TCP-Diffusion: A Multi-modal Diffusion Model for Global Tropical Cyclone Precipitation Forecasting with Change Awareness
Authors: Cheng Huang
Pan Mu
Cong Bai
Peter AG Watson
Venue: ICML 2025 poster (2025)
Keywords: Tropical Cyclone
Precipitation Forecasting
Diffusion Model
Primary area: applications->chemistry_physics_and_earth_sciences

Abstract: Deep learning methods have made significant progress in regular rainfall forecasting, yet the more hazardous tropical cyclone (TC) rainfall has not received the same attention. While regular rainfall models can offer valuable insights for designing TC rainfall forecasting models, most existing methods suffer from cumulative errors and lack physical consistency. Additionally, these methods overlook the importance of meteorological factors in TC rainfall and their integration with the numerical weather prediction (NWP) model. To address these issues, we propose Tropical Cyclone Precipitation Diffusion (TCP-Diffusion), a multi-modal model for forecasting of TC precipitation given an existing TC in any location globally. It forecasts rainfall around the TC center for the next 12 hours at 3 hourly resolution based on past rainfall observations and multi-modal environmental variables. Adjacent residual prediction (ARP) changes the training target from the absolute rainfall value to the rainfall trend and gives our model the capability of rainfall change awareness, reducing cumulative errors and ensuring physical consistency. Considering the influence of TC-related meteorological factors and the useful information from NWP model forecasts, we propose a multi-model framework with specialized encoders to extract richer information from environmental variables and results provided by NWP models. The results of extensive experiments show that our method outperforms other DL methods and the NWP method from the European Centre for Medium-Range Weather Forecasts (ECMWF).

TCP-Diffusion:
A Multi-modal Diffusion Model for Global Tropical Cyclone Precipitation Forecasting with Change Awareness
Cheng Huang'
Pan Mu
Cong Bai
Peter A. G. Watson 3
Abstract
(b)
TC Location
Deep learning methods have made significant progress in regular rainfall forecasting, yet the more hazardous tropical cyclone (TC) rainfall has not received the same attention. While regular rainfall models can offer valuable insights for designing TC rainfall forecasting models, most existing methods suffer from cumulative errors and lack physical consistency. Additionally, these methods overlook the importance of meteorologi- cal factors in TC rainfall and their integration with the numerical weather prediction (NWP) model. To address these issues, we propose Tropical Cy- a
Predpitation Area
(c) time steps
m time steps
TC Rolated Information
Precipitation
Forecasting Models
clone Precipitation Diffusion multi-modal model for forecasting TC precipita- tion given an existing TC in any location globally. It forecasts rainfall around the TC center for the next 12 hours at 3 hourly resolutions based on past rainfall observations and multi-modal envi- ronmental variables. Adjacent residual prediction (ARP) changes the training target from the abso- lute rainfall value to the rainfall trend and gives our model the capability of rainfall change aware- ness, reducing cumulative errors and ensuring physical consistency. Considering the influence of TC-related meteorological factors and the use- ful information from NWP model forecasts, we propose a multi-mode framework with special- ized encoders to extract richer information from environmental variables and results provided by NWP models. The results of extensive experi- ments show that our method outperforms other DL methods and the NWP method from the Eu- ropean Centre for Medium-Range Weather Fore- casts (ECMWF).
Figure 1. The difference between the regular precipitation forecast- ing (a) and TC (b) precipitation forecasting. Regular precipitation forecasting (a) usually focuses on specific fixed region, where the predicted area (blue box) does not move with the rainfall area (black dashed boxes). In TC precipitation forecasting (b), the pri- mary region of interest (blue boxes) moves with the TC. Sub-figure (c) represents the main prediction process of our model. The light blue box represents historical data, which is considered be the input of the forecasting model. The light orange box represents the TC rainfall that should be predicted. This paper just focuses on the prediction of TC rainfall.
1. Introduction
Tropical cyclone (TC) precipitation refers to substantial rain- fall events that accompany the formation, development, and movement of TCs. These precipitation events lead to severe disasters in the affected regions, like flooding, mud- slides, and landslides. These TC rainfall-related disasters cause more economic losses and deaths than strong winds (Wendler- "Wendler-Bosco Nicholson, 2022), yet most TC forecast- ing research focuses only on TC track and intensity while neglecting the TC precipitation. If the TC precipitation can be accurately predicted, preemptive measures may be taken to mitigate the disasters brought by TC rainfall, protecting people's 's lives and property. Therefore, it is important to accurately predict the precipitation around the TC center.
'College of Computer Science. Zhejiang University of Tech- nology. Hangzhou, China *Zhejiang Key Laboratory of Visual Information Intelligent Processing, Hangzhou, China "Scoool of Goographical Sciences, University Bristol, Bristol, United King- dom. Correspondence to: Cong Bai <congbaii zjut.edu.cn.
Proceedings of the ndnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).
Numerical weather prediction (NWP) is widely used for various weather forecasting tasks, including TC rainfall

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A Multi-modal Diffusion Model for Global Tropical Cyclone Precipitation Forecasting
forecasting. It simulates atmospheric dynamics, thermo- dynamics, and physical processes by solving the physical and mathematical equations that describe changes in wind, temperature, humidity, and pressure (Bai et al., 2020). It has achieved impressive results, but the development in
ing methods predict the absolute value of rainfall. How- ever, future rainfall can be understood the sum of the current rainfall and change in rainfall (ARain fallin Future) over time, which is shown in Figure 2.(c). Specifically:
NWP research has been gradual (Benjamin et al., 2018). Additionally, not all physical mechanisms of TCs are fully understood, which prevents the formulation of perfect phys- ical and mathematical equations for NWP (Xu et al., 2024). Furthermore, NWP typically runs supercomputer plat- forms, consuming extensive computational resources and time for predictions, when predicting a high-resolution re- sult. Nonlinear simulation also poses a significant challenge for NWP. Fortunately, the development of deep learning (DL) offers solutions to these NWP challenges. DL-based methods excel at modeling nonlinear processes, and the cost of model training and inference is relatively low, requiring only few Graphics Processing Units for regular Al tasks.
Rain f all Future
+ A Rain fall Future
We can train DL model to predict A Rainfall and use Equation I to obtain the absolute value of future rainfall, rather than predicting the absolute value of future rainfall di- rectly. This mechanism is advantageous because predicting the change in TC rainfall not only helps reduce cumulative errors but also ensures physical consistency meannng that changes in rainfall intensity and spatial patterns should align to some extent with historically observed trends. We de- fine this capability of a model as change awareness. Similar mechanisms are used in some NWP methods (Kalnay, 2003) and global weather forecasting models (Price et al., 2025; Nguyen et al., 2024; Oskarsson et al., 2024; Hu et al., 2023) to improve the accuracy and stability of meteorological fore- casts. Therefore, it is worth considering this mechanism in the TC rainfall prediction task.
DL methods have been applied to many meteorological tasks, like TC track and intensity prediction (Huang et al., 2022; 2023; 2025: Zhang et al., 2025), TC rainfall down- scaling (Vosper et al., 2023), global meteorological variable prediction (Bi et al., 2023; Lam al., 2023), and precipi- tation nowcasting (Bai et al., 2022; Yang al., 2024). For regular precipitation nowcasting, several works have used DL. Some previous works used a U-Net architecture net- work to predict rainfall (Gao et al., 2022; Xu et al., 2021). This could perform well on metrics like mean squared error, but gave predictions that were spatially smoother than real TC rainfall. Some research used the generative adversar- ial network (GAN) model to obtain more realistic rainfall predictions (Tian et al., 2019). Recently, due to issues with mode collapse and training instabilities in GAN models (Gao et al., 2024), researchers have applied diffusion mod- els (DMs) for better rainfall prediction (Asperti et al., 2023; Addison et al., 2022: 2024).
Extracting richer meteorological information: most pre- vious DL precipitation forecasting methods attempt to ex- tract sufficient information solely from the rainfall value data. However, the information in rainfall data alone is not adequate for DL. models to learn the patterns of TC rainfall. Various TC-related data can help people and DL models understand and predict the tendency of TC rainfall, shown in the light blue box in Figure L.(c). For instance, since rain- fall is wind-driven, TC wind distribution is critical. Thus, beyond direct rainfall data extraction, modeling synergistic effects of meteorological factors (e.g., wind-rainfall dynam- ics) is also essential to capture TC rainfall mechanisms.
These previous precipitation forecast models provide good reference for constructing TC precipitation models. How- ever, there are notable differences between the TC precipita- tion forecasting task that we consider here and regular pre- cipitation forecasting, as shown in Figure 1.(a) and (b). For example, regular precipitation forecasting usually focuses on specific fixed region, where the area being predicted does not move with the rainfall. In contrast, in this work, we focus on forecasting the TC precipitation, where the pri- mary region of interest and the corresponding environmental factors, such as terrain, will change dynamically with the movement of the TC. Therefore, it is valuable to investigate whether better methods can be developed for this task. We consider the three following approaches to improving TC rainfall prediction skills:
Integrating with NWP models: DL models can make use of global NWP predictions enhance forecasts of specific phenomena (Harris et al., 2022; Zhu et al., 2022; Antonio et al., 2024). If the NWP forecasts are produced using phys- ical equations, such postprocessing approaches allow useful information to be extracted from the embedded understand- ing. Therefore, we evaluate using specific information from NWP results to guide better predictions.
Based on these above potentially useful ideas, we propose TCP-Diffusion, a multi-modal diffusion model for global tropical cyclone precipitation forecasting with change aware- ness. This model can simultaneously forecast TC rainfall for multiple future time steps, at 3-hourly intervals, within the next 12 hours. The contributions are summarized as follows:
Changing the training goal: most precipitation forecast-
TCP-Diffusion can extract information from a rich
2

