Ningbo, a sub-provincial city in Zhejiang Province, China (Fig. 1a), covers a land area of 9816 km², has a population of 9.78 million people, and produced a GDP value of CNY 1814.77 billion in 2024. It is located on the southern wing of the Yangtze River Delta (28°51^′–30°33^′ N, 120°55^′–122°16^′ E), bordered by the East China Sea to the east and Hangzhou Bay to the north. The region is characterized by varied topography that includes northeastern plains and southwestern hills (Fig. 1b). The study area has a dense network of rivers, including one of the eight major water systems of Zhejiang Province. Two major rivers converge within the urban area, flowing north-eastward into the East China Sea. Ningbo experiences a subtropical monsoon climate with average annual rainfall of 1539 mm. Rainfall is concentrated from May to September, mainly during the monsoon and typhoon seasons. As one of the regions in China most frequently and severely affected by tropical cyclones, Ningbo has experienced multiple severe urban flood events triggered by typhoons (e.g., Haikui in 2012, Fitow in 2013, In-Fa in 2021, and Muifa in 2022). Observations reveal substantial spatiotemporal variability in typhoon-related rainfall, making Ningbo an ideal study area.

In this study, two sets of IDF curve fitting were conducted. The first was performed for the period 1980–2014, consistent with the data period coverage of existing IDF curves, which were published in 2015 and remain in current use. This period was selected because both the quantity and the quality of rainfall data have increased substantially since 1980, and the data naturally ended in 2014 based on the local practical conditions and demands of that time. The existing published IDF curves were derived using the complete mixed rainfall data, without distinguishing between typhoon and non-typhoon rainfall, and were focused primarily on short-duration events, with sliding windows of mainly of 6 h or less during sampling. Research indicates that most extreme hourly rainfall events are caused by non-typhoon systems that include surface fronts, vortex/shear lines, and weak synoptic forcing (Luo et al., 2016). Consequently, short-duration (e.g., hourly scale) extreme rainfall intensity/frequency information derived from complete mixed rainfall data will be higher than that derived from typhoon-only rainfall data. This can lead to fitted IDF curves with higher rainfall intensities for short durations. For long durations (> 6 h), the results from mixed rainfall data may be distorted. The second fitting utilized typhoon rainfall data that covered 1980–2024 (i.e., updated to include recent years) to capture how the features of IDF curves have changed over time (compared with those for the 1980–2014 period).

By comparing the results obtained under different distributions (Sect. S3), the Exponential distribution combined with the minimum sum of squared deviations criterion (Fig. 3) was found to be generally applicable across all stations for the final fitting results. The optimal fitted curves are obtained through deterministic stepwise optimization. Starting from initial guesses, the method uses gradient information to determine the direction and step size for parameter updates within allowable ranges, systematically approaching the best fit. The process stops when the maximum iteration limit is reached or the convergence condition is met, yielding a uniquely determined optimal solution. The fitted Cs / Cv ratios generally fall within the range of 2.5–4.0, concentrated predominantly between 3.0 and 3.5. These results are reasonable compared with the fixed values of Cs / Cv adopted in previous studies (Yu et al., 2021). It should be noted that the error threshold criterion mentioned in Sect. 2 was originally established only for short-duration events and did not distinguish between typhoon and non-typhoon rainfall. In this study, this criterion was used as a reference rather than being strictly enforced. Given the varied characteristics among different typhoons and the notable interannual differences in typhoon frequency, the threshold was reasonably relaxed. Furthermore, validation based on absolute error was found to be more suitable for assessing the results in this study. In practice, except for a very few cases where the absolute error was 0.06 mm min⁻¹, all other results satisfied the condition of being < 0.05 mm min⁻¹ (Sect. S4).

