5 i4 i5 i4 K6 i6 K6 i6 K7 K8 K7 K8 i8 i7 i8 i7 Figure 5. Longitude time cross-section of DTE (m 2 s 2 ) at 500 hpa averaged between 10 and 20 N from 0000 UTC 22 October to 1200 UTC 2 December (a) DTE with EX1 2, (b) DTE with EX1 EX3, (c) DTE with EX1 EX4, and (d) DTE with EX1 EX5 are shown. The cross marks and black, blue and red circles indicate the category classes of the initial disturbance, tropical depression, tropical storm, and typhoon (severe tropical storm) with the best track. Bold dotted lines represent the propagation of the convectively coupled equatorial waves extracted in Figure 2. The stronger DTE signals around the typhoons are marked as i1 i8, and K1 K8 represent the Kelvin waves corresponding to i1 i8. 5. Evaluation of the reduction of analysis spread The previous sections show that the influence of MISMO observations is propagated by convectively coupled equatorial waves. Hence a reduction of the analysis spread is also expected on the tracks of the waves. This section attempts to discuss the influence of the observations on analysis spread. Generally, the verification method takes the analysis error as the root mean square difference between geopotential heights from radiosonde and objective analysis (Anthes et al., 1989). However, difficulties in verification have recently been pointed out (Koh and Ng, 2009). In particular, assessment using this method is only possible in regions with many operational radiosonde observation points. This limitation in the method will become a crucial problem in the assessment over the Tropics, where operational observational data are sparse. Moreover, the objective analysis data could be constructed so that the difference from radiosonde data becomes zero. Consequently, we propose a new index for the analysis error reduction rate using the analysis ensemble spread referring to the forecast error reduction rate defined by Szunyogh et al. (2002). Here the analysis error reduction rate was estimated against geopotential height, as done in many studies. The reduction rate of the analysis ensemble spread (%) at each grid is defined by 100 Sz w/o Sz w S z, (5) w/o where S z w and Sz w/o are the analysis ensemble spread of geopotential height from experiments with and without the assimilation of MISMO data, respectively. Positive and negative values of this quantity suggest the improvement and degradation of the analysis accuracy, respectively. In assimilation processes with an ensemble Kalman filter, it is obvious that the spread is always reduced within the region covered by the local patch (65 88 E, 9 S 12 N) at the instant of the assimilation of the added observations, while remote effects out of the local patch are necessarily nontrivial because of the time evolution of the spread in forecast processes (in fact, there are many grid points with increased spread). Meanwhile, considering the fact that the spread distribution is affected by contamination with meaningless noise, as in the analysis ensemble mean, a significance test should be performed for the spread difference. The appearance frequency of the extracted significant spread

9 Propagation of Observation Impact through Tropical 649 (a)12z01nov. (I2) [116.5E,18.9N] (a) i7-18 hour [12Z 26 NOV.] Latitude (centered on Storm) Latitude (centered on Storm) Latitude (centered on Storm) (b) i70 hour [06Z 27 NOV.] Latitude (centered on Storm) (b) 12Z08NOV. (i4) [135.3E,15.4N] (c) 06Z27NOV. (I7) [138.5E,10.8N] Latitude (centered on Storm) Latitude (centered on Storm) (c) i hour [00Z 28 NOV.] (d) (i7) 0h: 06Z 27 NOV. Longitude (centered on Storm) Longitude (centered on Storm) Lag (hour) Figure 6. The horizontal distributions of vertically integrated DTE between 1000 and 100 hpa (shaded), sea-level pressure (contoured), and horizontal wind vectors at 700 hpa centred on the position of each typhoon, with the best track data at (a) 1200 UTC 1 November (i2 for Cimaron), (b) 1200 UTC 8 November (i4 for Chebi), and (c) 06 UTC 27 November (i7 for Durian). Longitude (centered on Storm) 10m/s 20m/s difference (%) is defined by 100 K s K, (6) where K and K s are the total number of grid points in a target domain and the number of grid points at which the significant spread differences are extracted, respectively. Hence this quantity reflects the frequency of the passage of the dynamic phenomena that can propagate the significant spread difference. Combining the reduction rate of the analysis ensemble spread (Eq. (5)) and the appearance frequency of the