Precipitation Estimation Based on Infrared Data with a Spherical Convolutional Neural Network

Lu Yi aKey Laboratory of Coastal Environment and Resources Research of Zhejiang Province, School of Engineering, Westlake University, Hangzhou, Zhejiang, China

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Zhangyang Gao bAI Research and Innovation Lab, School of Engineering, Westlake University, Hangzhou, Zhejiang, China

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Zhehui Shen cSchool of Earth Sciences and Engineering, Hohai University, Nanjing, Jiangsu, China

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Haitao Lin bAI Research and Innovation Lab, School of Engineering, Westlake University, Hangzhou, Zhejiang, China

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Zicheng Liu bAI Research and Innovation Lab, School of Engineering, Westlake University, Hangzhou, Zhejiang, China

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Siqi Ma bAI Research and Innovation Lab, School of Engineering, Westlake University, Hangzhou, Zhejiang, China

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Cunguang Wang dState Key Laboratory of Hydroscience and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing, China

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Stan Z. Li bAI Research and Innovation Lab, School of Engineering, Westlake University, Hangzhou, Zhejiang, China

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Ling Li aKey Laboratory of Coastal Environment and Resources Research of Zhejiang Province, School of Engineering, Westlake University, Hangzhou, Zhejiang, China

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Abstract

Precipitation is a vital process in the water cycle. Accurate estimation of the precipitation rate underpins the success of hydrological simulations, flood predictions, and water resource management. Satellite infrared (IR) data, with high temporal resolution and wide coverages, have been commonly used in precipitation inversion. However, existing IR-based precipitation retrieval algorithms suffer from various problems such as overestimation in dry regions, poor performance in extreme rainfall events, and reliance on an empirical cloud-top brightness–rain rate relationship. To resolve these problems, we construct a deep learning model using a spherical convolutional neural network to properly represent Earth’s spherical surface. With data input directly from IR bands 3, 4, and 6 of the operational Geostationary Operational Environmental Satellite (GOES), our new model of Precipitation Estimation based on IR data with Spherical Convolutional Neural Network (PEISCNN) was first trained and tested with a 3-month-long dataset, and then validated in a 2-yr period. Compared to the commonly used IR-based precipitation product PERSIANN-CCS (Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks–Cloud Classification System), PEISCNN showed significant improvement in the metrics of POD, CSI, RMSE, and CC, especially in the dry region and for extreme rainfall events. Decomposed with the four-component error decomposition (4CED) method, the overestimation of PEISCNN was averaged 47.66% lower than the CCS at the hourly scale. The PEISCNN model may provide a promising way to produce an improved IR-based precipitation product to benefit a wide range of hydrological applications.

Significance Statement

An IR-based precipitation algorithm is irreplaceable in satellite precipitation inversion, since an IR sensor can provide observations of high frequency, fine temporal resolution, and wide coverage. Considering the spherical nature of Earth’s surface which has been overlooked in previous IR-based precipitation retrieval algorithms, we proposed a new deep learning model PEISCNN, which can address the problems that exist in IR-based precipitation estimations such as overestimation in dry regions, deficiency in extreme rainfall events, and reliance on the empirical cloud-top brightness–rain rate relationship. PEISCNN provides a new insight to improve the accuracy of the satellite IR-based or multisensor-based precipitation estimation, and it has great potential to benefit a range of related hydrological research, applications in water resource management, and flood predictions.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Lu Yi and Zhangyang Gao are co-first authors.

Corresponding authors: Stan Z. Li, stan.zq.li@westlake.edu.cn; Ling Li, liling@wetlake.edu.cn

Abstract

Precipitation is a vital process in the water cycle. Accurate estimation of the precipitation rate underpins the success of hydrological simulations, flood predictions, and water resource management. Satellite infrared (IR) data, with high temporal resolution and wide coverages, have been commonly used in precipitation inversion. However, existing IR-based precipitation retrieval algorithms suffer from various problems such as overestimation in dry regions, poor performance in extreme rainfall events, and reliance on an empirical cloud-top brightness–rain rate relationship. To resolve these problems, we construct a deep learning model using a spherical convolutional neural network to properly represent Earth’s spherical surface. With data input directly from IR bands 3, 4, and 6 of the operational Geostationary Operational Environmental Satellite (GOES), our new model of Precipitation Estimation based on IR data with Spherical Convolutional Neural Network (PEISCNN) was first trained and tested with a 3-month-long dataset, and then validated in a 2-yr period. Compared to the commonly used IR-based precipitation product PERSIANN-CCS (Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks–Cloud Classification System), PEISCNN showed significant improvement in the metrics of POD, CSI, RMSE, and CC, especially in the dry region and for extreme rainfall events. Decomposed with the four-component error decomposition (4CED) method, the overestimation of PEISCNN was averaged 47.66% lower than the CCS at the hourly scale. The PEISCNN model may provide a promising way to produce an improved IR-based precipitation product to benefit a wide range of hydrological applications.

Significance Statement

An IR-based precipitation algorithm is irreplaceable in satellite precipitation inversion, since an IR sensor can provide observations of high frequency, fine temporal resolution, and wide coverage. Considering the spherical nature of Earth’s surface which has been overlooked in previous IR-based precipitation retrieval algorithms, we proposed a new deep learning model PEISCNN, which can address the problems that exist in IR-based precipitation estimations such as overestimation in dry regions, deficiency in extreme rainfall events, and reliance on the empirical cloud-top brightness–rain rate relationship. PEISCNN provides a new insight to improve the accuracy of the satellite IR-based or multisensor-based precipitation estimation, and it has great potential to benefit a range of related hydrological research, applications in water resource management, and flood predictions.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Lu Yi and Zhangyang Gao are co-first authors.

Corresponding authors: Stan Z. Li, stan.zq.li@westlake.edu.cn; Ling Li, liling@wetlake.edu.cn

1. Introduction

Precipitation is a dominant driving factor in the water cycle, dictating the variations of the subsequent hydrological variables and processes such as evapotranspiration, soil moisture, river discharge, and groundwater. The spatiotemporal distributions of these hydrological variables in turn cause different impacts on human societies in the aspects of agriculture, flood, water resource management, and ecological environment (Hossain et al. 2010; Kucera and Lapeta 2014; Rohatyn et al. 2018; Flossmann et al. 2019; Wang et al. 2019). Generally, precipitation can be measured by in situ gauge stations or ground-based weather radar in some developed regions. These measurements are usually considered as the ground truth, but they are severely limited by poor point-to-area representativeness, wind-induced deviation, sparse observation networks in the economically poor areas, and the observation limitations over oceans and remote locations (Steiner et al. 1999; Lorenz and Kunstmann 2012; Fortin et al. 2015). As the technique of remote sensing developed, global precipitation estimation has become a reality (Sorooshian et al. 2011). The satellite precipitation products have helped to break the limitation of hydrology research in especially ungauged regions and enable research upscaled from local watersheds to continents, and even the globe (Yong et al. 2010; Hou et al. 2014; Papalexiou and Montanari 2019).