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A Multi-modal Diffusion Model for Global Tropical Cyclone Precipitation Forecasting
set of meteorological variables, learn the rules of TC rainfall development, and make skilful predictions for global tropical cyclones. To our knowledge, it is the first global TC precipitation forecasting work based on DI..
time step), both in terms of the overall intensity and the spatial and temporal structure.
3. Model Design
TCP- ICP-Diffusion is a temporal DM-based method. The denois- ing process is performed by a neural network, which we call Environmentally
Adjacent Residual Prediction (ARP) is proposed to make our model focus on the rainfall change between adjacent time steps, learn a coherent temporal evolution of the TC rainfall, and have the capability of rainfall change awareness. This mechanism can reduce cumu- lative errors and ensure physical consistency, making the results more realistic and accurate.
3DUNet (EA-3DUNet) (described in detail below). As shown in Figure 2.(b), it can Histor- ical Dataza Encoder, Historical Dataid Encoders and Fu- ture Dalazz Encoder to extract TC rainfall information from rainfall related data, 2D environmental factor data, scalar TC variable and future prediction data. 3DUNet is designed to further extract spatiotemporal future features from the information provided by different encoders. The inherent abilities of DMs enables making predictions that have struc- ture that resembles real rainfall data. The information from all the inputs helps the predicted rainfall values more closely match the real rainfall data. In the following section, we will introduce the details of TCP-Diffusion. We have released the code at Diffusion.
A multi-modal framework is built with several encoder modules to extract extensive information from vari- ous meteorological historical data and future predic- tions provided by NWP. This framework can represent the TC rainfall more comprehensively and provide "bridge" between DL models and NWP models.
We show that our model achieves the best perfor- mance compared to state-of-the-art (SOTA) DL pre- cipitation forecasting methods and outperforms NWP methods from authoritative meteorological agencies
3.1. Adjacent Residual Prediction (ARP)
like ECMWF.
In the TC rainfall forecasting task, predicting the rainfall value directly difficult because weather systems exhibit chaotic characteristics. Some NWP methods improve the accuracy and stability of forecasts by keeping the weather change their prediction goal (Kalnay, 2003). Inspired by this idea, we find the capability of change awareness is helpful to our model, so we replace the direct prediction of rainfall value with predicting the adjacent residual A between rainfall at adjacent time steps (A Rainfall). We call this mechanism Adjacent Residual Prediction. AG can be calculated
2. Task Definition
Different from regular precipitation forecasting, where the predicted regions are fixed, our TC precipitation forecasting task focuses on the 10a by 10t rainfall field around the TC center, which moves with the TC. We denote the final output of our work as Y = ( 9.+2...... -a ................................ mn where th+t represents the rainfall prediction around the TC center time steps into the future. Here, rep- resents the input time steps and m represents the out- put time steps. The input data we used can be divided into two parts, as shown in the left part of Figure 2.(b): the first part is historical observation data (Xnistoricat = (Xf, Xx .2..... "x."......"""....... X,)), where X is the input data at the t time step and it includes the rainfall value data, A Rainfall, the 2-Dimension environment data, and scalar TC variables, like TC intensity and track. The second part is the future prediction data from an NWP system (X fuuture = (xf,
A
X X
Xaan
(2)
where X and X are the absolute rainfall data at t time step and t- time step respectively. In our work, in ad- dition to the absolute rainfall data, we add adjacent residual sequence D2 (A), A2 ... A ".....,
where A is calculated by the Equation 2, which shown as the A Rainfall in Figure 2.(b). The direct output sequence of our DL model is D,, { A where An++ is the adjacent residual we predict between rain- fall of time step n + t and + t. The final prediction y (0n-1, 0 Onter ... (n+m) can be computed as:
, x! m }), where X/ de- notes the prediction data at future / time step. Overall, imag- ine a TC developing. just like shown in Figure 1.(c). We obtain all the input data X (Xhistorioat X { and then we input them to our model TCP-Diffusion TCP- Diffusion will extract the TC information from the in- put data and make a rainfall prediction Y. The aim is for Y to be as close as possible to the real TC rainfall (Y = [1n+1. yn+2..... yn+es.... }, where yn+e rep- resents the real rainfall around the TC center at the future
Agtt ..... Aptm),
N X X
Antz
(3)
Y is obtained by the accumulation of the latest historical TC rainfall data X X and the ARP Ay.
3

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A Multi-modal Diffusion Model for Global Tropical Cyclone Precipitation Forecasting
(a)
Step N
Step
Step s-1
Step
(c)
Denoise
Denoise
Denoise
Denoise
Denoise
Bainf curemt
(b)
Historical
Dataga
Output
Loss
Encoder
fullsurre
Noise
Rainfall
Historical Data Encoder
Scalar TC variables
A Rainfall
Both Training and Inference Path
Futtre
U-Net encoder
environment data
Dataza Encoder
Inference
Future prediction data
Training Path
U-Net decoder
Ratef aullre
Step embeding
Conditions embeding
Figure 2. The framework of TCP-Diffusion. Sub-figure (a) shows the inference stage of TCP--Diffusinn (black+red arrows). Our model will use N loop denoising processes to obtain the future rainfall change Rain fall Fature from noise input. The sub- sub-figure (b) shows model structure of the denoising process and shows training stage TTCP-Diffusse (blacktgreen arrows). In the training stage, the Output will be used calculate the loss and update the parameters of TCP-Diffusion (green arrow). In the inference stage, the Output will used get future rainfall change A RRin flll Future with noise at Step (red arrow). The sub-figure (c) shows the process (Equation of getting the final predicted TC rainfall Rainfalll F with the latest rainfall Rain fallCarrent and the future rainfall change Rain Future-
3.2. Diffusion Model
where ai = a,
a, =1 1 3., 3, E (0, 1) is predefined by an incremental variance schedule.
The prediction process of DMs involves removing noise from completely random noise r step by step, shown in Figure (.).) Based on the DMs' generation process, our training goal is teach our model to perform accurate denoising based on the specific step and the given infor- mation. Specifically, the training goal is to make the noise f. predicted by our model close possible to the noise N}. N
For the denoising process, we build EA-3DUNet, which is defined follows:
f. EAADU N (Xnisstorr X future: Dÿ s,
(5)
where r is the added random noise, EA3DU is the trainable model, and f. is the predicted noise. Thus, our training goal can be defined as:
added to the target at the s-th step, a hyper-paramett
L( |r.. f
(6)
DMs typically include two processes: a forward noising process and reverse denoising process. The forward process has trainable parameters, quire training a DL model. According to the training goal mentioned above, we need obtain the sequence DR where D is s-th-step noised real adjacent residual D2 = x+++1 n++ ,...,. A n+t ,..., Ax+m]. Following (Ho al., 2022), D could be calculated using random noise r, (0, 1), step s, and the D (the original data without noise). The forward process is defined follows:
where 0 represents all the trainable parameters in our model. ra calculated by Equation 4.
does
For the inference phase, we consider a random noise r as the D' (Ho al., 2020) and use the following Equation to denoise D. step by step to obtain the D which is equivalent to Dy:
3.
D Vo (D
f.) + OsC
VI
Ci
where f. the predicted noise added at s-th step, o2 is a variance hyperparameter. C~ N20 1) is random noise.
Dú = Vo, vI Varrs
(4)

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A Multi-modal Diffusion Model for Global Tropical Cyclone Precipitation Forecasting
which plays a critical role in generating high-quality predic- tion in the inference phase (Ho et al., 2020).
Considering that our data has time dimension, we build Historical Dataza Encoder with 3D Convolutional Neural Networks (CNNs) to encode all 2D data with time infor- mation first. To reduce computational resources, we use one module to encode these data, so we concatenate them to get XiszD = [Xrains 2 XPLEnes Tsl. This process defined as follows:
Overall, the training phase (Figure 2.(b)) and inference phase (Figure 2.(a) and (c)) can be represented by the fol- lowing pseudocode. Here, q(-) denotes the data distribu- tion from which samples are drawn. Specifically, ((D,)) represents the distribution of the target variable, while q( ((Xnistory) and [[(Xfutrre) represent the distributions of historical and future input features, respectively.
Chis2D = (onood((Nie20)) Wh12D)
(8)
where WhisDD is the encoder parameters. Chie2D represents the features encoded from X and serves as the initial feature input to 3DUNet for further feature extraction.
Algorithm 1 Training
I: repeat
2: D2 ~ (Dy))
3: 8 ~ Uniform (1,,m,,(,1.,
The scalar TC variable Xse does not have a 2D structure, build Historical Data Encoder with Multilayer Perceptron (MLP) and Transformer (Vaswani et al., 2017) layers to encode X and obtain the temporal information.
4:
D2 = Vo + vI ast
5:
Xnistory ~ q( ((Nnistory)
6:
X futture (og((futuu) future)
7:
(0,
The main process is as follows:
X future; D 8,,,, 8) 9: Take gradient descent step on Vellr - f|
8:
F F= nel
Cmlp ob (b(Se: W Wmip)
(9)
10: until converged
ChislD Transformer(emttp Watten)
(10)
Algorithm 2 Inference
where & is denoted as an MLP module, which is used for getting the features Cmip of different variables. W is the parameters of ø. The Transformer module is used for obtaining the temporal information of X Watten is the parameter of Transformer and ChisiD the encoded features of X Xse
1: DW ~ N),
2: Xhistorg (Xhisstryy)
3: Xjuture ~ (X [ future)
4: for ,...., do
5: 6~ N>N00, 1) if >,,,,,,,,, else =
6: f= neADDnne((Naaan (Dz
X Susures Dr 8, s)
7: L -
Vi-w. f) + O,E
Future Prediction Data Encoder Future prediction data X future contain future information and some physical in- formation provided by NWP, which differs from Historical data. It is challenging for single module to encode these data containing different types of information at the same time (Alzubaidi et al., 2021). Therefore, we build a Future Dataza Encoder to encode these data and try to obtain more specific features. We use modified Resnet- 18 (He et al., 2016) to obtain the vector. The main process of Future
8: end for
9: Use Equation.3 to get y
10: return Y
3.3. Environmentaaly- 3DUNet (EA-3DUNet)
EA-3DUNet is the neural network component of TCP- Diffusion. It can extract various features from multi-modal data sources. Due to the differing characteristics and di- mensions of these heterogeneous metcorological data, we need to build multiple encoders to embed these data. There- fore, we build the Historical Data Encoder for Rainfall Data and Environment Data, and the Future Prediction Data Encoder for future prediction data. To better extract temporal and spatial information from these data, we build 3DUNet with temporal and spatial attention mechanism. We will introduce all these modules in the following sec- tions.
Datazd Encoder is follows:
efuture Resnet(X (eaunee(Xuuurree future, W Wre
(11)
where Resnet the Resnet-18 model, W Wrests the param- eters, and ffuure is the condition extracted from X fatare and used for guiding our model to make better prediction.
3DUNet 3DUNet (Çişek al., 2016) is the core com- ponent of EA-3DUNet and is classical DL structure for tasks involving 2D data with time information. It usually includes three parts shown in Figure 2.(b): U-Net encoder (U-Neten). U-Net decoder (U-Netae). and the bottleneck between encoder and decoder. There are several modules in U-Netan and UNNeetde called module and moduleae
Historical Data Encoder Rainfall Data Xyain- adjacent residual data Dr,, ERA5 surface data XsfEmes and ERA5 pressure level data X Yreae are two-dimensional (2D) data.
5

