An enlarged map showing the observed and simulated trajectories of TC Batsirai from CTL and the sensitivity experiments around Réunion Island (Fig. 6a) highlights the orographically modified TC track. All simulations (blue, green, magenta, and orange lines) produce nearly identical trajectories until the system passes north of Mauritius (∼ 57° E) around 09:00 UTC on 2 February. However, a relatively weaker TC is simulated in FLT_all and FLT_mdg (minimum MSLP ∼ 942 hPa; green and magenta lines in Fig. 4) compared to CTL and FLT_reu (minimum MSLP ∼ 938 hPa; blue and orange lines in Fig. 4). After approximately 12:00 UTC of 2 February (Fig. 6a), as TC Batsirai propagates north of the region between Mauritius and Réunion Island (section i), the TC in both FLT_all and FLT_mdg continues to move southwestward, approaching closer to Réunion Island (green arrow). In contrast, the tracks in the other two simulations – CTL and FLT_reu – are deflected more westward (blue arrow).

On 3 February, when TC Batsirai moves north of Réunion Island (section ii), all simulations show a general southwestward propagation (blue and green dashed lines in Fig. 6a), with minimum MSLP values ranging from 940 to 950 hPa (Fig. 4). Nevertheless, FLT_all and FLT_mdg simulate a weaker TC (minimum MSLP ∼ 950 hPa; green and magenta lines in Fig. 4) compared to CTL and FLT_reu (minimum MSLP ∼ 945 hPa). Although the overall southwestward motion in section ii is similar across simulations, the distinct track orientations established in section i (westward versus southwestward) lead to differences in proximity to Réunion Island. Consequently, the minimum distance between the TC centre and the northern coast of Réunion Island decreases to ∼ 107 km in FLT_all and FLT_mdg around 06:00 UTC on 3 February, compared to ∼ 145 km in CTL and FLT_reu. On 4 February (section iii), the TC tracks in all simulations shift from southwestward to slightly west-northwestward, in closer agreement with IBTrACS.

Interestingly, the TC evolution simulated in CTL and FLT_reu – in terms of both trajectory and intensity – is nearly identical, suggesting that the terrain effect of Réunion Island on TC Batsirai during its nearby passage is negligible. At the same time, the mesoscale terrain of Madagascar appears to play a crucial role in modifying the track of TC Batsirai, bringing it closer to Réunion Island, whereas its influence on TC intensity in the vicinity is relatively minor.

The five-day accumulated precipitation distributions are shown in Fig. 7. TC-induced precipitation (Fig. 7a) is evident along the storm trajectory, with intense rainfall (∼ 500 mm over five days; blue shades) in the southern part of the cyclone over the ocean. Two other regions of heavy precipitation are notable: (i) ≥ 800 mm in the mountainous regions of Réunion Island, and (ii) ≥ 500 mm in the southeastern foothills of Madagascar. Over Réunion Island, consistent with Fig. 2b, intense precipitation exceeding ∼ 1000 mm over three days is confirmed to areas with terrain elevations above 1000 m, peaking at 3032 mm on the southern mountain peak. The simulated localized heavy precipitation over the mountainous region of Réunion Island is absent in FLT_reu, in a manner nearly identical to FLT_all. The difference in five-day accumulated precipitation between CTL and FLT_reu (Fig. S1b iin the Supplement) indicates that approximately 96 % of the localized heavy precipitation (e.g. 2906 mm) can be attributed to the steep terrain of Réunion Island. Notably, this orographically induced precipitation is confined to mountainous region above 1000 m (see Fig. 1 for topography). Although the simulated TC Batsirai in FLT_reu tracks farther north of Réunion Island, nearly identical to CTL (orange line in Fig. 6a), the localized heavy precipitation of approximately 3000 mm is absent in FLT_reu, similar to FLT_all. Furthermore, the differences in precipitation over Réunion Island between FLT_all and FLT_mdg, are negligible, indicating that the terrain effect of Réunion Island is highly localized and does not significantly influence precipitation beyond the island.

