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    Effect of Tb and albedo thresholds on the capture of daytime rain area and rain volume during the summer of 2006 over central and eastern conterminous United States: The numbers next to the dashed threshold lines represent the percentages of missed–underestimated rain area and volume. The numbers are obtained after implementation of the two previously suggested thresholds of 253 K and 0.4 on a pool of high-resolution bispectral grid boxes with RR > 0.1 mm h−1. Corresponding RR data are obtained from ground radar observation: (a) relative frequency distributions of Tb under rain condition, (b) distribution of normalized rain volume with respect to the corresponding Tb value, (c) relative frequency distributions of albedo under rain condition, and (d) distribution of normalized rain volume with respect to the corresponding albedo value.

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    Schematic overview of the algorithm development–calibration and precipitation estimation steps.

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    Demonstration of cloud patches and different threshold layers for an event at 1915 UTC 6 Jul 2006: (a) map of IR Tb, (b) map of smoothed albedo, (c) IR temperature-based cloud patches, (d) albedo-based cloud patches, (e) IR temperature threshold layers, and (f) albedo threshold layers. Cloud-type labels in (a) and (b) are obtained through comparison with Fig. 4. The zones Pt and Pa, shown in (c) and (d) are examples of patches captured by one cloud-patch segmentation approach and not by the other.

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    Schematic representation of a simple cloud classification scheme using different layers of cloud temperature–height and reflectance.

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    Evaluation statistics for all four scenarios using 30 days of 6-h (0900–1500 LST) high-resolution (4 km) RR over the whole study area: (left) categorical statistics including (a) ETS, (c) POD, (e) FAR, and (g) BIASa and (right) quantitative statistics including (b) CORR, (d) RMSE, and (f) BIASq. Note that perfect score for both BIASa and BIASq is 1.

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    Visual assessment of performances of the studied scenarios using a rain event at 1615 UTC 24 Aug 2006 over Arizona: (a) IR Tb (K), (b) normalized albedo, (c) radar RR, (d) IR-based cloud patches, (e) smoothed albedo image prior to cloud segmentation, (f) RR estimate from scenario IR/IR, (g) albedo-based cloud segmentation, (h) RR estimate from scenario IR/IRandVIS, (i) RR estimate from scenario VIS/IRandVIS, and (j) RR estimate from scenario CMB. Note that columns are associated with (left) IR-based and (middle) albedo-based cloud patches.

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    Fig. B1. Visual representation of the contingency table.

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Daytime Precipitation Estimation Using Bispectral Cloud Classification System

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  • 1 Center for Hydrometeorology and Remote Sensing, and Department of Civil and Environmental Engineering, Henry Samueli School of Engineering, University of California, Irvine, Irvine, California
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Abstract

Two previously developed Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN) algorithms that incorporate cloud classification system (PERSIANN-CCS) and multispectral analysis (PERSIANN-MSA) are integrated and employed to analyze the role of cloud albedo from Geostationary Operational Environmental Satellite-12 (GOES-12) visible (0.65 μm) channel in supplementing infrared (10.7 mm) data. The integrated technique derives finescale (0.04° × 0.04° latitude–longitude every 30 min) rain rate for each grid box through four major steps: 1) segmenting clouds into a number of cloud patches using infrared or albedo images; 2) classification of cloud patches into a number of cloud types using radiative, geometrical, and textural features for each individual cloud patch; 3) classification of each cloud type into a number of subclasses and assigning rain rates to each subclass using a multidimensional histogram matching method; and 4) associating satellite gridbox information to the appropriate corresponding cloud type and subclass to estimate rain rate in grid scale. The technique was applied over a study region that includes the U.S. landmass east of 115°W. One reference infrared-only and three different bispectral (visible and infrared) rain estimation scenarios were compared to investigate the technique’s ability to address two major drawbacks of infrared-only methods: 1) underestimating warm rainfall and 2) the inability to screen out no-rain thin cirrus clouds. Radar estimates were used to evaluate the scenarios at a range of temporal (3 and 6 hourly) and spatial (0.04°, 0.08°, 0.12°, and 0.24° latitude–longitude) scales. Overall, the results using daytime data during June–August 2006 indicate that significant gain over infrared-only technique is obtained once albedo is used for cloud segmentation followed by bispectral cloud classification and rainfall estimation. At 3-h, 0.04° resolution, the observed improvement using bispectral information was about 66% for equitable threat score and 26% for the correlation coefficient. At coarser 0.24° resolution, the gains were 34% and 32% for the two performance measures, respectively.