Taking Yinzhou station as an example, the intensity–frequency curves of typhoon, non-typhoon, and complete rainfall data at 1, 6, 12, and 24 h are compared in Fig. 4. In this study, typhoon events were defined in terms of onset and termination based on their definition. For non-typhoon rainfall data and complete rainfall data, however, because no further differentiation of other weather systems is made, individual rainfall events lack clear physical boundaries. Therefore, a unified time-interval threshold is required to delineate independent rainfall processes and ensure consistency in the delineation criteria. When delineating rainfall processes from the complete rainfall data, the 24 h interval can ensure, to the greatest extent possible, that impact events of different typhoons are separated correctly. While this threshold may merge some short-duration storms separated by less than 24 h into a multi-peak, long-duration process, it does not exclude the storms themselves. Under the annual maximum sampling framework adopted in this study, processes are first delineated and then a moving window is applied. The peak rainfall intensity within any merged process is still retained and has the opportunity to be selected as the annual maximum value. Correspondingly, for non-typhoon rainfall data and complete rainfall data, the rainfall process is considered to have ended when a period of at least 24 consecutive hours without precipitation occurs thereafter. When the green line lies above the blue line, this indicates that typhoons are more likely to produce rainfall of a given intensity and that, for the same exceedance probability, they can generate more intense extreme rainfall. Comparison of the four subplots clearly shows that the blue and green curves begin to intersect at duration of 6 h and longer (Fig. 4b–d). As duration increases, the intersection position gradually moves toward the location of higher probability (Fig. 4c and d), indicating that the statistical characteristics of extreme rainfall exhibit clear dependence on duration and weather system. For short-duration extreme precipitation (e.g., 1 h) non-typhoon systems (such as the Meiyu front or severe convective weather) exhibit greater hazard potential (Fig. 4a). For long-duration extreme precipitation (e.g., 12 and 24 h; Fig. 4c and d, respectively), the rainfall intensity induced by typhoons can more readily reach or even exceed the levels associated with non-typhoon scenarios. This confirms quantitatively that typhoon systems are a key risk source for extreme precipitation under low frequency and long duration (e.g., those with a 100-year return period). The longer the duration, the greater the contribution of typhoons becomes to the statistical characteristics of extreme rainfall (Fig. 4b–d). Compared with non-typhoon convective systems with shorter lifespans and smaller spatial scales, the vast and more persistent rotational structure of typhoons enables them to sustain highly efficient moisture transport and convergent uplift over extended periods, thereby achieving substantial advantage in generating extreme accumulated rainfall. The above conclusions are generally applicable across all stations (Sect. S5), although minor differences exist.

This study compared the fitted results with currently published IDF curves. Intensities of typhoon rainfall at specific return periods are generally lower than those from the published IDF curves for short durations, but markedly higher for long durations, particularly for events with duration exceeding 6 h (Fig. 5a). Moreover, the differences are more pronounced for long durations after the data update (Fig. 5a). This reflects an essential difference in the dominant weather systems and physical mechanisms responsible for extreme rainfall across different durations. It is necessary to distinguish rainfall types (e.g., typhoon-type versus general-type) for differentiated design. The variation in intensity of typhoon rainfall with duration is more notable compared with the current IDF curves, and tends to stabilize after the 24 h processes (Fig. 5a). The newly developed curves reflect the unique characteristics of typhoons, exhibiting greater randomness and uncertainty. The primary hazard period is concentrated within 24 h, after which rainfall enters a phase of attenuation or stabilization. The applicability of the published IDF curves for extrapolating long-duration extreme rainfall intensities is limited (Fig. 5b). Designs based solely on the current IDF curves might result in insufficient drainage capacity for long-duration events. For urban drainage design, the intensity of typhoon rainfall within the 24 h window is a critical control target. Additionally, the hourly rainfall intensities produced by typhoons under high return periods remain comparable to the values of the published IDF curves at medium return periods (Fig. 5a). The non-typhoon weather systems make a greater contribution to extreme precipitation on the hourly scale, while typhoons, although responsible for a lesser contribution, remain capable of generating substantial hourly intensities. Extreme precipitation at longer durations (e.g., 24 h) driven by typhoon systems is characterized by higher accumulated rainfall rather than by instantaneous peak intensities of short-duration processes of convective weather systems (Fig. 5b). Comparison of the fitted results from different time periods revealed that the rainfall intensities derived from the 1980–2024 series are markedly higher than those obtained from the 1980–2014 series, with greater increase observed for longer durations compared with shorter ones (Fig. 5a). This indicates that the impact of typhoon precipitation has continued to intensify in recent years. Under the current changing conditions, precipitation events with high intensity and long duration that were previously less common are now more likely to occur (Fig. 5c). However, as indicated by the fitted data, this trend reflects an increase in the occurrence probability of such events, rather than a change in their extreme intensity.