The basic particle (cloud droplet) diameter of precipitation ranges from 1 to 100 μm. Electromagnetic waves with identical spectra can distinguish raindrops from other objects and thus further detect the precipitation rate (Neu and Prather 2012; Subramanian et al. 2017; Arulraj and Barros 2019; Sun and Liang 2020; Tang et al. 2020). According to the different wavelengths of the electromagnetic wave received or emitted by the sensor equipped on satellite, the precipitation estimation algorithms can be classified into four main types: visible/infrared (VIS/IR), passive microwave (PMW), active microwave (precipitation radar, PR), or multisensor precipitation estimation (MPE) (Zhang et al. 2016; Arulraj and Barros 2019; Nguyen et al. 2020; Tang et al. 2020).

The VIS band can detect the spectral reflections of clouds but is rarely applied due to its sole availability in the daytime. The thermal IR band can capture the low temperature radiation of precipitation cloud and estimate precipitation intensity through the inversed cloud-top brightness temperature (Tb) following the physical assumption that colder Tb corresponds to more intensive rainfall rate (RR) (Arkin and Meisner 1987; Behrangi et al. 2009). Compared to the VIS/IR band, the microwave band has an incomparable ability of giving the information inside the precipitable cloud through detecting radar reflectivity, and higher precipitation estimation accuracy than the VIS/IR (Bauer et al. 1995; Ebert and Manton 1996). However, it is affected by the phase state of water condensate, raindrop spectrum, and precipitation temperature, as well as the precipitation heterogeneity in the radar image pixel. Moreover, both the PMW and the PR radar suffer from coverage gaps resulting from its installation on the low-Earth-orbit (LEO) satellites. In the past two decades, a number of MPE algorithms were developed based on data of multiple sensors such as CMORPH (Joyce et al. 2004), TMPA (Huffman et al. 2007), GsMap (Okamoto et al. 2005), and IMERG (Hou et al. 2014).

Despite the MPE developments, the IR-based algorithm remains indispensable for satellite precipitation inversion, since the IR sensor can afford imageries steadily with high frequencies, fine temporal resolution, and wide coverages, which enables precipitation estimation of the same quality and capacity (Sadeghi et al. 2019; Nguyen et al. 2020). The successor of TRMM, i.e., the famous IMERG, takes as much LEO-PMW data as possible, while it also applied the GEO-IR precipitation estimates with a Kalman filter where the LEO-PMW are too sparse (Hou et al. 2014). Various IR-based algorithms were developed based on the TbRR relationship with traditional inversion methods, including those of Griffith–Woodley (Griffith et al. 1978), GOES precipitation index (GPI; Arkin and Meisner 1987), outgoing longwave radiation (OLR)-based precipitation index (OPI; Xie and Arkin 1997), and GOES multispectral rainfall algorithm (GMSRA; Ba and Gruber 2001). In 1997, Hsu et al. (1997) introduced the artificial neural network to construct the relationship between Tb and the pixel RR, created the initial IR-based precipitation estimation model with artificial intelligence, named as the Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Network (PERSIANN) package. Instead of direct pixel-to-pixel fitting of the infrared cloud images to the rainfall rate, Hong et al. (2004) applied image segmentation and objective classification to sort cloud images into a set of disjointed cloud-patch regions, and generated the PERSIANN-CCS (Cloud Classification System) product with resolutions of 0.04° and 30 min. Tao et al. (2018) utilized the IR and water vapor channels from the operational Geostationary Operational Environmental Satellite (GOES) to develop PERSIANN-SDAE (stacked denoising autoencoders technique). However, PERSIANN-SDAE cannot efficiently use the information from neighborhood pixels due to an inefficient structure for learning from image datasets. To overcome such inefficiency, Sadeghi et al. (2019) applied the convolutional neural networks (CNNs) and developed PERSIANN-CNN. To deal with the climatology effect on precipitation accuracy, Nguyen et al. (2020) constructed different Tb–RR relationships for dry and wet areas with the PMW data, and proposed the PERSIANN Dynamic Infrared–Rain Rate Model (PDIR) upon the PERSIANN-CCS framework.

From the preliminary PERSIANN to the latest proposed PDIR, the machine learning (ML) approach demonstrated its great potential in the IR-based precipitation inversion (Ashouri et al. 2015; Pan et al. 2019; Wang et al. 2021). However, existing IR-based ML algorithms have much room for improvement to resolve problems such as overestimates in dry regions, underestimates in wet regions, deficiency in detecting extreme rainfall events, and uncertainty with the determination of the Tb threshold and the selection of physical input data. Recently, precipitation estimation approaches based on machine learning have been developed that move beyond reliance on physical equations or parameters (Shi et al. 2017; Snderby et al. 2020; Trebing et al. 2021). Unlike the commonly used one-channel input, Wang et al. (2020) applied three IR data and two derived physical parameters and proposed a novel end-to-end deep learning–based algorithm of the infrared precipitation estimation using a convolutional neural network (IPEC). Ravuri et al. (2021) presented a deep generative model for precipitation nowcasting directly from radar data, while not indirectly from radar-based wind estimates. As pointed out by Sadeghi et al. (2019), due to the complexity and nonlinear behavior of precipitation, applying more direct and advanced data-driven methodologies to automatically extract features beyond human knowledge from the input data may be a good way to improve the precipitation estimation accuracy. Seeking for the data driving free of physical constraints and avoiding inductive biases, we tried to directly use the IR data in the deep learning model to realize direct optimization. Moreover, we noted that all these IR-based ML algorithms make an assumption that data from satellite images are from a flat surface, despite the fact that Earth’s surface is spherical. This ignores the continuous and non-Euclidean characteristic of Earth’s surface. The projection in such a flat surface assumption will cause space-varying distortions and make translational weight sharing ineffective (Cohen et al. 2018) and may hinder algorithm performance (Defferrard et al. 2020). Therefore, applying CNN in a straightforward way when capturing complex meteorological patterns inevitably introduces feature distortions. How to avoid such feature distortions and further improve the precipitation estimation accuracy? To address these problems and issues, we applied a spherical convolutional neural network (SCNN), which is constructed on a triangular mesh, to approximate Earth’s spherical surface. Unlike the application of learnable weights to aggregate neighborhood information in ordinary CNN, spherical convolution uses a message passing mechanism to exchange information with neighboring nodes. SCNN can eliminate systematic error caused by projection and enhance its generalization ability through its rotational equivalent extracted features (Esteves et al. 2018; Cohen et al. 2019). Moreover, SCNN can learn SO(3) (three-dimensional rotation group) equivariant representations to describe the state of three-dimensional rotation of geometric spherical features, which the CNN could not but has been shown to be important for climate forecast (Cohen et al. 2019). Based on SCNN, we developed a new deep learning model called PEISCNN (Precipitation Estimation based on IR data with Spherical Convolutional Neural Network), which takes a spectral perspective and uses Chebyshev convolution kernels as filters. Furthermore, we used original IR data without intermediate parameterization to avoid introduction of additional uncertainty and errors.

