Global expansion of tropical cyclone precipitation footprint

Domain: earth_science
Published: 2024-06-06
Editorial outcome: major_revision

Abstract
Precipitation from tropical cyclones (TCs) can cause massive damage from inland floods and is becoming more intense under a warming climate. However, knowledge gaps still exist in changes of spatial patterns in heavy TC precipitation. Here we define a metric, DIST30, as the mean radial distance from centers of clustered heavy rainfall cells (>30 mm/3 h) to TC center, representing the footprint of heavy TC precipitation. There is significant global increase in DIST30 at a rate of 0.34 km/year. Increases of DIST30 cover 59.87% of total TC impact areas, with growth especially strong in the Western North Pacific, Northern Atlantic, and Southern Pacific. The XGBoost machine learning model showed that monthly DIST30 variability is majorly controlled by TC maximum wind speed, location, sea surface temperature, vertical wind shear, and total water column vapor. TC poleward migration in the Northern Hemisphere contributes substantially to the DIST30 upward trend globally.

Introduction
Tropical cyclones (TCs) have a large area footprint and strong destructive power which threatens lives and property1–3. TC impact is mainly due to strong winds, storm surges in coastal areas, and heavy precipitation4,5. Future climate model projections generally indicate a decrease in the global average frequency of TCs and an increase in the global average intensity of TCs6. An increased TC rainfall rate is expected with a warming climate due to the Clapeyron–Clausius scaling of water vapor in the atmosphere7–11. However, recent studies based on satellite rainfall measurements12,13 demonstrate that the TC rainfall rate shows a decreasing trend in the inner-core of the rain band with increases in the outer bands. This reverse pattern could be associated with both atmospheric stability and the higher availability of water vapor triggered by warmer sea surface temperature (SST)12,13. TC rainfall area is another key factor to affect TC rainfall distribution, which increases with increasing relative SST14, defined as the difference between the local SST and the average SST over the tropical oceans.

Although many prior studies12,13,15–17 discuss the changes in TC rainfall rates and accumulated TC precipitation, we still need more knowledge of the spatial structure of TCs and their connection with climate change. Rainfall is controlled by different mechanisms in different parts of the TC. While convective rainfall dominates in the inner core of the TC driven by atmospheric updraft, the outer TC bands generally have stratiform precipitation18. Recent studies19,20 also find that TC precipitation in the inner core and outer region is controlled by TC intensity and environmental conditions. In addition, the majority of TC precipitation research uses rainfall metrics (e.g., mean or median) based on arbitrary radii (e.g., 100 km and 500 km) from the TC center6,10,15. However, different definitions of TC rainfall rate can be challenging for multi-model comparisons10. Furthermore, the within radii averaging approach may not be an accurate description of the TC rainfall risk because of the high spatial variabilities in TC rainfall in both the core and outer band areas21,22.

While there is consensus that the TC rainfall rate will increase with a warmer climate following the Clausius-Clapeyron equation, the actual fractional rainfall increase varies above or below the 7% °C−1 theoretical rate with SST warming among different models23,24. There is an urgent need to understand mismatches between models and observations, particularly how the fractional rainfall increase will likely change when one moves from the TC center by certain distances10. Therefore, here we define a TC rainfall metric DIST30 as the mean radial distance from centers of clustered heavy rainfall cells (>30 mm/3 h) weighted by their rainfall rate (see Methods) to the TC center. As compared with the existing spatial metrics25–27 for TC rainfall, the DIST30 has a more generalized description of the distance from the center of clustered heavy rainfall cells to each TC center. It provides a more direct approach to understanding the potential major inland flood risk caused by heavy TC rainfall. DIST30 is constructed based on a 41-year quality controlled high-resolution global precipitation data set (MSWEP). Our results indicate that DIST30 has increased at an average rate of 0.34 km/year globally, with stronger increases observed in ocean-land boundary areas and mid-latitudes in the northern hemisphere. Based on our interpretable machine learning algorithm (XGBoost), the TC maximum sustained wind speed (central pressure), location of the TC, SST, vertical wind shear, and total column water vapor are the most important factors. DIST30 shows a particularly strong positive relationship with vertical wind shear in mid-latitudes which explains the recent global increasing trend in DIST30.

Results
Global increases in distance from TC center and extreme rainfall
Besides high interannual and interdecadal variabilities, the global annual mean DIST30 (Fig. 1a) demonstrates a statistically significant increasing trend (at a 95% significance level) with a slope of 0.34 km/year between 1980 and 2020. In addition, we calculated and compared the frequency of extreme TC rainfall (30 mm/3 h) within different bins of distance to each TC center between 1980–1999 and 2000–2020 (Fig. 1b, c). Both low latitudes (≤25°) and mid-latitudes (>25°) observe decreased relative frequency of extreme TC rainfall within 200 km of the TC center. While the low latitude has a 5.02% decrease, the mid-latitude has a larger 22.60% decrease. Conversely, we observe increases in the relative frequency of extreme TC rainfall beyond 200 km from the TC center in both low and mid-latitudes. The low latitudes show a 13.11% increase, but a 43.33% increase in mid-latitudes. To further validate trends found in extreme TC rainfall, we also defined DIST50 as the distance between the TC center and extreme rainfall clusters larger than 50 mm/3 h. DIST50 shows a consistent upward trend of 0.36 km/year (Supplementary Fig. 1a) similar to DIST30, with a smaller change in the relative frequency in low latitudes (−3.02% beyond 200 km from the TC center and −21.54% within 200 km of the TC center; Supplementary Fig. 1c).

Spatial distribution of changes in DIST30
To further investigate the spatial variations of DIST30, we calculated temporal differences of DIST30 between the late period (2001–2020) and the early period (1980–1999) (ΔDIST30) for every 4° grid cell (Fig. 2). The results show that DIST30 increases for 59.87% (8.79×107 km2) and only decreases for less than 40.13% (5.89×107 km2) of the total TC impact areas (Fig. 2 and Supplementary Table 1). The areas with positive ΔDIST30 greater than 25, 50, 75, and 100 km take 39.03% (5.73×107 km2), 22.06% (3.24×107 km2), 12.01% (1.76×107 km2), and 7.41% (1.09×107 km2) amount of the global total TC impact areas, respectively (Supplementary Table 2). Among six ocean basins, only the Northern Indian basin experiences a general reduction in DIST30. In the other five ocean basins, increasing trends of DIST30 are more frequent than decreasing trends. The Western North Pacific basin has the largest proportion of areas with DIST30 growth (2.20×107 km2, 25.06% of global area with DIST30 increase), and the areas with positive ΔDIST30 greater than 25, 50, 75, and 100 km take 39.76% (1.35×107 km2), 21.49% (7.30×106 km2), 10.62% (3.61×106 km2), and 7.49% (2.54×106 km2) of the total TC impact areas in Western North Pacific basin, respectively (Supplementary Table 2). The Northern Atlantic basin has the second largest proportion of areas with DIST30 growth (1.92×107 km2, 21.80% of global area with DIST30 increase), and the areas with positive ΔDIST30 greater than 25, 50, 75, and 100 km take 43.73% (1.29×107 km2), 22.64% (6.68×106 km2), 13.79% (4.07×106 km2), and 7.36% (2.17×106 km2) amount of the total TC impact areas in Northern Atlantic basin, respectively (Supplementary Table 2).

In addition, we examined coastal grid cells (defined as grid cells with both land and sea) and found they have slight growth in DIST30. From a total of 4.73×107 km2 of land and sea boundary areas, slightly more than half (54.02%, representing 2.56×107 km2) present an increasing trend in DIST30. More growths in DIST30 are observed in populated coastal areas including eastern coastal areas of China, Japan islands, Korean peninsula, and eastern Australia, since we have observed that 7.33×106 km2 (61.84%) of Western North Pacific basin boundary areas and 4.93×106 km2 (63.55%) of South Pacific basin boundary areas showed increases of DIST30. In general, the areas experiencing increases of DIST30 have elevated risk of heavy precipitation far from the TC center, and they take the majority of the TC impact areas globally, indicating a global expansion of TC precipitation footprint and flood risk. In contrast, we observe a downward trend in DIST30 in the North Indian basin coastal areas (1.67×106 km2, 32.71% of the area with increasing trends). Other ocean basins only observed slight increases or no trend in DIST30.