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A Multi-modal Diffusion Model for Global Tropical Cyclone Precipitation Forecasting
respectively. In each module, we build different blocks (blue cuboids) capture features from various aspects. Over all, the 3DUNet receives the feature map from the Historical Dataid Encoder and the condition information from Future Daland Encoder. Additionally, step s is also included in the condition information to inform the model how much noise to remove at the current stage. Then, the 3DUNet predicts the noise (f+) added at the step s. Finally, there are two pathes shown in Figure 2.(b). In the training stage (green arrow), we could calculate the loss between actual noise rs and P.s to optimize the parameters of our model. In the inference stage (red arrow), f, could be used for obtaining Dy- using Equation 7. The main process of 3DUNet is shown in Appendix.B.
Model Name
ETS-6 t
ETS-24 +
ETS-60
TAM 4
Persistence
0,41640
0.14530
0.00564
0,44558
U-Net
0.44169
0.10587
0
0.47452
PreDiff'
0,38453
0.11931
0.00430
0.53617
NowcastNet
0.42180
0.08990
0.00016
0,56954
ICP-Diffusion 0.43788
0.14703
0.00644
0.42344
Higher better, Lower is better.
Bold values are the best. Underlined values are the second best.
Table 1. Comparison with other SOTA DL methods. Equitable Threat Score (ETS) is used to evaluate the prediction skill of each model. ETS-6, ETS-24, and ETS-60 are used to show the prediction skill for light (>6 mm/3hr), medium (>24 mm/3hr), and high (>60 mm/3hr) rainfall respectively. TE shows the total precipitation forccasting skill of different methods and, with unit mm/3hr. The results here represent the overall performance each model for lead times of 3, 6, 9, and 12 hours.
4. Dataset and Evaluation Methods
4.1. Dataset
cipitation: PreDiff, which is DM-based (Gao et al., 2024), and NowcastNet (Zhang et al., 2023). We also compare TCP-Diffusion with a basic baseline, persistence forecast- ing, using the last observed rainfall field for each future prediction (Panofsky, 1963). Since TCP-Diffusion is prob- abilistic prediction model, to ensure the stability of the re- sults presented, we conducted eight tests on the test set. For each test, the evaluation metries were calculated, and the final results were obtained by averaging the metrics across these eight tests. Additionally, the individual results from each test are provided in Table 5 in Appendix.D.2.
We collected various TC rainfall-related data for our TCP- Diffusion model to comprehensively represent TC rainfall. A total of 1877 TCs spanning from 1980 to 2020 are col- lected, covering the six major ocean areas. These TC data are divided into three sets: training set (1751 TCs), valida- tion set (87 TCs), and test set (126 TCs from 2018 2020). We divided the data into two parts: X Aisttorica and X future- Details of the data we used are in Appendix.A.
4.2. Evaluation Metrics
Equitable Threat Score (ETS) The Equitable Threat Score (ETS) (Gandin & Murphy, 1992) is a metric used to evaluate the accuracy of precipitation forecasts. Com- pared to the Critical Success Index (CSI) (Schaefer, 1990), a more popular metric, it considers the effects of random chance, providing a more equitable assessment of fore- cast model's 's performance (Manzato & Jolliffe, 2017). The definition of ETS is given in Appendix.C. C. We use this met- ric to show the performance for predicting light, medium, and heavy rainfall, setting thresholds 6 mm/3hr (ETS-6), 24 mm/3hr (ETS-24), and 60 mm/3hr (ETS-60) respectively.
Qualitative Analysis. Figure 3 shows an example of pre- dictions from TCP-Diffusion and other DL methods for a forecast of TC Dumazile. Comparing with the determinis- tic U-Net rainfall prediction model, the DM-based models (Predif and TCP-Diffusion) can give more realistic rainfall predictions with fine spatial detail, such as the shape of the rain band. U-Net and NowcastNet produce predictions that are too spatially smooth. This is one of the reasons we chose DMs as the basis for our TC rainfall prediction model. When comparing our TCP-Diffusion with PreDiff in this example, our model provides more accurate results and does better at predicting the increasing trend of precip- itation intensity with time, because the ARP mechanism gives our model the capability to track the rainfall change. We show two samples from TCP-Diffusion, generated using different noise inputs. We also show all 8 samples from TCP-Diffusion in Figure 9 in Appendix.D. D. Overall, they have similar large-scale rainfall trends and structures. This means that the information extracted from other input data, such as historical TC rainfall and 2D environmental vari- ables, can guide our model to make reasonable and realistic forecasts. Overall, these results indicate that can produce rainfall predictions that have realistic spatial and temporal structure, performing better in this example than the other DL. methods.
Total Precipitation Mean Absolute Error (TPMAE) This is the absolute difference between real TC rainfall Y and the predicted rainfall V averaged over the 10 spatial domain, to show the prediction skill of different methods at predicting total TC rainfall.
5. Results
5.1. Comparison with State-of-the-art DL. Methods
TCP-Diffusion is compared with a deterministic DL method: U-Net (Çiçek et al., 2016). We also compare our model with two generative DL. methods developed for nowcasting pre-
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A Multi-modal Diffusion Model for Global Tropical Cyclone Precipitation Forecasting
Ground Truth
U-Nlt
PreDiff
NowcastNlet
TCP-Diff #1
TCP-OIf #2
Previous haurs Prevtous -9 hours
3 hours
h
9 houns
Previous
Present
12 hours
10 20
20
50 100
Precioltation (mm/3h)
Figure 3. The prediction results of different DL methods TC Dumazile in the North Indian Occan 03/03/2018 06:00. The first column is the previous 4 timesteps of rainfall data used as input. The second column is the future TC rainfall we want to predict. Each subsequent column from the left shows the predictions from different DL method. "TCP-Diff #1" and "TCP-Diff #2" samples from our TCP-Diffussie model with different initial random noise
Quantitative Analysis. To further demonstrate the effec- tiveness of method, we calculate and compare various metrics the entire test set, as shown in Table 1. We also show the performance of ICP--Diffusie other methods at lead times of 3, 6, 9, and 12 hours sepa- rately in Figure 8 in Appendix.D. D. The lead time indicates the amount time between the issuance of a forecast and the actual occurrence of the weather event. For light rainfall pre- diction (ETS-6), U-Net achieves the best performance, with TCP-Diffusion ranking second. However, U-Net performs poorly for moderate and heavy rainfall predictions. For higher rainfall thresholds and TAMAE, our TCP-Diffusion method achieves the best performance. Especially heavy rainfall prediction, CCF-Diffusion shows a substantial im- provement compared to other DI. models. is also the only model that performs better than Persistence forecasting, in- dicating the value of designing specialised system for the task of TC rainfall prediction. We also show some analysis about why Persistence forecasting performs better than the other three DL models in Appendix.D.
predicts a slightly lower precipitation intensity. However, for more moderate rainfall intensities, TCP-Diffusion has more realistic frequency than PreDiff, as shown in the circled region in Figure 4. We also present the distribution of rainfall prediction from TCP-Diffusion and compared methods at each lead-time in Figure 10 in Appendix.D.
compared with
Analysis of TC Rainfall's Radially Averaged Power Spectral Density We use the Radially Averaged Power Spectral Density (RAPSD) to help demonstrate that our model better captures the spatial structure of large-scale TC rainfall systems, shown in Figure 5. If the power spectral density curve predicted by the model is closer to the ground truth MSWEP at a given spatial frequency, it indicates that the model captures the rainfall variability at that spatial scale more effectively. The low wavenumber region corresponds to large-scale weather systems, such as fronts and tropical cyclones. As observed in Figure 5, the power spectral den- sity of TCP-Diffusion is closer MSWEP compared to PreDiff in the low wavenumber region, indicating that our method achieves better capture of rainfall characteristics at the TC scale. We also show the RAPSD of rainfall predic- tion from TCP-Diffusion and compared methods at each lead-time in Figure 11 in Appendix.D.
Analysis of TC Rainfall Frequency Distribution. Fig- ure 4 shows histograms of rainfall rates for observations and forecasts by each DL method. We find that the performance of DM-based models, PreDiff and TCP-Diffusion, is much better than that of non-DMMbased models, especially in pro- ducing a realistic frequency of the heaviest rainfall rates. Our method predicts a slightly higher frequency of the heav- iest precipitation intensities than is observed, while PreDiff
5.2. Comparison with NWP Methods
We also compare our model with two state-of-the-ar NWP methods. We select the precipitation forecast data in THOR- PEX Interactive Grand Global Ensemble (TIGGE) provided

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A Multi-modal Diffusion Model for Global Tropical Cyclone Precipitation Forecasting
Distribution of Rainfall Intensity
Average RAPSD Across Datasets
NEWEP
10
MSWEP
U-Net
107
NowcastNst TCP Diffusion
10
PreDiff
NowcastNet
Power Spectral Density
TCP-Diffusion
10
10º
10
Frequency
1.0
10
10a
10a
"102
20
150
Wavenumber (1/m)
10
Figure 5, Radially Averaged Power Spectral Density (RAPSD) analysis across datasets. The plots compare the power spectral density of predicted rainfall using different models over range of wavenumber. In the low wavenumber region, higher power spectral density represents that the displayed data belongs to large-scale weather systems, such as fronts and tropical cyclones. The power spectral density of CCP-Diffusion in the low wavenumber region is closer to the ground truth rainfall (MSWEP). indicating that our method achieves better capture of rainfall characteristics at the TC scalc. Note the logarithmic vertical axis.
20
40 60
30
100
120
340
Rainfall Intensity (mm/33rr
Figure 4. TC rainfall frequency distributions of different DL fore- casting methods. The grey histogram is the distribution of MSWEP observations. The coloured lines show histograms of rainfall rates from different DL forecasting methods. The circular magnified re- gion more clearly shows differences between these methods in the indicated span of rainfall intensity. Note the logarithmic vertical axis.
Model Name ETS-6 f
ETS-241
ETS-60
ERA5-IFS
0,20172
0.01646
0.51
5.3. Ablation Studies
ECMWF-IFS
0.30193
0.08348
0.00255
0,50661
TCP-Diffusion
0,41238
0.12790
0.00444
0.47446
To demonstrate the effectiveness of individual components of our model, an ablation study is conducted. As shown in Table 3, comparing the results from the model with and without ARP in the first two rows, we find that changing the regular rainfall value prediction to the adjacent resid- ual prediction results in an improvement in ETS of about 0.1-15.0% This indicates that predicting the adjacent resid- ual reduces cumulative errors. Then, due to the rich and important TC environment information from multi-modal meteorological data, the model with M and ARP (third row) performs better than the model with only ARP, showing an improvement of about 5.6-13 13.0% in ETS and a reduction in
Table Comparison with the ERAS-IFS and ECMWF-IFS NWP methods. The forecast diagnostics are the same as in table 1.
by ECMWF (ECMWF, 2006), denoted ECMWF-IFS.
This has higher skill than the ERAS-IFS (ECMWF, 2017). However, the spatial resolution of ERA5-IFS results is lower than that of ECMWF-IFS results, which means the costs of getting ERAS-IFS results is lower than that of ECMWF- IFS results and makes ERA5-IFS results more practical to use as the future prediction data X future in training. As ECMWF-IFS forecasts in the TIGGE archive for 6- hourly rather than 3-hourly precipitation, we sum 3-hourly TCP-Diffusion forecasts within each 6-hour interval. Addi- tionally, ECMWF-IFS forecasts start at 12 am and 12 pm UTC each day, so we use TCP-Diffusion to forecast TC rainfall from the same start times. Thus, the test samples in this table are different from those in Table 1.
ARP M F
ETS-6 1
ETS-24 1
ETS-60 1
TPMART
0,39109
0.12474
0.00453
0,50109
0.40634
0.13014
0.00521
0.50043
0.42926
0. 0.14253
0.00589
0.44632
0.43788
0.14703
0.00644
0.42344
Table 3. Ablation studies. ARP means the contribution that we change the regular rainfall value prediction the adjacent residual prediction. M means we not only consider the information from TC rainfall but also consider the TC-related environment informa- tion extracted from multi-modal meteorological data. F means we combine our DI. model with the NWP method by using the predictions provided by NWP to guide the prediction process of our method.
As shown in Table 2, our method achieves better ETS for all rainfall thresholds and better TF than the ECMWF- IFS. This means that low-cost, low-quality NWP methods (ERAS-IFS), when augmented by DL techniques, have the potential to surpass the performance of high-cost, high- quality NWP approaches (ECMWF-IFS).
8