The rest of the paper is organized as follows. First, it describes the study area, applied datasets, proposed algorithm, and model evaluation metrics. Then, it shows the model evaluation results at hourly, daily, monthly, seasonally, and yearly scales over wet and dry regions and for different rainfall intensities. Finally, the conclusions and recommended future works are presented.

2. Data

a. Study area

A central region in the United States covering the latitudes from 30° to 45°N and the longitudes from 90° to 105°W was selected as the study area (Fig. 1) for three main reasons: 1) the radar data in the region are available and of high quality, suitable for proper training and effective verification of the deep learning model (PEISCNN); 2) the collected data in the area could present good diversity in precipitation events that the PEISCNN would like to model; and 3) the topography and climate in this area is of good diversity and the regional climate varies from semiarid steppe to subhumid subtropical and humid; these spatially variant climate conditions allow investigation on the precipitation accuracy in different climatic regions.

Fig. 1.
Fig. 1.

Location and the elevation of study region.

Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0081.1

b. Study data

For the purpose of model training and evaluation, three datasets were utilized, that is, GOES IR images, National Centers for Environmental Prediction (NCEP) Stage IV, and PERSIANN-CCS. We selected band 3 (∼6.5 μm), band 4 (∼10.7 μm), and band 6 (∼13.3 μm) from the GOES IR data as the input of PEISCNN. While band 3 can measure the midlevel water vapor which is crucial for precipitation, band 4 allows detection of the surface/cloud-top temperature, which affects the saturated water vapor pressure and possible transformation of water vapor to liquid water, and band 6 reflects the cloud height (Wang et al. 2020). For the convective precipitation process, the more water vapor, colder cloud-top temperature, and higher cloud-top height implies heavier precipitation. It is worth noting again that data of these three bands are used with no intermediate parameterization to directly drive PEISCNN.

The GOES IR imageries were obtained from the National Oceanic and Atmospheric Administration (NOAA) Comprehensive Large Array-data Stewardship System (CLASS; https://www.avl.class.noaa.gov/saa/products/welcome), with its spatiotemporal resolutions of 4 km and 30 min. The radar–gauge-combined Stage IV data were obtained from NCEP (https://data.eol.ucar.edu/dataset/21.093) and applied as the ground truth in model training and as the baseline for model evaluation, since it is of high quality with spatiotemporal resolutions of 4 km and 60 min and undergoes detailed manual quality control (Lin 2011). Among the PERSIANN family algorithms mentioned in section 1, only three of them (PERSIANN, CCS, and PDIR) have been applied and generated products. The IR-based algorithm PERSIANN-CCS is applied in the advanced satellite precipitation product IMERG. Moreover, the CCS product are used as the benchmark in the accuracy assessments for the latest proposed IR-based and machine learning–based algorithms of the PDIR (Nguyen et al. 2020) and IPEC (Wang et al. 2020). Therefore, the PEISCNN was compared to the CCS for performance evaluation. The CCS has spatiotemporal resolutions of 0.04° and 30 mins, it can be downloaded from the Center for Hydrometeorology and Remote Sensing (CHRS) data portal (http://chrsdata.eng.uci.edu/) estimation.

3. Methodology

a. Algorithm architecture

We consider examining the nonlinear transformation between spherical signals, namely, X S2 × ℝc, where S2 is the spherical surface of Earth and X is a signal vector in c-dimensional real space. The term X is actually sampled from the sphere S2, with the latter being non-Euclidean. Therefore, applying traditional convolutional neural networks (CNNs) inevitably introduces feature distortion in complex meteorological patterns when the data are considered as a projection of spherical signals onto a plane. To overcome this problem, we introduce a method that applies convolution to the sphere. Specifically, we sample the vertices of the inscribed regular polyhedron of the sphere (Fig. 3), construct a k-nearest neighbor (kNN) graph of these sampling points, and apply a graph neural network to perform the convolution. To regress the long-tail distribution data, we further use a Kullback–Leibler (KL) divergence term in the loss function to impose distribution constraints. We adopt the U-Net (Ronneberger et al. 2015) as the overall neural network architecture as shown in Fig. 2.

Fig. 2.
Fig. 2.

The neural network architecture for PEISCNN where the U-Net is used, and convolution is performed on a kNN graph defined on a sphere (see details below). ConvBnPool (graph convolution + batch normalization + graph pooling) denotes a series of layers consisting of graph convolution, batch normalization, and pooling. The Gj are the graph signals after j times ConvBnPool with G0 as the input graph signal and G10 as the output signal, and the corresponding Li means the ith level of the icosahedron, whose vertices are laid on by the nodes of Gj. The first five series of ConvBnPool layers are all made up of down-pooling, while the last five series of layers up-pool the signals.

Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0081.1

1) Spherical sampling

As shown in Fig. 3, we aim to construct a kNN graph G(V, X, Y, E) to apply graph convolutional neural networks, where V = {υ1, υ2, …, υn} is the set of points located on the sphere surface, X = {x1, x2, …, xn} is the feature vectors of each point, Y = {y1, y2, …, yn} is the set of targets corresponding to each xi, and E = {ei,j}, ei,j ∈ {0, 1} is the set of edges between points. We sample V from the vertices of the icosahedral spherical mesh (Baumgardner and Frederickson 1985) and improve the resolution by recursively breaking the mesh triangles at the midpoints of the edges (Jiang et al. 2019). Denoting nf, ne, and nυ as the number of faces, edges, and vertices, respectively, of the spherical mesh, for a level-l mesh, we have
nf=20×4l;ne=30×4l;nυ=nenf+2.
Once V is known, we construct the kNN graph of vertexes to get E based on the spherical geodesic distance. Note that X and Y can be directly sampled from the set of spherical points V. The essential problem is to learn a mapping ϕ:G(V,X,E)Y^, such that YY^ is minimized.
Fig. 3.
Fig. 3.

(a) Loop subdivision scheme. The triangle 1–2–3 is subdivided by inserting new vertices 4, 5, 6 at the edge centers and is replaced by the four triangles 1–4–6, 4–2–5, 6–5–3, and 4–5–6. (b) The subdivided icosahedron projected to the sphere. Subdivision levels are 0, 1, and 2 with 12, 42, and 162 vertices.

Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0081.1

2) Spherical convolution

The mapping constitutes a cascade of spectral graph convolutions as the network layers, in which a spectral graph convolution can be expressed as Θ* Gx = gα( L)x = UTgα( L) Ux, where * is the convolution or cross-correlation operation, * G means convolution on graph g, x is the input signal on the graph node, UTΛ U is the eigendecomposition form of the graph Laplacian L, and gα(⋅): ℝ → ℝ is a filter defined on graph spectra with α as the parameter for learning. We use Chebyshev polynomials (Defferrard et al. 2016) on the spectral of Laplacian to approximate gα, which can be written as gα=k=0KαkTk(Λ), where K is the highest order and {Tk} is the Chebyshev polynomials. The Chebyshev convolution kernel can be recursively calculated by
{Tk(Λ)=2ΛTk1(Λ)Tk2(Λ),fork>1T1(Λ)=ΛT0(Λ)=I.
In Fig. 2, with Gj(Vj, Xj, Ej) as the input graph signal to the jth layer and XjR|Vj|×Cj, the graph convolution is given by
Conv(Gj):Gj(Vj,Xj,Ej)Gj(Vj,Xj,Ej),
where XjR|Vj|×Cj+1.

3) Spherical pooling

To reduce the computational cost and improve the receptive field of convolutional kernels, we introduce the down-pooling and up-pooling operations. First, we interpolate the nodes to replace changed to make up the missing values of the raw IR data. Then, we sample nodes between adjacent resolution levels by down-pooling (the first 5 layers) or up-pooling (the last 5 layers) operations (Fig. 4) for all 10 layers in PEISCNN (Fig. 2). Similar to the average pooling in CNN, we also aggregate neighborhood node features through mean operation. For each vertex of the spherical triangular mesh, we use the spherical k-nearest neighbors interpolation method (Trempe 2019) for its IR and perception value from the original data, including longitude, latitude, and data values.

Fig. 4.
Fig. 4.

Down-pooling or up-pooling operation for each layer in PEISCNN. We sample or interpolate nodes between adjacent resolution levels to form down-pooling or up-pooling operation in each layer of the PEISCNN algorithm. The newly created node feature is the average of its neighbors’. For example, x7=(1/6)i=16xi,x10=(1/2)(x8+x9).

Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0081.1

In Fig. 2, with Gj(Vj, Xj, Ej) as the output graph signal from the jth convolution, the graph pooling can be formulated as
Pool(Gj):Gj(Vj,Xj,Ej)Gj+1(Vj+1,Xj+1,Ej+1),
where |Vj+1| < |Vj| if using down-pooling, and vice versa.

4) Loss function

The total loss function contains a Huber loss to regress the pointwise precipitation and KL divergence to regularize the global precipitation distribution, which reads
L=H(y^,y)+λKL[P(y^),P(y)],
where y^ and y are the pointwise predicted and real precipitation value, and λ is a hyperparameter. KL(⋅, ⋅) is the KL divergence between two density functions P(y^) and P(y), both of which are obtained by the kernel density estimation (KDE). The term H(⋅, ⋅) is the Huber loss written as
H(y^,y;δ)={12y^y22,y^y1<δδy^y112δ2,y^y1δ,
where δ is a manually specified threshold, and we choose δ = 5 based on test results for extensive numerical experiments. The KDE is
P(x|{yi}i=1n)=1nhi=1nKer(xyih),
where Ker(t)=(1/2π)exp(t22/2) is Gaussian kernel, h is a fixed hyperparameter, and we set h = 2.5 according to the experiments done by Wang et al. (2020).

b. Experiment design

Given the high spatiotemporal resolutions of the input GOES IR and Stage IV data, we carried out the experiments at the resolutions of hourly and 4 km. Two experiments were designed (Table 1): a short-term experiment to train and test the PEISCNN model and a long-term experiment to validate the accuracy of the model in different spatiotemporal scales and analyze the reasons for its advantages and disadvantages.

Table 1

Information about the experiment design.

Table 1

c. Metrics for evaluating model performance

To evaluate the accuracy of the PEISCNN precipitation estimations, comparisons with the PERSIANN-CCS product were made, both against the ground truth of the Stage IV. Three categories of metrics shown in Table 2 were employed. The first category contains the root-mean-square error (RMSE) and correlation coefficient (CC), which describe the continuity and consistency between the estimates and Stage IV data. The second category of metrics is the skill scores commonly used in meteorological studies, including the bias score (BIAS), false alarm ratio (FAR), probability of detection (POD), and critical success index (CSI). BIAS is an indicator of how well the model predicts the number of rainfall event occurrences. FAR denotes the fraction of forecasts detected by the model which turn out to be wrong. POD, commonly known as the hit rate, represents the ratio of correct estimates to the number of events that occurred. CSI is one of the most frequently applied and comprehensive skill scores for summarizing square contingency tables and combining the characteristics of hints and random detections. The third category is the statistical indicator of mean error (ME) obtained by summing the difference between the estimates and the Stage IV data. To avoid the offsetting of the positive and negative biases, the four-component error decomposition (4CED) method (Zhang et al. 2021) was employed. The ME was decomposed into the hit positive bias (HPB), hit negative bias (HNB), false alarm bias (FB), and the missed bias (MB), thus helping to track the sources of the error and provide feedback for improving the retrieval algorithms.

Table 2

Statistical metrics used in the model evaluation. The terms PP,i and PO,i denote the estimated and observed (Stage IV) precipitation values for the ith grid, where PP,i˙ and PO,i˙ are their means, respectively. The variable A represents the number of precipitation events estimated by the model and also observed as shown by the reference data, B represents the number of precipitation events estimated by the model but not observed, and C represents the number of precipitation events not estimated by the model but observed.

Table 2

Moreover, the normalized Taylor diagram was also used to further show the model performance at larger temporal scales through three variables including standardized deviations, pattern correlations, and relative bias (%) between the estimates and the reference Stage IV data. The diagram is applied to compare the spatial patterns of temporal means at daily and monthly scales. The threshold to distinguish rain and no rain was set to 0.1 mm h−1 or 1 mm day−1 in this study.

4. Results and discussion

a. Performance of PEISCNN in training and testing

The PEISCNN model was trained and tested with the ground truth Stage IV over June, July (training period), and August (testing period) in 2016. The total precipitation over the two periods was calculated by summing the model-generated hourly precipitation rates at each grid and compared to the CCS result against the Stage IV data. As shown in Figs. 5a and 5d, the precipitation in the study area decreases from the east to the west, with the highest rate at the southeast corner near the Gulf of Mexico (Fig. 1) where ample water vapor passes by the atmosphere in the summer. Overall, the CCS largely overestimated the regional total precipitation amount especially in the west dry and southeast wet regions. In contrast, the PEISCNN showed much fewer errors in the west dry regions, with some underestimations in the east. Such opposite deviations of the CCS and the PEISCNN estimates are also evident in the hourly temporal series of the spatial mean precipitation (averaged over the whole region, Fig. 5g). Compared to the maximum hourly Stage IV, the overestimation of the CCS was by 63.91%, while PEISCNN showed underestimation with 24.63%.