Modeling DIST30 using machine learning
Drawing on high-resolution dynamical General Circulation Models (GCMs) and downscaled Regional Climate Models (RCMs), many studies discuss the sensitivity of TC rainfall rate (Clausius-Clapeyron Scaling) to global climate warming scenarios9,23,24,28–32. To understand factors that determine the TC rainfall footprint, we developed XGBoost models for global and ocean basin wide monthly values of DIST30 based on TC characteristics (e.g., central pressure and maximum sustained wind speed) and environmental factors (SST, relative 2-meter air temperature, vertical wind shear). XGBoost is a powerful decision tree-based machine learning approach33 that repeatedly generates new trees from the initial poor performers (‘weak learners’) intending to improve the model fit (see Methods for further detail). A variables list is shown in Supplementary Tables 3 and 4. The XGBoost model demonstrates decent out-of-sample prediction performances, with the ratio of the explained variance (R2) = 0.51, root mean square error (RMSE) = 70.48 km, and mean absolute error (MAE) = 47.34 km. Similarly, models for different ocean basins (Supplementary Fig. 2) also show consistent performance (R2 ranging from 0.46 to 0.57, RMSE ranging from 66.66 to 77.90 km, MAE ranging from 43.74 to 50.77 km). All indicate that our XGBoost models have decent prediction performance without overfitting and are reliable sources for model interpretations.

The SHapley Additive exPlanations (SHAP) value34 (see Methods) is an interpretable artificial intelligence (AI) approach that represents the contribution from each feature to each individual prediction. Therefore, a larger than zero SHAP value indicates a positive contribution from a feature to the mean prediction of the response variable (here DIST30) and vice versa. Here we define the feature importance as the absolute value of all positive and negative contributions of each feature which reflects the sensitivity of DIST30 to the specific feature. Figure 3b demonstrates the 8 top-ranked features for the global DIST30 models. The TC maximum intensity (VMAX) and Latitude (LAT) rank as the most important variables in the global DIST30 model, followed by the central pressure (PRES), vertical wind shear (WS), and relative 2-meter air temperature (RT2M). In addition, we demonstrated the detailed interactions between DIST30 and four top-ranked features in the XGBoost models (Fig. 3c–f) as well as their spatial distributions (Fig. 4).

DIST30 generally has a negative relationship with VMAX (Fig. 3c), with different sensitivities within different VMAX ranges. Negative contributions to DIST30 (smaller DIST30) are generally associated with a higher VMAX (>70 knots, ~Category 1 hurricane intensity). The magnitude of negative contributions of SHAP is stabilized when VMAX is larger than 70 knots. Strong convective precipitation from a well-developed TC system in the tropics is usually located near the eyewalls35,36, within a short distance to the TC center. In contrast, the DIST30 SHAP increases abruptly when the VMAX is reduced below 70 knots, which could be related to the Extratropical Transition (ET) of TCs. As TCs undergo the ET, warm-core tropical systems change to cold-core mid-latitude cyclones. These mid-latitude systems are generally larger with a more widespread distribution of precipitation than well-developed TCs in the tropics. As the eyewall disappears, the heavy precipitation center for ET storms usually moves further away from the storm center. In Fig. 3d we can observe a clear pattern such that a higher absolute value of LAT is associated with a larger DIST30, whilst mid-latitude regions (20°N to 40°N and 20°S to 40°S) have more frequent observations of lower VMAX. The translation speed of TC also increases as it moves to higher latitudes37, contributing to the asymmetry of TC precipitation21,38 and possibly to the increase in DIST30. In addition to the general positive relationships with latitude, a small number of high DIST30 SHAP values are also located in low latitudes (between 20°S and 20°N, Fig. 3b) and have low VMAX. These are possibly associated with scattered tropical thunderstorms in less organized tropical storm systems with weak wind intensity (<40 knots). The eyewalls of those systems are not well defined, and the center of the thunderstorms with heavy precipitation can be far away from the center.

The vertical wind shear (WS) demonstrates a general positive but non-linear relationship with the DIST30 SHAP values (Figs. 3e and 4c), with complexities when WS is below 15 knots. Higher WS is likely to expand the TC rainfall area and introduce higher rainfall rates far from the TC center39,40; this phenomenon is particularly strong in the mid-latitudes when TCs are translating to regions with lower relative sea surface temperature (green and yellow dots in Fig. 3e). More frequent larger WS SHAP values also occur at higher latitudes (Fig. 4c), reflecting the latitudinal gradient. Previous studies have identified WS as one of the key factors that increase the TC precipitation asymmetry21,38,41,42. Positive vertical wind shear SHAP values are scattered across different ocean basins in the northern hemisphere (Fig. 4c) and are slightly stronger in the southern hemisphere. The lower range of WS (<10 knots) demonstrates both negative and positive contributions to the DIST30 SHAP values and those cases are more likely to happen in warmer SSTs (Fig. 3e), indicating a lower sensitivity of DIST30 to the WS in the tropics.

The relative 2-meter air temperature (RT2M) also demonstrates a nonmonotonic relationship with DIST30—a negative relationship when the RT2M is lower than 1 K but a weak positive relationship when the RT2M is higher than 1 K. This non-monotonic relationship could be caused by several factors. The RT2M decreases with latitudes, so larger DIST30 (ET systems) correspond to lower RT2M in higher latitudes, whilst in the tropics, higher RT2M corresponds to higher SST. Higher SST is likely to support more latent heat to the TC system. Interestingly, the SHAP values for the Relative SST (Supplementary Fig. 5h) also demonstrate a positive relationship with DIST30 when it is above 0 K, but the absolute SST has both positive and negative contributions to DIST30 (Supplementary Fig. 5g). Both observations and numerical models have previously demonstrated that the area of TC rainfall increases as the relative SST increases for mature TCs in the tropics, potentially caused by the influences from Relative SST to TC size, relative humidity, and potential intensity14. But the TC rainfall area is less sensitive to the absolute SST in the tropics14. Our analysis also indicates that higher total precipitable water vapor (TCWV) is generally associated with larger DIST30 (Supplementary Fig. 5i). This is also consistent with the previous analysis13, which demonstrates that there is a positive relationship between TCWV and rainfall intensity in the TC outer region, while there is a negative relationship between TCWV and rainfall intensity in the TC inner core. Spatially, a very strong latitudinal gradient is also evident for the SHAP value for RT2M (Fig. 4d).

Interpreting trends in DIST30
In previous sections, we have discovered that after TCs’ own characteristics (VMAX and PRES), vertical wind shear is the most important environmental variable explaining DIST30, and displays a strong positive but non-linear relationship. Therefore, here we provide additional analysis to explain temporal trends in global DIST30 by splitting our monthly DIST30 data into three parts according to latitude: the tropics between 25°S and 25°N, mid-latitudes of the northern hemisphere (>25°N), and mid-latitudes of the southern hemisphere (>25°S).

In the tropics, DIST30 demonstrates a slight increasing pattern but with low confidence (Fig. 5a, p-value≈0.11). Meanwhile, we identified a statistically significant (p-value≈0.00) decreasing trend in vertical wind shear in the tropics. Lower vertical wind shear is likely to create a more favorable environment for cyclone genesis to survive and evolve into stronger TCs43,44 in the tropics. Meanwhile, lower vertical wind shear is not likely to directly disperse the rain field and increase the DIST30 in the tropics because of its lower sensitivity in the tropics (SHAP value in Fig. 3e). We did find a weak increasing pattern in the annual frequency of DIST30 in the tropics (p-value≈0.29, Fig. 5c), which could be related to the reduced vertical wind shear. Recent studies have also identified increased SST in the tropics globally45,46. Both the more surviving TCs and more latent heat supplied from the ocean surface are likely to contribute to the slightly increasing precipitation footprints (DIST30) of TCs within the tropics.