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A Multi-modal Diffusion Model for Global Tropical Cyclone Precipitation Forecasting
MAE This demonstrates the significance of building dif- ferent encoder modules to extract TC rainfall-related infor- mation, addressing the deficiency of information provided only by the TC rainfall field. Finally, our complete model TCP-Diffusion including NWP forecast inputs (fourth row) achieves a 2.0-9.3% improvement in ETS over the model with only M and ARP. This demonstrates that using fore- casts provided by NWP to guide DL prediction can enhance skill. (Though note that the scores for our model without using future forecast data still improve upon those of other benchmarks for ETS at high thresholds and TPM AE shown in table 1, showing that the method can improve skill even when future forecast data is unavailable.) Overall, due to the contributions of A ARP, M, and F, our final model TCP- Diffusion achieves an improvement in ETS scores of about 11.9-42.19 % over the baseline original spatio-temporal diffu- sion model across the different metrics.
TCP-Diffusion method significantly improves TC rainfall forecasts while reducing cumulative errors and ensuring physical consistency. These advancements have the poten- tial to enhance disaster preparedness and mitigation strate- gies, provide actionable insights for climate resilience, and improve the overall efficiency and effectiveness of global weather prediction systems.
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6. Conclusion
In this paper, we propose the TCP-Diffusion model for fore- casting TC precipitation in the region around a given track location, applicable anywhere in the world. TCP-Diffusion uses the ARP mechanism to predict changes in rainfall and framework with multiple encoders to extract information from numerous relevant variables, including historical TC rainfall data, TC-related environmental data, and forecast data from NWP models. These guide and control our model to make better predictions. TCP-Diffusion produces pre- cipitation predictions with realistic spatial variability. It achieves higher skill scores than existing rainfall forecasting methods and leading NWP system, the ECMWF IFS. In the future, our model can be applied as a component of a forecasting system that includes track and intensity forecasts to produce overall predictions of TC properties.
Alzubaidi, L., Zhang, J., Humaidi, A. J., Al-Dujaili, A., Duan, Y., Al-Shamma, O., Santamaria, J., Fadhel, M. A., Al-Amidie, M., and Farhan, L. Review of deep learn- ing: concepts, cnn architectures, challenges, applications, future directions. Journal of big Datu, 8:1-74, 2021.
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This work is partially supported by the Zhejiang Provin- cial Natural Science Foundation of China under Grant No. LRG25F020002 and No. LR21F020002, Natural Science Foundation of China under Grant No. 62202429, U24A20221 and Zhejiang Provincial Natural Science Foun- dation of China under Grant No. LY23F020024. Peter A. G. Watson was supported by a NERC Independent Research Fellowship (Grant No. NE/S014713/1).
CGRS.2002.316633
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Impact Statement
This work aims to advance the accuracy and reliability of tropical cyclone (TC) rainfall forecasting, addressing a critical gap in weather prediction. By leveraging deep learning and integrating meteorological factors with nu- merical weather prediction (NWP) models, the proposed
Benjamin, S. G., Brown, J. M., Brunet, G., Lynch, P., Saito, K., and Schlatter, T. W. 100 years of progress

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A Multi-modal Diffusion Model for Global Tropical Cyclone Precipitation Forecasting
MSWEP
30
9-600
0,0075
t-600
U-600
15
v-600
25
277
10
0.0085
20
0.0060
5
15
0.0055
275
-5
100
10
0.0050
-10
-15
0.0045
24
274
16
-15
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3500
Z-600
43200
t2m
300
sst
300
msi
Topography
290
101000
-4000
43000
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100800
260
100600
42800
296
270
100400
42500
260
100200
-5000
294
100000
42400
250
98800
5500
Figure The visualization presents part of the historical data on TC Dumazile North Indian Ocean 03/03/2018 06:00. MSWEP the rainfall values. q-600, 1-600, u-600, v-600, z-600 represent the Specific Humidity, Temperature, Wind, V Wind, and Geopotential Height at the 600 hPa pressure level respectively, 12m, sst, msl and topography represent the 2m Temperature, Sea Surface Temperature, Mean Sea Level Pressure, and Topography respectively around the TC center.
A. The Details of Data
We divided the data into parts: X Nistorical and X future. We collected total of 1877 TCs spanning from 1980 to 2020 contained in the International Best Track Archive for Climate Stewardship (IBTrACS) dataset (Knapp et al., 2010), covering the six major ocean areas. These TC data are divided into three sets: training set, validation set, and test set. The test set contains 126 TCs from 2018 to 2020. For the other two datasets, we randomly selected 95% of the TCs from 1980 to 2018 as the training set (1751 TCs) and 5% as the validation set (87 TCs). Due to the time cost DMs inference, we use approximately 5% of the data to validate and determine our best checkpoint in the training run. Some of the Nhistoricnt are visualized Figure for one TC one time and some of the X future are visualized in Figure
A.1. Historical Data
Rainfall Data The rainfall dataset that we use (Xrain) is the Multi-Source Weighted-Enseminee Precipitation (MSWEP)(Beck al., 2019) global precipitation product. This has 3-hourly 0.1 resolution available from 1979 about hours from real-time. We focus only the rainfall field around the TC center, we crop and obtain rectangular data covering 10" by 10" region around the TC center.
Environment Data We also collect critical meteorological variables including surface data and pressure level data (200 hPa, 600 hPa, 850 hPa, and 925 hPa) from ERAS (ECMWF, 2017), and TC attributes data. The surface data, denoted as XsfEnv include 2m temperature, sea surface temperature, mean sea level pressure, and topography. ERA5 pressure level data, denoted as XPIEnes consists of 5 variables: temperature, specific humidity, U-component of wind, V-component of wind, and geopotential height. We perform the same operations as with Xyains focusing on the 10 by 10" region around the TC center.
We also use several scalar TC variables, which we call Xs. and includes TC intensity, movement velocity, the month and the track location. Xs. is collected and calculated from the IBTIACS dataset.
A.2. Future Prediction Data.
is necessary for DL models to better understand the physical processes of TC rainfall. However, incorporating the physical mechanisms TC rainfall development into DL model design challenging. Physically- -based NWP methods can predict TC rainfall using various equations, such as Dynamical Equations, Thermodynamic Equations, Moisture Equations, and
12