significant spread difference (Eq. (6)), we define the following index as the analysis error reduction Figure 7. The horizontal distributions of vertically integrated DTE between 1000 and 100 hpa (shaded), sea-level pressure (contoured), and horizontal wind vectors at 700 hpa centred on Durian at (a) 1200 UTC on 26, (b) 0600 UTC on 27, (c) 0000 UTC on 28 November, and (d) the longitude time cross-section of DTE averaged between the centre and 10 south of Durian (shaded and contoured every 1 m 2 s 2 ) and lagged several hours with respect to the time of the passage of the Kelvin waves. The dashed lines in (d) represent phase speeds of 10 and 20 m s 1. rate: 100 Sz w/o Sz w S z w/o K s K. (7)

10 650 Q. Moteki et al. Note that the significance test for the spread is a necessary but not a sufficient condition for an actual reduction in analysis uncertainty because the spread could be a qualitative but not a quantitative error reference. Although it is expected that the change of horizontal patterns for the new index in Eq. (7) could qualitatively reflect that of analysis uncertainty fields in the OSEs, another validation using independent data with higher quality than an objective analysis is needed for obtaining the sufficient conditions. Figure 8 presents the horizontal distribution of the vertically integrated analysis ensemble spread: the vertically averaged analysis spread reduction rate in the layer of hpa averaged from 22 October to 2 December for geopotential height. In EX1 without assimilation of MISMO data (Figure 8(a)), spread of more than 100 m is widely distributed in the vicinity of the Maldives Islands over the Indian Ocean. In EX2 with assimilation of MISMO data (Figure 8(b)), the large spread is clearly reduced not only over the Indian Ocean but also over Africa and the tropical Western Pacific. In fact, the significant analysis spread reduction rates are distributed over such regions (Figure 8(c)). A noteworthy feature in Figure 8(c) is that the shape of the region of significantly reduced spread (the region where the analysis spread reduction rate exceeds 0.5% and the appearance frequency exceeds 2%) resembles that of the Matsuno Gill pattern of the heat source response in the Tropics (Matsuno, 1966; Gill, 1980). This correlation strongly corroborates the notion that Kelvin waves and ER waves are the dominant dynamic phenomena for propagating the observation information. Also, this is consistent with the results in Figure 4 that the Kelvin and ER components are predominant in the DTE signal propagation. Weakly degraded regions in the midlatitudes are explained by type II error in a significance test because the appearance frequency in such regions is very small (<2%) and the degraded regions disappear at higher confidence levels (i.e. 98% and 99%). To the west of the MISMO region, the analysis spread reduction rate and the appearance frequency in the region between 10 Sand10 N are very small. This suggests that the contribution of the advection by easterly winds is small. In the subtropical region (latitudes higher than 10 Sand 10 N), although the appearance frequency sharply decreases to the west of 60 E, the region of reduced spread prevails to the western coastal regions of Africa. TotheeastoftheMISMOregion,theanalysisspread is more reduced than those to the west, and the region of reduced spread extends to the central Pacific between 20 Sand20 N. This suggests that Kelvin waves have a powerful effect on enlarging the region of reduced spread, and their effect prevails up to km or more. From the perspective of improving the accuracy of the objective analysis over the entire Tropics, increasing the radiosonde observations that capture Kelvin waves will be one of the most effective approaches. Figure 8 shows that the horizontal distribution of the time-averaged analysis spread reduction rate is dynamically reasonable. However, when assessing the time variation of this index for individual phenomena, it is important to pay more attention to the behaviour of the index. Before investigating the time variation, Figure 9 shows characteristics of the vertical profiles of the analysis spread reduction rates for different areas (0 20 N; E, E, and E). These three areas were selected because they cover the tracks of typhoons Cimaron, Chebi, and Durian. Above 500 hpa, the analysis spread in all areas was found to be reduced, and the analysis spread reduction rate tended to decrease with distance from the locations of the additional