DIST30 in mid-latitudes of the northern hemisphere demonstrates a very strong increasing trend (p-value≈0.00). We believe this is the major contributor to the global increasing trend in DIST30, since both the tropics and southern hemisphere mid-latitudes (Supplementary Fig. 7) demonstrate weak increases of DIST30. The strong increasing trend of DIST30 beyond 25°N can be explained by changes in both vertical wind shear and the frequency of TCs entering the mid-latitudes. In contrast to the decreasing pattern in the tropics, the vertical wind shear in the northern hemisphere at higher latitudes demonstrates a weakly increasing signal (Fig. 5e, p-value≈0.33). More importantly, a very strong increase is evident for the annual DIST30 observation frequency beyond 25°N (Fig. 5f, p-value≈0.00). It is probable that more TCs survived beyond 25°N, translated toward mid-latitudes, and then encountered relatively higher vertical wind shear. Those TCs undergoing extratropical transition are usually associated with more asymmetric distribution of rain fields and enlarged DIST30, which was also demonstrated by the high sensitivity of DIST30 to WS in mid-latitudes from our SHAP analysis (Fig. 3e). Interestingly, we only observe those strong temporal trends in DIST30 in the higher latitudes of the northern hemisphere. In the southern hemisphere, no statistically significant trend has been identified in DIST30, vertical wind shear, and observation frequency beyond 25°S (Supplementary Fig. 7).

The poleward migration of TCs was first described by Kossin et al.47 and has been discussed by recent studies48–52. The poleward migration of TC intensity can be explained by the expansion of the Inter Tropical Convergence Zone (ITCZ) and the tropical Hadley circulation under a warming climate, which changes the environment for TC genesis and development, including the vertical wind shear, SST, and steering flows. Some studies identified a more distinct poleward migration of TCs in the Western North Pacific basin48,50,53. Here we discovered that the vertical wind shear in the tropics has become more favorable to TC genesis and evolution globally in the last 41 years. More TCs moved to higher latitudes in the northern hemisphere and interacted with stronger vertical wind shear. Those processes could work together and cause substantial increases of larger TC precipitation footprint (DIST30) globally. Supplementary Figs. 3–6 also show SHAP relationships between all included features and the global DIST30 from our XGBoost modeling.

Methods
Data
The International Best Track Archive for Climate Stewardship (IBTrACS) v04 dataset63 was acquired for the period 1980 to 2020, which includes TC position, minimum sea-level pressure, and the maximum sustained wind speed. The TC-related precipitation data were drawn from the Multi-Source Weighted-Ensemble Precipitation (MSWEP) v2 dataset, which takes advantage of the complementary strengths of in-situ-, satellite-, and reanalysis-based data to provide reliable estimates of precipitation on a global scale64. The MSWEP v2 data provides a complete record of precipitation over both ocean and land after 1980 and its length matches with the satellite-based TC location records. The land and sea boundary shape file were obtained from the UCLA Geoportal (see Data availability section).

TC information and precipitation extraction
All TCs with wind speeds in the best track dataset on both land and ocean during 1980-2020 are used in this study, but only including records at 00:00, 03:00, 06:00, 09:00, 12:00, 15:00, 18:00, and 21:00 UTC. The MSWEP dataset covers the period 1980-2020 with a temporal resolution of 3 h. Here the Precipitation of TCs is defined as accumulated 3-h MSWEP precipitation within 500 km of the TC center15. To facilitate the calculation of the distance from the TC center, we first adjust the latitude values (rounding the latitude up for the Northern Hemisphere and down for the Southern Hemisphere) and resample the TC precipitation field to 25 km resolution using the Albers projection. In the Albers projection, standard parallels are set to the adjusted latitude of TC center ±10°. The number of rows and columns of the TC precipitation field after resampling is 41, and the coordinates of the TC center are (21, 21), which we note here as the TC center X0, Y0.

DIST30 and DIST50
DIST30 is the distance from the center of clustered heavy rainfall cells (>30 mm/3 h) to each TC center, which is given:

DIST30 = (Σ_{i=1}^{N} dist_i × P_i) / (Σ_{i=1}^{N} P_i) (1)

where:

P_i = precipitation, if precipitation ≥ 30 mm per 3 hours (2)

where N is grid number within 500 km from the TC center, precip_i is the TC precipitation in the i-th grid (unit: mm/3 h), dist_i is the distance between the TC center and the i-th grid (unit: km).

The definition of DIST50 is the same as DIST30 but the threshold of heavy rainfall is 50 mm/3 h.

Trend detection for time series
The linear trends in Figs. 1a, 5, and Supplementary Figs. 1a, 7 are estimated using simple linear regression. Shaded areas in Fig. 1a and Supplementary Fig. 1a are the 95% confidence bounds. In this work, the significance of linear trends in Fig. 1a and Supplementary Figs. 1a are using the F-test65 (the regress() function and the LinearModel.fit() function in Matlab R2016a). The Mann-Whitney test66 is used on the regression model of time series based on the 99% significance level (the ranksum() function in Matlab R2016a).

The surface area of grid
Based on the ref. 67, the surface area of each raster is given:

A = R^2 × (θ_2 - θ_1) × (sinφ_2 - sinφ_1) (3)

where A is the surface area (unit: km^2), θ_1 and θ_2 is longitude (unit: radians), φ_1 and φ_2 is latitude (unit: radians), R is the radius of the earth (R = 6371.39, unit: km). Here we created a mesh of grids boxes with 0.25°×0.25° by size. Then the monthly mean value of DIST30 is calculated for each grid and used as the response variable for the XGBoost models.

Land and sea boundary
If a grid cell includes both land and sea, we define the grid cell as the land and sea boundary.

XGBoost model
Boosting trees is a decision tree-based machine learning approach33. The algorithm starts with weak learners, and new trees are generated to reduce the errors of trees in previous rounds. The objective function of XGBoost is written as follows:

L(t) = Σ_{i=1}^{n} l(y_i, ^y_i^{(t-1)} + f_t(X_i)) + Ω(f_t) (4)

where L is a differentiable convex loss function measuring the difference between the prediction ^y_i and the target value y_i. The term Ω is a penalization for the complexity of the regression tree functions. The model is trained in an additive manner so ^y_i^{(t)} is the prediction of the i-th instance at the t-th iteration and f_t is greedily added to minimize the objective L and improve the model performance. The XGBoost has already been successfully used to reconstruct precipitation isotope records in Europe68 and historical hurricane wind records69. We used the caret R package caret (v6.0-93) to streamline the model training process of the XGBoost model (R package xgboost v1.7.3.1). The whole data was sliced into five equal-size samples that are with random data selections. For each data slice, we trained the XGBoost with the remaining 4/5 of data with 5 folds cross-validation. A set of different parameters combinations have been tested (number of rounds, maximum tree depth, subsample ratio of columns when constructing each tree, etc.) using the caret package to achieve the best model fitting, cross-validation, and out-of-sample prediction results. The model is used to predict the observed DIST30 for each 1/5 testing slice. All out-of-sample predictions for five slices are collected and compared with the observation for model predictive performance evaluation. We repeated the process for the entire globe and six ocean basins.