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A Multi-modal Diffusion Model for Global Tropical Cyclone Precipitation Forecasting
q-850
0.014
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Figure 7. The visualization of the Future Prediction Data for the TC Dumazile in the North Indian Occan at 03/03/2018 06:00. These data are all collected from ERA5. The q-850, t-850, u-850, and v-850 represent the forecast data for Specific Humidity, Temperature, U Wind, and V Wind at 850 hPa pressure level respectively. The tp, msl, and (2m represent Total Precipitation, Mean Sea Level Pressure, and 2m Temperature, respectively.
Radiative Transfer Equations, based on physical mechanisms. The prediction data are thus based on explicit physical laws. DL models are good at extracting information from data. Therefore, we also consider X future as input data for model, providing future information based on physical laws some extent. All X future used is provided by the ensemble mean of the ERA5 (ERA5-IFS) (ECMWF, 2017). Here, opted for the low-resolution ERA5-IFS dataset over the high-resolution ECMWF-IFS (ECMWF, 2006) for our training data due to ERAS-IFS's & broader temporal coverage and higher temporal resolution. Additionally, the cost of generating ERA5-IFS is lower owing to its coarser spatial resolution. Moreover, our results reported in the main text showed that incorporating ERAS-IFS enhances the predictive performance of our model, surpassing that achieved with the high-quality ECMWF-IFS. There are many variables at the 200 or 850 hPa pressure levels, such as temperatur, specific humidity, U-component of wind, and V-component of wind. Total precipitation, 2m temperature, and mean level pressure are also collected.
B. Development of the model
B.1. The Setting of Hyper- Sypee-paramettrs
In designing our method, we established consistent hyperparameters to enable greater flexibility for other users. This allows users to apply CCP-Diffusion to similar tasks and tailor the model by adjusting specific hyperparameters according to their needs. The time steps for input data n and future prediction m are both set to 4, meaning our model extracts information from 12 hours historical and ERA5 prediction data to predict accurate future 12-hour TC rainfall data. The denoising step N is set to 200, but users can modify
control the model inference time. For B., we use the Cosine Schedule 3, 1 cos cos(Ts/(3) (N N 1)), which controls the level of noise addition the specific step The a, in Equation in the main paper is related to 8, and is set as vB,. The count of modules K in U-Netan and U-Neta, Ne is set as 4. People can use it to adjust the size of our model.
it:
B.2. Hardware Details
The experiments in this work were conducted using an NVIDIA A100 GPU with 256GB of RAM. The deep learning models were developed and trained using PyTorch (version 1.10) as the primary framework. The training process took approximately 72 hours to achieve the optimal checkpoint. During inference, each sample takes around 1.253 seconds to process. We also compare different methods' training and inference time-cost in Table 4, In addition, the environment included essential Python libraries such as NumPy (version 1.21), SeiPy (version 1.7), and CUDA Toolkit (version 11.4) for
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A Multi-modal Diffusion Model for Global Tropical Cyclone Precipitation Forecasting
U-Net
PreDiff
NowcastNet
TCP-Diffusion
ECMWF-IFS
Training (h)
5
67
52
72
Inference (s/sample)
0.0062
9,401
0,0052
1.253
30min
Table 4, Training and inference time-cost of TCP- CCD-Diffusion and compared methods.
GPU acceleration.
B.3. The Detail of 3DUNet
3DUNet (Çişek et al., 2016) is the core component of EA-3DUNet and is classical DL structure for tasks involving 2D data with time information. It usually includes three parts shown in Figure 2.(b): U-Net encoder (U-Neten), U-Net decoder (U-Nelad), and the bottleneck between encoder and decoder. There are several modules in U-Neten and U-Neldee called moduleen and modulede respectively. In each module, we build different blocks (blue cuboids) to capture features from various aspects.
Specifically, in the encoder module (moduleen), shown the blue cuboids in U-Nelen in Figure 2, stack two CNN blocks, one spatial attention (SA) block, one temporal attention (TA) block, and down-sampling block. The network progressively performs downsampling by stacking several module Each moduleen receives the feature map from the previous module and also the conditions eMei1D and ffuture from the Historical Datais Encoder and Future Datazd Encoder, respectively. Additionally, step s is also received to inform the model how much noise to remove at the current stage, We concatenate these conditions to form the final condition Cond- U-Neten as follows:
[ehis e futures 8]. The main process of
module en (Chis2D, Cond, Wen.) module (c/m) Cond, Wen.) if 1.
if 1,
(12)
on
where module is the depth-i module in U-Nelen, E 2 K}. of the module module (the first module receives Ehis2D from the historical data encoder. Subsequent module (i > 1) receive ein11 from module
K is hyper-parameter. Won, is the parameters
The module between U-Nelen and U-Nelde the Bottleneck. The Bottleneck also contains two CNN blocks, one SA block, and one TA block. The main process as follows:
Emid Bottleneck(( K Cond, W W
(13)
where Emid is the output of the Bottleneck and Weeck is the parameter of Bottleneck.
For U-Netae: its structure is similar to that of U-Neten- They both include K modules with similar architecture. In modulede. there are two CNN blocks, one SA block, one TA block and the final up-sampling block. There are also skip connections between U-Neten and U-Netde- Thus, the definition of U-Netat is as follows:
module's (ouuulledeemmsss Cond, e'e Wdes) if = K,
(14)
module's (c Cond, e W de.)
if K.
where module's, is the depth-i module in U-Netae: i E {K.... 2, 13. Wae. is the parameters of the module If module', is the deepest one (i = K), module receives the Emid from the Bottleneck. if module is not the deepest (+1 one (i < K), module's, receives the e++ from module de if i = 1, ede is the final output of EA-3DUNet, which means f. -e Then, we could calculate the loss between re and f, to optimize the parameters of our model.
C. The Definition of Metrics
C.1. Equitable Threat Score (ETS)
The Equitable Threat Score (ETS) (Gandin & Murphy, 1992) is statistical measure used to evaluate the accuracy of precipitation forecasts. Compared to the more popular metric, the Critical Success Index (CSI)(Schaefer, 1990), it provides a more robust assessment of forecast model's performance (Manzato & Jolliffe, 2017). The definition of ETS is as follows:
(NA NN) Ne) R(a)=
(15)
NA + NB + No + ND
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A Multi-modal Diffusion Model for Global Tropical Cyclone Precipitation Forecasting
NA R(a)
ETS NA + NB + Nc R(a)
(16)
where NA. NB, Nc, and ND represent the number of correctly predicted precipitation events, the number of false alarms, the number of missed precipitation events, and the number of correctly predicted no-precipitation events respectively, R((a) denotes the expected number of correct forecasts due to random chance.
In addition, we also use this metric to show the performance of different methods for light, moderate, and heavy rainfall prediction. Thus, we set thresholds 6 mm/3hr (ETS-6), 24 mm/3hr (ETS-24), and 60 mm/3hr (ETS-60) to show the prediction skill for each rainfall category respectively. We need to do some processing before we calculate the ETS, which is shown as follows:
if TT,
Y
(17)
0 if <T.
1 if TT,
Y7
(18)
0
ifY <..
where E (6,24, 60) is the rainfall intensity threshold. Then we use Vy and Yr to calculate ETS-T via Equations 15 and 16.
C.2. Total Precipitation Mean Absolute Error MAE)
In addition to comparing the prediction skills of different methods light, moderate, and heavy rainfall, we also want to evaluate the performance of total precipitation forecasting in the region covered by TC. This critical index for representing the intensity of TC rainfall. Therefore, we use Total Precipitation Mean Absolute Error (TP (A) to show the prediction skill of different methods in total rainfall prediction. The definition of MAE is follows:
Yiu
Peja
TPMAE-
(19)
hwm
where & and w represent the height and the width of the TC rainfall data respectively and m represents the total number of time steps that we want to predict. Yije and Vize are the observed and predicted rainfall at the given grid point and time respectively.
D. Extended Experiments
D.1. Results at Different Lead-times
In the main text, we have shown the overall performance of our model compared to other models. Now, we will demonstrate and compare their predictive performance at each lead time point-3-hour, 6-hour, 9-hour, and 12-hour. As illustrated in Figure 8, we evaluate the performance of each method using the metrics ETS-6, ETS-24, ETS-60, and TPMSE. For ETS-6, the Unet model achieves the best performance, with TCP-Diffusion ranked second. However, for the remaining metrics, our method consistently outperforms the others. Notably, the ETS-60 results indicate that non-diffusion-based models do not perform well. Overall, TCP-Diffusion not only excels overall performance but also demonstrates strong predictive accuracy at each lead time point. Besides, the prediction lead time increases, the performance of all deep learning methods declines to varying degrees. In the future, extending the duration of rainfall prediction and improving its accuracy will be the focus of subsequent research efforts.
D.2. Results of Multiple Tests
TCP-Diffusiae is probabilistic prediction model, which generates different results for different noise inputs. To ensure the reproducibility of the metric results for our model presented in the main text, we produced 8 separate samples for each TC case in the test set, with each test using independent random noise drawn from a normal distribution in the diffusion process. As a result, we obtained independent prediction outcomes. After calculating the metrics for these outcomes, the results are shown in Table 5. From the experimental results, can be observed that the performance of our model across multiple tests remains relatively stable on these metrics, with low standard deviations.
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A Multi-modal Diffusion Model for Global Tropical Cyclone Precipitation Forecasting
TPNat
0:35
U-kt
Prebiff
0.18
PreOfff
U-Nett
0.006
U-Net PreD
ProDiff
U-bat
0.50
Nowcasttett TCP Offfusion
0.16
Nowcantlee
0.005
Nieeaatthet TCP: Diffusion
Neweentiee
TCP-D musion
TCNDifusion
Velves
0.45
0.12
0.004
Volues
0.5
0.003
0.40
0.10
0.002
2.08
0.35
3.06
00011
0.3
0.000
3h
6h
9
12
h
6
9h
12
3h
6h
hh
12h
3h
6h
9h
hhh
Lead Time
Lead Time
Lead Time
Lead Time
Figure& 8. Comparison with SOTA deep learning methods for lead times of h, h 9 h. and 12 h on ETS-6 (a), ETS-24 (b), ETS-60 (c), and TP MSE (d).
Sample/Statistic
ETS-6 1
ETS-24
ETS-60
TAMA
TCP-Diffusionst
0.43862
0.14848
0.00726
0,42403
TCP-Diffusionf*
0.43867
0.14698
0.00619
0,41968
TCP-Diffusion##
0,43782
0.14735
0.00674
0.42340
TCP-Diffusiontt4
0.43735
0.14651
0.00646
0.42527
TCP-Diffusion#5
0,43860
0,14802
0.00632
0.42131
TCP-Diffusion#6
0,43715
0.14621
0.00633
0,42406
TCP-Diffusion#7
0,43716
0.14591
0.00601
0,42265
TCP-Diffusion##8
0.43767
0.14678
0.00623
0,42713
VCP-Diffusion--ent mean
0.43788
0.14703
0.00644
0,42344
ICC-Diffusion-std
0.00066
0.00088
0.00039
0.00229
Table 5. Performance metrics of based on 8 independent tests, where TCR- I to (CR-Diffusionffs represent the results of the to 8th predictions. The rows TCR- Diffusion mean and TCR- RR--Diffusion--ee std summarize mean and standard deviation these tests, respectively.
We also visualized the results of each prediction, as shown in Figure 9. The eight samples exhibit an overall trend consistent with the ground truth, with an enhancement rainfall intensity. This demonstrates the effectiveness of our APR mechanism, showing that our model can accurately perceive future changes in rainfall trends and provide predictions aligned with these changes. Besides, the eight samples display differences in rainfall patterns and intensity, effectively simulating the chaotic nature of tropical cyclone rainfall. These multiple possible predictions are valuable for forecasters to determine the uncertainty range of the future TC rainfall. This approach aligns with the ensemble forecasting method in meteorology, which is widely used to address chaotic weather systems.
D.3. Analysis of Persistence's Good Performance
Persistence forecasting performs better than the other DL methods except TCP. Diffusion for most evaluation metrics, as shown in Figure 1. There may be two reasons for this situation. On the one hand, these DL methods are designed for traditional rainfall prediction tasks, focusing only on a fixed region, meaning the observation window does not change with the movement of the rain band. Our TC rainfall prediction task focuses on the precipitation in the region around the TC center, and the observation window changes with the movement of the TC. There are some differences between these two tasks. Therefore, some novel ideas proposed for traditional rainfall prediction tasks may not be suitable for TC rainfall prediction. This means that simply applying previous rainfall forecasting methods to TC rainfall forecasting is insufficient, highlighting the value of proposing the designed with consideration of the special features of TC. On the other hand, because we keep the observation window always centered around the TC, there is always rainfall in the center of the observation window, and the rainfall intensity usually does not change much over several hours. The rainfall also primarily concentrated in the central region. Therefore, when calculating the metrics, this makes Persistence forecasting strong baseline.
There is an interesting phenomenon:
model, which is
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A Multi-modal Diffusion Model for Global Tropical Cyclone Precipitation Forecasting
Ground Truth
TCP- #1
TCP- #?
TCP-DHt #
TEPOFT #4
TCP-D/ff #5
TEPOIT #6
TCP-0Hf #7
TCPD eB
Frevioes Tours Fresious 6 hours Previous hours
hours
Presstn
10
Prodpitatoon
22
30
50 100
Figure 9. The prediction results of different TCP-Diffusion samples on the TC Dumazile in the North Indian Ocean at 03/03/2018 06:00. The first column is the previous 4 timesteps of rainfall data used as input. The second column is the future TC rainfall want predict. TCR-Diff#1 to TCR-DiftWS represent the results of the 1st to 8th tests on this sample.
(n)
Dicniiuution of Sainfal Intenstyy h
(b)
Dist bistiinutionoo of Paintall Intendity 6
(c)
Distr bution of Rointal intersity 9
(d)
Dustriuutoon of Rointail interstyy 12 h
Hamadde
Frequency
Fresuency
Frenuwnzy
20
00
20
1/ 30 Intensity (mm/3he)
10
65 20 19
d0 us 20
3mm03300
Intersity tmm/3hei
intensily (mm/30r)
Figure 10. TC rainfall forecasting distributions different DL methods for lead times of (a), 6h (b), 9h (c). and 12h (d). The grey histogram is the distribution of MSWEP observations. The coloured lines show histograms of rainfall rates from different DL forecasting methods. Note the logarithmic vertical axis.
D.4. Analysis of TC Rainfall Frequency Distribution at Different Lead-times
We also present the TC Rainfall Frequency Distribution predictions for lead times of 3-12 hours, shown in Figure 10. The results are consistent with those displayed in Figure 4 of the main text, showing that the distribution of predictions by TCCP-Diffusion is overall closer to the ground truth rainfall, particularly in the distribution of medium-to-lot low rainfall intensities, which account for a larger proportion.
D.5. Analysis of TC Rainfall's Radially Averaged Power Spectral Density at Different Lead-times
We use the Radially Averaged Power Spectral Density to help demonstrate that our model better captures the spatial structure of large-scale TC rainfall systems, as shown in Figure 11. If the power spectral density curve predicted by the model is closer to the ground truth MSWEP at a given spatial frequency, it indicates that the model captures the rainfall variability at that spatial scale more effectively. The low wavenumber region corresponds to large-scale weather systems, such as fronts and tropical cyclones. The RAPSD results of different lead times are similar to that shown in Figure 5.
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A Multi-modal Diffusion Model for Global Tropical Cyclone Precipitation Forecasting
(a)
NAPS Acuos Datmsts leading 25
(c)
SAPSO Acres Deteadt bestire d:
10
Hotee
30*
HOMer
10
Prebir
10
Pra Newecstteet K. stgn
10 Rustin
-24
10
10
We rooo 12s01
(b)
1AP50 ACTOS DIOSeS bodiine 56
(d)
HAPSO Acoss Dscasets leadine 32h
101
No
Novccatitt TCR-0m..es
TCP
10
10
10"
WevETATber 125mm)
Figure/ 11. Radially Averaged Power Spectral Density (RAPSD) analysis across datasets for lead times of 3h (a), 6h (b), 9h (c), and 12h (d). The plots compare the power spectral density of predicted rainfall using different models wavenumber region, higher power spectral density represents that the displayed data belongs to large-scale weather systems, such as fronts and tropical eyclones. The power spectral density of TCP-Diffusion in the low wavenumher region is closer to the ground truth rainfall (MSWEP), indicating that our method achieves better capture of rainfall characteristics at the TC scale. Note the logarithmic vertical axis.
range of wavenumber. In the low
Ground Tuth
TCR-Diffusion
Previous 46 hours Previous 4 hours
Previous FRours
hhuur
12 hours
Present
Precia
Precio tetion Cmm/3s))
Figure 12. The prediction results of TCP-DDiffusiie and FuXi.
D.6. Comparison with Large Weather Model
We also compare our model with a ttateoof-theaut large weather model FuXi(Chen et al., 2023). We obtain the results (6- 12h) of FuXi and TCP-Diffusion of 349 samples of the year 2020. Due to differences in the comparison samples as well as the predicted lead times, the TCP-Diffusion data presented in this table vary slightly from those in Table I of the main text. As shown in Table 6 and Figure 12, we observe that FuXi performs poorly and tends to significantly overestimate rainfall intensity. We suspect is because FuXi is designed for global variable prediction and thus lacks the ability to capture localized rainfall details associated with tropical cyclones. This highlights the importance of designing models that are specifically centered on tropical cyclone. Such targeted modeling enables a more accurate and localized understanding of rainfall associated with typhoons, which is critical for disaster prevention and early warning.
Model Name
ETS-6
ETS-24
ETS-60 1
TP MAA
FuXi TCP-Diffusion
0.02770
0.03113
0
5.10396
0.39493
0.10348
0.00489
0.46302
Table 6. The performance of TCP-Diffusion and FuXi on TC precipitation prediction. The forecast diagnostics are the same as in table 1.
18