observations. The decrease was associated with a decrease in the appearance frequency of the significant spread difference. However, the analysis spread reduction rate below 600 hpa is much smaller than that in the upper layers. This could be due to the facts that the spatial representativeness of the observations becomes smaller and that the amplitude of waves basically becomes smaller in the lower layers than those in the upper layers. Unlike the upper layers, negative values are seen in the regions of E and E (indicated by closed and open rectangles). The degradation in the lower layers at 0600 UTC (valid at about LST) was more remarkable than that at 0000 UTC, 1200 UTC, and 1800 UTC (not shown). One of the reasons for the negative values could be the estimation error of the analysis ensemble spread over land. A larger estimation error of the spread could be caused by the imperfection of the model s boundary layer schemes (e.g. vertical diffusion, surface flux). If the estimation error ofthespreadoverlandislargerthanthatovertheocean, a type II error of the significance test could result. Based on this problem in the lower layers, the analysis spread reduction rate between 500 and 100 hpa was found to be more appropriate for application to individualphenomena. In order to investigate the difference of the improvement between each typhoon case, Figure 10 shows the time series of the analysis spread reduction rates between 500 and 100 hpa averaged in the degree box centred on each typhoon position. As for Cimaron, although the relationship between the analysis spread reduction rate and the Kelvin waves K1 and K2 is indistinct, the remarkable reduction rates of 2.7% and 3.7% appear 6 h before and 24 h after the passage of Kelvin wave K3 (Figure 10(a)). As for Chebi, larger analysis spread reduction rates of 1 4% correspond tothepassagesofthekelvinwaves(figure10(b)).among the seven peaks where there is a jump of values above 0.5%, the five peaks appear within 12 h of the Kelvin wave passage (indicated by the shaded zones). The analysis field around Durian has a great spread reduction of 2 13% before 30 November (Figure 10(c)). These large values could be due to successive passages of Kelvin waves within a shorter period (about 5 days). Also, Durian could be susceptible to the Kelvin waves because Durian moved in lower latitudes than Cimaron and Chebi. In fact, the analysis spread reduction rates for all three typhoons have a significant dependence on latitudinal position, as shown in Figure 11. We found that the analysis spread reduction rate exponentially decreases with increasing latitude. The meridional gradient is consistent with the decay curve of the amplitude of the Kelvin wave calculated from linear theory (indicated by the solid line). The height anomaly of the Kelvin wave component from linear theory (e.g. Andrews et al., 1987) is written as = cû 0 exp( β 2c y2 + z 2H s ), (8) where c = 16 m s 1 is a typical phase speed that is roughly estimated from Figure 2 (corresponding to the Rossby radius of approximately 830 km), û 0 = 3ms 1 is a representative zonal wind speed over the equator, β is the meridional gradient of the Coriolis parameter, y is the distance from

11 Propagation of Observation Impact through Tropical 651 (a) (b) (c) Figure 8. Horizontal distribution of the vertically integrated analysis ensemble spread (coloured every 10 m between 50 and 130 m and contoured every 50 m) in (a) EX1 and (b) EX2 and (c) the vertically averaged analysis spread reduction rate (coloured) and the appearance frequency of the significant spread difference (contoured every 2% between 2% and 10%) in the layer of hpa averaged from 22 October to 2 December against geopotential height. Black dashed rectangles in (c) represent the area used to compute averages in Figure 9. the Equator, z = 5000 m is a representative geopotential height, and H s = 7300 m is a scale height in the tropical troposphere. The actual latitudinal positions are shifted northward by 10 because the degree box can be taken as the average position. This latitudinal dependency of the analysis spread reduction rate also corroborates the finding that the dominant phenomenon in propagation of observation information to the east is the Kelvin waves. Another factor that should contribute to the analysis spread reduction rate is the effect of the duration of the additional observations. The time-averaged analysis spread reduction rates for Cimaron, Chebi, and Durian, which are 0.31%, 