Machine learning models are not only adept at delivering robust prediction performance but can also unveil essential insights into underlying physical processes. One strength of certain machine learning models, like XGBoost, is their ability to identify intricate and non-linear relationships between input features and outputs. To interpret our trained models, we employed the SHapley Additive exPlanations (SHAP) value method, which draws inspiration from Shapley Values in game theory. It offers a systematic mechanism to allocate significance values to individual model features, helping to quantify the influence of each feature on the model’s predictions by considering all potential feature combinations. The Shapley value can be mathematically represented by:

φ_j(v) = Σ_{S⊆{1,...,p}∖{j}} (|S|!(p - |S| - 1)! / p!) × (v(S ∪ {j}) - v(S)) (5)

Here, S represents a subset of the p features the model utilizes, and x is the feature value vector of the instance under study. v_x(S) denotes the prediction for feature values in set S, marginalized over features outside of set S. Calculating the exact SHAP value becomes computationally demanding as it requires evaluating all feature combinations both with and without a particular feature, especially as the feature count grows. To mitigate this computational challenge, approximations like the Monte-Carlo Sampling introduced by Štrumbelj et al.70 have been proposed. We use the SHAP value to both rank the feature importance and analyze how DIST30 interacts with each individual feature. For our analysis, we harnessed the R package “shapviz” to compute and visualize the SHAP values for all environmental forcing variables in our XGBoost model.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Review recommendafion: Major revision\nThis study invesfigated the long-term changes in TC precipitafion in terms of a spafial scale. In this study,\nan index called DIST30 was developed to represent the spafial scale of heavy precipitafion of TCs.\nDIST30 showed a significant increase globally, with considerable spafial variability. Factors influencing\nDIST30 were examined using a XGboost model, and the verfical wind shear was idenfified as a key factor of long-\nterm changes in DIST30. Recent studies have highlighted long-term changes in TC precipitafion based on\nobservafional data. Previous studies mainly focused on changes in TC precipitafion rates, without\ndetailed characterisfics of precipitafion structure. Therefore, this study is important in illuminafing the\ndetailed characterisfics of TC precipitafion. However, there are methodological ambiguifies hindering the\nderivafion of key conclusions of this study. Considering the importance of the research topic, a major\nrevision is necessary for publicafion. Detailed comments are provided below.\nMain comments:\n1. An interpretafion of the physical meaning of DIST30 needs to be added to the manuscript. The key\nfindings of this study are based on the DIST30. DIST30 represents the average distance from the TC\ncenter weighted by precipitafion rates. DIST30 can reflect the complex characterisfics of TC precipitafion\nstructure. For example, if the same precipitafion paftern moves away from the TC center, DIST30 will\nincrease. This means that the intensity and area of precipitafion remain constant, but only the posifion\nfrom the TC center changes. On the other hand, if precipitafion decreases in the inner-core and increases\nin the outer regions as described by Tu et al. (2021), DIST30 will increase. It is difficult to understand how\nthe changes in DIST30 mean the changes in precipitafion structure of TCs based on the current analysis.\nTherefore, it is necessary to clearly explain what characterisfics of TC precipitafion DIST30 can represent\nand the advantages of using DIST30.\n2. In connecfion with the above comment, it would be beneficial to emphasize the purpose of examining\nDIST30 further. Previous studies have analyzed the precipitafion structure of TCs using various indices. A\ncommonly used index represenfing the spafial scale of precipitafion is areal extent. In addifion, the\ndispersion index (Zick and Matyas 2016; Zhou and Matyas 2021; Kim and Matyas 2024) is very similar to\nDIST30 but differs in that it is weighted by area rather than precipitafion rates. Emphasizing the\nadvantages of DIST30 compared to exisfing methods would enhance the significance of the research.\nZick, S. E. & Matyas, C. J. A Shape metric methodology for studying the evolving geometries of synopfic-\nscale precipitafion pafterns in tropical cyclones. Ann. Am. Assoc. Geogr. 106, 1217–1235. hftps:// doi.\norg/ 10. 1080/ 24694 452. 2016. 12064 60 (2016).\nZhou, Y. & Matyas, C. J. Regionalizafion of precipitafion associated with tropical cyclones using spafial\nmetrics and satellite precipitafion. GISci. Remote Sens. 58, 542–561. (2021).\nKim, D., & Matyas, C.J. Classificafion of tropical cyclone rain pafterns using convolufional autoencoder.\nSci Rep 14, 791 (2024).\n3. It would be befter to discuss the long-term quality of precipitafion data (MSWEP). Is there any\ndifference in the quality between periods that include satellite data such as TRMM/GPM and periods\nthat do not? Is there any potenfial impact this could have on the analysis of long-term changes?\n4. It is necessary to revise the interpretafion of trends in DIST30. According to the XGboost model,\nDIST30 has a negafive relafionship with VMAX and a posifive relafionship with VWS. In the tropics, VWS\nis significantly decreasing, which does not explain the increase in DIST30. Furthermore, SST is increasing\nin the tropics, which is favorable for the increase in VMAX. That is, if VMAX increases, DIST30 could\ndecrease, which contradicts the findings of this study. Addifionally, in the mid-lafitudes, while DIST30 is\nsignificantly increasing, the increase in VWS is not significant. The increase in the sample number of\nDIST30 in the mid-lafitudes (Fig. 5f) may not fully explain the increase in DIST30, as the annual mean\nDIST30 in Figure 5d may not be related to sample numbers. Removing linear trends in Figs. 5d and 5f\nwould likely result in a lower correlafion between DIST30 and Obs Freq.\nSpecific comments:\n(Abstract) It would be befter to provide the definifion of DIST30. For example, the mean radial distance\nof heavy precipitafion area weighted by precipitafion rate.\n(Line 50) There is a typo. “precipitafion”\n(Line 55) This sentence would be as follows: “TC rainfall rate shows”\n(Line 63-66) Several studies also support that the variabilifies of TC rain in the inner-core and outer\nregion are different. Here are some relevant references.\nKim, D., Park, DS.R., Nam, C.C. et al. The parametric hurricane rainfall model with moisture and its\napplicafion to climate change projecfions. npj Clim Atmos Sci 5, 86 (2022).\nKim, D., Park, D.-S.R. & Matyas, C. J. Spafial variafions in tropical cyclone rainfall over the western North\nPacific according to ENSO phase. J. Clim. 36, 1697–1710. (2023).\n(Figs 1b,c) It would be helpful to examine the changes in precipitafion rates between the periods of\n1980-1999 and 2001-2020, not only focusing on the frequency of heavy precipitafion. It will be possible\nto see how the increase in DIST30 is associated with changes in precipitafion structure.\n(Fig 2) Only the changes in area of grids where DIST30 increased or decreased was interpreted in the\nmanuscript. However, it is also necessary to interpret the changes in DIST30 magnitude for each ocean\nbasin.\n(Line 123) It would be befter to define land and sea boundaries more clearly. Do the boundary include\nland? Or does it mean grids that have fracfions of both land and sea?\n(Figs 3c-f) The colors in the scafter plot have not been interpreted.\n(Line 176-182, 200-201) I agree that VWS can induce asymmetry in TC rain and contribute to the increase\nincrease in rain area and DIST30. Addifionally, the non-linear relafionship between sea surface temperature and\nDIST30 is consistent with Kim et al. (2021). In Kim et al. (2021), TC rain area increased solely with sea\nsurface temperature in the tropics and was controlled by VWS in the mid-lafitudes.\nKim, D., Ho, C.-H., Murakami, H. & Park, D.-S.R. Assessing the influence of large-scale environmental\ncondifions on the rainfall structure of Atlanfic tropical cyclones: An observafional study. J. Clim. 34,\n2093–2106. (2021).", "reviewer_2": "The authors defined a novel metric, DIST30, which represents the footprint of heavy TC precipitafion\nbased on a high-resolufion satellite precipitafion product and the global TC record over the past 41\nyears. They showed that DIST30 has increased significantly globally at a rate of 0.34 km per year.\nSpafially, DIST30 increases by 59.87% of the total TC impact area (8.79×107 km2), especially in the\nwestern North Pacific, the northern Atlanfic and the southern Pacific.