A box centered on Réunion Island (55–56° E, 20.8–21.5° S; rectangle in Fig. 7) is used to analyze hourly precipitation over land during the passage of TC Batsirai. The five-day evolution of the maximum hourly precipitation over Réunion Island (Fig. 8a) reveals (i) persistent heavy precipitation (≥ 10 mm h⁻¹) lasting approximately 60 h in CTL (light blue bars within the grey-shaded period from 18:00 UTC on 1 February to 07:00 UTC on 4 February), whereas (ii) only three hours of heavy precipitation are simulated in FLT_reu (yellow bars from 14:00 to 16:00 UTC on 3 February). During this period, the peak hourly precipitation reaches 96 mm h⁻¹ in CTL, compared to only 26 mm h⁻¹ in FLT_reu. A sharp increase in hourly precipitation to above 50 mm h⁻¹ occurs at 00:00 UTC on 3 February in CTL, and very intense precipitation (≥ 50 mm h⁻¹) persists for nearly one day while TC Batsirai passes near Réunion Island (section ii marked in Fig. 6a). After 4 February, when the TC moves away from the island, FLT_reu produces little to no precipitation, whereas CTL continues to simulate weak to intense precipitation ranging from 2 to 30 mm h⁻¹. Even with the TC at a distance, southwesterlies prevailed around the Réunion Island region, supplying low-level moisture toward the mountain slopes (data not shown). The consistent ascent of this moist air along the slope prolongs the precipitation.

A comparison between CTL and FLT_all (Figs. 4, 6, and 7) clearly demonstrates that the steep orography of Réunion Island critically influences the precipitation distribution, including both five-day accumulated and hourly rainfall. To further investigate the orographically induced low-level winds and moisture fields responsible for the persistent heavy precipitation over Réunion Island, a detailed analysis was conducted. Figure 9 shows the horizontal distributions of reflectivity and low-level moisture flux convergence at three selected times (indicated by red dots on the x-axis of Fig. 8a): 12:00 UTC on 2 February, prior to the onset of very intense precipitation (exceeding 50 mm h⁻¹) over Réunion Island; 00:00 UTC on 3 February, corresponding to the onset of very intense precipitation; and 12:00 UTC of 3 February, during the very intense precipitation period. During this period, the TC eye was located between 18.5 and 20° S (Fig. 9a–c), while the southern spiral rainbands passed across the island.

At 12:00 UTC on 2 February, the TC eye was located north of Mauritius, while reflectivity exceeding 25 dBZ was observed over Réunion Island, associated with a thin outer spiral rainband (Fig. 9a). Relatively weak southeasterly flow (8–10 m s⁻¹) prevailed at low altitudes around the island, generating a relatively small Froude number (Fr ≤ 0.3). Fr is a dimensionless parameter defined as Fr =U0/Nh, where U0 is the mean wind speed below the terrain height, N is the Brunt-Vaisala frequency, and h is the height of the mountain peak; Fr is proportional to the square root of the ratio of upstream flow's kinetic energy required to lift a fluid parcel over the terrain. Under such small-Fr condition, low-level winds flowed around the terrain, generating two distinct wind structures: (i) divergence (≤-20 g m⁻³ s⁻¹, red shading in Fig. 9d) on the windward side (e.g., the southeastern foothills) and (ii) convergence (≥ 40 g m⁻³ s⁻¹, blue shading) on the lee side (e.g. the northwestern slope). Another notable feature is that the ambient low-level southeasterlies converge with the deflected flow along the eastern coast (delineated by the green dashed line). In contrast, these wind structures are absent in FLT_reu at the same time (Fig. 10a, d). Although the TC is located north of Mauritius, similar to CTL, and relatively weak southeasterlies prevail at low levels, Réunion Island remains relatively calm in FLT_all.

At 00:00 UTC on 3 February, the TC approached closer to Réunion Island, and more pronounced convective regions with reflectivity exceeding 45 dBZ are evident over the southeastern and northern mountainous regions of the island at an altitude of 3 km (Fig. 9b), accompanied by a complex pattern of moisture convergence and divergence at low levels (Fig. 9e), similar to that seen at previous time (Fig. 9d) but with increase intensity. With TC approach, further intensified low-level southeasterlies (10–20 m s⁻¹) prevailed around the island, with Fr increasing to ∼ 0.4. The flow partially split and moved around the mountain foothills, resulting in (i) a rounded region of moisture divergence (≤-50 g m⁻³ s⁻¹, delineated by the yellow dashed contour) on the windward side near the foothills, and (ii) a strong moisture convergence region (≥ 80 g m⁻³ s⁻¹, delineated by the blue dashed contour) on the lee side. On the windward side, the partially split low-level flow continuously converges with the environmental southeasterlies, leading to localized moderate moisture convergence (∼ 20 g m⁻³ s⁻¹, blue shading) along the southeastern coast, as outlined by the green dashed contour in Fig. 9e. Meanwhile, the partially split low-level flow was uplifted over the southeastern mountain slope, generating complex wind patterns (Fig. 9e). These dynamical features correspond well with the enhanced reflectivity observed over the mountainous terrain.

In contrast, the strong reflectivity cores and organized low-level moisture flux patterns evident in CTL at 00:00 UTC are absent in FLT_reu at the same time (Fig. 10b, e). While the positions of the TC center in CTL and FLT_reu were similarly located between 19 and 20° S (Figs. 9a–c, 10a–c), spiral rainbands passed over the island. Unlike in CTL, relatively strong reflectivity and pairs of convergence and divergence were seen in FLT_reu only where the convective clouds existed within the spiral rainbands.

The vertical cross-sections along the A–B line of equivalent potential temperature (θe) and vertical wind (Fig. 11) indicate that low-level warm and moist air (θe≥350 K) is partially uplifted along the windward mountain slope from below 500 m to above 2.5 km. Very high θe values (≥ 356 K) extend from the southeastern coast to the mountain summit (∼ 1.8 km). The uplifted warm and moist air (θe≥ 350 K) reaches altitudes up to 4 km above the mountain crest, while a deeper moist layer, extending to about 5 km, is evident on the lee side (i.e., northwestern offshore of the island), where pronounced orographically induced moisture flux convergence occurs (delineated by the blue dashed contour in Fig. 9e). In addition to the partially deflected flow around the terrain and the associated wind convergence on the lee side, descending motion is also apparent along the downwind slope. The combined effects of low-level wind convergence and vertical uplift, likely enhanced by accelerated gravity-wave dynamics on the lee side, appear to play a crucial role in deepening the moist layer downstream of the island.

In contrast, in FLT_reu (Fig. 11b), the warm and moist air (θe≥352 K) remains confined below 1 km, and is distributed relatively homogeneously along the cross-section, with a drier air mass (θe≤350 K) above. The comparison between CTL and FLT_reu (Fig. 11) clearly demonstrates that the high terrain of Réunion Island plays a critical role in lifting the abundant low-level moisture advected by TC Batsirai to altitudes above 4 km on the windward side and near the mountain crest, thereby contributing to the intense precipitation over the mountainous region.

During 00:00–12:00 UTC on 3 February, spiral rainbands continued to pass over the island in CTL (Fig. 9b–c), and convective regions (reflectivity ≥ 45 dBZ) persisted over the mountainous areas. Compared with the reflectivity distribution at 12:00 UTC on 2 February (Fig. 9a), the spiral rainbands became further thickened, and the convective regions within the rainbands expanded by 12:00 UTC on 3 February (Fig. 9c), particularly in the southern sector of the TC. During this period, the dominant low-level winds shifted from southeasterly to easterly with TC propagation, with wind speeds slightly strengthening to exceed 25 m s⁻¹ at 10 m altitude. Consequently, orographically induced ascent on the windward side – especially along the eastern coast – and moisture convergence on the lee side became more pronounced (moisture flux convergence ≥ 100 g m⁻³ s⁻¹; Fig. 9e–f). In contrast, in FLT_reu (Fig. 10b–c, e–f), the convective regions and orographically induced wind patterns observed in CTL are absent. Instead, increased reflectivity and wind convergences associated with convective clouds within the spiral rainbands are apparent as similarly produced in CTL (Fig. 9).

An enlarged map showing the observed and simulated trajectories of TC Batsirai from CTL and sensitivity experiments around eastern Madagascar (Fig. 6b) highlights the orographically modified TC track. Similar to the behavior near Réunion Island (Fig. 6a), the simulated trajectories in FLT_all and FLT_mdg are nearly identical (green and magenta lines in Fig. 6b), whereas those in CTL and FLT_reu closely resemble one another (blue and orange lines) during the approach to landfall over eastern Madagascar. In both FLT_all and FLT_mdg, after passing the lee side of Réunion Island (west of ∼ 54.5° E; see also Fig. 6a), the TC turned more directly westward until making landfall along the eastern coast of Madagascar. In contrast, a more southwestward propagation is evident in CTL and FLT_reu. As a result, landfall in FLT_all and FLT_mdg occurred approximately 30 km north of the location indicated by IBTrACS and simulated by CTL (black and blue solid lines).

Regarding landfall timing, in both FLT_all and FLT_mdg, TC Batsirai reached the southeastern coast (i.e., near 48.5° E) at approximately 00:00 UTC on 5 February, about 12 h earlier than in CTL (00:00 UTC vs. 12:00 UTC; green and blue lines, respectively). At landfall, nearly identical minimum MSLP value (∼ 955 hPa) were simulated across the experiments (00:00 UTC on 5 February for FLT_all and FLT_mdg; 12:00 UTC on 5 February for CTL and FLT_reu; Fig. 4). The comparison between CTL and FLT_all suggests that the high terrain of Madagascar exerted only a minor influence on TC intensity, whereas its impact on the TC trajectory – particularly the timing and location of landfall – was more substantial. At the same time, the comparison between FLT_mdg and FLT_reu indicates that the influence of Réunion Island on the trajectory and intensity of the TC as it approached eastern Madagascar is negligible.

After landfall, the simulated trajectories of TC Batsirai in the absence of realistic Madagascar orography (i.e., FLT_all and FLT_mdg) continue to propagate westward to northwestward across the island. In contrast, simulations incorporating realistic Madagascar topography (i.e., CTL and FLT_reu, blue and orange lines in Fig. 6b) exhibit a gradual southwestward motion, consistent with the IBTrACS observation (black line).

The comparison of the five-day accumulated precipitation distributions between CTL and FLT_all (Fig. 7a–b) indicates that more than 1000 mm of precipitation was concentrated at the foothills of the southeastern slope of Madagascar, of which approximately 82 % (∼ 830 mm) was induced by the high terrain. Owing to the deflected TC trajectory in the flat-terrain experiment (FLT_all), and additional ∼ 220 mm of precipitation (maximum difference of -224 mm over 5 d; bluish area in Fig. 7b) was simulated along the central eastern coastal region (∼ 20° S). In contrast, no significant precipitation was produced over the inland region. The differences in precipitation over southeastern Madagascar between FLT_all and FLT_mdg are negligible. Likewise, the precipitation differences between CTL and FLT_reu are minimal, indicating that the terrain of Madagascar exerts a dominant control on the localized heavy precipitation over the southeastern slope.

Approximately 150 mm of additional precipitation is produced in FLT_all over the downslope of the mountainous region (bluish area in Fig. 7b), resulting from the continued westward to northwestward propagation of the simulated TC across the island (Fig. 6b).

The comparison of hourly precipitation between CTL and FLT_all over eastern Madagascar (45.8–51.0° E, 18.2–22.8° S; see analysis domain in Fig. 7) is presented in Fig. 8b. In CTL, the steep terrain produces sustained heavy precipitation (≥ 10 mm h⁻¹) for 19 consecutive hours beginning at 05:00 UTC on 5 February (grey-shaded period), with a peak intensity of 92.8 mm h⁻¹ at 15:00 UTC on 5 February. In contrast, under flat-terrain conditions (FLT_all), heavy precipitation persists for only 4 h and reaches a lower peak value of 44.5 mm h⁻¹. Consistent with the earlier landfall of TC Batsirai in FLT_all, the peak precipitation occurs earlier – at 00:00 UTC on 5 February, coinciding with landfall along the eastern coast – whereas in CTL the peak is observed later, at 15:00 UTC on 5 February. Furthermore, the precipitation differences over eastern Madagascar – particularly along the terrain foothills – between FLT_all and FLT_mdg are negligible, indicating that the terrain effect of Réunion Island has little influence on the localized precipitation over Madagascar.

To examine the detailed orographic effects of the steep terrain of Madagascar on long-lasting localized heavy precipitation, horizontal distributions of low-level reflectivity and vertical velocity were analyzed at three selected times (01:00, 07:00, and 13:00 UTC on 5 February; marked by three red dots along the x-axis in Fig. 8b; see Fig. 12) and compared with simulations without realistic topography (FLT_all) at corresponding times when TC Batsirai is similarly situated as in CTL (16:00 and 22:00 UTC on 4 February, and 04:00 UTC on 5 February; Fig. 13).

At 01:00 UTC on 5 February, when the TC eye was located offshore of eastern Madagascar (∼ 50.5° E, 20.5° S; Fig. 12a), it appeared relatively larger than when the storm passed near Réunion Island at 12:00 UTC on 3 February (Fig. 9c). An asymmetric ring of intense reflectivity (≥ 45 dBZ; Fig. 12a), accompanied by weak upward motion (≥ 0.2 m s⁻¹; yellowish region in Fig. 12d), was evident in the eyewall region over the ocean. In contrast, weakened spiral rainbands with reflectivity below 30 dBZ were observed in the southern sector of the system. Meanwhile, over the mountainous terrain (500 m topographic contour shown by the grey solid line in Fig. 12a), multiple scattered convective cells with intense reflectivity (≥ 45 dBZ) were identified. These convective regions coincided with strong low-level upward motion (≥ 1.5 m s⁻¹, red shades in Fig. 12d). Toward this region, southeasterlies (∼ 10 m s⁻¹) prevailed at low altitudes with Fr ∼ 0.6, indicating that they contribute to both wind convergence and lifting along the foothills. In contrast, simulations without realistic topography (FLT_all) exhibit near-zero vertical velocities over eastern Madagascar (Fig. 13d) and a corresponding absence of spiral rainbands with reflectivity in the range of 20–30 dBZ in the coastal region, which are evident in CTL (delineated by the black dashed contour in Fig. 12a).

At 07:00 UTC on 5 February, the TC eye made landfall along the eastern coast, while an asymmetric but further thickened eyewall with intense reflectivity remained evident (Fig. 12b). In particular, in the southern half of the TC eyewall (21–22° S, 48–50° E), eyewall structures are identifiable through intense reflectivity (≥ 45 dBZ) with further strengthened upward motion (≥ 2 m s⁻¹), induced by the convergence of intensified TC-associated southeasterlies (∼ 15 m s⁻¹) with orographically modified and weakened southerlies (∼ 10 m s⁻¹) along the mountain foothills (Fig. 12e). Correspondingly, Fr increased to ∼ 1.0. The role of terrain in generating this local wind convergence along the coastal mountainous ridge becomes more evident when compared with FLT_all. The simulation without realistic topography (FLT_all) shows homogenous strong southeasterlies (∼ 15 m s⁻¹) associated with the TC in the eastern coastal region (Fig. 13e), and correspondingly, convective regions are absent in this region (Fig. 13b).

Horizontal and vertical cross-sections of equivalent potential temperature (θe) along the A–B line (marked in Fig. 12e) at 07:00 UTC on 5 February are shown in Fig. 14. These reveal that a large volume of warm and moist air (θe ≥ 350 K) was advected toward the southeastern coastal region by intense southeasterlies (Fig. 13a). The region of elevated θe extends along the coast in the southern part of the TC, whereas relatively dry air (θe ≤ 347 K) is advected in the northern part. In the coastal region, three notable features are observed (Fig. 14b): (i) warm and moist air (θe ≥ 350 K) concentrated from the surface to ∼ 1.2 km altitude, (ii) a deep warm and moist layer (θe ≥ 347 K) extending above 5 km altitude with the TC eyewall, and (iii) local wind convergence between orographically modified weaker winds and relatively stronger cyclonic easterlies below 1 km height (delineated by the grey dashed contour). Notably, at the mountain foothills, an accumulation of warm and moist air (θe ≥ 350 K) is observed from the surface up to ∼ 2.3 km, about 1° from point A (indicated by a red arrow in Fig. 14b), whereas relatively dry air (θe ≤ 347 K, grey shading) dominates above the mountainous ridge.

The TC Batsirai made landfall along the southeastern coast around 12:00 UTC on 5 February, and by 13:00 UTC (Fig. 12c), the TC eye was no longer discernible. However, the southern portion of the cyclone (21–24° S, 46–49° E) still exhibited expanded and intensified convective regions (reflectivity ≥ 45 dBZ), particularly over mountainous terrain where strong upward motion (≥ 2 m s⁻¹) was observed, along with further strengthened horizontal winds (≥ 25 m s⁻¹; Fr ≥ 1.4). In contrast, simulations without realistic topography (FLT_all) exhibit very weak upward motion (≤ 0.5 m s⁻¹) in the southern sector of the TC (yellowish area in Fig. 13f). At the same time, FLT_all shows (i) a reduced area with reflectivity ≥ 45 dBZ in the southern half of the cyclone, and (ii) a horizontally expanded area with reflectivity exceeding 20 dBZ (Fig. 13c). These features – including reduced convective area, expanded stratiform regions, disappearance of the eye, and asymmetric wind fields – are characteristic of the decay phase of a landfalling TC (Tuleya and Kurihara, 1978; Chan et al., 2022). Moreover, as the FLT_all-simulated TC propagates across Madagascar, the orographically induced scattered convective regions and intense upward motions along the mountain foothills – prominent in CTL (Fig. 12c, f) – are entirely absent in FLT_all (Fig. 13c, f). Similar distributions of reflectivity and vertical velocity at low altitudes are also found in FLT_mdg, resembling those in FLT_all.