Fig. 5.
Fig. 5.

Overestimation by the CCS and underestimation by the PEISCNN were generally found in the training and testing periods over the study area (mm). (a)–(c) The total precipitation of the ground truth Stage IV, and absolute errors of the CCS and the PEISCNN estimates compared with the Stage IV data in the training period, respectively. (d)–(f) The corresponding results in the testing period. (g) The spatial mean of the hourly Stage IV data, and CCS and PEISCNN estimates. (Here and in the other figures, the arrow in the color bar indicates existing extended values.)

Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0081.1

1) Performance at hourly scale

The skill scores and error indices of the hourly CCS and PEISCNN estimates were calculated over all grids and subsequently analyzed with the statistics shown in Fig. 6 and Table 3. The BIAS values (>1) of PEISCNN estimates deviated from the perfect value (1) more than those (<1) of CCS estimates for both the training and testing periods, showing false alarm biases (Fig. 6a). Correspondingly, the FAR values of PEISCNN estimates were higher (Fig. 6b). These indicated that the PEISCNN-predicted precipitation had a wider coverage than the Stage IV at the hourly scale. Despite these drawbacks, the POD of PEISCNN estimates exhibited remarkable improvements over CCS estimates (Fig. 6c); in particular, the average, 10th and 90th percentile POD values were 0.31, 0.27, and 0.28 higher than those of CCS in the testing period, respectively. This indicates a better performance of PEISCNN in correctly estimating the rainfall events as observed, with higher hit rates than those of CCS. As a result, the comprehensive skill index CSI of PEISCNN was much closer to its perfect value (Fig. 6d), with the mean CSI values exceeding those of CCS by 7.14% and 25.00% over the training and testing periods, respectively (Table 3). Moreover, the PEISCNN RMSEs showed considerable decreases (Fig. 6e), with the mean values 0.16 and 0.14 mm lower than those of CCS for the training and testing periods, respectively (Table 3).

Fig. 6.
Fig. 6.

BIAS, FAR, POD, CSI, RMSE (mm), and CC values of the hourly CCS and PEISCNN estimates compared against the Stage IV data.

Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0081.1

Table 3

Skill scores and error indices of the hourly CCS and PEISCNN estimates compared against the Stage IV data. IDs 0 and 1 denote the CCS and PEISCNN cases in the training period, respectively; and IDs 2 and 3 denote the CCS and PEISCNN cases in the testing period, respectively.

Table 3

2) Performance at grid scale

At the local grid scale, the PEISCNN estimates showed similar BIAS and FAR trends to those found for the whole region as discussed above. However, PEISCNN again was found to outperform CCS at most grids in terms of POD, CSI, RMSE, and CC (Fig. 7). In particular, the grid-mean values of these four indices for PEISCNN turned out to be 87.85% higher, 24.90% higher, 15.87% lower, and 1.34% higher than the corresponding CCS values in the testing period, respectively. The accumulative statistical distributions of the four skill scores and the two error indices over all grids were also compared between PEISCNN and CCS estimates (Fig. 8). For the majority of the grids, PEISCNN performed better in the hit rate and comprehensive accuracy as indicated by the results of POD, CSI, RMSE, and CC.

Fig. 7.
Fig. 7.

POD, CSI, RMSE (mm), and CC of the local hourly precipitation estimates from the CCS and PEISCNN.

Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0081.1

Fig. 8.
Fig. 8.

Accumulated distribution curves of the skill scores and error indices.

Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0081.1

3) Performance at daily and monthly scales

The hourly CCS and the PEISCNN estimates were aggregated to daily and monthly values. The standardized deviations, pattern correlations, and relative bias (%) of the daily and monthly mean CCS and PEISCNN estimates over the whole grids were calculated against the Stage IV data and compared using the normalized Taylor diagram (Fig. 9). The results of PEISCNN, much closer to the REF lines than those of CCS, showed a better performance of the former with higher CC, and lower relative error and standard deviations.

Fig. 9.
Fig. 9.

Normalized Taylor diagram of the daily and monthly mean CCS and PEISCNN estimates.

Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0081.1

In summary, the above evaluations showed that over the training and testing periods, the precipitation estimates produced by the PEISCNN algorithm outperformed those of CCS in the hit rate, missing bias, RMSE, and comprehensive index CSI across different temporal (hourly, daily, and monthly) and spatial (local grids and whole region) scales.

4) Comparison to the ordinary CNN

Except for the CCS, the PEISCNN was compared to the ordinary CNN against Stage IV as well. Since there is no generated product of the well-known PERSIANN CNN algorithm, and there are no public algorithms for precipitation estimation based on CNN either, we constructed the ordinary CNN based on IPEC. The source code of the constructed CNN can be downloaded from https://github.com/gaozhangyang/Precipitation_Estimation. Using the same training and testing dataset, PEISCNN achieve a competitive performance, as shown in Table 4. To ensure the comparability, the evaluated index kept the same with that applied in the research of Wang et al. (2020).

Table 4

The performance index for ordinary CNN and PEISCNN.

Table 4

b. Robustness and spatiotemporal characteristics of the PEISCNN estimates in validation

To further test the robustness and generalization ability of the PEISCNN algorithm in different seasons, a 2-yr-long (2016 and 2017) modeling, which contains wet and dry seasons, was carried out. Over these two years, the spatial mean and local maximum of the total precipitation measured by the Stage IV reached 1687 and 5103 mm, respectively. The east part of the region remained wetter than the west over the period (Fig. 10a). Compared with the spatial distribution of the 3-month total regional precipitation amount (Fig. 5), the 2-yr accumulated CCS showed more sever overestimation in most parts of the study area, and the overestimation in the west and underestimation in the east of the 2-yr accumulated PEISCNN estimations (Figs. 10b,c) were amplified as well. The ME of the local total precipitation between the two IR-based estimates and the ground truth ranged from −2454 to 3126 mm for the CCS and from −2349 to 1908 mm (smaller) for the PEISCNN. On average (over time), the spatial mean hourly precipitation rate estimated by PEISCNN deviated from the ground truth given by the Stage IV data by −0.017 mm h−1 (underestimate), compared with 0.037 mm h−1 overestimated by CCS, and the maximum deviation of the PEISCNN estimates was lower (Fig. 10d).

Fig. 10.
Fig. 10.

Deviation magnitude of the PEISCNN underestimation was smaller than that of the CCS overestimation over the validation period (2016–17). (a) Total precipitation given the Stage IV data over period. (b),(c) The absolute errors of total precipitations estimated by CCS and PEISCNN from that of the Stage IV data, respectively. (d) The time series of the deviations of hourly CCS and PEISCNN estimates from the Stage IV data. The inset shows plots of CCS and PEISCNN estimates vs the Stage IV data. (e)–(h) The spatial means of the hourly HPB, HNB, FB, and MB for CCS (red line) and PEISCN (blue line) estimates.

Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0081.1

To quantify the severity of deviations from the ground truth, the ME of CCS and PEISCNN estimates (against the Stage IV data) were further decomposed using the 4CED method to compute the four error components, HPB, HNB, FB, and MB. The spatial mean values of these error components (Figs. 10e–h) showed that compared with the CCS results, PEISCNN’s HNB was 76.92% higher on average over the period, but its HPB, FB, and MB values were 58.82%, 42.47%, and 25.00% lower, respectively. While the spatial mean underestimation of PEISCNN (−0.079 mm h−1) was slightly greater than that of CCS (−0.07 mm h−1) by 12.86%, the overestimation of PEISCNN (0.056 mm h−1) was significantly lower than that of CCS (0.107 mm h−1), equivalent 47.66% improvement. The underestimation of PEISCNN mainly resulted from the negative bias in the hit rate (Figs. 10e–h). In the PEISCNN, the features of neighboring nodes were aggregated with the summation operation during the message passing process. The norm of feature vectors after message aggregation changed with the number of neighboring nodes. The dramatic reduction of neighbor nodes of the boundary points resulted in boundary effect in the PEISCNN (Fig. 10c).

1) Temporal characteristics of the PEISCNN estimates

The hourly precipitation estimates by CCS and PEISCNN in the validation period, averaged over the whole region (spatial mean), were further aggregated to daily, monthly, seasonal, and annual values. According to the Stage IV measurements, the annual average precipitation for the region was 848.7 and 838.1 mm yr−1 in 2016 and 2017, respectively. The precipitation showed notable peaks in April and July (Fig. 11b) and overall higher rates in the wet seasons of spring and summer (Fig. 11c).

Fig. 11.
Fig. 11.

Spatial mean precipitation given by the Stage IV data, CCS, and PEISCNN at daily, monthly, seasonal, and annual scales. Q1, Q2, Q3, Q4 denote the four quarters of February–April, May–July, August–October, and November–January, respectively.

Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0081.1

At the daily scale, the performances of CCS and PEISCNN in estimating the average precipitation over the region appeared to be similar except for the overestimation and underestimation biases, respectively (Fig. 11a). While the correlation coefficient of the CCS estimates was slightly higher, the RMSE of the PEISCNN estimate was lower. Comparison between Figs. 10d and 11a showed that the overestimation of CCS at the daily scale was reduced, as a result of the smearing effect associated with summing of hourly rainfall events over daily cycles. The monthly PEISCNN estimates improved with CC increased to 0.885 (0.059 higher than that of CCS) and RMSE kept lower. Although CCS captured most of the monthly and seasonal variation signals, it overestimated significantly for December 2016 and April 2017 and overestimation persisted over the period between these months (Fig. 11b). This led to large relative errors of 105.05% and 49.39% in the CCS monthly estimates for the 2016 winter and 2017 spring, respectively (Fig. 11c). In contrast, the relative errors of the PEISCNN estimates were significantly lower in magnitude; the relative errors in the summer, autumn, and winter of 2016 were −9.081%, −10.372%, and −12.326%, respectively. At the annual scale, the relative errors of CCS and PEISCNN estimates were 25.138% and −15.912% in 2016, and 37.792% and −16.702% in 2017, respectively (Fig. 11d). Overall, PEISCNN outperformed CCS in estimating the average precipitation rate over the region at different time scales.

2) Spatial characteristics of the PEISCNN estimates

The spatial variations of the local total precipitation over both the training/testing period and validation period (Figs. 5a and 10a) revealed a decreasing trend of the precipitation rate from the east to the west across the study region. To explore how PEISCNN and CCS performed differently in dry and wet regions, the hourly CCS and PEISCNN estimates were evaluated based on the skill scores and 4CED method in three local regions with high, medium, and low terrain heights (denoted as RegH, RegM, and RegL in Fig. 1b), which have low (dry), medium (moderate), and high (wet) precipitation rates, respectively.

As shown in Fig. 12, the PEISCNN estimates in the three local regions again showed higher values of BIAS and FAR, but PEISCNN outperformed CCS in terms of POD, CSI, RMSE, and CC. The mean CSI values for the cases shown in the Fig. 12d, from the left to right, are 0.190, 0.191, 0.197, 0.194, 0.222, 0.222, 0.130, 0.147, 0.150, 0.126, 0.167, and 0.167, respectively. Except for RegH in the dry season, the accuracies of the PEISCNN estimates in the three regions were better than those of the CCS estimates; both performed better in the wet seasons than in the dry season and better in the wet region than in the dry region. Compared to the CCS results, the PEISCNN CSI improved by 1.71% in the wet season and worsened by 3.03% in the dry season within RegH. The new algorithm performed better over the other two local regions with improved CSI in both wet and dry seasons, by 15.82% and 13.93% over the RegM and 12.82% and 11.66% over the RegL.

Fig. 12.
Fig. 12.

Skill scores and error indices for the CCS(C) and PEISCNN(P) estimates in the regions of high (H), medium (M), and low (L) terrain heights.

Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0081.1

The ME of the 2-yr-long hourly CCS and PEISCNN estimates for each grid in the three local regions were calculated and decomposed to HPB, FB, HNB, and MB with the method of 4CED. As illustrated in Fig. 13, the ME of PEISCNN estimates was lower than that of CCS estimates in all three regions. The CCS results showed high overestimation (OE) in RegH and high underestimation (UE) in RegL. This appears to be a general problem with existing IR-based precipitation algorithms (including CCS), which tend to underestimate in wet regions and overestimate in dry regions due to their sole reliance on cloud-top brightness temperature readings (Nguyen et al. 2020). The PEISCNN algorithm seems to be less affected by this problem. The PEISCNN OE were significantly lower than the CCS OE, by 56.14%, 50.00%, and 29.98%, respectively, in RegH, RegM, and RegL. To a lesser extent, the PEISCNN UE were higher than the CCS UE, by 11.37%, 15.65%, and 11.24% in the corresponding regions. While the overestimation of CCS was mainly caused by high FB, the underestimation of PEISCNN can be mainly attributed to large levels of HNB. Future work to further improve the accuracy of PEISCNN should pay more attention to reduction of the hit negative bias especially in wet regions.

Fig. 13.
Fig. 13.

Mean error (ME), overestimation (OE), underestimation (UE), hit positive bias (HPB), hit negative bias (HNB), false alarm bias (FB), and missed bias (MB) of the CCS and PEISCNN estimates in the regions with high (RegH), medium (RegM), and low (RegL) terrain heights over the validation period against the Stage IV data (mm). OE = HPB + FB, and UE = HNB + MB.

Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0081.1

3) Accuracy of PEISCNN in conditions of different rainfall intensities

The daily CCS and PEISCNN estimates were also compared in conditions of different rainfall intensities. According to the Stage IV data, the highest average daily precipitation rate over the study area was 18.4 mm day−1. Taking 1 mm day−1 as the critical rate for the rainfall condition, we divided the precipitation intensities into four sections: [1, 5), [5, 10), [10, 15), and ≥15 mm day−1. The skill scores and error indices of the CCS and PEISCNN estimates under these conditions were calculated as listed in Table 5. The results showed that PEISCNN did not always outperform the CCS. Two consistent improvements by PEISCNN are lower RMSE for all rainfall intensity ranges and better performance with all indices for the heavy rainfall condition (≥15 mm day−1). The PEISCNN CSI was 0.059 lower than that of CCS in the [1, 5) range. As the rainfall intensity increased, PEISCNN started to show improvement with CSI 0.041 higher and RMSE 11.607 mm lower than those CCS values in the heavy precipitation range (≥15 mm day−1). These results indicated the better performance by PEISCNN under heavy rainfall conditions and the need for further improvement for light rainfall.

Table 5

Skill scores and error indices of the CCS and PEISCNN estimates in conditions of different rainfall intensities. Bold indices show improvements, and italic indices are worse.

Table 5

4) Accuracy of the PEISCNN for extreme rainfall events

Extreme precipitation events may account for a large portion of the total annual precipitation (Dettinger 2013) and have the potential to trigger regional floods. Therefore, accurate estimation of extreme precipitation is vital for precipitation retrieval algorithms. Although the definition of extreme precipitation varies with location and the time scale considered (Pendergrass 2018), here we applied the extreme precipitation index Rx5day (maximum 5-day precipitation) (Sun and Miao 2018) to determine the first-ranked extreme events in the wet and dry seasons. The two 5-day periods covering from 26 to 30 April 2017 (W-event, wet season) and from 3 to 7 October 2017 (D-event, dry season) were selected and evaluated in detail.

As shown in Fig. 14, for the W-event, CCS overestimated significantly while the PEISCNN estimates better fit with Stage VI data. The deviations of both estimations were less for the D-event than for the W-event. The skill scores fluctuated with the rainfall rates (Fig. 14). It was clear that the IR-based algorithms show better performance in the heavier rainfall period, with lower BIAS and FAR but higher POD and CSI. Although the PEISCNN BIAS and FAR values were higher than those of CCS, the PEISCNN POD was higher, resulting in overall higher CSI, especially for the extreme precipitation event in the dry season. It can be concluded that PEISCNN outperformed CCS for both extreme events, with improvement of 12.76% and 32.49% in terms of CSI, and 42.57% and 100.83% in POD, respectively.

Fig. 14.
Fig. 14.

Skill scores for the hourly precipitation of the two extreme events in the wet and dry seasons, respectively.

Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0081.1

5. Conclusions

IR-based precipitation inversion is an important approach in hydrometeorological studies based on remote sensing data thanks to high temporal resolutions of readily available satellite infrared data. However, an effective method is needed to leverage rich information contained in the IR data to achieve better accuracy for precipitation estimation. In this study, we focused on developing a deep learning algorithm, PEISCNN, that considers the spherical nature of Earth’s surface from which satellite IR data are acquired—which has been overlooked previously. To avoid introduction of additional uncertainty due to parameterization, our PEISCNN model is a spherical convolutional neural network model working directly on the original IR band 3, 4, and 6 data from the GOES. PEISCNN was first trained and tested over a period of 3 months and validated further over 2 years. Comprehensive evaluations of PEISCNN’s performance based on a set of skill scores and error indices over different spatial and temporal scales were performed in comparison with CCS—a commonly used IR-based ML model for precipitation inversion.

PEISCNN was found to be highly efficient and outperform CCS overall. The mean CSI of the hourly PEISCNN estimates in the testing period was 25.00% higher than that of CCS estimates. Over the validation period, overestimation by PEISCNN at the hourly scale was 47.66% lower than that by CCS. The much-reduced overestimation outweighed the 12.86% higher underestimation by PEISCNN than that by CCS. Furthermore, PEISCNN significantly outperformed CCS in extreme events. Results from the error decomposition analysis suggest improved accuracy of the PEISCNN model mainly results from its better performance for the extreme events and the significant reduction of the overestimation in the dry areas.

Despite the improvement made by PEISCNN, further work should be carried out to solve the boundary effect problem and reduce the model’s hit negative bias and false alarm bias, especially in the wet regions. Future research should also explore how other precipitation-related information, such as the terrain surface elevation, atmosphere water vapor, cloud height, and convective system mechanism, can be incorporated to further the model accuracy. While the PEISCNN algorithm is underpinned by the spherical convolutional neural network, which distinguishes PEISCNN from other machine learning models for precipitation estimation, whether the advantage of PEISCNN will become more profound when applied to a larger region remains a question to be addressed. Notwithstanding the further developments, the current version of PEISCNN will serve as good starting point for producing accurate precipitation products based on the satellite IR data and has the potential to benefit a range of related hydrological research and applications in water resource management and flood predictions.

Acknowledgments.

This research was funded by the National Natural Science Foundation of China (42101035 and 4197060711), Zhejiang Provincial Natural Science Foundation of China (LQ21D010005), China Postdoctoral Science Foundation (2020M671815) and the Postdoctoral Fellowship supported by the Hangzhou Municipal Government of Zhejiang Province in China.

Data availability statement.

The source code and data analyzed in this research are openly available in OneDrive at PEISCNN supplementary.

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  • Tao, Y. M., K. Hsu, A. Ihler, X. Gao, and S. Sorooshian, 2018: A two-stage deep neural network framework for precipitation estimation from bispectral satellite information. J. Hydrometeor., 19, 393408, https://doi.org/10.1175/JHM-D-17-0077.1.

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  • Trebing, K., T. Staǹczyk, and S. Mehrkanoon, 2021: SmaAt-UNet: Precipitation nowcasting using a small attention-UNet architecture. Pattern Recognit. Lett., 145, 178186, https://doi.org/10.1016/j.patrec.2021.01.036.

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    • Search Google Scholar
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  • Shi, X. J., Z. H. Gao, L. Leonard, H. Wang, D. Y. Yeung, W. K. Wong, and W. C. Woo, 2017: Deep learning for precipitation nowcasting: A benchmark and a new model. arXiv, 1706.03458v2, https://doi.org/10.48550/arXiv.1706.03458.

    • Search Google Scholar
    • Export Citation
  • Snderby, C. K., and Coauthors, 2020: MetNet: A neural weather model for precipitation forecasting. arXiv, 2003.12140v2, https://doi.org/10.48550/arXiv.2003.12140.

    • Search Google Scholar
    • Export Citation
  • Sorooshian, S., and Coauthors, 2011: Advancing the remote sensing of precipitation. Bull. Amer. Meteor. Soc., 92, 12711272, https://doi.org/10.1175/BAMS-D-11-00116.1.