\nThe authors also used the XGBoost model, which showed strong performance in both predicfing and\ninterprefing DIST30. They also used Shapley Addifive exPlanafions (SHAP) to interpret the XGBoost\nmodel. The results showed that the monthly DIST30 variability is mainly controlled by the variafions of\nthe maximum TC wind speed, TC locafion, sea surface temperature, verfical wind shear and total water\ncolumn. In parficular, the DIST30 shows a very strong posifive relafionship with verfical wind shear. And\nmore frequent TCs migrafing to higher lafitudes in the northern hemisphere is the main contributor to\nthe recent global upward trend in DIST30.\nThe research topic is certainly plausible and important. The manuscript is well-organized and well-\nwriften. The novelty of the research is jusfified. Therefore, I recommend that this manuscript be\naccepted for publicafion after a minor revision.\nMinor comments:\n In the methods secfion, the authors have randomly selected data for the XGBoost model. Would it be\nwise to use 30 years of data for training and 10 years of data for tesfing?\n The authors should provide the architecture of the XGBoost model.\n RMSE alone is not sufficient to evaluate the performance of the XGBoost model. Authors are\nencouraged to use more metrics such as mean absolute error, Nash-Sutcliffe efficiency, correlafion\ncoefficient, etc.", "reviewer_3": "Review of “Global Expansion of Tropical Cyclone Precipitafion Footprint” by Qin et al.\nSummary:\nIn this manuscript, the authors define a new TC rainfall index, DIST30, to describe the precipitafion\ndistribufion, and it is found that tropical cyclone (TC) precipitafion footprint has shown a significant\nexpansion in recent several decades. The study presents valuable insights into the field of TC\nprecipitafion.\nOverall, the paper is well organized, and its presentafion is good. However, some issues associated with\nthe data, methods and mechanisms sfill need to be clarified and improved before the manuscript can be\nconsidered for publicafion.\nComments:\n1. The use of MSWEP precipitafion data is noted, but the predominant reliance on reanalysis data,\nespecially in the earlier periods, raises concerns about the robustness of the findings. It is essenfial to\nexplore the ufilizafion of alternafive satellite-based precipitafion datasets (e.g., TRMM or GPM) to\nvalidate and supplement the findings.\n2. L96: The term \"relafive frequency of extreme TC rainfall\" and the physical significance of DIST30\nrequire clear definifion and clarificafion to enhance reader understanding.\n3. L35-36: “Spafially, DIST30 increases by 59.87% of the total TC impact area (8.79×107 km2)”. The\nstatement regarding the increase in DIST30 lacks a clear explanafion of how this increase leads to an\nincrease in the total TC impact area. Further clarificafion on this relafionship is necessary for a\ncomprehensive understanding of the results.\n4. The “monthly DIST30” calculafion and its relafionship with various influencing factors need further\nexplanafion.\n5. The study suggests a strong influence of wind shear on DIST30, but the presented results seem\ninconsistent with this conclusion. The observed minimal change in DIST30 in tropical regions, despite a\nsignificant decrease in verfical wind shear, as well as the conflicfing pafterns in higher lafitudes, require\nfurther clarificafion.\n6. L50: \"precipitafion\".\n7. L229-230: There is a discrepancy between the figure capfions and the figure. The authors should\nensure that the capfions accurately reflect the content of the respecfive figure."}, "author_response": "Reviewer #1 (Remarks to the Author):\nReview recommendation: Major revision\nThis study investigated the long-term changes in TC precipitation in terms of a spatial scale. In\nthis study, an index called DIST30 was developed to represent the spatial scale of heavy\nprecipitation of TCs. DIST30 showed a significant increase globally, with considerable spatial\nvariability. Factors influencing DIST30 were examined using a XGboost model, and the vertical\nwind shear was identified as a key factor of long-term changes in DIST30. Recent studies have\nhighlighted long-term changes in TC precipitation based on observational data. Previous studies\nmainly focused on changes in TC precipitation rates, without detailed characteristics of\nprecipitation structure. Therefore, this study is important in illuminating the detailed\ncharacteristics of TC precipitation. However, there are methodological ambiguities hindering\nthe derivation of key conclusions of this study. Considering the importance of the research topic,\na major revision is necessary for publication. Detailed comments are provided below.\n[Answer] Many thanks for your comments and suggestions. We have carefully revised our\nmanuscript based on your suggestions. We hope those changes significantly improved the\nquality of the manuscript.\nMain comments:\n[Comment #1] An interpretation of the physical meaning of DIST30 needs to be added to the\nmanuscript. The key findings of this study are based on the DIST30. DIST30 represents the\naverage distance from the TC center weighted by precipitation rates. DIST30 can reflect the\ncomplex characteristics of TC precipitation structure. For example, if the same precipitation\npattern moves away from the TC center, DIST30 will increase. This means that the intensity\nand area of precipitation remain constant, but only the position from the TC center changes. On\nthe other hand, if precipitation decreases in the inner-core and increases in the outer regions as\ndescribed by Tu et al. (2021), DIST30 will increase. It is difficult to understand how the changes\nin DIST30 mean the changes in precipitation structure of TCs based on the current analysis.\nTherefore, it is necessary to clearly explain what characteristics of TC precipitation DIST30\ncan represent and the advantages of using DIST30.\n[Answer] Thanks for your valuable comment. The physical meaning of DIST30 is the mean\nradial distance of the area of heavy precipitation of 30 mm per 3 hours weighted by the\nprecipitation rate to the TC center, reflecting the relative position of the extreme TC\nprecipitation to the TC center. The value of DIST30 is determined by precipitation in both the\ninner core and outer regions, as well as the precipitation structure of the TC. For example,\nComment Fig. 1 presents two precipitation profiles of TC, which are the distance series of rain\nrate. The profiles have similar precipitation in the inner core and outer regions, but differ in\ntheir value of DIST30 due to the different precipitation structure of TC.\nDIST30 can partially describe the complexity of TC precipitation structure. Higher value of\nDIST30 indicates that the most extreme precipitation related to the TC occurs farther away\nfrom the center. It is an important indicator to understand potential flood impacts from heavy\nTC rainfall. It is important to note that DIST30 is a numerical value calculated solely from the\nTC precipitation profile (the distance series of TC rain rate) shown in Comment Fig. 1. We\nacknowledge that the full TC precipitation structure still cannot be completely captured by the\nvalue of DIST30, which is a limitation of using DIST30. We plan to incorporate the evolution\nand structure of TC rainfall in our future research.\nWe have modified the definition of DIST30 in the main text to better reflect its physical\nmeanings in the new text (lines 33-34, lines 82-85). We have also included more discussion\nabout the precipitation in both the inner core and outer regions in the discussion section (lines\n343-350).\nComment Fig. 1. The distance series of TC rain rate. The profiles have similar precipitation in\nthe inner core and outer regions, but differ in their value of DIST30 due to the different\nprecipitation structure of TC.\n[Comment #2] Previous studies have analyzed the precipitation structure of TCs using various\nindices. A commonly used index representing the spatial scale of precipitation is areal extent.\nIn addition, the dispersion index (Zick and Matyas 2016; Zhou and Matyas 2021; Kim and\nMatyas 2024) is very similar to DIST30 but differs in that it is weighted by area rather than\nprecipitation rates. Emphasizing the advantages of DIST30 compared to existing methods\nwould enhance the significance of the research.\nZick, S. E. & Matyas, C. J. A Shape metric methodology for studying the evolving geometries\nof synoptic-scale precipitation patterns in tropical cyclones. Ann. Am. Assoc. Geogr. 106,\n1217–1235. https://doi.org/10.1080/24694 452. 2016. 12064 60 (2016).\nZhou, Y. & Matyas, C. J. Regionalization of precipitation associated with tropical cyclones\nusing spatial metrics and satellite precipitation. GISci. Remote Sens. 58, 542–561. (2021).\nKim, D., & Matyas, C.J. Classification of tropical cyclone rain patterns using convolutional\nautoencoder. Sci Rep 14, 791 (2024).