Marked regional spatial variations are observed across county-level areas. As a representative coastal station, Beilun station exhibits distinct characteristics of typhoon precipitation. For this region, typhoons not only are the primary cause of high-impact extreme precipitation with long duration but also possess extreme hazard potential on short-duration scales, which is comparable to that of non-typhoon weather systems (Fig. 6a). Compared with Yinzhou station, Beilun station experiences considerably higher rainfall intensities. This phenomenon is related to its geographic location, which is more directly exposed to typhoons. The intensity at stations such as Fenghua and Ninghai is notably higher than that at Yinzhou station (table omitted). This difference is attributed primarily to the amplification effect of complex terrain on typhoon precipitation. Additionally, comparison of fitting results based on two periods, i.e., 1980–2014 and 1980–2024, across various stations revealed that extending the observation series generally leads to increase in typhoon rainfall intensity for the same duration and return period. This trend is most pronounced for Yuyao station and Cixi station, both located in northern Ningbo, as illustrated in Fig. 6b for Yuyao station. Statistics further show that the increase in rainfall intensity is driven primarily by a higher frequency of extreme precipitation rather than the surpassing of historical rainfall maxima. Under changing conditions, extreme precipitation from typhoons is transitioning from a “rare anomaly” into a “more frequent and high-risk phenomenon,” and thereby giving rise to new challenges for existing flood control and drainage systems.

The contribution of typhoons to extreme rainfall increases considerably with longer duration, and this characteristic is universal. The more severe impacts of extreme typhoon rainfall on the coastal and mountainous areas of the study region suggest that the recent increase in typhoon impacts is characterized by notable spatial non-uniformity. Additionally, thorough analysis of how these extreme 24 h rainfall records are realized through specific typhoon precipitation processes, including their spatiotemporal patterns, is crucial for rational design of drainage systems, reservoir operation strategies, and effective emergency management. Based on these findings, this study systematically extracted the key spatial and temporal patterns of rainfall by examining representative historical typhoon rainfall processes. Gridded data are available only from 1998 onward; therefore, to ensure consistency in the analysis of temporal and spatial patterns of rainfall, both analyses were based on station and gridded data from 1998 onwards.

The rainfall processes underlying the annual maximum 24 h rainfall sequences used for curve fitting at meteorological stations across Ningbo were extracted, and three distinct temporal patterns (Fig. 7d–f) were identified among the clustered rainfall processes (Fig. 7a–c). The proportions of the rainfall processes in the three categories were 33.77 %, 22.73 %, and 43.51 %; the corresponding mean peak rainfall coefficients were 0.79, 0.24, and 0.51. Additionally, as described in Section 2, each 24 h process was divided equally into three consecutive 8 h sub-phases. The proportion of event-total rainfall occurring in the sub-phase with the largest rainfall accumulation, averaged by category, was 60.69 %, 56.09 %, and 62.69 %, respectively. All differences in these indicators between categories were statistically significant. Temporal rainfall patterns in Ningbo are characterized primarily by the late-peaked pattern (Fig. 7d) and the central-peaked pattern (Fig. 7f). The late-peaked pattern and the early-peaked pattern (Fig. 7e) exhibit relatively typical single-peak structures, with rainfall being more concentrated and hourly rainfall intensity displaying a relatively abrupt pattern. The central-peaked pattern (Fig. 7f) is more uniform and moderate, featuring a double-peak structure.