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A Multi-modal Diffusion Model for Global Tropical Cyclone Precipitation Forecasting
Stages
ETS-6
ETS-24 t
ETS-60 1
TP MAME
Formation
0.34965
0,07112
0.00077
0.41756
Others
0.45679
0.16220
0.00745
0,42621
Dissipation
0.28706
0.04400
0.00110
0.38850
All
0.43788
0. 0.14703
0.00644
0.42344
Table performance TCP-Diffussion on formation, dissipation, and other phases. The forecast diagnostics are same as table 1.
Intensity
ETS-66 t
ETS-244
ETS-60
MAM
Tropical Storm
0.33051
0.06312
0.00086
0.40756
Severe Tropical Storm
0.39824
0.09811
0.00286
0.40902
Typhoon
0.43464
0.12800
0.00695
0.42457
Strong Typhoon
0.49420
0.20603
0.01046
0.46508
Super Typhoon
0.52014
0.23882
0.01120
0.42191
All
0.43788
0.14703
0.00644
0.42344
Table 8. The performance of TCC--Diffusion on different cyclone intensities. The forecast diagnostics are the same as in table 1.
D.7. Performance of TCP-Diffusion on Different TC Lifecycle-phases
From the results shown in Table 7, we observe that the model performs relatively worse in terms of ETS during the Formation and Dissipation phases, Interestingly, the metric is better in these phases compared to others. This may be attributed to the unstable and irregular rainfall cloud structures during the formation and dissipation stages, which make spatial pattern prediction more difficult. However, rainfall intensity tends to fluctuate less drastically in these stages compared to the active and more intense phases of the TC lifecycle, where extreme values dominate and may introduce higher prediction error. These findings offer useful insights for future work, such as phase-aware modeling or adaptive loss functions.
D.8. Performance of TCP-Diffusion on Different TC Intensities
From the results shown Table 8, we observe that the ETS scores consistently improve with increasing cyclone intensity. In contrast, the metric tends degrade intensity increases. This pattern is consistent with our earlier observations in the lifecycle-phart phasee analysis 7. A likely explanation is that lower-intensity cyclones (e.g., Tropical Storm and Severe Tropical Storm) tend to exhibit unstable and irregular cloud structures, making spatial rainfall prediction more difficult. However, their overall rainfall intensity is more stable, which may lead to fewer false alarms. On the other hand, higher-intensity cyclones (e.g., Strong Typhoon and Super Typhoon) are structurally more organized, resulting in more predictable rainfall spatial patterns. Yet, the rainfall intensity becomes more variable and extreme, which increases the difficulty accurate intensity estimation and may negatively affect the metric. These results reinforce the need for adaptive modeling approaches that account for both cyclone intensity and lifecycle phase, which plan explore in future work.
D.9. The Visualizations Predictions from an NWP Method and TCP-Diffusion
We have shown the comparison of skill scores of ECMWF-IFS and TCP-Diffusion. Here, we also visualize the results from ECMWF-IFS and TCP-Diffusion. As shown in Figure 13, the forecasting results of our method also contain many details. Sample and Sample 2 are different, but their trends of rainfall intensity changes are also similar.
19

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A Multi-modal Diffusion Model for Global Tropical Cyclone Precipitation Forecasting
Previous- 6 hours Previous 99 hours
Preveuu hours
hours
12 hours
Precipitation (mm/3h)
Figure The prediction results NWP (ECMWF-IFS and ERA5-IFS) and TCP-Diffusion on TC Olivia Eastern Pacific at 03/09/2018 12:00. The first two columns are the past 4 timesteps of rainfall data input TCP-Diffusion The third column is the target observed future TC rainfall. The right columns are the predictions from ERA5-IFS, ECMWF-IFS and CCP-Diffussio (TCP-Diff' and TCP-Diff #2) respectively.
20