\n[Answer] Thanks for providing that suggestion. They are great studies and good references for\nour study. We agree that both the areal extent and the dispersion index are the useful index for\nrepresenting the spatial scale of precipitation. As mentioned from the comment, DIST30 is\nsimilar to the dispersion index in some ways, but differs in that it is weighted by heavy\nprecipitation rate instead of area. We do believe that both the dispersion index (Zick and Matyas,\n2016) and our DIST30 provides some perspectives of the spatial distribution of the TC rainfall.\nIn the future, it would be interesting to combine both the area and intensity information in a\nnew index and track their global patterns.\nWe have added a brief discussion that emphasizes the advances of our DIST30 as compared to\nexisting methods starting from line 85.\n[Comment #3] It would be better to discuss the long-term quality of precipitation data\n(MSWEP). Is there any difference in the quality between periods that include satellite data such\nas TRMM/GPM and periods that do not? Is there any potential impact this could have on the\nanalysis of long-term changes?\n[Answer] Many thanks for raising that important point. In this study, we selected the MSWEP\ndata because it is the longest available high resolution precipitation product with global\ncoverage. It starts from the beginning of satellite age (~1980) and matches with the reliable\nglobal TC record. We agree that the MSWEP uses a data fusion approach to merge precipitation\ndata from different sources (satellites, reanalysis, rain gauges, etc) and there are inevitably\ninconsistencies in those original data sources for MSWEP. Like what you have mentioned, there\ncould be potential impact from those inconsistencies (as the case that TRMM is only available\nsince 1998) in interpreting our long-term changes, but there is no other data source available to\nvalidate the trend before the 2000. In order to test the consistency in different data, we finished\nan independent test based on a different precipitation data (TRMM Multi-satellite Precipitation\nAnalysis Precipitation, TMPA). Results (Comment Fig. 2) show that our findings are\nconsistent based on two different precipitation data after 2000. The DIST30 based on the TMPA\ndata shows an upward trend of 0.20 km/year between 2000 and 2019 (Comment Fig. 2a), with\nhigher relative change in low latitudes (+16.82% beyond 200 km from TC center and -9.24%\nwithin 200 km from TC center; Comment Fig. 2b), and in mid latitudes (+0.25% beyond 200\nkm from TC center and -0.21% within 200 km from TC center; Comment Fig. 2c). In general,\nthose patterns agree with the DIST30 trends/patterns from MSWEP after 2000, as well as the\nwhole upward trend in DIST30 since 1980. We have also added more justification about why\nwe are choosing the MSWEP data in the Data section of Methods, from line 430 to 432.\nComment Fig. 2. As with Fig. 1, but for TMPA precipitation data. a, annually time series of\nglobally averaged DIST30. b, relative frequency of > 30 mm per 3 hours precipitation in low\nlatitude (≤25°). c, relative frequency of > 30 mm per 3 hours precipitation in mid-latitude (>25°).\nBlue lines are for the early period (2000-2009) and red lines are for the late period (2010-2019).\n[Comment #4] It is necessary to revise the interpretation of trends in DIST30. According to the\nXGboost model, DIST30 has a negative relationship with VMAX and a positive relationship\nwith VWS. In the tropics, VWS is significantly decreasing, which does not explain the increase\nin DIST30. Furthermore, SST is increasing in the tropics, which is favorable for the increase in\nVMAX. That is, if VMAX increases, DIST30 could decrease, which contradicts the findings\nof this study. Additionally, in the mid-latitudes, while DIST30 is significantly increasing, the\nincrease in VWS is not significant. The increase in the sample number of DIST30 in the mid-\nlatitudes (Fig. 5f) may not fully explain the increase in DIST30, as the annual mean DIST30 in\nFigure 5d may not be related to sample numbers. Removing linear trends in Figs. 5d and 5f\nwould likely result in a lower correlation between DIST30 and Obs Freq.\n[Answer] Many thanks for the comments and suggestions. In the SHAP analysis of DIST30\n(Fig. 3), we can observe a general negative relationship between DIST30 SHAP and VMAX\n(Fig. 3c), as well as a general negative relationship between DIST30 SHAP and Wind Shear\n(Fig. 3e). The negative relationship for VMAX is most sensitive when VMAX is below 70 kt,\nwhich could be more related to the situation in the midlatitude where the storm intensity\ndecreased but the rain band gets more disbursed. And the curve almost flattened when the\nVMAX is larger than 70 kt (~category 1 hurricane intensity). So, this indicates that there is a\nweak DIST30 sensitivity to larger ranges of VMAX, which mostly likely happens over warm\nocean water in the tropics. Here we also demonstrate the SHAP value change for SST (included\nas SI Fig. 5g, here Comment Fig. 3). The SST SHAP also demonstrates different patterns\nwithin different ranges, when the SST is below 299K (~26℃, an important threshold for TC\ngenesis and development) there are more positive contributions dominate (corresponding to\nlarger DIST30), but there are both positive and negative contributions to DIST30 when the SST\nis above 299K. Both relationships for VMAX and SST indicate a complex non-linear\nrelationship between VMAX and DIST30, particularly for well-developed TCs over the tropics.\nThe relationship for Wind Shear’s SHAP is also highly non-linear, and generally agrees with\nthe relationships in VMAX and SST. That is, when the wind shear is lower (< 0 kt), the SST is\nhigher (red color in Fig. 3d), there are both positive and negative contributions from the wind\nshear to DIST30, but the averaged contribution is negative (black line below zero) and smaller\nDIST30 is corresponding to this part of data. But when the wind shear is much larger, RSST\ndrops to much lower ranges in higher latitude, and most of the SHAP contributions from wind\nshear are positive for this range.\nIn Fig.5a, the trend of DIST30 in the midlatitude could be influenced by both observation\nfrequency and wind shear. The increasing trends in DIST30 and Obs Freq for mid latitudes\ngenerally agree with each other after 1990, except that the Obs Freq has a sudden dip in year\n2009. The 2009 dip significantly changed the 5 year moving average curve but does not change\nthe general increasing trend in the Obs Freq. But the wind shear time series does not have this\nsudden drop in 2009, instead the wind shear has a spell of above average observations after\n2009. As indicated from the SHAP plot, the DIST30 has high sensitivity to vertical shear in mid\nlatitudes, The increasing trend in DIST30 has not been influenced significantly by the one big\ndrop of Obs Freq in 2009, the slightly increased wind shear could play an important role\nparticularly after 2009. We also created a linear regression (Comment Fig. 4) for the 5-year\nsmoothed DIST30 in the northern hemisphere based on the 5-year smoothed WS and Obs Freq.\nIt indicates that the WS and Freq can capture the DIST30 variability well from a simple linear\nmodel. And estimated parameters for both WS and Obs Freq are both positive. Comment Fig.\n4 also indicates the mid-latitude DIST30 in northern hemisphere is generally positive correlated\nwith both the vertical wind shear and the frequency of observation. We have made some\nmodifications in the original description and discussions in the manuscript (multiple places in\nresult and conclusion sections).\nComment Fig. 3. The SHAP value for SST.\nComment Fig. 4. The fitted vs observed the smoothed DIST30 in the mid-latitudes of northern\nhemisphere, linear model is constructed based on smoothed Wind Shear (WS) and the observed\nfrequency (OBSFreq). The linear model function for the DIST30 is displayed in the figure, with\nR2 displayed between the observed DIST30 and fitted DIST30. Black line is a linear line fitted\nthe scatter dots (black) and red dash line is for y=x line.\nSpecific comments:\n[Comment #5] (Abstract) It would be better to provide the definition of DIST30. For example,\nthe mean radial distance of heavy precipitation area weighted by precipitation rate.\n[Answer] Thanks for your valuable suggestion. We have updated the definition of DIST30 in\nAbstract as well as its physical meaning from line 33 to line 37: “Here we define a novel metric,\nDIST30, as the mean radial distance from centers of clustered heavy rainfall cells (> 30 mm/3\nhours) to the TC center. DIST30 represents the footprint of heavy TC precipitation based on\nhigh-resolution precipitation data and the global TC record over the past 41 years for which\nsatellite observations are available.”\n[Comment #6] (Line 50) There is a typo. “precipitation”\n[Answer] Thanks for your careful reading. We have corrected this typo.