057%, and 3.18%, respectively, could include effects of the duration of additional observations. Table II shows the time-averaged analysis spread reduction rate from EX2 to EX5 for each typhoon. The rates for Cimaron, Chebi, and Durian are interpreted as follows: Cimaron: The assimilation of the MISMO data from 3 days before genesis in EX2 for 17 days (22 October 7 November) results in a 0.17% higher spread reduction rate than assimilation from 6 days after genesis in EX3 for 5 days (1 November 5 November). Chebi: The assimilation of MISMO data from 16 days before genesis in EX2 for 25 days (22 October 15 November) results in a 0.53% higher spread reduction rate than assimilation from 7 days before genesis in EX3 for 5days(1 5November),and results in a 0.31% higher spread reduction rate than assimilation from 2 days before genesis in EX 4 for 10 days (6 5 November). Durian: The assimilation of the MISMO data from 33 days before genesis in EX2 for 42 days (22 October 2 December) results in a 3.09% higher spread reduction rate than assimilation from 24 days before genesis in EX3 for 5days(1 5November), results in a 3.10% higher spread reduction rate than assimilation from 18 days before genesis in EX4 for 10 days (6 15 November), and

12 652 Q. Moteki et al. Table II. Time-average analysis spread reduction rate (%) in the layer of hpa against geopotential height for Cimaron, Chebi, and Durian. The period for taking average is indicated in parentheses. Experiment no. TY0619 Cimaron (0000 UTC 25 October 1200 UTC 7 November 2006) EX2 EX3 TY0620 Chebi (0600 UTC 7 November 0000 UTC 15 November 2006) EX2 EX3 EX4 TY0621 Durian (1200 UTC 24 November 1800 UTC 9 December 2006) EX2 EX3 EX4 EX5 Analysis spread reduction rate (averaged period) 0.50% (0000 UTC 1 November 1200 UTC 7November) 0.33% (0000 UTC 1 November 1200 UTC 7November) 0.57% (0600 UTC 7 November 0000 UTC 15 November) 0.04% (0600 UTC 7 November 0000 UTC 15 November) 0.26% (0600 UTC 7 November 0000 UTC 15 November) 3.18% (1200 UTC 24 November 1200 UTC 2 December) 0.09% (1200 UTC 24 November 1200 UTC 2 December) 0.08% (1200 UTC 24 November 1200 UTC 2 December) 0.53% (1200 UTC 24 November 1200 UTC 2 December) Difference from EX2 0.17% 0.53% 0.31% 3.09% 3.10% 2.65% results in a 2.65% higher spread reduction rate than assimilation from 17 days before genesis in EX5 for 16 days (16 November 2 December). This comparison of the time-averaged analysis spread reduction rates objectively indicates the importance of the duration of additional observations. That is, a longer duration of observations makes a greater contribution to the improvement of analysis, and the positive impact of the additional observations remains in the analysis cycle after stopping the assimilation of additional observations. 6. Discussion This study shows the contribution of synoptic-scale waves over the Tropics in dispersing the impact signals of the MISMO data in the OSEs. Here we discuss the following two issues: (1) the advantage of our approach, and (2) supposed concerns on the analysis ensemble spread as a reference of the analysis error. As for the first issue, we tried to assess the impact of observations from analysis experiments, though it was usually evaluated from forecast experiments in most previous studies. One of the major characteristics of our approach is that the scale of impact signals in analysis experiments does not grow over a period of analysis cycles. In contrast, the scale in forecast experiments grows monotonically with respect to forecast time. The signals at a certain scale during a long period are more suitable for investigating the influences relating to various phenomena than those growing monotonically. In addition, significant data impact extracted by a significance test using the analysis ensemble spread was consistent with the variation of dynamic phenomena. This is potentially a great advantage to traditional assessments of OSEs by forecast experiments. As for the second issue, we need to pay attention to the fact that the analysis ensemble spread has several unsolved problems on quantitative agreement with the analysis errors (Houtekamer and Mitchell, 1998; Whitaker and Hamill, 2002). The problems depend on various factors relating to system settings of an ensemble Kalman filter (ensemble size, localization scheme, covariance inflation scheme, etc.) and a forecast model (parameterizations of cloud physics and boundary layer, etc.). Also, estimation of the spread is affected the magnitude of observation errors which cannot be flow-dependent estimated. Thus, the index proposed in section 5 cannot be used for the quantitative assessment of the reduction rate of the analysis error. In addition, our approach using the spread is based on the premise that the additionally assimilated observations can detect actual phenomena with high quality. Even if unrealistic random noises were assimilated, Kalman filter processes would provide a decrease of spread and fake improved grid points would appear. In the case that the amplitude of given noises is sufficiently smaller than