Reviews:
[{"review_id": "CU8304F0Dj", "reviewer": "Reviewer_NZjq", "summary": "The article proposes a multimodal diffusion model that integrates data on rainfall, environment, tropical cyclone attributes, and meteorological predictions to generate precipitation due to tropical cyclones globally. Its results outperform other deep learning methods and numerical weather prediction (NWP) models. Among its contributions, the algorithm can predict precipitation globally, demonstrates that forecasting temporal changes in precipitation is more effective, and integrates multidimensional meteorological information.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for recognizing our work and for your valuable comments and stylistic recommendations. These suggestions will help us further improve the quality of this manuscript. We will incorporate the corresponding revisions in the camera-ready version. Below are our responses to the issues you raised.\n\n**Q1:Would it be possible to provide access to at least a subset of the dataset or a simplified version of the model during the review process?**\n\nA1:We have created an anonymous GitHub repository (https://anonymous.4open.science/r/TCP-Diffusion-ICML-review/README.md) that includes the testing code and a subset of the test data for our method. \n\n**Q2:Have the authors considered benchmarking their model against probabilistic forecasting techniques, especially in terms of uncertainty quantification?**\n\nA2:We have compared our method with PreDiff, which is also a probabilistic forecasting approach. While we have not explicitly benchmarked uncertainty quantification metrics against PreDiff at this stage, we have evaluated the stability of our predictions. As shown in Table 5, the standard deviation of our method's results is notably small, indicating that our model performs consistently across the dataset.\n\n**Q3:How adaptable is TCP-Diffusion to future improvements in NWP methodologies? Would retraining be necessary with every update to the NWP model, or can the framework accommodate updated inputs dynamically?**\n\nA3:Currently, our model does not dynamically adapt to different NWP methodologies. This is primarily because different NWP models may produce outputs with varying resolutions, spatial-temporal scales, and embedded physical assumptions. Existing offline deep learning frameworks, including ours, typically require consistent input characteristics and cannot yet generalize across heterogeneous NWP outputs without retraining. We greatly appreciate this insightful suggestion—it highlights a direction for making our work more practically applicable. In future research, we plan to incorporate adaptability to diverse NWP models into our framework design.\n\n**Q4:Could the authors clarify whether the model also improves fine-scale precipitation patterns, or does it tend to smooth out small-scale variability?**\n\nA4:Compared to deterministic forecasting methods, our model provides richer details in the prediction of fine-scale precipitation patterns. As illustrated in Figures 3 and 9, especially around the TC center, our method is capable of capturing the shape and structure of heavy rainfall regions. In contrast, deterministic baselines such as U-Net tend to smooth out these localized high-intensity features. This demonstrates the advantage of our probabilistic diffusion-based approach in preserving small-scale variability.\n\n**Q5:Could the authors provide insights into whether there is a feasible way to optimize the model's computational efficiency while maintaining its accuracy?**\n\nA5:As shown in Table 4, our method requires longer training time compared to some traditional deep learning models, and the inference time is also slightly higher than that of non-diffusion approaches. However, given the complexity of the TC precipitation forecasting task, we believe the computational cost of our model remains reasonable. Furthermore, our method is significantly more computationally efficient than NWP systems.\n\nIn terms of model design, we adopt a hybrid architecture combining CNNs and Transformers. For high-dimensional data, we utilize CNNs, which are computationally efficient and lightweight. For lower-dimensional inputs, we use Transformers, which, though more computationally intensive, offer stronger feature extraction capabilities—allowing for a more fine-grained understanding.\n\nAdditionally, we are exploring model transfer strategies, where a pre-trained large model is adapted to downstream tasks like TC precipitation forecasting. This would allow us to fine-tune only a small portion of the parameters while leveraging the representational power of the large model. This direction represents a promising way to further enhance computational efficiency and is a focus of our future research.\n\n**Q6: Does the model show any systematic underprediction or overprediction of extreme precipitation events?**\n\nA6: We conducted a focused evaluation on extreme precipitation events, which account for approximately 6.73% of the total test samples. The results show that our model tends to slightly overpredict these events, with an average overestimation of about 0.206 mm per 3 hours.\n\nThese findings provide valuable insights for future improvements. In particular, we plan to explore techniques such as weighted loss functions or targeted fine-tuning to better handle rare but high-impact precipitation extremes. Addressing this challenge is critical for enhancing the model’s reliability under severe weather conditions.\n\n***If you have more questions, We'd like to discuss them with you during the author-reviewer discussion period.***", "claims_and_evidence": "The authors provide a detailed, clear, and extensive description of the prediction of precipitation changes, the diffusion model, and its solution architecture. The description of their claims is convincing. However, the submission did not include code or data. Having access to them could increase confidence in their results. The authors suggest that the code and data will be available once the article is accepted.", "methods_and_evaluation_criteria": "The total precipitation mean absolute error, the radially averaged power spectral density, quantifying the precipitation's accuracy, spatial structure, and realism. The paper's metrics make sense in the context of the problem.", "theoretical_claims": "I reviewed the concept of ARP, which is straightforward. The diffusion model is standard and generally accepted. The algorithms on which I am providing comments.", "experimental_designs_or_analyses": "I verified the results and the quantitative and qualitative analysis, the precipitation frequency distribution, and the power spectral density. I did not find any issues with them.", "relation_to_broader_scientific_literature": "The article reviews the related literature, including current approaches based on numerical methods and Deep Learning. I find the review to be comprehensive.", "essential_references_not_discussed": "Recently, on December 4, 2024, the article \"Probabilistic Weather Forecasting with Machine Learning\" was published. I believe the results presented in that article would complement some of the elements described in this article.", "other_strengths_and_weaknesses": "Overall, I observe a well-formulated article with a strong experimental foundation. Elements such as ARP have been successfully leveraged. The diffusion model for precipitation prediction follows the trend of utilizing them to determine meteorological variables.\nI would have liked to review the code and associated data. While the results appear promising, having access to them would have strengthened my confidence in the approach. Additionally, I include some stylistic recommendations later in my review.", "other_comments_or_suggestions": "*** I recommend using elements such as \\text{Rainfall}_{\\text{Current}} when writing text within math environments in LaTeX.\n\n*** ablation for \\Delta Rainfall as oppose to total rainfall\n*** ablation to computing rainfall everywhere need as opposed to the TC moving center\n\n*** X_t^h is called input data in line 138 (first column). I believe you want to call it historical\n** embedding in Figure 2.\n\n*** check equation in line 203, left column\n\n*** use same fonts to name in the text (line 206, first column) and equation (5). Now that you are correcting that, add ',' or '.' at the end of the equations, as needed.\n\n*** change \"the following pseudocode\" to \"the pseudocode in Algorithm 1 (or 2, as needed)\"?\n\n*** include input/outputs and variable description in the algorithms\n\n*** pathes, line 259 right column\n\n*** Predif, line 312 right column", "questions_for_authors": "1. Would it be possible to provide access to at least a subset of the dataset or a\n simplified version of the model during the review process?\n\n\n2.  Have the authors considered benchmarking their model against probabilistic forecasting\n techniques, especially in terms of uncertainty quantification?\n\n\n\n\n3. How adaptable is TCP-Diffusion to future \nimprovements in NWP methodologies? Would retraining be necessary with every update to the NWP model,\n or can the framework accommodate updated inputs dynamically?\n\n\n4. Could the authors clarify whether the model also improves fine-scale precipitation patterns,\n or does it tend to smooth out small-scale variability?\n\n5. Could the authors provide insights into whether there is a feasible way to optimize the\n model's computational efficiency while maintaining its accuracy?\n\n6. Does the model show any systematic underprediction or overprediction of \nextreme precipitation events?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "2QgYg7bFxM", "reviewer": "Reviewer_caD7", "summary": "This paper proposes a diffusion model to do precipitation nowcasting relative to a predefined tropical cyclone. The idea is to track the location of a tropical cyclone and to do nowcasting relative to the tracked location. The proposed model also incorporates additional information for the forecasting including IFS, tropical cyclone information, and historical reanalysis. The model acheives a state-of-the-art result compared to other baselines on the newly task.\n\n## Update after rebuttal\nI appreciate the efforts of the authors to clarify and address my concerns. Unfortunately, I would not recommend to accept the manuscript in its current version. The manuscript lacks an appropriate comparison to standard baselines for global tropical cyclone precipitation forecasting i.e., using global/regional weather forecast. This comparison should have been made before the main submission and the rebuttal period. The results from the FuXi model are irrelevant since the model was trained on different target.\nMoreover, as mentioned in the rebuttal, I would not consider ARP as a novel contribution since many works in weather forecast proposed this technique before. Finally, the  persistence baseline still achieves a similar skill to the proposed model.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for recognizing our work, including the novelty of the task itself, the comprehensiveness of our experiments, and the clarity of the manuscript. We also understand the reviewer’s concerns regarding our use of IFS data. Below are our responses to some of the issues raised, and we hope they can help alleviate some of your concerns.\n\n**Q1: The model relies a lot on the IFS forecast from ECMWF.**\n\n1. Comparing the first row in Table 1 with the third row in Table 3 (the model version without IFS), we can observe that our method still slightly outperforms the persistence baseline overall. Furthermore, even without IFS inputs, our model achieves better performance than other deep learning-based baselines, as also mentioned in Lines 413-418 (right column) of the manuscript.\n\n2. Our work is, to our knowledge, the first to integrate deep learning methods with NWP (specifically IFS data) for TC precipitation forecasting. As one of the contributions of this work, integrating with NWP can improve the performance of our model, which supports the effectiveness of this contribution and offers useful insights for broader weather forecasting tasks.\n\n3. The acquisition and usage of IFS data will be further simplified. Please refer to the details in the response to the Q1 of Reviewer Ndz5, point 2.\n\n**Q2: The ablation study of ARP is currently missing.**\n\nIt is possible that our explanation of Table 3 was not sufficiently clear. In fact, the ablation study of the ARP mechanism is already presented in the first and second rows of Table 3. The first row corresponds to the original baseline of our method without ARP, while the second row shows the results after incorporating the ARP mechanism. The performance improvement demonstrates the effectiveness of ARP.\n\n**Q3: Using ARP is a well-known technique for weather forecast see i.e., GenCast**\n\nWe appreciate the reviewer for bringing GenCast (published in December 2024) to our attention. We have carefully studied the paper and will cite and briefly discuss it in our camera-ready version. Notably, we found that the Residual Prediction in GenCast shares conceptual similarities with our ARP module, which further supports the value of residual modeling in weather-related prediction tasks.\n\nOur ARP design was inspired by the denoising process in diffusion models. Just as diffusion models iteratively refine predictions by removing noise, we view precipitation forecasting as a residual step-by-step accumulation process, as discussed in Lines 102-108 (left column) of our paper. We later found theoretical support for this idea in Chapter 6 of Atmospheric Modeling, Data Assimilation and Predictability, which further reinforced the motivation for adopting ARP in our framework. To the best of our knowledge, this is the first work to apply the ARP mechanism to the task of TC precipitation forecasting. We believe our work can provide inspiration for future research on specialized weather forecasting tasks. \n\n**Q4: Compare with global forecast model FuXi.(For the 2nd point of Methods And Evaluation Criteria)**\n\nWe appreciate the reviewer’s suggestion and have supplemented additional experiments to address this point. Among existing large global forecasting models, FuXi (FuXi: a cascade machine learning forecasting system for 15-day global weather forecast) is currently the only one capable of providing global-scale precipitation predictions. However, FuXi does not publicly release official predictions for the total precipitation (TP) variable. So, we reproduced the FuXi model using the official codebase and evaluated its performance on TC precipitation. From the results, we observe that FuXi performs poorly and tends to significantly overestimate rainfall intensity. More details are shown at the link:https://limewire.com/d/HHv6Z#HXP582VLSv\n\n\n**Q5: Concern about the practicality of the approach for real-world scenario. (For the 1st point of Methods And Evaluation Criteria)**\n\nRegarding ERA5, although it is a reanalysis product, near real-time access is possible through collaboration with ECMWF. For instance, Pangu-Weather also utilizes ERA5 reanalysis data and has already been adopted within ECMWF's operational forecasting system for real-time prediction. Therefore, we believe the use of ERA5 in research and applied forecasting scenarios is reasonable and increasingly practical. \n\nFor IFS data, the generation time is shorter than that of ERA5 data. Moreover, since we use low-resolution IFS data, the required time is further reduced. This has been mentioned in Lines 427-428 (left column). \n\n**Q6: How ARP is going to reduce accumulative errors?**\n\nA similar concern was raised by Reviewer Ndz5, and we have addressed it in our response to their Q3. Please refer to that response for detailed clarification.\n\n***Owing to space constraints, we would be glad to elaborate further on Experimental Designs Or Analyses (Point 2) or other questions during the author-reviewer discussion period.***", "claims_and_evidence": "- L58-60: Using $\\Delta^{t}_{x}$ is a well-known technique for weather forecast see i.e., GenCast (https://doi.org/10.1038/s41586-024-08252-9). However, how Adjacent Residual Prediction (ARP) is going to reduce accumulative errors? $\\Delta$ is actually accumulate errors with rollout. That is why some works use continuous or direct forecast i.e., https://arxiv.org/pdf/2312.03876. There is also no ablation study on this claim.\n\n- Without IFS, the prediction is not better than persistence baseline. Compare the first row in Table 1 with the third row in Table 3. I think the improvement comes from the IFS forecast itself since this forecast includes precipitation and correlated variables as well.", "methods_and_evaluation_criteria": "- Concern about the practicality of the approach for real-world scenario:\nAs far as I know ERA5 can't be obtained in real-time. IFS forecasts also need time to be generated. I thin the experimental setting is not realistic.\n\n- I think a better evaluation would be to compare to precipitation nowcasting centering around the center of the TC for the proposed model with other baselines that do forecasting but without centering on TC (i.e., this can be done using global forecast).\n\n- Table-2 ECMWF-Ifs: I think the reason why the proposed model is better than IFS is because IFS forecasts the precipitation similar to ERA5. While the proposed model was trained and evaluated against different rainfall Data (MSWEP). It is also not clear if the evaluation was done using total precipitation or just rain.", "theoretical_claims": "The paper doesn't include proofs.", "experimental_designs_or_analyses": "- I think an ablation about Adjacent Residual Prediction (ARP) or  $\\Delta^{t}_{x}$ is currently missing in the paper.\n \n- PreDiff performs worse than a persistence baseline while in the original paper it achieves much higher performance than a persistence baseline (see Table 1 https://arxiv.org/pdf/2307.10422). I think the baselines should be evaluated with out centering or at least they should have a positional encoding to adapt for the task.", "relation_to_broader_scientific_literature": "Precipitation nowcasting is performed in an absolute sense i.e., over a specific domain or on a global grid. The main contribution of this paper is to do nowcasting of precipitation in relation to a tropical cyclone movement. The novelty is to track the location of the tropical cyclone and then to do prediction relative to the tracked location.", "essential_references_not_discussed": "The paper cited main references reasonably.", "other_strengths_and_weaknesses": "Strength:\n- It is novel to perform precipitation nowcasting relative to tracked trobicla cyclone.\n- The paper includes many experiments and ablation studies which make understanding the method clearer.\n- The concept of the proposed method is well explained, and the paper is written concisely.\n\nWeakness:\n- The model relies a lot on the IFS forecast from ECMWF.\n- The paper argues that predicting relative change in precipitation is better than predicting precipitation nowcasting on a global or regional scales. However, there is no experiment to support this argument.", "other_comments_or_suggestions": "Please check equation 6. What type of loss function was used? Do you mean MSE?", "questions_for_authors": "1- Why CNN3d was chosen to handle 2D data and a transformer to handle 1D data? And why Resnet? It is not clear from the text i.e., one can use transformer also for 2D data.\n\n2- Do other baselines use the same input information as the proposed model? And what about the IFS forecast, do other baselines use this information?\n\n3- Did you report the baseline scores for the eight test sets similar to the proposed model? see Table 5.