\n[Comment #7] (Line 55) This sentence would be as follows: “TC rainfall rate shows”\n[Answer] Thanks for your suggestion. We have updated this sentence “However, recent studies\nbased on satellite rainfall measurements12,13 demonstrate that the TC rainfall rate shows a\ndecreasing trend in the inner-core of the rainband with increases in the outer bands.”\n[Comment #8] (Line 63-66) Several studies also support that the variabilities of TC rain in the\ninner-core and outer region are different. Here are some relevant references.\nKim, D., Park, DS.R., Nam, C.C. et al. The parametric hurricane rainfall model with moisture\nand its application to climate change projections. npj Clim Atmos Sci 5, 86 (2022).\nKim, D., Park, D.-S.R. & Matyas, C. J. Spatial variations in tropical cyclone rainfall over the\nwestern North Pacific according to ENSO phase. J. Clim. 36, 1697–1710. (2023).\n[Answer] Thanks for your recommendation. They are great studies and good references for our\nstudy. We have added the new sentence “Recent studies19,20 also find that TC precipitation in\nthe inner core and outer region is controlled by TC intensity and environmental conditions” in\nthe Introduction section.\n[Comment #9] (Figs 1b, c) It would be helpful to examine the changes in precipitation rates\nbetween the periods of 1980-1999 and 2001-2020, not only focusing on the frequency of heavy\nprecipitation. It will be possible to see how the increase in DIST30 is associated with changes\nin precipitation structure.\n[Answer] Thanks for your valuable comment. Following your suggestion, we have examined\nthe changes in rain rates between the periods 1980-1999 and 2001-2020 (Comment Fig. 5). It\nwas observed that rain rates decreased more during the latter period (2001-2020) at the location\ncloser to the center of the TC compared to the previous period (1980-1999), which is roughly\nconsistent with the findings of Tu et al. (2021). The changes in precipitation structure between\nthe two time periods can partially explain the rise in DIST30.\nIn addition, according to the physical meaning of DIST30, we also plot the distance series of\ntotal heavy precipitation (> 30 mm per 3 hours) in Comment Fig. 6. We observe that the\nchanges in heavy precipitation structure between the two time periods are similar to the relative\nfrequency of precipitation exceeding 30 mm per 3 hours in Fig. 1b-c. This observation can also\nexplain the increase in DIST30.\nComment Fig. 5. The distance series of mean TC rain rates between the periods of 1980-1999\nand 2001-2020. a, in low latitude (≤25°). b, in high latitude (>25°). Blue lines are for the early\nperiod (1980-1999) and red lines are for the late period (2001-2020).\nComment Fig. 6. As with Comment Fig. 5, but the sum of rain that exceeds 30 mm per 3\nhours. a, in low latitude (≤25°). b, in mid latitude (>25°). Blue lines are for the early period\n(1980-1999) and red lines are for the late period (2001-2020).\n[Comment #10] (Fig 2) Only the changes in area of grids where DIST30 increased or decreased\nwas interpreted in the manuscript. However, it is also necessary to interpret the changes in\nDIST30 magnitude for each ocean basin.\n[Answer] Thanks for your valuable suggestion. We have listed the details of the areas of\nmagnitude of the differences in DIST30 between the late period (2001-2020) and the early\nperiod (1980-1999) in Supplementary Table 2 by following your suggestion. Some\ndescriptions are added between line 134 and 137.\n[Comment #11] (Line 123) It would be better to define land and sea boundaries more clearly.\nDo the boundary include land? Or does it mean grids that have fractions of both land and sea?\n[Answer] Thanks for your valuable point. Yes, if a grid has the fractions of both land and sea,\nwe define the grid as the land and sea boundary in this study. A more detailed description has\nbeen added in line 151.\n[Comment #12] (Figs 3c-f) The colors in the scatter plot have not been interpreted.\n[Answer] Thanks for raising this important point. The color in the SHAP scatter plot means the\nsecond independent variable that has the largest covariance with the main independent variable\nas in the x axis. Some variable colors have complex relationships with the main independent\nvariable and hard to interpret physically, such as the Atlantic Multidecadal Oscillation (AMO)\nand VMAX in Fig. 3c. Some variable colors actually provide valuable additional information\nfor the physical interpretation of the main independent variable, such as the relative sea surface\ntemperature (RSST) and VS in Fig. 3e. We have added more information in the figure caption\nand some revised discussion in the text.\n[Comment #13] (Line 176-182, 200-201) I agree that VWS can induce asymmetry in TC rain\nand contribute to the increase in rain area and DIST30. Additionally, the non-linear relationship\nbetween sea surface temperature and DIST30 is consistent with Kim et al. (2021). In Kim et al.\n(2021), TC rain area increased solely with sea surface temperature in the tropics and was\ncontrolled by VWS in the mid-latitudes.\nKim, D., Ho, C.-H., Murakami, H. & Park, D.-S.R. Assessing the influence of large-scale\nenvironmental conditions on the rainfall structure of Atlantic tropical cyclones: An\nobservational study. J. Clim. 34, 2093–2106. (2021).\n[Answer] Thanks for your valuable comments, we believe the relationships between VWS and\nDIST30 agrees with the previous findings for the TC rain area, particularly in mid-latitudes.\nWe also added the suggested literature in our discussion.\nReviewer #2 (Remarks to the Author):\nThe authors defined a novel metric, DIST30, which represents the footprint of heavy TC\nprecipitation based on a high-resolution satellite precipitation product and the global TC record\nover the past 41 years. They showed that DIST30 has increased significantly globally at a rate\nof 0.34 km per year. Spatially, DIST30 increases by 59.87% of the total TC impact area\n(8.79×107 km2), especially in the western North Pacific, the northern Atlantic and the southern\nPacific.\nThe authors also used the XGBoost model, which showed strong performance in both\npredicting and interpreting DIST30. They also used Shapley Additive exPlanations (SHAP) to\ninterpret the XGBoost model. The results showed that the monthly DIST30 variability is mainly\ncontrolled by the variations of the maximum TC wind speed, TC location, sea surface\ntemperature, vertical wind shear and total water column. In particular, the DIST30 shows a very\nstrong positive relationship with vertical wind shear. And more frequent TCs migrating to\nhigher latitudes in the northern hemisphere is the main contributor to the recent global upward\ntrend in DIST30.\nThe research topic is certainly plausible and important. The manuscript is well-organized and\nwell-written. The novelty of the research is justified. Therefore, I recommend that this\nmanuscript be accepted for publication after a minor revision.\n[Answer] Many thanks for your comments and suggestions. We have addressed all of them\npoint by point and hope they improve the clarity and quality of the manuscript.\nMinor comments:\n[Comment #1] In the methods section, the authors have randomly selected data for the XGBoost\nmodel. Would it be wise to use 30 years of data for training and 10 years of data for testing?\n[Answer] Thanks for the comment and the valuable question. We have identified an increasing\ntrend in DIST30 in 41 years of data and indicate there could be temporal changes in physical\nprocesses that control the DIST30 variability. So, the DIST30 data is non-stationary, and we\nwill not be able to get very good out of sample prediction performance if we are using previous\n31 years of data to train the model and last 10 years for testing. There will also potential under-\nsample issues because there is large uncertainty in annual climate variabilities and TC locations.\nOur main purpose for this article is to develop XGBoost model that can identify important\nfactors/processes that possibly control the monthly DIST30 variability and have decent amount\nof out-of-sample prediction skills to avoid over-fitting. However, the current model may not\ncapture the non-stationarity in the time series and the complex inter-annual changes in global\nTC activities very well. We have trained two new XGBoost models, one based on 1980-2010\ndata and the other based on 1990-2020 data. Then we tested the model prediction performance\nusing 2011-2020 data and 1980-1989 data, respectively. Although both models have good\nperformance when predicting data within their time range (with R2>0.5), Comment Fig. 7 a&b\nshowed that their prediction performance for years never appeared in the model deteriorate\nfrom the randomly selected 5 slice hold-out cross validation (Fig. 3a) because of the non-\nstationarity in processes controlling the DIST30. Note that the LAT and WS demonstrates\nhigher importance rank in the 1990-2020 model than 1980-2010 model, this is consistent with\nour argument that increases in TCs moving to the mid-latitudes and wind shear change in the\nmid-latitudes in the northern hemisphere after 1990 play important role in the increasing\nDIST30 trend globally. Therefore, challenges are still existed in training a ML model to\nskillfully predict possible future changes in DIST30 under climate change, as well as their\nannual variabilities. Since DIST30 is a feature of TC, the future works need to be first focused\non developing ML models that can predict annual variabilities of regional and global TC genesis\nand locations well.