13 Propagation of Observation Impact through Tropical 653 (a) E, 0-20N E, 0-20N E, 0-20N K1 K2 K3 DB TD TS TY (a) DB TD TS TY K3 K4 K5 (b) (b) E, 0-20N E, 0-20N E, 0-20N K6 K7 K8 DB TD TS TY (c) Figure 9. Vertical profiles of the analysis spread reduction rate averaged from 22 October to 2 December against geopotential height for (a) above 500 hpa and (b) below 500 hpa. Black and white rectangles and white circle indicate the areas averaged for 0 20 N in the meridional direction and E, E, and E in the zonal direction, respectively. the original spread, such noises can be eliminated by a significance test. However, in the case of assimilating noises with large amplitudes, erroneous decreases of the spread should be significant. Thus, for our approach, it is a given fact that the additionally assimilated observations are realistic and are quality controlled before the calculation of the OSEs. 7. Conclusion This paper described the propagation of the influence of additional radiosonde observations during MISMO through convectively coupled equatorial waves. MISMO was conducted over the Indian Ocean during the period from October to December 2006 and captured several convectively coupled equatorial waves as well as the onset of large-scale convection associated with intraseasonal variation. Propagation of the impact signals of the additional observations was investigated using ALERA. Dynamically Figure 10. The time series of the area-averaged analysis spread reduction rate for the degree box centred on each typhoon position in the layer of hpa against geopotential height for (a) Cimaron, (b) Chebi, and (c) Durian. +,,, and represent the category classes of the initial disturbance, tropical depression, tropical storm, and typhoon, respectively. The open circle represents the fact that there is no grid with a significant difference in the spread in the box. The shaded zones indicate the period of ±12 h from the passages of the Kelvin waves K1 K8. meaningless signals due to the model s truncated spectral basis were successfully eliminated by a significance test using the analysis ensemble spread. On the basis of the temporal and spatial distributions of the indices, propagation of the influence of the MISMO data through equatorial waves is summarized in the schematic illustration of Figure 12. Grey eastward and westward arrows represent the propagations of the impact signals through eastward- and westward-propagating waves, respectively. The eastward-propagating waves such as Kelvin waves and MJO make a significant contribution to propagation of the influence of MISMO data, and the influence extends up to the central Pacific. The analysis fields around typhoons Cimaron, Chebi, and Durian, which were generated over the tropical Western Pacific during MISMO, were affected

14 654 Q. Moteki et al. LATITUDE CIMARON 7 CHEBI 6 DURIAN ANALYSIS ERROR REDUCTION RATE Figure 11. Scatter plot of the area-averaged analysis spread reduction rate versus meridional positions for Cimaron (open circle), Chebi (open triangle), and Durian (closed rectangle). Solid lines indicate the latitudinal dependence of the amplitude of the Kelvin wave from linear theory. The dashed line is the same as the solid line but is shifted northward by 10. Figure 12. Schematic illustration of the propagation of the influence of MISMO radiosondes. The region that is directly influenced in the vicinity of the additional observations is surrounded by a solid line. The significantly improved region is surrounded by a dashed line. Grey eastward and westward arrows represent propagations of the impact signals through equatorial waves. The impact on a tropical cyclone through Kelvin waves over the tropical Western Pacific is indicated by arrows extending to the north from the Equator. by the MISMO data through Kelvin waves and the analysis ensemble spread around the typhoons were significantly reduced. The reduced