Using the current published IDF curves for Yinzhou station and the Chicago hyetograph method, the 24 h rainfall series at 5 min intervals was calculated. The rainfall peak coefficients for Ningbo, corresponding to Fig. 7d–f, were also applied, with the return period set to 100 years. Subsequently, the hourly rainfall pattern structure was derived by accumulating rainfall over 12 consecutive 5 min intervals. It can be observed that the rainfall distribution in the Chicago hyetograph is excessively concentrated within a very short period, with the proportion of rainfall during the peak period exceeding 0.4 (Fig. 7g–i). In contrast, typhoon rainfall patterns show more moderate hourly intensity and gradient variations, differing considerably from the patterns generated by the Chicago hyetograph method. Therefore, it is recommended that the Chicago hyetograph not be applied directly as the temporal rainfall pattern for long-duration rainfall processes.

The spatial distribution of rainfall varies among typhoon events in Ningbo. The spatial grid is densely distributed, enabling a more detailed description of the spatial distribution structure of each rainfall event compared with data from the sparse meteorological stations. Consequently, rainfall data for the grids corresponding to the occurrence time of the targeted 24 h events were extracted to facilitate a more refined and realistic analysis of the spatial pattern of rainfall. The accuracy of gridded data must be verified. It is also important to note that this accuracy refers to how closely the spatial structure of the rainfall is represented by the gridded data compared with station data, not as a comparison of specific rainfall amounts. The consistency between the two types of data was assessed using three indices. First, the Spearman's rank correlation coefficient was employed to examine their monotonic relationship (Fig. 8a). Second, rainfall intensities from both datasets were ranked and grouped into five equal percentiles (quintiles), and the adjacent percentile matching rate was calculated as the proportion of grids with a percentile difference of ≤ 1 (Fig. 8b). Third, a spatial pattern shift index was constructed using rainfall magnitude-based weights to quantify the normalized displacement of rainfall centres between the two datasets (Fig. 8c). The median Spearman's rank correlation coefficient was 0.638 (Fig. 8a), reflecting acceptable agreement between the gridded data and station observations in terms of spatial precipitation ranking. The median adjacent percentile match rate reached 0.803 (Fig. 8b), meaning that the precipitation category for most processes differs by no more than one level between the two datasets. With a median value of 0.031 (Fig. 8c), the spatial pattern shift index revealed that the precipitation centroids of the two datasets are aligned almost perfectly. All three metrics consistently showed that the gridded data reliably captured the spatial rainfall distributions reflected by the station observations.