* Current affiliation: Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California

Corresponding author address: Ali Behrangi, Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, MS 183-301, Pasadena, CA 91109. Email: ali.behrangi@jpl.nasa.gov

This article included in the International Precipitation Working Group (IPWG) special collection.

Abstract

Two previously developed Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN) algorithms that incorporate cloud classification system (PERSIANN-CCS) and multispectral analysis (PERSIANN-MSA) are integrated and employed to analyze the role of cloud albedo from Geostationary Operational Environmental Satellite-12 (GOES-12) visible (0.65 μm) channel in supplementing infrared (10.7 mm) data. The integrated technique derives finescale (0.04° × 0.04° latitude–longitude every 30 min) rain rate for each grid box through four major steps: 1) segmenting clouds into a number of cloud patches using infrared or albedo images; 2) classification of cloud patches into a number of cloud types using radiative, geometrical, and textural features for each individual cloud patch; 3) classification of each cloud type into a number of subclasses and assigning rain rates to each subclass using a multidimensional histogram matching method; and 4) associating satellite gridbox information to the appropriate corresponding cloud type and subclass to estimate rain rate in grid scale. The technique was applied over a study region that includes the U.S. landmass east of 115°W. One reference infrared-only and three different bispectral (visible and infrared) rain estimation scenarios were compared to investigate the technique’s ability to address two major drawbacks of infrared-only methods: 1) underestimating warm rainfall and 2) the inability to screen out no-rain thin cirrus clouds. Radar estimates were used to evaluate the scenarios at a range of temporal (3 and 6 hourly) and spatial (0.04°, 0.08°, 0.12°, and 0.24° latitude–longitude) scales. Overall, the results using daytime data during June–August 2006 indicate that significant gain over infrared-only technique is obtained once albedo is used for cloud segmentation followed by bispectral cloud classification and rainfall estimation. At 3-h, 0.04° resolution, the observed improvement using bispectral information was about 66% for equitable threat score and 26% for the correlation coefficient. At coarser 0.24° resolution, the gains were 34% and 32% for the two performance measures, respectively.

* Current affiliation: Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California

Corresponding author address: Ali Behrangi, Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, MS 183-301, Pasadena, CA 91109. Email: ali.behrangi@jpl.nasa.gov

This article included in the International Precipitation Working Group (IPWG) special collection.

1. Introduction

With continuous improvement over the past three decades, satellite precipitation estimation techniques now offer the means to map both occurrence and distribution of global rain rate. With the deployment of the first Special Sensor Microwave Imager (SSM/I; Hollinger et al. 1987), passive microwave (PMW) remote sensing of precipitation was recognized as the most reliable source of instantaneous precipitation estimates (Adler et al. 2001; Ebert et al. 1996). To date, all passive microwave sensors are carried on low Earth orbiting (LEO) satellites, thus restricting the temporal resolution of global precipitation mapping products. Although improvements in temporal resolution of global PMW coverage will be achieved through the Global Precipitation Measurement (GPM) mission, observations will remain constrained by ∼3-h-average revisit time and ∼10-km gridbox resolution (Hou et al. 2008). Currently, the growing demand from various scientific communities for global finer-scale precipitation estimates can only be addressed by utilizing a combination of LEO mounted sensors along those carried by geosynchronous Earth orbiting (GEO) satellites. In general, GEO sensors provide higher temporal and spatial resolution imagery in the visible (VIS) and infrared (IR) ranges of the electromagnetic spectrum. These observations, typically obtained at 0.04° (latitude–longitude grid boxes) every hour or less, are adequate to study cloud and precipitation evolution processes. Many combined precipitation estimation algorithms have been introduced and made operational during the past few years. Although some of these products depend on GEO single infrared channel to track cloud motions or fill the gap of PMW rain estimate [the Climate Prediction Center morphing method (CMORPH; Joyce et al. 2004) and the Tropical Rainfall Measuring Mission Multisatellite Precipitation Analysis (TMPA; Huffman et al. 2007)], others use infrared data as a main rain estimator after being adjusted by PMW estimate. Among the latter class of methods are the passive microwave-calibrated infrared algorithm (PMIR; Kidd et al. 2003), the Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN) algorithm (Hsu et al. 1997; Sorooshian et al. 2000), the Naval Research Laboratory Global Blended-Statistical Precipitation Analysis (NRLgeo; Turk and Miller 2005), and the Self-Calibrating Multivariate Precipitation Retrieval algorithm (SCaMPR; Kuligowski 2002).

Infrared-based algorithms use a variety of techniques to establish a relationship between cloud-top brightness temperature (Tb) and rain rate (RR). Among these techniques are the histogram matching (e.g., Hong et al. 2004; Huffman et al. 2007; Kidd et al. 2003; Manobianco et al. 1994; Todd et al. 2001; Turk et al. 2003) or power-law regression (e.g., Kuligowski 2002; Martin et al. 1990; Vicente et al. 1998). In practice, the Tb–RR relationship is not unique and it varies substantially with time, location, and cloud type, requiring rapid adjustment in time and space and identification of cloud-type systems. Clearly, the limited information conveyed by Tb value at each grid box is insufficient to recognize the corresponding cloud type. As such, some techniques have supplemented satellite gridbox information by extracting a suite of local textural features of clouds using neighboring grid boxes (Sorooshian et al. 2000; Wu et al. 1985) or using multispectral data (Ba and Gruber 2001; Behrangi et al. 2009b; Kurino 1997; among others). Using the self-organizing feature map (SOFM; Kohonen 1984) classification method and multispectral data from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) on board the Meteosat second generation (MSG) satellite, Behrangi et al. (2009a) developed a multispectral precipitation estimation algorithm (PERSIANN-MSA). The algorithm classifies input features into a predetermined number of clusters, calculates mean rain rate for each multidimensional cluster, and extends the commonly used Tb–rain-rate histogram matching technique (e.g., Huffman et al. 2007; Kidd et al. 2003; Todd et al. 2001) to multiple dimensions. As described in Behrangi et al. (2009a), the multidimensional histogram matching technique establishes a relationship between the multidimensional input features and rain rate. A preliminary evaluation of PERSIANN-MSA shows encouraging results (Behrangi et al. 2009a), arguably because of its ability to address two key problematic areas for infrared-only algorithms: 1) screening out no-rain thin clouds (e.g., cirrus) and 2) estimating rain from relatively warm clouds.

Analyzing a number of synoptic types including cold fronts, mesoscale convective systems, warm fronts, and cold-air convection, Cheng et al. (1993) concluded that the performance of rain area delineation using satellite data varies with synoptic type. Therefore, further distinction of different satellite grid boxes can be obtained by supplementing gridbox information with its reference cloud system type. For practical purposes, a group of connected satellite grid boxes called “patch” can be delineated to represent a cloud system. One early example of patch-based algorithm is the Griffith–Woodley technique (GWT; Griffith et al. 1978; Woodley et al. 1980), in which the lifetime of a cloud patch, which they defined as the area where Tb < 253 K, is tracked and maximum cloud area and cloud area in each stage are used to derive the stage’s rainfall volume. The Negri–Adler–Wetzel technique (NAWT, Negri et al. 1984) simplifies GWT to drive instantaneous rain estimates and by that eliminates the need to predetermine maximum cloud area. The convective–stratiform technique (CST; Adler and Negri 1988) is also another example of patch-based methods in which the temperature difference between cloud coldest grid box and the mean temperature of its neighboring grid boxes is used to distinguish between convective and stratiform clouds and then to assign rain rate to each of them. Xu et al. (1999) proposed the cloud-patch analysis (CPA) method to estimate rainfall after removing a large portion of no-rain clouds using infrared imagery and an inductive decision tree. In contrast to most of the previous patching techniques, CPA does not use a fixed threshold of 253 K to delimit clouds. Instead, a pair of microwave rain rate and data is used to delineate rain areas. More recently, Hong et al. (2004) reported a cloud-patch classification system (CCS) labeled PERSIANN-CCS that relies on infrared-only images. PERSIANN-CCS implements image processing and pattern classification techniques to derive rain rate through the following steps: 1) cloud patches are segmented using a fixed threshold 253 K, using the incremental temperature threshold (ITT) method; 2) cloud-patch features, representing cloud-patch coldness, geometry and texture properties are extracted; 3) the extracted features are classified into a number of groups using SOFM; and 4) for each patch class, an individual Tb–RR relationship is established through employment of histogram matching technique and fitting a nonlinear exponential function into the redistributed pixels. PERSIANN-CCS has been found successful in deriving rain rate from cold clouds (Hong et al. 2004). However, the predefined cloud/clear-sky temperature threshold (253 K, similar to GWT) restricts the method’s ability to detect and estimate the intensity of rain from warmer clouds. In addition, the method has difficulties removing no-rain thin cold clouds associated with few synoptic types (e.g., anvils of a convective synoptic).

During daytime hours, the combined use of visible and infrared data has been found effective to alleviate parts of the problem associated with warm rainfall and cold cirrus clouds (Behrangi et al. 2009b; Cheng et al. 1993; Grassotti and Garand 1994; Griffith et al. 1978; Hsu et al. 1999; King et al. 1995; Lovejoy and Austin 1979; O’Sullivan et al. 1990; Tsonis and Isaac 1985). The potential effect of considering visible information is illustrated in Fig. 1, which is constructed using the dataset described in section 2. As shown in Figs. 1a,b, by filtering rain grid boxes with Tb > 253 K, approximately 42% of daytime summer rainfall can be missed over the study region (the U.S. landmass east of 115°W). This is about 30% of the total rain volume determined by radar during the study period (June–August 2006). Part of the missed rainfall, mainly from warm thick clouds, can be captured if reflectance of clouds during daylight is accounted for. Figures 1c,d show that optically thick clouds with albedo >0.4 (Ba and Gruber 2001; Rosenfeld and Lensky 1998) can contain about 77% of the rain area and 82% of daytime rain volume.

In this paper, building on the two distinct PERSIANN-CCS and PERSIANN-MSA algorithms, a comparative visible–infrared rain-rate estimation study is developed to investigate the value of using a visible channel in rain estimation from Geostationary Operational Environmental Satellite (GOES). The combination of the CCS and MSA algorithms allows us to test the utility of visible and infrared images in delineating cloud patches as well as in determining rain rates associated with each grid box. For this purpose, four scenarios are developed and evaluated in which visible or infrared images are used for cloud-patch segmentation, classification, and final high-resolution estimation of rain intensity for each satellite grid box. The best scenario is eventually expected to address drawbacks attributed to infrared-only rain estimation techniques. Input dataset for the study are outlined in section 2. In section 3, the proposed method will be described. In section 4, the scenarios and overall evaluation statistics for the case study along with a single rainfall event–based assessment are reported. Section 5 contains discussions; a summary and conclusions are provided in section 6.

2. Dataset and study area

Three months (June, July, and August 2006) of half-hourly high-resolution (0.04° × 0.04°) GOES-12 VIS (0.65 μm) and IR (10.8 μm) images were collected from the National Oceanic and Atmospheric Administration/National Environmental Satellite, Data, and Information Service (NOAA/NESDIS) Environmental Satellite Processing Center (ESPC). The study is performed over the landmass of the eastern and central United States, east of 115°W. Limiting the western boundary to 115°W reduces the effect of oblique pixels, especially in the northwestern United States. Following previous studies (Cheng et al. 1993; King et al. 1995; Behrangi et al. 2009b), the albedo images are first normalized using inverse cosine of sun zenith angle (SZA). Only grid boxes with SZA < 60° are used in this study to reduce uncertainties associated with albedo normalization during early morning and late afternoon hours (Behrangi et al. 2009b; King et al. 1995).

Hourly accumulated 0.04° latitude–longitude gridded radar rain-rate estimates were obtained from the National Centers for Environmental Prediction (NCEP) Environmental Modeling Center (EMC; Lin and Mitchell 2005). The rain-rate observation was assumed as “uniformly distributed within each hour” to allow for comparison with half-hourly GOES data and a mask representing the effective beam height of 3 km (Maddox et al. 2002) was used to retain only the more reliable radar measurements. Calibration and verification periods were selected by a simple odd–even yearday criterion with odd days chosen for training and model development and even days being retained for evaluation and comparison.

3. Method

As described in section 1, PERSIANN-CCS algorithm includes four key steps, which are cloud segmentation, cloud-patch feature extraction, cloud-patch classification, and rain-rate estimation. PERSIANN-MSA, which is a multispectral gridbox-based approach, furnishes an alternative method for rain-rate estimation through multidimensional histogram matching method described in section 1. Figure 2 is a schematic overview of the major steps involved in the proposed algorithm. Briefly, the algorithm starts with the development–calibration phase (Fig. 2, left) in which the first step is segmenting clouds into a number of predefined cloud patches. The K-means classifier is then used to classify cloud-patch features into clusters representing different cloud types. Subsequently, gridbox-scale features are extracted for each cloud-patch type and the K-mean classifier is applied again to obtain subclasses of finescale classification of cloud grid boxes. The multidimensional histogram matching method is then used to calculate rain rate for each subclass using ground radar rain-rate observations. In the estimation and validation phase (Fig. 2, right), each individual satellite VIS or IR image is similarly processed to segment clouds into patches; extract patch scale features; and, using the cloud-type clusters obtained in the development–calibration phase, assign each patch to the appropriate cloud type. The estimation procedure continues by extracting gridbox-scale features for each cloud type and then assigning each gridbox value to its corresponding subclass using the grid-scale cluster maps, which are also identified during the development–calibration phase. The known rain rate associated with each cluster is then assigned to the grid box. This described procedure is independent of the algorithm’s spectral dimension. In the bispectral application, which is investigated herein, the approach is used to test four different scenarios in which IR and VIS information is used individually or in combination at various stages of the classification and estimation. In this section, the key algorithmic components shown in Fig. 2 are described in detail.

a. Cloud-patch segmentation

Cloud segmentation is a fundamental step in which the object (cloud system here) is first defined for later description and recognition. Both Tb and albedo images are independently used to segment clouds into a number of independent patches using the ITT approach of Hong et al. (2004). The ITT technique was originally applied to the IR imagery to segment clouds colder than 253 K into a number of independent patches (Hong et al. 2004). Without ITT, by implementing a fixed threshold, all connected grid boxes with Tb less than 253 K are segmented into a single large cloud patch and information regarding cloud systems within the large patch is lost. Complete description of the ITT method and its implementation to IR imagery is available in Hong et al. (2004). In brief, the method uses a fixed threshold of 253 K (similar to Griffith et al. 1978; Woodley et al. 1980; Xu et al. 1999) and subdivides cold clouds into number of patches using topographically top-down hierarchical thresholds from cloud-top cold core to cloud warm edge. The major steps are 1) selection of a fixed upper boundary threshold (e.g., 253 K), not only to delineate cloud area but also to obtain a distinct cloud system; 2) locating the local minimum temperatures (seeds) within the cold clouds; and 3) incrementally increasing the temperature threshold for each seed to include neighboring satellite grid boxes until the border of other seeded regions or cloud-free areas are reached. It must be mentioned that, although the method performs well for cold clouds, applying a fixed threshold (253 K) on IR image to discern the initial cloudy region can result in significant elimination of rain-producing warm clouds (Fig. 1).