\nComment Fig. 7. a. prediction of DIST30 for 2011-2020 by using a XGBoost model trained\nby data of 1980-2010; b. prediction of DIST30 for 1980-1989 by using a XGBoost model\ntrained by data of 1990-2020. c. feature importance calculated as the SHAP value for eight top\nranked features with the most importance for the XGBoost model trained by data of 1980-2010;\nd. feature importance calculated as the SHAP value for eight top ranked features with the most\nimportance for the XGBoost model trained by data of 1990-2020.\n[Comment #2] The authors should provide the architecture of the XGBoost model.\n[Answer] Many thanks for your suggestions, we have added more description about the\nXGBoost model and the SHAP value in the new manuscript to improve the clarity.\n[Comment #3] RMSE alone is not sufficient to evaluate the performance of the XGBoost model.\nAuthors are encouraged to use more metrics such as mean absolute error, Nash-Sutcliffe\nefficiency, correlation coefficient, etc.\n[Answer] Thanks for your valuable suggestion, we have added the MAE in the new Fig. 3 to\nprovide more robust metrics for model evaluation. We have included the R2 already, which is a\nsquared correlation coefficient. Since the focus here is not to compare different ML approaches,\nwe will save Nash-Sutcliffe efficiency and other metrics for future ML algorithm comparison\nstudies.\nReviewer #3 (Remarks to the Author):\nReview of “Global Expansion of Tropical Cyclone Precipitation Footprint” by Qin et al.\nSummary:\nIn this manuscript, the authors define a new TC rainfall index, DIST30, to describe the\nprecipitation distribution, and it is found that tropical cyclone (TC) precipitation footprint has\nshown a significant expansion in recent several decades. The study presents valuable insights\ninto the field of TC precipitation.\nOverall, the paper is well organized, and its presentation is good. However, some issues\nassociated with the data, methods and mechanisms still need to be clarified and improved before\nthe manuscript can be considered for publication.\n[Answer] Many thanks for your comments. We have carefully edited the corresponding parts\nand hopefully those further improved the quality and clarity of the presentation.\nComments:\n[Comment #1] The use of MSWEP precipitation data is noted, but the predominant reliance on\nreanalysis data, especially in the earlier periods, raises concerns about the robustness of the\nfindings. It is essential to explore the utilization of alternative satellite-based precipitation\ndatasets (e.g., TRMM or GPM) to validate and supplement the findings.\n[Answer] Thanks for your valuable suggestion. In the latest version, we have discussed the\nresults based on a different precipitation data (TRMM Multi-satellite Precipitation Analysis\n(TMPA) Precipitation) by following your suggestion. Our new results (Comment Fig. 8) show\nthat our findings are consistent based on two different precipitation data between 2000 and 2019.\nThe DIST30 with the TMPA data shows an upward trend of 0.20 km/year (Comment Fig. 8a)\nin the 20 years that are available, which is similar to the 0.34 km/year trend based on 41 years\nof MESWEP data. There are higher changes for relative rain rate frequency in low latitudes\n(+16.82% beyond 200 km from TC center and -9.24% within 200 km from TC center,\nComment Fig. 8b), but lower changes in mid latitudes (+0.25% beyond 200 km from TC center\nand -0.21% within 200 km from TC center; Comment Fig. 8c). We hope this extra analysis\nsolidifies the findings that we had previously. In addition, we have also added more justification\nabout why we are choosing the MSWEP data in the Data section of Methods, from line 430 to\n432.\nComment Fig. 8. As with Fig. 1, but for TMPA precipitation data. a, annually time series of\nglobally averaged DIST30. b, relative frequency of > 30 mm per 3 hours precipitation in low\nlatitude (≤25°). c, relative frequency of > 30 mm per 3 hours precipitation in mid-latitude (>25°).\nBlue lines are for the early period (2000-2009) and red lines are for the late period (2010-2019).\n[Comment #2] L96: The term \"relative frequency of extreme TC rainfall\" and the physical\nsignificance of DIST30 require clear definition and clarification to enhance reader\nunderstanding.\n[Answer] Thanks for your valuable comment. In Fig. 1b&c, the x-axis indicates the distance\nfrom the center of the TC, while the y-axis represents the relative frequency of extreme\nprecipitation at that distance occurring over a given time period. If the relative frequency of\nextreme precipitation occurrences over small distances decreases, and the relative frequency of\nextreme precipitation occurrences over large distances increases, the DIST30 calculated by\nEquation 1 becomes larger.\n[Comment #3] L35-36: “Spatially, DIST30 increases by 59.87% of the total TC impact area\n(8.79×107 km2)”. The statement regarding the increase in DIST30 lacks a clear explanation of\nhow this increase leads to an increase in the total TC impact area. Further clarification on this\nrelationship is necessary for a comprehensive understanding of the results.\n[Answer] Thanks for raising that point. Here the majority areas experienced increases in\nDIST30, indicating more areas are experiencing elevated risk of heavy precipitation far away\nfrom the TC center. We added some clarification for the meaning of our findings in line 158 to\n161.\n[Comment #4] The “monthly DIST30” calculation and its relationship with various influencing\nfactors need further explanation.\n[Answer] Thanks for your question. In this study, the monthly DIST30 is calculated as the\naverage of all DIST30s for each month within each 0.25° × 0.25° boxes, we added descriptions\nin the captions of Fig. 3 and method section in line 467.\n[Comment #5] The study suggests a strong influence of wind shear on DIST30, but the\npresented results seem inconsistent with this conclusion. The observed minimal change in\nDIST30 in tropical regions, despite a significant decrease in vertical wind shear, as well as the\nconflicting patterns in higher latitudes, require further clarification.\n[Answer] Thanks for raising that point. Yes, we agree that relationships between the wind shear\nand DIST30 are complex and nonlinear (Fig. 3e). In the tropics, the wind shear (WS) is\ngenerally lower and the DIST30 has low sensitivity to vertical shear in the tropics, with both\npositive and negative contributions to DIST30 (Fig. 3e, when WS is below 15 knots). So, the\nDIST30 is less sensitive to changes in WS in the tropics and reduced wind shear in the tropics\ndoes not significantly decrease the DIST30 over the topics. However, generally theories\nmentioned that reduced WS in the tropics will likely benefit TC genesis and growth. In the mid-\nlatitudes, the DIST30 has higher sensitivity to the wind shear following a general positive\nrelationship. As more TCs entering midlatitude and a slightly increased WS in midlatitude, we\nare observing a strong increasing trend of DIST30 in midlatitudes in the northern Hemisphere.\n[Comment #6] L50: \"precipitation\".\n[Answer] Thanks for your careful reading. We have corrected this typo.\n[Comment #7] L229-230: There is a discrepancy between the figure captions and the figure.\nThe authors should ensure that the captions accurately reflect the content of the respective\nfigure.\n[Answer] Thanks for your careful reading. We apologize for the discrepancy between the\ncaptions and the figure in Fig. 4. In the latest version, we have updated the captions in Fig.\n4c&d."}, {"round": 2, "reviewer_comments": {"reviewer_1": "Review recommendafion: Accept\nThe authors have appropriately answered the quesfions raised and accordingly revised the manuscript.\nTherefore, I recommend the publicafion of this paper. Please correct the typos found throughout.", "reviewer_2": "I recommend this manuscript for publicafion.", "reviewer_3": "Second review of \"Global Expansion of Tropical Cyclone Precipitafion Footprint\" by Qin et al. (NCOMMS-\n24-06089A)\nI greatly appreciate the authors' substanfial revisions and detailed responses to my earlier concerns, and\nI am safisfied with the current revised version. I recommend that this manuscript be accepted for\npublicafion."}, "author_response": ""}]

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