\n\n4- Why U-Net is better for ETS-6? Is there any explanation?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Ia2SkvwReE", "reviewer": "Reviewer_Ndz5", "summary": "This paper addresses two key challenges in medium-range tropical cyclone forecasting: current methods suffer from cumulative errors and the lack of physical consistency. A multi-modal model is proposed, equipped with ARP mechanism to focus on rainfall change to reduce cumulative errors. The integration of NWP system helps to enhance physical consistency.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for recognizing the value of integrating our method with NWP. We also understand your concerns regarding the potential impact of using NWP data on the flexibility of our approach. These insights will serve as valuable guidance for our future research. Below, we provide responses to your questions, and we hope they will help address some of your concerns about our method.\n\n**Q1: The flexibility of the method is limited to some extent due to the use of NWP data.**\n\nWe appreciate the reviewer’s concern regarding the flexibility and real-world applicability of our method.\n1. Please note that our model also provides a version that does not rely on IFS forecasts. As shown in Table 3 (Row 3), our model without IFS still outperforms other deep learning baselines listed in Table 1. This is also discussed in Lines 413-418 (right column) of the manuscript. Therefore, our approach remains functional and competitive even in the absence of IFS inputs.\n2. ECMWF has announced that it will make its forecast data fully open starting in October 2025 (https://www.ecmwf.int/en/about/media-centre/news/2025/ecmwf-achieve-fully-open-data-status-2025). This will significantly reduce the difficulty of accessing IFS forecasts, making it increasingly feasible to incorporate them in practice. We believe our work offers a timely exploration of how to leverage such forecasts effectively in deep learning frameworks.\n3. we emphasize that IFS and deep learning are not mutually exclusive; rather, their integration can lead to more accurate and efficient forecasts. To our knowledge, this work is the first to integrate NWP forecasts with deep learning for TC precipitation prediction. While IFS captures physical laws through numerical simulation, deep learning excels at learning hidden patterns from data. Our design—which directly feeds IFS outputs into a dedicated encoder for representation learning—offers a simple yet effective fusion strategy. This approach may serve as a useful reference for future efforts in combining NWP with data-driven models across various forecasting tasks.\n\n**Q2: The difference with DiffCast, Pangu and Fengwu.**\n\nWe would like to clarify the unique contributions of our model and how they differ from prior works:\n1. **Difference from DiffCast**: While both our approach and DiffCast involve residual prediction, the underlying concepts are fundamentally different. In our model, we view precipitation forecasting as an accumulative process of rainfall changes over time, where the model directly learns to generate the adjacent residual (future rainfall change) rather than the absolute future value. This is reflected in lines 102-108 (left column).\n\n    In contrast, DiffCast models the residual between a deterministic forecast and the ground truth, as shown in Section 4.2 of their paper. Their diffusion module acts more as a correction mechanism to add details to the output of a deterministic backbone, rather than directly modeling rainfall evolution through temporal differences. Although DiffCast is an inspiring work, our method tackles a different formulation and learning objective. We will discuss this paper in the camera-ready version.\n2. **Difference from Pangu and Fengwu**: The motivation for using multimodal meteorological inputs in our work is distinct. The prediction targets of Pangu and Fengwu are the future states of multiple variables themselves, hence multimodal inputs are a natural part of the task.\n\n    In contrast, we focus solely on predicting TC rainfall, and we incorporate multimodal inputs to compensate for the limitations of using rainfall data alone, especially in capturing TC rainfall dynamics. Our design emphasizes the integration of environmental and physical information to enhance prediction quality, addressing a gap in existing regular precipitation forecasting models.\n\n3. **Empirical Validation**:\n    As shown in our ablation results (Table 3), both the proposed ARP and the multimodal input design (M) contribute significantly to model performance. This supports the value of our innovations, particularly in the context of TC precipitation forecasting.\n\n**Q3: It is necessary to visualize the residual prediction and show the contribution of how it can reduce cumulative errors.**\n\nThe residual prediction visualizations are shown at this link: https://limewire.com/d/HHv6Z#HXP582VLSv. Please refer to this link for detailed results.\n\nRegarding its role in reducing cumulative errors, predicting residuals rather than absolute rainfall values allows the model to estimate smaller relative shifts at each time step. As a result, even if there are minor prediction errors at individual steps, their cumulative impact is less severe. This approach helps mitigate long-term drift and leads to more stable multi-step forecasts.\n\n***Owing to space constraints, we would be glad to elaborate further on Methods and Evaluation Criteria (Point 2) or other questions during the author-reviewer discussion period.***", "claims_and_evidence": "The flexibility of the method is limited to some extent. Since the future data from an NWP system is necessary, when such data is not accessible, the system seems to stop working. Also NWP system generally requires large-scale computations. If this is the case, it significantly increase the latency for the predictions.", "methods_and_evaluation_criteria": "- The overall contribution could be limited. The idea of the adjacent residual prediction is very similar to DiffCast (CVPR2024). What’s your unique model design contributing to TC prediction compared to this method? The idea of using multmodal meteorological factors has been explored in other works such as Pangu and Fengwu.\n- Line 258-260, the encoding mechanism is a combination of concatenation and convolution operations. What’s the phylosophy for such computations? Will transformers/attention mechanisms be better? There are many multimodal features fusion methods are available, justifications for the design are expected to be clearly outlined.\n\nYu, Demin, et al. \"Diffcast: A unified framework via residual diffusion for precipitation nowcasting.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.", "theoretical_claims": "There is no theoretical proofs relevant to this study.", "experimental_designs_or_analyses": "- More experiments can be conducted on diverse datasets or similar extreme weather prediction such as lightning.\n- It is necessary to visualize the residual prediction and show the contribution of how it can reduce cumulative errors.", "relation_to_broader_scientific_literature": "This work proposes an idea of using residual information to better capture the spatial and temporal information to medium-range TC precipitation forecasting.", "essential_references_not_discussed": "The references is good to the reviewer.", "other_strengths_and_weaknesses": "Strengths\n- It considers the influence of TC-related meteorological factors and the useful information from NWP model forecasts. Even though DL methods outperform traditional NWP, the results of NWP can still be useful.\n\nWeaknesses\n- The significance of the task and input selection is not clear to me, as mentioned in previous review questions. Since the future data from an NWP system is required, when the future data is not accessible, the system may fail to work.", "other_comments_or_suggestions": "N/A", "questions_for_authors": "Please see my comments in other sections.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "9HwSlOzSkT", "reviewer": "Reviewer_5hd2", "summary": "This paper introduces TCP-Diffusion, a multi-modal diffusion model for tropical cyclone precipitation forecasting. It leverages an Adjacent Residual Prediction (ARP) mechanism to predict rainfall changes, integrates numerical weather prediction data, and employs an Environmentally-Aware 3D U-Net within a diffusion framework. The study evaluates the model against deep learning and numerical baselines, reporting improvements in predicting medium and heavy rainfall.\n\n## update after rebuttal\nThank you for the author's response. However,  from my perspective, the quality of this paper still needs to be improved to meet ICML's standards. Therefore, I will maintain my score.", "questions": "", "limitations": "", "rating": 2, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for acknowledging the contributions of our ARP mechanism. We also understand your concerns regarding the motivation behind using both NWP data and the diffusion model. Below, we provide detailed responses to these questions, and we hope they will help alleviate some of your concerns about our method.\n\n**Q1: A strong motivation for using a diffusion model over other deep learning approaches (e.g., VAEs, Transformers) for precipitation forecasting is not clearly provided.**\n\nWe would like to clarify the motivation for choosing diffusion models over other representation learning-based approaches.\n1. TC precipitation exhibits chaotic behavior and inherent uncertainty, which makes probabilistic forecasting more suitable than deterministic approaches. This is supported by the theoretical discussion in Atmospheric Modeling, Data Assimilation and Predictability, particularly Section 6.5, which states:\"*The chaotic behavior of the atmosphere requires the replacement of single ‘deterministic’ forecasts by ‘ensembles’ of forecasts.*\" Deterministic models like VAEs can be seen as single forecasts, whereas diffusion models naturally resemble ensemble forecasting by sampling multiple possible futures. This makes them well-aligned with the demands of real-world atmospheric prediction, especially under extreme conditions such as TCs.\n\n2. Previous methods—including deterministic models like U-Net, VAEs, and Transformer-based architectures—often produce over-smoothed forecasts with limited fine-grained spatial details. We briefly discuss these issues in Lines 69–86 (left column) of the paper. In contrast, diffusion models naturally incorporate noise and denoising processes, allowing them to generate more detailed and realistic outputs.\n\n**Q2: The paper describes the use of physical processes only from the results of NWP, but incorporating more TC-related information as model input is an intuitive approach rather than one inspired by physical principles. (For Weaknesses 1 and 4)**\n\nIt is true that our approach adopts a relatively simple yet effective strategy to integrate deep learning with NWP forecasts. However, to the best of our knowledge, this is the first work that combines deep learning with NWP data specifically for TC precipitation forecasting. While the idea may appear intuitive in hindsight, however, the novelty must be evaluated before the idea existed. The inventive novelty was to have the idea in the first place. If it is easy to explain and obvious in hindsight, this in no way diminishes the creativity (and novelty) of the idea.\n\nIn our approach, we do not directly embed physical equations into the model (such as PINNs), but instead let the model learn the embedded physical knowledge present in the IFS forecast. This is a simple yet practical alternative to explicitly encoding physical constraints, especially considering the complexity of modeling TC precipitation—a highly nonlinear and chaotic process.\n\nThat said, we fully agree that incorporating meteorological physics in a more explicit way (e.g., through constraint-aware loss functions or hybrid physics-ML models) is a promising direction. Bridging the gap between data-driven modeling and physical interpretability is part of our long-term research vision.\n\n**Q3: Is incorporating NWP outputs in the model truly reasonable?**\n\nReviewer Ndz5 raised a similar concern, which we responded to in Q1. For a more detailed explanation, please refer to that response.\n\n\n**Q4: The ablation study of individual encoders (historical vs. future data) is missing. Additionally, while different lead times are tested, a deeper analysis of how performance degrades over time is missing.** \n\nWe would like to clarify that ablation experiments on the historical and future data encoders were indeed included in Table 3. Specifically, the third row in Table 3 represents our model with the ARP and multimodal encoder (M), but without the historical encoders and future data encoders. The fourth row shows the full version of our model, which includes both historical and future encoders. The performance improvement between these two rows demonstrates the effectiveness of integrating NWP forecasts and our encoder designs.\n\nRegarding performance degradation over time, it is a well-known challenge in sequential forecasting tasks. In our setting, this issue is particularly pronounced due to the chaotic nature of atmospheric systems, where small disturbances can amplify over time and lead to substantial divergence in predictions (as described by the butterfly effect). We will provide a more comprehensive analysis in Section D.1 (Line 755) of the camera-ready version.\n\n**Q5: The performances of our method on different TC lifecycle stages and intensities.**\n\nThe results are shown at https://limewire.com/d/HHv6Z#HXP582VLSv. Please refer to this link for detailed results.\n\n***If you have more questions, We'd like to discuss them with you during the author-reviewer discussion period.***", "claims_and_evidence": "The paper’s claims are generally supported by experimental results. However, the motivation for using a diffusion model instead of other representation learning-based methods for the prediction task is not clearly justified.", "methods_and_evaluation_criteria": "The paper’s methodological approach is generally well-structured. However, the study presents various comparative experiments, but it does not explicitly assess how well the model adapts to different TC lifecycle stages (e.g., formation, intensification, dissipation).", "theoretical_claims": "No Theorems are presented in this paper.", "experimental_designs_or_analyses": "The experimental setup follows standard practices, utilizing benchmark meteorological datasets (ERA5, ECMWF-IFS, MSWEP) and established evaluation metrics (ETS, TP-MAE). However, while ARP’s contribution is evaluated, the paper does not analyze how individual encoders (historical vs. future data) affect performance separately. Additionally, while different lead times are tested, a deeper analysis of how performance degrades over time is missing.", "relation_to_broader_scientific_literature": "The paper builds upon existing work by referencing deep learning (DL) applications in meteorology, numerical weather prediction (NWP), and generative models. It builds upon prior work in precipitation forecasting, particularly U-Net-based methods and generative adversarial networks (GANs), and extends recent applications of diffusion models in atmospheric prediction.", "essential_references_not_discussed": "The paper appears to have included most of the essential references needed to understand its contributions.", "other_strengths_and_weaknesses": "**Other Strengths:**\n\n1.\tThe paper applying diffusion models to tropical cyclone precipitation forecasting is an interesting attempt.\n2.\tThe ARP mechanism helps mitigate cumulative errors and ensures temporal consistency in forecasts.\n3.\tThe topic of applying AI tools for climate research is a hot topic.\n\n**Other Weaknesses:**\n\n1.\tThe paper describes the use of physical processes only from the results of numerical weather prediction (NWP), but incorporating more TC-related information as model input is an intuitive approach rather than one inspired by physical principles. Instead of seeing a combination of existing deep learning modules for precipitation forecasting, I would prefer to see a novel deep learning design explicitly guided by meteorological physics.\n2.\tSensitivity to different cyclone intensities or unseen meteorological conditions is not analyzed, which could impact generalization.\n3.\tA strong motivation for using a diffusion model over other deep learning approaches (e.g., VAEs, Transformers) for precipitation forecasting is not clearly provided.\n4.\tI appreciate the authors' effort, but the work lacks sufficient appeal from a machine learning contribution perspective (e.g., introducing new meteorological or physics-informed machine learning approaches). As a result, it may be more suitable for a good meteorology-focused journal.", "other_comments_or_suggestions": "N/A", "questions_for_authors": "1.\tIs incorporating NWP outputs in the model truly reasonable? Traditional numerical weather prediction (NWP) methods involve significant computational costs. If a new deep learning-based approach still depends on NWP results, it does not improve forecasting speed, making it difficult to apply in rapidly changing precipitation prediction scenarios. Could you clarify how this approach balances efficiency and accuracy?\n2.\tThe motivation for choosing a diffusion model over alternatives like VAEs, normalizing flows, or Transformers is not clearly explained. What specific properties of diffusion models make them particularly suited for TC precipitation forecasting?\n3.\tHave ablation studies been conducted to evaluate the individual contributions of different encoders (historical vs. future data)? How does model performance change when certain encoders are removed or altered?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper proposes a method to predict tropical cyclone precipitation with a diffusion model. There is substantial disagreement between the reviewers. Reviewer NZjq argues that the paper offers a meaningul contribution and that the paper has sufficient quality. The reviewer engaged in a discussion with the authors, which appears to have clarified the main questions. The other reviewers recommend Weak reject. Reviewer caD7 argues that the comparison with baselines is not strong because the baseline should have been trained on the same data. The other main concern by this reviewer is that Adjacent Residual Prediction (ARP) is not a novel contribution. Reviewer 5hd2 argues that the contribution is limited and that the motivation to use a diffusion model instead of other models is not strong enough. In light of the good results and the fact that the problem tackled has been understudied, I am not too concern about the novelty issues. Even if the methodological novelty is limited, which I will not discuss, that would not justify the rejection of a well-written paper that offers a method with good results on an important application. What is important is that the authors adjust their claims of novelty to reflect the actual literature, as suggested by the reviewers. I would make a similar point about the baselines. The main contribution of the paper, in my view, is to apply machine learning on a important though understudied problem and obtain good results that have not been shown before. Whether similar results could be obtained with other methods is an interesting question but to me not a strong reason for rejection. Regarding the comments about the quality of the paper, my impression is that the paper is well written and other reviewers have not raised this point.

For these reasons, I lean towards recommending accepting the paper despite the average score under the threshold.
Decision: Accept (poster)