    • Search Google Scholar
    • Export Citation
  • Steiner, M., J. A. Smith, S. J. Burges, C. V. Alonso, and R. W. Darden, 1999: Effect of bias adjustment and rain gauge data quality control on radar rainfall estimation. Water Resour. Res., 35, 24872503, https://doi.org/10.1029/1999WR900142.

    • Search Google Scholar
    • Export Citation
  • Subramanian, A., A. Weisheimer, T. Palmer, F. Vitart, and P. Bechtold, 2017: Impact of stochastic physics on tropical precipitation in the coupled ECMWF model. Quart. J. Roy. Meteor. Soc., 143, 852865, https://doi.org/10.1002/qj.2970.

    • Search Google Scholar
    • Export Citation
  • Sun, C., and X. Z. Liang, 2020: Improving US extreme precipitation simulation: Sensitivity to physics parameterizations. Climate Dyn., 54, 48914918, https://doi.org/10.1007/s00382-020-05267-6.

    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
  • Tang, G. Q., M. P. Clark, S. M. Papalexiou, Z. Q. Ma, and Y. Hong, 2020: Have satellite precipitation products improved over last two decades? A comprehensive comparison of GPM IMERG with nine satellite and reanalysis datasets. Remote Sens. Environ., 240, 111697, https://doi.org/10.1016/j.rse.2020.111697.

    • Search Google Scholar
    • Export Citation
  • Tao, Y. M., K. Hsu, A. Ihler, X. Gao, and S. Sorooshian, 2018: A two-stage deep neural network framework for precipitation estimation from bispectral satellite information. J. Hydrometeor., 19, 393408, https://doi.org/10.1175/JHM-D-17-0077.1.

    • Search Google Scholar
    • Export Citation
  • Trebing, K., T. Staǹczyk, and S. Mehrkanoon, 2021: SmaAt-UNet: Precipitation nowcasting using a small attention-UNet architecture. Pattern Recognit. Lett., 145, 178186, https://doi.org/10.1016/j.patrec.2021.01.036.

    • Search Google Scholar
    • Export Citation
  • Trempe, P., 2019: Spherical k-nearest neighbors interpolation. arXiv, 1910.00704v1, https://doi.org/10.48550/arXiv.1910.00704.

  • Wang, C. G., J. Xu, G. Q. Tang, Y. Yang, and Y. Hong, 2020: Infrared precipitation estimation using convolutional neural network. IEEE Trans. Geosci. Remote Sens., 58, 86128625, https://doi.org/10.1109/TGRS.2020.2989183.

    • Search Google Scholar
    • Export Citation
  • Wang, F., D. Tian, L. Lowe, L. Kalin, and J. Lehrter, 2021: Deep learning for daily precipitation and temperature downscaling. Water Resour. Res., 57, e2020WR029308, https://doi.org/10.1029/2020WR029308.

    • Search Google Scholar
    • Export Citation
  • Wang, X. Q., G. Kinsland, D. Poudel, and A. Fenech, 2019: Urban flood prediction under heavy precipitation. J. Hydrol., 577, 123984, https://doi.org/10.1016/j.jhydrol.2019.123984.

    • Search Google Scholar
    • Export Citation
  • Xie, P., and P. A. Arkin, 1997: Global precipitation: A 17-year monthly analysis based on gauge observations, satellite estimates, and numerical model outputs. Bull. Amer. Meteor. Soc., 78, 25392558, https://doi.org/10.1175/1520-0477(1997)078<2539:GPAYMA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Yong, B., L. L. Ren, Y. Hong, J. H. Wang, J. J. Gourley, S. H. Jiang, X. Chen, and W. Wang, 2010: Hydrologic evaluation of multisatellite precipitation analysis standard precipitation products in basins beyond its inclined latitude band: A case study in Laohahe basin, China. Water Resour. Res., 46, W07542, https://doi.org/10.1029/2009WR008965.

    • Search Google Scholar
    • Export Citation
  • Zhang, J., and Coauthors, 2016: Multi-Radar Multi-Sensor (MRMS) quantitative precipitation estimation initial operating capabilities. Bull. Amer. Meteor. Soc., 97, 621638, https://doi.org/10.1175/BAMS-D-14-00174.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, Y. H., A. Z. Ye, P. Nguyen, B. Analui, S. Sorooshian, and K. Hsu, 2021: New insights into error decomposition for precipitation products. Geophys. Res. Lett., 48, e2021GL094092, https://doi.org/10.1029/2021GL094092.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Location and the elevation of study region.

  • Fig. 2.

    The neural network architecture for PEISCNN where the U-Net is used, and convolution is performed on a kNN graph defined on a sphere (see details below). ConvBnPool (graph convolution + batch normalization + graph pooling) denotes a series of layers consisting of graph convolution, batch normalization, and pooling. The Gj are the graph signals after j times ConvBnPool with G0 as the input graph signal and G10 as the output signal, and the corresponding Li means the ith level of the icosahedron, whose vertices are laid on by the nodes of Gj. The first five series of ConvBnPool layers are all made up of down-pooling, while the last five series of layers up-pool the signals.

  • Fig. 3.

    (a) Loop subdivision scheme. The triangle 1–2–3 is subdivided by inserting new vertices 4, 5, 6 at the edge centers and is replaced by the four triangles 1–4–6, 4–2–5, 6–5–3, and 4–5–6. (b) The subdivided icosahedron projected to the sphere. Subdivision levels are 0, 1, and 2 with 12, 42, and 162 vertices.

  • Fig. 4.

    Down-pooling or up-pooling operation for each layer in PEISCNN. We sample or interpolate nodes between adjacent resolution levels to form down-pooling or up-pooling operation in each layer of the PEISCNN algorithm. The newly created node feature is the average of its neighbors’. For example, x7=(1/6)i=16xi,x10=(1/2)(x8+x9).

  • Fig. 5.

    Overestimation by the CCS and underestimation by the PEISCNN were generally found in the training and testing periods over the study area (mm). (a)–(c) The total precipitation of the ground truth Stage IV, and absolute errors of the CCS and the PEISCNN estimates compared with the Stage IV data in the training period, respectively. (d)–(f) The corresponding results in the testing period. (g) The spatial mean of the hourly Stage IV data, and CCS and PEISCNN estimates. (Here and in the other figures, the arrow in the color bar indicates existing extended values.)

  • Fig. 6.

    BIAS, FAR, POD, CSI, RMSE (mm), and CC values of the hourly CCS and PEISCNN estimates compared against the Stage IV data.

  • Fig. 7.

    POD, CSI, RMSE (mm), and CC of the local hourly precipitation estimates from the CCS and PEISCNN.

  • Fig. 8.

    Accumulated distribution curves of the skill scores and error indices.