spread of the analysis fields around the typhoons resulted from two factors: (1) the latitudinal positions of the typhoons and (2) the duration of the observations. The analysis spread around Durian was especially reduced due to a combination of both factors; that is, it moved in lower latitudes than Cimaron and Chebi did, and it was generated during the latter part of the MISMO period. The ER waves also made a significant contribution to propagation of the influence of MISMO data. As a result, the shape of the region of reduced spread by the MISMO observations (surrounded by the dashed line) resembles the Matsuno Gill pattern of the heat source response in the Tropics. This implies that the MISMO observations widely affect the analysis through the Kelvin and Rossby waves, which are the major dynamic factors propagating the influence of the observations. Although the advection with easterly winds is also a candidate for contributing to propagation of the influence of the observation, there is almost no analysis spread reduction to the west of the MISMO region over the equator. This suggests that propagation of the analysis error information by advection is very small and limited compared to that by synoptic-scale waves. In addition, because the region of reduced spread to the west reaches up to latitudes higher than 20,interaction processes could have occurred between the equatorial waves and phenomena in the midlatitudes. Although specific interaction processes were not discussed in this paper, they should be one of the important future issues for understanding the impact of the MISMO data. Also, considering the fact that dominant dynamic phenomena vary with different regions and seasons, data impact should be investigated in various regions and seasons. In particular, although the contribution of the MJO could be significant, a re-evaluation of the MJO contribution would be needed since the period of the OSE was not sufficiently long relative to the time-scale of the MJO. It is necessary to conduct OSEs for a sufficiently long period (more than 2 months) in future studies. Acknowledgements We thank members of the observing system research and ensemble data assimilation group of JAMSTEC for support for this work. We also thank Drs Masaki Katsumata, Hiroyuki Yamada, Biao Geng, Mikiko Fujita, and Masanori Yoshizaki of JAMSTEC/RIGC for fruitful discussions. Two anonymous reviewers and the associate editor Dr Martin Leutbecher provided us with very constructive comments that helped clarify many aspects of this study. We used the Earth Simulator under the support of JAMSTEC for creating ALERA datasets. The AFES-LETKF system was developed by collaborative research among the Japan Meteorological Agency,theEarthSimulatorCenter,JAMSTEC,andthe Chiba Institute of Science. Global OLR data were provided by NOAA ( References Andrews DG, Holton JR, Leovy CB Middle Atmosphere Dynamics. Academic Press: San Diego, CA. Anthes RA, Kuo YH, Hsie EY, Lownam S, Bettge TW Estimation of skill and uncertainty in regional numerical-models. Q. J. R. Meteorol. Soc. 115: Bessafi M, Wheeler MC Modulation of south Indian ocean tropical cyclones by the Madden Julian oscillation and convectively coupled equatorial waves. Mon. Weather Rev. 134: Enomoto T, Yoshida A, Komori N, Ohfuchi W Description of AFES 2: improvements for high-resolution and coupled simulations. In High Resolution Numerical Modelling of the Atmosphere and Ocean, Ohfuchi W, Hamilton K (eds). Springer: New York; Fourrie N, Marchal D, Rabier F, Chapnik B, Desroziers G Impact study of the 2003 North Atlantic THORPEX Regional Campaign. Q. J. R. Meteorol. Soc. 132: Frank WM, Roundy PE The role of tropical waves in tropical cyclogenesis. Mon. Weather Rev. 134: Gill AE Some simple solutions for heat-induced tropical circulation. Q. J. R. Meteorol. Soc. 106: Gruber A, Krueger AF The status of the Noaa outgoing longwave radiation data set. Bull. Am. Meteorol. Soc. 65: Hall JD, Matthews AJ, Karoly DJ The modulation of tropical cyclone activity in the Australian region by the Madden Julian oscillation. Mon. Weather Rev. 129: Hodyss D, Majumdar SJ The contamination of data impact in global models by rapidly growing mesoscale instabilities. Q. J. R. Meteorol. Soc. 133: Houtekamer PL, Mitchell HL Data assimilation using an ensemble Kalman filter technique. Mon. Weather Rev. 126: Hunt BR, Kostelich EJ, Szunyogh I Efficient data assimilation for spatiotemporal chaos: a local ensemble transform Kalman filter. Physica D 230: