Abstract

Compared to ground precipitation measurements, satellite-based precipitation estimation products have the advantage of global coverage and high spatiotemporal resolutions. However, the accuracy of satellite-based precipitation products is still insufficient to serve many weather, climate, and hydrologic applications at high resolutions. In this paper, the authors develop a state-of-the-art deep learning framework for precipitation estimation using bispectral satellite information, infrared (IR), and water vapor (WV) channels. Specifically, a two-stage framework for precipitation estimation from bispectral information is designed, consisting of an initial rain/no-rain (R/NR) binary classification, followed by a second stage estimating the nonzero precipitation amount. In the first stage, the model aims to eliminate the large fraction of NR pixels and to delineate precipitation regions precisely. In the second stage, the model aims to estimate the pointwise precipitation amount accurately while preserving its heavily skewed distribution. Stacked denoising autoencoders (SDAEs), a commonly used deep learning method, are applied in both stages. Performance is evaluated along a number of common performance measures, including both R/NR and real-valued precipitation accuracy, and compared with an operational product, Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks–Cloud Classification System (PERSIANN-CCS). For R/NR binary classification, the proposed two-stage model outperforms PERSIANN-CCS by 32.56% in the critical success index (CSI). For real-valued precipitation estimation, the two-stage model is 23.40% lower in average bias, is 44.52% lower in average mean squared error, and has a 27.21% higher correlation coefficient. Hence, the two-stage deep learning framework has the potential to serve as a more accurate and more reliable satellite-based precipitation estimation product. The authors also provide some future directions for development of satellite-based precipitation estimation products in both incorporating auxiliary information and improving retrieval algorithms.

1. Introduction

Precipitation is one of the major driving forces for the hydrological cycle. Accurate precipitation measurement is the key to the success of many hydrological applications. Many natural disasters, such as flood events, are the direct results of extreme precipitation (AghaKouchak and Nakhjiri 2012; Ajami et al. 2008; Anderson et al. 2008; Liu et al. 2015). To better manage water resources and cope with the direct impacts of extreme weather, it is important to provide precipitation measurements at high spatiotemporal resolutions, with good spatial coverage especially over remote areas. There are three types of commonly used precipitation measurements: gauge networks, radar systems, and satellite-based precipitation measurements. Both gauge and radar networks have limited coverage over certain areas. For example, in remote areas, a gauge network is likely to be sparse, owing to the harsh environment and difficulty of maintaining the equipment. Radar networks are good at flat areas but often fail to provide good coverage in mountainous areas (Ajami et al. 2008; Bellerby and Sun 2005; Habib et al. 2014; Huffman et al. 2007; Nasrollahi et al. 2013; Liu et al. 2017; Yang et al. 2017a).

Compared to gauge and radar networks, satellite-based precipitation estimation products provide near-real-time high-resolution hydrometeorological information, which supports weather observation and forecasts and disaster preparation and management. They have the advantage of global coverage and high spatiotemporal resolution. Such information is particularly valuable for remote regions without sufficient access to ground measurements, like oceans, deserts, and developing countries. Also, for extreme events, satellite instruments can monitor the full evolution of these events in high resolution (Nguyen et al. 2014; Scofield and Kuligowski 2003).

Instead of directly measuring precipitation, the satellite-based precipitation estimation products rely on cloud and other information from geosynchronous-Earth-orbiting (GEO) and low-Earth-orbiting (LEO) satellites and then estimate the rainfall intensity (Hsu et al. 1997; Weng et al. 2003). Infrared (IR) data and passive microwave (PMW) data from GEO and LEO satellites are the most commonly used data sources. PMW data have the advantage of being directly retrieved from actual hydrometeor content, whereas IR data are limited to cloud-top information (Behrangi et al. 2009a; Kummerow and Giglio 1995). One feature of precipitation estimation products based on only GEO satellites is that they allow the creation of long archives of consistent data. This is essential for long-term climate monitoring and operational applications, where hydrological models require long periods of consistent precipitation data to calibrate. Another drawback of PMW data is their low temporal resolution (Marzano et al. 2004). This can be improved by using multiple satellites in the Global Precipitation Measurement (GPM) program (Hou et al. 2008). GEO satellites’ IR data have a high spatial and temporal resolution and thus can be useful for monitoring the evolution of a local precipitation event (Behrangi et al. 2009b). Many satellite-based precipitation estimation products have been recently developed and made operational by combining IR and PMW data (Hong et al. 2004; Hsu et al. 1997; Huffman et al. 2007; Joyce et al. 2004; Kidd et al. 2003; Kuligowski 2002). Some products provide different versions of precipitation estimations to satisfy different needs of precipitation measurements, such as near-real-time monitoring and long-term climate analysis.

One widely used, data-driven, satellite-based precipitation estimation product is Precipitation Estimation from Remotely Sensed Information Using Artificial Neural Networks (PERSIANN), developed by Hsu et al. (1997). PERSIANN extracts features for each pixel at 0.25° × 0.25° longitude and latitude, like cloud-top brightness temperature average and standard deviation of nearby pixels. Then it uses a self-organizing feature map, an unsupervised neural network algorithm, to assign pixels to proper groups. Finally, it uses exponential regressions to estimate the precipitation amount for each pixel. Hong et al. (2004) further developed the algorithm and applied it to cloud patches in higher spatial resolution, 0.04° × 0.04° longitude and latitude, to produce the product PERSIANN–Cloud Classification System (PERSIANN-CCS). PERSIANN and PERSIANN-CCS are both IR-based precipitation estimation products.

Some studies have incorporated multiple channels of GEO satellite data, because the IR cloud-top brightness temperature data alone do not contain sufficient information for accurate precipitation retrieval (Ba and Gruber 2001; Behrangi et al. 2009b). One common choice is visible (VIS) wavelength cloud albedo data because they provide high-quality precipitation measurements during daytime (Behrangi et al. 2010; Capacci and Conway 2005; Hsu et al. 1999). The obvious drawback for VIS data is that they are not available at night. Similarly, the combination of IR data with information from the water vapor (WV) channel was also shown to be quite effective for improving precipitation estimation (Behrangi et al. 2009a; Martin et al. 2008; Tao et al. 2016b; Tjemkes et al. 1997).

Therefore, one direction to improve the accuracy of precipitation estimation products is using available data more effectively, such as the information from the VIS and WV channels of the GEO satellites. The retrieval algorithm, which directly generates precipitation estimates from the input data, also plays a critical role in producing accurate precipitation estimates. According to Sorooshian et al. (2011), the key to making the best use of available and new datasets to improve the accuracy of satellite-based precipitation estimation products is to take advantage of any advanced methodology that can extract valuable and useful information related to rainfall. In recent years, deep learning algorithms, also known as deep neural networks (DNNs), have been widely applied in many fields, including signal and image processing, computer vision, and language, in part for their ability to perform complex feature extraction (Bengio 2009; Hinton et al. 2006; LeCun et al. 2015). According to many recent studies (Glorot et al. 2011; Hinton et al. 2006; Lu et al. 2013; Tao et al. 2016a, 2018; Vincent et al. 2008; Yang et al. 2017b, 2018), the DNN techniques have proven to be effective at dealing with many real-world classification and prediction problems and have been considered a major breakthrough in many applications. One particular advantage of DNNs is their capability to automatically extract useful features from the data, which can be then used for estimation and prediction. The success of deep learning algorithms in signal and image processing suggests a major potential for improving the accuracy of satellite precipitation estimation, especially when merging additional information from multiple GEO satellite channels.

In previous works, Tao et al. (2016b, 2017) presented promising performances of the application of DNNs on precipitation estimation. More specifically, Tao et al. (2016b) discussed the benefits of applying DNNs and incorporating the Kullback–Leibler (KL) divergence for precipitation estimation. The comparison between DNNs and shallow neural networks demonstrated the effectiveness of the methodology. In addition, Tao et al. (2017) successfully applied DNNs to binary precipitation identification from bispectral satellite information and demonstrated its effectiveness in correctly delineating the precipitation regions. Also, the improved performance by adding information from the water vapor channel demonstrated the value of the additional data. Such a model can serve as the first step of a satellite-based precipitation estimation product. In this paper, we build on top of our previous works to estimate precipitation using a two-stage model, where we first delineate precipitation regions and then estimate the rainfall intensity. This is an initial analysis for a new satellite-based precipitation estimation product.

The goal of this paper is to report on the development of a two-stage precipitation estimation procedure driven by state-of-the-art deep learning algorithms and using bispectral satellite information, consisting of IR and WV channels from a GEO satellite. The specific objectives of this paper are to report on

  1. design of a deep learning framework that is capable of extracting useful features from bispectral satellite information to support producing accurate precipitation estimates with consistently high quality,

  2. evaluation of the effectiveness of the proposed methodology on both binary precipitation identification and precipitation amount estimation by comparing its performance with an operational product,

  3. evaluation of the performance of the proposed deep neural network model through a large-domain experiment over the United States to test its potential for future application at the global scale, and

  4. assessment of the advantages and limitations of the developed deep neural network structure and identification of potential future developments in improving the accuracy of satellite-based precipitation estimation products.

The paper is organized as follows. Section 2 explains the detailed process and structures of the DNNs used in this study. Section 3 describes the study region, data used, and the specific experimental design. Section 4 presents results for the models developed in this study, comparing them to existing predictions from operational products. Finally, the main conclusions and recommended future work are discussed in section 5.

2. Methodology

Satellite-based precipitation products require high spatiotemporal resolution for hydrometeorological applications, often at an hourly scale and finer than 0.25° × 0.25° (approximately 25 km × 25 km) longitude and latitude resolution. At this scale, the precipitation estimates are expected to be highly skewed. That is, no rain pixels are dominant, while pixels with heavy rain are rare. Critically, however, an important purpose of the satellite-based precipitation estimation is to track rainfall events, especially rare heavy rainfall events that may lead to environmental disasters.

To develop a reliable structure for satellite-based precipitation estimation products, we need to consider multiple objectives and provide multiple performance measurements. Table 1 provides the commonly used performance verification measurements for precipitation estimation, including performance for rain/no-rain (R/NR) classification and precipitation amount estimation regression. These measurements are used to evaluate performances of precipitation estimation models with references to the ground observations.

Table 1.

Common verification measurements for satellite-based precipitation estimation products. TP denotes the number of true positive events, MS denotes the number of missing events, FP denotes the number of false positive events, TN denotes the number of true negative events, denotes the estimation average, denotes the observation average, denotes pixel estimation, denotes pixel observation, and N denotes the amount of observations.

Common verification measurements for satellite-based precipitation estimation products. TP denotes the number of true positive events, MS denotes the number of missing events, FP denotes the number of false positive events, TN denotes the number of true negative events,  denotes the estimation average,  denotes the observation average,  denotes pixel estimation,  denotes pixel observation, and N denotes the amount of observations.
Common verification measurements for satellite-based precipitation estimation products. TP denotes the number of true positive events, MS denotes the number of missing events, FP denotes the number of false positive events, TN denotes the number of true negative events,  denotes the estimation average,  denotes the observation average,  denotes pixel estimation,  denotes pixel observation, and N denotes the amount of observations.

Because of the skewness of the precipitation data and the main application of precipitation data in hydrometeorology, a reliable satellite-based precipitation product needs to satisfy both R/NR identification and rainfall amount estimation. First of all, a precipitation estimation model needs to be capable of distinguishing R/NR pixels, whose accuracy is usually measured by probability of detection (POD), false alarm ratio (FAR), and critical success index (CSI), as introduced in Table 1. Then, such a model needs to accurately estimate the rainfall amount, for both pixels with light and heavy rain. Since these objectives may be at odds with one another, the model needs to be able to trade off between improvement and balanced performance.

To tackle this multiobjective problem, we develop a two-stage model. The first stage includes a binary R/NR classification model, which focuses on correctly identifying pixels with precipitation and eliminating the massive amount of no-precipitation pixels. The second stage is a precipitation amount regression model, which focuses on estimating amounts accurately, while preserving the skewed distribution.

The overview of the two-stage model’s process is presented in Fig. 1. The bispectral imageries are first fed into the R/NR classifier, where a DNN with binary output is deployed. Then for pixels classified as without precipitation, the predicted values are set to zero. For pixels classified as with precipitation, the corresponding bispectral imageries are fed into the second stage, consisting of another DNN with real-valued precipitation amount output.

Fig. 1.

Overview of the two-stage model process. The first stage is R/NR classification, as shown in Fig. 2. The second stage is precipitation amount estimation, as shown in Fig. 3.

Fig. 1.

Overview of the two-stage model process. The first stage is R/NR classification, as shown in Fig. 2. The second stage is precipitation amount estimation, as shown in Fig. 3.

The structures of DNNs for the two stages are presented in Figs. 2 and 3, respectively. For both neural networks, the inputs of the model are 15 pixel × 15 pixel bispectral satellite patches. The resolution of the pixels is at 0.08° × 0.08° latitude and longitude in this study. The output of the first stage is the probability of R/NR for the centered pixel of the patch. The output of the second stage is the real-valued rainfall amount for the centered pixel of the patch, which was previously classified as having precipitation. The training techniques used in both stages are stacked denoising autoencoders (SDAEs), widely used DNN training techniques taking advantage of unsupervised feature extraction. Briefly speaking, SDAEs incorporate two steps. First, an autoencoder (AE) is used to extract features from the raw input images. An AE learns the internal representations by reconstructing the input information. Figure 4 presents the structure of an AE (Tao et al. 2017). Second, AEs are applied to the DNNs (Figs. 2, 3) to get the precipitation estimates. More technical details for SDAEs and their application to the first stage are discussed in detail in Tao et al. (2017).

Fig. 2.

Structure of the DNN used in the first stage: the input layer is IR and WV imageries, and the output layer is the probabilities of R/NR for the centered pixel.

Fig. 2.

Structure of the DNN used in the first stage: the input layer is IR and WV imageries, and the output layer is the probabilities of R/NR for the centered pixel.

Fig. 3.

Structure of the DNN used in the second stage: the input layer is IR and WV imageries, and the output layer is the precipitation amount for the centered pixel.

Fig. 3.

Structure of the DNN used in the second stage: the input layer is IR and WV imageries, and the output layer is the precipitation amount for the centered pixel.

Fig. 4.

Structure of an AE (Tao et al. 2017).

Fig. 4.

Structure of an AE (Tao et al. 2017).

In this paper, we focus on the second-stage, real-valued rainfall amount estimation. As mentioned before, the skew of the precipitation data is a major challenge for a precipitation estimation product. Specifically, for a data-driven model using mean squared error (MSE) as its cost function, the model tends to be conservative and avoids predicting large values, since they are rare and the costs are high if the prediction is not accurate. Thus, the desire to predict realistic events, including large rainfall events, makes MSE unsuitable as the sole cost function for training our model. To ameliorate this issue, in this study we add a KL divergence term in addition to the MSE term in the cost function. KL divergence measures the difference of two distributions, which can be expressed as

 
formula

where P and Q are two distributions of a continuous random variable x, and p(x) and q(x) are the corresponding density functions.

That is, in addition to the pointwise difference measured by MSE, we also incorporate a cost corresponding to the difference between the observed rainfall amount’s distribution and the estimates’ distribution, captured by KL divergence. In the training process, a weighted average of the MSE and the KL divergence is applied as the cost function. The weights are set to be 1:100 with experiments of different combinations (1:10, 1:100, and 1:1000; Tao et al. 2016b).

Table 2 summarizes the combination of the other key parameters we used in the classification and regression models, respectively. These parameters were selected based on the previous experiments for precipitation estimation using DNN methods (Tao et al. 2016b, 2017).

Table 2.

Key parameters used in the two-stage model.

Key parameters used in the two-stage model.
Key parameters used in the two-stage model.

3. Experimental design and data used

The data used in this study incorporate satellite imageries, ground observations, and precipitation estimates from operational products. The satellite imageries are the inputs of the precipitation estimation model. The IR (10.8 μm) and WV (6.7 μm) channels from the Geostationary Operational Environmental Satellite (GOES) serve as inputs. The combination of the two channels has been shown to be helpful for precipitation identification and estimation (Ba and Gruber 2001; Behrangi et al. 2009a,b). The IR channel measures cloud-top brightness temperature, which provides information on precipitable clouds. The WV channel measures the intensity of water vapor over the mid- to upper levels, which is a necessary condition in the formation of precipitation. Both channels are at 0.04° × 0.04° latitude and longitude (approximately 4 km × 4 km) spatial resolution at a half-hourly scale. In this study, the National Centers for Environmental Prediction (NCEP) Stage IV radar and gauge precipitation data (http://www.emc.ncep.noaa.gov/mmb/ylin/pcpanl/stage4/) serve as ground observations. The Stage IV data are at 0.04° × 0.04° latitude and longitude spatial resolution at an hourly scale. PERSIANN-CCS (Hong et al. 2004), a widely used satellite-based precipitation estimation product, serves as a baseline model for performance comparisons.

The study period covers the summer (June–August) and the winter (December–February) seasons for 2012–14 at 0.08° × 0.08° latitude and longitude (approximately 8 km × 8 km) spatial resolution and hourly temporal resolution. The data were simply processed by averaging raw values within each grid. The reason for this data processing is for the potential of taking advantage of useful data sources with lower resolution in the future, such as PMW data and numerical model predictions. To properly validate the methodologies, the data of the summer and winter seasons of 2012–13 in the central United States (30°–45°N, 90°–105°W) are used to calibrate the models, and the data of the next year (2013–14) over a larger coverage area of the United States (30°–45°N, 85°–115°W) serve as verification data. The average precipitation observed by Stage IV radar over the verification periods and regions are presented in Fig. 5. During the training process, the training dataset is used to calibrate the parameters and prevent overfitting. Specifically, the training data, data from the summer and winter seasons of 2012–13, are randomly divided into two parts in a ratio of 75:25. The model is calibrated with the former, and its performance is evaluated with the latter to prevent overfitting. We did not distinguish between the seasons for the models because the potential usages of such models are global. In addition, the evaluation of large-scale applications is necessary before promoting such models to near-real-time operational products. Thus, in the verification, we applied the model to a larger coverage area of the United States (30°–45°N, 85°–115°W) to assess its generalization ability. The satellite data are normalized to between 0 and 1 for the best practice of serving as inputs for the DNNs. Higher values mean lower brightness temperatures, which often correspond to higher precipitation rates. This normalization helps to accelerate the training process of DNNs (Vincent et al. 2008).

Fig. 5.

Stage IV averaged precipitation amount (mm h−1) observations over the large coverage area of the United States (30°–45°N, 85°–115°W): (a) summer (June–August 2013) and (b) winter (December 2013–February 2014).

Fig. 5.

Stage IV averaged precipitation amount (mm h−1) observations over the large coverage area of the United States (30°–45°N, 85°–115°W): (a) summer (June–August 2013) and (b) winter (December 2013–February 2014).

4. Results and discussion

In this section, we evaluate the performance of the two-stage model in the verification periods (summer 2013 and winter 2013/14) over the large coverage area of the United States (30°–45°N, 85°–115°W), in comparison with the data of PERSIANN-CCS. The definitions of the measurements used for verification are presented in section 2. For all measurements, we also present the performance gain with respect to PERSIANN-CCS.

Table 3 summarizes the overall R/NR classification performance of PERSIANN-CCS and the two-stage model over the verification periods of the large coverage area of the United States (30°–45°N, 85°–115°W). The two-stage model shows significant performance gain (32.56% in CSI) in precipitation identification compared to PERSIANN-CCS. More specifically, the two-stage model has a 23.30% performance improvement in POD compared to PERSIANN-CCS (0.418 compared to 0.339) while the performance improvement of FAR is 16.19% (0.528 compared to 0.630). The overall promising performance demonstrates the capability of the two-stage model in delineating precipitation regions correctly.

Table 3.

Summary of R/NR classification performances over the verification periods (including both summer 2013 and winter 2013/14) of the large coverage area of the United States (30°–45°N, 85°–115°W).

Summary of R/NR classification performances over the verification periods (including both summer 2013 and winter 2013/14) of the large coverage area of the United States (30°–45°N, 85°–115°W).
Summary of R/NR classification performances over the verification periods (including both summer 2013 and winter 2013/14) of the large coverage area of the United States (30°–45°N, 85°–115°W).

More detailed information about the performances of the models over different seasons in the verification periods over the large coverage area of the United States are provided in Table 4. In the summer and winter seasons, over 20% increases in POD can be detected in the two-stage model compared to PERSIANN-CCS (22.57% and 21.02% performance gains, respectively), while FAR remains similar to PERSIANN-CCS for the summer season (2.09% performance gain) but has a significant improvement for the winter season (40.85% performance gain). Compared to PERSIANN-CCS, the overall improvements shown in CSI are higher for the winter (45.45% performance gain) than the summer (16.67% performance gain).

Table 4.

Summary of precipitation estimation performance over the large coverage area of the United States for summer 2013 and winter 2013/14.

Summary of precipitation estimation performance over the large coverage area of the United States for summer 2013 and winter 2013/14.
Summary of precipitation estimation performance over the large coverage area of the United States for summer 2013 and winter 2013/14.

Figures 6 and 7 present the maps of POD, FAR, and CSI of the PERSIANN-CCS and the two-stage model over the large coverage area in the summer and winter verification periods, respectively. The region between the black dotted lines is the calibration region, on which the model was calibrated. The warm colors indicate high measurement values, while cold colors indicate low measurement values. The white color indicates that less than 50 precipitation pixels are observed at that location during the corresponding period. High values are desirable for POD and CSI, while low values are desirable for FAR. Figures 6a and 6b show that the two-stage model uniformly outperforms PERSIANN-CCS over the middle to eastern part of the area. For FAR (Figs. 6c,d), the performance of the two models is almost the same, which is consistent with the FAR values presented in Table 3 (0.537 and 0.526 for PERSIANN-CCS and the two-stage model, respectively). Compared to PERSIANN-CCS, the two-stage model shows significant improvement in CSI (Figs. 6e,f), especially in the central to eastern region. More specifically, 84.4% of the pixels show better performance in CSI with the two-stage model compared to PERSIANN-CCS, as presented in Table 5. The improved performance found in the northeast and southeast particularly demonstrates the model’s ability to extend to unfamiliar regions. However, in the western part of the area, no significant improvement can be visually distinguished. This might be because the model was not trained in this region and thus the improvement is not as significant. Similarly, Fig. 7 presents the results for the winter season. In CSI, an obvious improvement can be observed over the mideastern part of the map, centered around Illinois. There are also identifiable improvements in the northwest part of the map, where enough precipitation pixels are present in the verification period. Specifically, 80.7% of the pixels show better performance in CSI with the two-stage model, compared to PERSIANN-CCS, as presented in Table 5. Overall, performance improvements are significant and consistent geographically for both seasons.

Fig. 6.

POD, FAR, and CSI of PERSIANN-CCS and the two-stage model over the large coverage area of the United States for summer 2013 (June–August). (a),(b) POD; (c),(d) FAR; and (e),(f) CSI. The white color means that less than 50 precipitation pixels in the location are observed within corresponding periods.

Fig. 6.

POD, FAR, and CSI of PERSIANN-CCS and the two-stage model over the large coverage area of the United States for summer 2013 (June–August). (a),(b) POD; (c),(d) FAR; and (e),(f) CSI. The white color means that less than 50 precipitation pixels in the location are observed within corresponding periods.

Fig. 7.

As in Fig. 6, but for winter 2013/14 (December–February).

Fig. 7.

As in Fig. 6, but for winter 2013/14 (December–February).

Table 5.

Percentage of pixels with better performance in the two-stage model, compared to PERSIANN-CCS over the large coverage area of the United States for summer 2013 and winter 2013/14.

Percentage of pixels with better performance in the two-stage model, compared to PERSIANN-CCS over the large coverage area of the United States for summer 2013 and winter 2013/14.
Percentage of pixels with better performance in the two-stage model, compared to PERSIANN-CCS over the large coverage area of the United States for summer 2013 and winter 2013/14.

Table 6 provides the overall precipitation estimation performances of PERSIANN-CCS and the two-stage model over the verification periods of the large coverage of the United States. The two-stage model has significant improvement in all three measurements, compared to PERSIANN-CCS. The two-stage model reduces average bias and average MSE by 23.40% and 44.52%, respectively (0.036 compared to 0.047 and 0.562 compared to 1.013, respectively). At the same time, the two stage model has 27.21% higher Pearson’s correlation coefficient (COR), compared to PERSIANN-CCS (0.374 compared to 0.294). The overall performance demonstrates the ability of the two-stage model to estimate precipitation amounts more accurately.

Table 6.

Summary of precipitation estimation performance over the large coverage area of the United States (including both summer 2013 and winter 2013/14).

Summary of precipitation estimation performance over the large coverage area of the United States (including both summer 2013 and winter 2013/14).
Summary of precipitation estimation performance over the large coverage area of the United States (including both summer 2013 and winter 2013/14).

Figure 8 presents maps of the average bias of PERSIANN-CCS and the two-stage model precipitation over the large coverage area of the United States averaged over the warm and cold verification periods, respectively. Again, the region between the black dotted lines is the calibration region, on which the model was calibrated. In summer (Figs. 8a,b), the two-stage model outperforms PERSIANN-CCS and reduces the overestimation in the northwest and the south areas while both models show similar patterns of underestimation in the southeast area. In winter (Figs. 8c,d), the two-stage model reduces the overestimation in the middle to western area but introduces more underestimation in the eastern area of the map, compared to PERSIANN-CCS. The specific performance measures for both seasons are displayed in Table 7. Moreover, as presented in Table 8, compared to PERSIANN-CCS, 59.3% and 62.8% of the pixels show better performance in average bias with the two-stage model in the summer and winter seasons, respectively. As bias is not directly included in the objective function used in this algorithm, the percentages of the pixels with improvement are not very high though the overall biases are reduced for summer and winter, respectively.

Fig. 8.

Averaged bias (mm h−1) of (a),(c) PERSIANN-CCS and (b),(d) the two-stage model output over the large coverage area of the United States (30°–45°N, 85°–115°W) for (top) summer (June–August 2013) and (bottom) winter (December 2013–February 2014).

Fig. 8.

Averaged bias (mm h−1) of (a),(c) PERSIANN-CCS and (b),(d) the two-stage model output over the large coverage area of the United States (30°–45°N, 85°–115°W) for (top) summer (June–August 2013) and (bottom) winter (December 2013–February 2014).

Table 7.

Summary of precipitation estimation performance over the large coverage area of the United States for summer 2013 and winter 2013/14.

Summary of precipitation estimation performance over the large coverage area of the United States for summer 2013 and winter 2013/14.
Summary of precipitation estimation performance over the large coverage area of the United States for summer 2013 and winter 2013/14.
Table 8.

Percentage of pixels with better performance in the two-stage model, compared to PERSIANN-CCS over the large coverage area of the United States for summer 2013 and winter 2013/14.

Percentage of pixels with better performance in the two-stage model, compared to PERSIANN-CCS over the large coverage area of the United States for summer 2013 and winter 2013/14.
Percentage of pixels with better performance in the two-stage model, compared to PERSIANN-CCS over the large coverage area of the United States for summer 2013 and winter 2013/14.

Figure 9 presents the average MSE of PERSIANN-CCS and the two-stage model precipitation over the large coverage area of the United States, averaged in the warm and cold verification periods, respectively. The region between the white dotted lines is the calibration region, where the model was calibrated. Warm colors indicate strong differences compared to Stage IV observations, while cold colors indicate small differences. Figures 8a and 8b show significant decreases in MSE throughout the whole enlarged coverage area for the two-stage model in the summer season, compared to PERSIANN-CCS. Besides the main study region (the central United States), significant improvements can be found in the northwest and northeast regions. Specifically, MSEs are less than 3 (mm h−1)2 for most pixels for the two-stage model (Fig. 9b). Similarly, Figs. 9c and 9d show significant improvements of the two-stage model in the winter season, especially in the central to western area, where most pixels’ MSEs are less than 0.4 (mm h−1)2 for the two-stage model (Fig. 9d). In the east, improvement can also be identified by the reduced area with MSEs larger than 0.8 (mm h−1)2. In summary, a consistent and significant improvement can be found in the MSE of the two-stage model across the enlarged coverage area, compared to PERSIANN-CCS. Specific calculations are displayed in Table 7. Moreover, as presented in Table 8, compared to PERSIANN-CCS, nearly all (96.0% and 97.9% for the summer and winter seasons, respectively) pixels show better performance in average bias with the two-stage model. These high percentages show the effectiveness of the algorithm since MSE is optimized directly through part of the objective function.

Fig. 9.

As in Fig. 8, but for averaged MSE [(mm h−1)2].

Fig. 9.

As in Fig. 8, but for averaged MSE [(mm h−1)2].

Table 7 provides detailed values of average bias, average MSE, and COR for PERSIANN-CCS and the two-stage model in different seasons over the large coverage area of the United States. There are 10.00% and 34.55% decreases in the average biases for the two-stage model for the summer and winter seasons, compared to PERSIANN-CCS (0.036 compared to 0.040 and 0.036 compared to 0.055, respectively). More obvious improvement can be found in the MSE, where the two-stage model has 39.80% and 57.14% decreases in the summer and winter seasons, respectively. In addition, compared to PERSIANN-CCS, the COR for the two-stage model is 57.14% higher in the winter season and 5.96% higher in the summer season. The overall performance gain is higher for the winter season than the summer season.

To demonstrate the performance of the two-stage model on specific events, Figs. 10 and 11 present snapshots from an event at 1400 and 1800 UTC 1 June 2013. IR and WV imageries are also included for comparison. Overall, the two-stage model (Figs. 10d, 11d) captures the narrow shape of the rainfall over Kansas and Missouri fairly well and the separate small region with precipitation on the border of Missouri and Arkansas. On the contrary, PERSIANN-CCS (Figs. 10c, 11c) gives a fatter shape to the rainfall and misses the precipitation in the east. At 1800 UTC, the two-stage model (Fig. 11d) captures the locations with the peak rainfalls much better than PERSIANN-CCS (Fig. 11c). These shifts of the rainfall shape and locations might be due to its critical assumption of low brightness temperature leading to high rain rates. It demonstrates that the two-stage model is capable of better capturing the shape of the rainfall coverage and its peak area. It can extract more useful precipitation-related features from the bispectral information and captures some rainfall that PERSIANN-CCS fails to identify.

Fig. 10.

(a) IR and (b) WV imageries (K) and snapshots (mm h−1) of (c) PERSIANN-CCS, (d) the two-stage model, and (e) the radar observation over the central United States at 1400 UTC 1 Jun 2013.

Fig. 10.

(a) IR and (b) WV imageries (K) and snapshots (mm h−1) of (c) PERSIANN-CCS, (d) the two-stage model, and (e) the radar observation over the central United States at 1400 UTC 1 Jun 2013.

Fig. 11.

As in Fig. 10, but for 1800 UTC 1 Jun 2013.

Fig. 11.

As in Fig. 10, but for 1800 UTC 1 Jun 2013.

To analyze the uncertainty sources of the two-stage model, Table 9 provides the MSE introduced by the two stages for the summer and winter seasons, respectively. The misidentification of R/NR pixels contributes the most to the total MSE (74.9% and 54.6% for the summer and winter seasons, respectively). These results are not surprising given the low percentage of pixels with precipitation and the difficulties in accurately delineating the precipitation regions. This demonstrates the importance of improving the accuracy of the classification of R/NR.

Table 9.

Uncertainty analysis for the two-stage model over the large coverage area of the United States for summer 2013 and winter 2013/14.

Uncertainty analysis for the two-stage model over the large coverage area of the United States for summer 2013 and winter 2013/14.
Uncertainty analysis for the two-stage model over the large coverage area of the United States for summer 2013 and winter 2013/14.

5. Conclusions and future work

This study applies deep learning techniques to develop a two-stage framework for precipitation estimation from bispectral satellite imagery. The first stage is a rain/no-rain (R/NR) classification model, aiming to delineate precipitation regions. The second stage is a precipitation amount estimation model, focusing on estimating the pointwise precipitation amount accurately while preserving its highly skewed distribution. The model is calibrated in the central United States and evaluated on a large area of the United States (30°–45°N, 85°–115°W).

The experiments show significant improvements for the two-stage model in both R/NR classification and precipitation amount estimation, compared to PERSIANN-CCS over the study area of the United States. In the R/NR classification, the performance gain in CSI for the two-stage model is 32.56%, compared to PERSIANN-CCS. In precipitation amount estimation, the two-stage model is 23.40% lower in average bias, 44.52% lower in average MSE, and 27.21% higher in COR. In addition, the improvement is greater for the winter season than the summer.

The experimental results demonstrate the effectiveness of the two-stage deep learning framework for precipitation estimation from bispectral satellite information over unfamiliar areas, in both the R/NR classification and real-valued amount estimation. The model is capable of capturing the relationship between the satellite information and the precipitation even at new geographic locations, which is an important prerequisite for a model to serve as a satellite-based precipitation estimation product with global coverage. However, we also notice that the model’s performance outside the training region is not as good as within the training region. Larger and more diverse training data may lead to a more stable model.

The current application is an initial step as a proof of concept for a full, large-scale application. Further experiments are extremely important for the preparation of the model to serve as an operational product. For example, it is likely helpful to calibrate the parameters with samples from a larger study region, such as the entire continental United States, to better capture the variability in forms of precipitation. More evaluation and analysis, such as comparisons between other global products with both IR and WV inputs, are also extremely useful to further validate the methodology. Work is in progress to evaluate the model in multiple locations, within the United States and abroad, to better evaluate the global performance of the model toward full global implementation.

Acknowledgments

Financial support for this study is made available from the National Science Foundation Cyber-Enabled Sustainability Science and Engineering program (CCF-1331915), the NASA Earth and Space Science Fellowship (NNX15AN86H), the NASA Minority University Research and Education Project (MIRO NNX15AQ06A), the U.S. Department of Energy Clean Energy Research Center for Water-Energy Technology program (DOE Prime Award DE-IA0000018), and the California Energy Commission (CEC Award 300-15-005).

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Footnotes

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