The processes under each temporal category were further divided into two subcategories according to the position of the areas of heavy rainfall and the spatial dispersion characteristics of the precipitation. The statistical significance tests under each temporal pattern indicated marked differences in the structural indices between the two spatial rainfall patterns. Overall, the spatial patterns of rainfall can be summarized into the following two types. The first type can be described as the dispersed type, which predominates among the observed cases (Fig. 9a–c). This type is characterized by widespread rainfall coverage, with relatively scattered areas of heavy precipitation. The sample proportions for the three specific spatial patterns were 26.62 % (Fig. 9a), 12.99 % (Fig. 9b), and 37.66 % (Fig. 9c). The median proportions of rainfall contributed by the top 30 % of grids ranked by rainfall amount were 43.81 %, 43.52 %, and 42.70 % across the three rainfall patterns, while the corresponding values for the bottom 30 % were 16.55 %, 17.89 %, and 18.76 %, respectively. This type exhibits a reasonably uniform overall distribution, with centres of heavy rainfall scattered over high-elevation mountainous areas and with a gentle rainfall gradient. The second type is characterized by concentrated rainfall, with localized centres of heavy rainfall that account for a substantial proportion of the total regional rainfall (Fig. 9d–f). It also displays a markedly pronounced northward offset. Among the three specific spatial patterns, the sample proportions were 7.14 % (Fig. 9d), 9.74 % (Fig. 9e), and 5.84 % (Fig. 9f), with the latter accounting for the lowest share. Across the three rainfall patterns, the median proportions of rainfall contributed by the top 30 % of grids (ranked by rainfall amount) were 67.67 %, 58.69 %, and 63.77 %, while those for the bottom 30 % were 4.18 %, 8.16 %, and 6.53 %, respectively. The formation of this type might be more complex, potentially influenced by the inherent characteristics of typhoons (Yu et al., 2017; Li and Zhao, 2019; Lai et al., 2024) or by interactions between typhoons and other weather systems such as westerly troughs (He et al., 2020). This can be attributed to exceptionally abundant or sustained moisture transport, or to convergence, resulting in stronger localized impacts.

Analysis of the spatial and temporal patterns of typhoon rainfall revealed that intrinsic typhoon characteristics and underlying surface properties both play important roles. The counterclockwise circulation of a typhoon shapes its asymmetric moisture transport, which is typically strongest on its northern side (Li and Zhao, 2019; Wu et al., 2024). The transport of warm and moist air from the eastern sea, driven by typhoons, creates favourable moisture conditions that facilitate the formation of heavy rainfall along the coast (Fig. 9d and f). As this warm, moist airflow, driven by the Coriolis force and pressure gradients, moves toward land, it interacts dynamically with complex underlying terrain (Feng et al., 2024; Wu et al., 2024; Wang et al., 2026). In areas with trumpet-shaped topography, pronounced windward slopes, or curved coasts, the airflow is forced to converge and ascend, greatly enhancing local updrafts and precipitation efficiency (Cheng et al., 2025), thereby shaping the final distribution of the centres of heavy rainfall (Fig. 9a–c). Rainfall over mountainous areas can sometimes intensify abruptly. Under typhoon conditions, the dynamic forcing of terrain on airflow can rapidly trigger or enhance convection within a short period. Additionally, the complex thermal properties of the underlying surface in mountainous regions tend to accumulate unstable energy locally, which can be released abruptly. These conditions might cause rainfall intensity to increase sharply over time (Fig. 7d and e) and exhibit localized intensification spatially (Fig. 9d and e). Unlike in mountainous regions, over the northern plains and other gently sloping areas where terrain forcing is weak, the occurrence of widespread heavy rainfall induced by typhoons often requires effective dynamic and thermal coordination with other large-scale weather systems such as westerly troughs and shear lines (Fig. 9d and f).

Further statistics were computed regarding the characteristics of typhoon intensity, translation speed, and track during the 24 h rainfall process of typical typhoons. Based on the median and mean values, stronger typhoons are associated with a larger and more dispersed spatial distribution of rainfall (Fig. 10a and b), while a slower average translation speed is associated with a longer duration within a certain region scale, resulting in stronger and more localized rainfall (Fig. 10c and d). For the central-peaked and spatially concentrated pattern, the regional concentration of rainfall might be related to other factors. In terms of track characteristics, cases with stronger local influence correspond to typhoon track endpoints that are further north (Fig. 10e). As the track endpoint moves further northwest, the typhoon rainfall impact area tends to extend further toward inland areas of the northwest (Fig. 10e and f). The overall tracks of typhoons are predominantly north-eastward and north-westward, with north-westward tracks being more frequent (Fig. 10g). This implies that, for the processes examined in this study, typhoons affecting the Ningbo region are mainly of the north-westward-track type. Combined with the rotational characteristics of typhoons, such tracks can bring a continuous supply of water vapor from the eastern sea.