Availability of visible channel during daytime provides additional information about the thickness of clouds. A number of albedo-based cloud segmentation case studies were examined, through which albedo images were processed using ITT concept to segment cloud patches. A fixed albedo threshold of 0.4 representing lower band for optically thick clouds (e.g., Rosenfeld and Lensky 1998; Ba and Gruber 2001) was used, and seeds were initiated at the maximum albedo spots within the thick clouds. Prior to albedo-based cloud segmentation, a 3 × 3 smoothing (low pass) filter was applied to the albedo image for slight smoothing and noise reduction. Because it moderates the high variances that exist between neighboring grid boxes, the smoothing process appears to result in improved cloud segmentation phase. Overall, using the albedo image, clouds were reasonably segmented into a number of distinct patches. Figure 3 displays an example in which cloud patches (Figs. 3c,d) are derived from brightness temperature and smoothed albedo images (Figs. 3a,b). Region Pa in Fig. 3d represents those patches generated from clouds warmer than 253 K, whereas zone Pt in Fig. 3c includes cold thin patches with albedo less than 0.4. Therefore, cloud segmentation using bispectral observation results in generation of supplementary patches, enabling the identification of warm cloud areas prior to the rain-rate estimation phase.

b. Cloud-patch feature extraction

Clouds are complex three-dimensional structures of water vapor and depending on their type may yield intense, mild, or no precipitation. Cloud types are usually distinguished based on their appearance, vertical extent, and how high in the sky they form. Therefore, for automatic classification of clouds, a number of cloud-patch features need to be extracted from satellite imagery to represent both height and appearance of cloud patches. Because of the adiabatic lapse rate in the atmosphere, a strong relationship exists between cloud-top altitude and temperature. Similar to PERSIANN-CCS, three temperature threshold levels (253, 235, and 220 K) were used to articulate the vertical extent of each individual cloud patch (see Fig. 3e). Using visual inspections and evaluations, three albedo thresholds levels (0.4, 0.55, and 0.65) were identified as appropriate to scale cloud thickness (Fig. 3f). A mature convective patch is expected to run across all three albedo and temperature thresholds and to appear very cold, bright with high local gradient at cloud top. However, a stratus cloud patch, depending on its altitude and thickness, can present different combinations of coldness and reflection intensities with lower standard deviation and local gradient at cloud top. Cross comparison between cloud patches (Fig. 3) and simple classification of cloud types (shown in Fig. 4) illustrates how different threshold levels (Figs. 3e,f) can provide useful insights into identifying cloud types and as a result improve the final classification of clouds. Note that the labels in Figs. 3a,b provide additional examples, which are obtained from their corresponding cloud patches (shown in Figs. 3c,d) in conjunction with the simple cloud-type classification shown in Fig. 4.

Using the aforementioned thresholds and to quantify, improve, and automate the cloud classification process, a number of representative statistical indices was identified for each albedo-based and temperature-based cloud patch (Table 1). Here, feature or input feature refers to any input that is introduced into the classification step. For example, each of the indices in Table 1 is called a feature, and the collection of features that are associated with each cloud patch is called a “vector” of features. Description of the cloud-patch features are provided in appendix A. These features are selected to capture coldness–reflectance, geometry, and image textural properties of cloud patches using the bispectral information from Tb and albedo. Table 2 demonstrates how combination of cloud-patch features can assist to further distinguish between different cloud-patch types described in Fig. 4. As seen in the table, the combination of brightness temperature textural information (e.g., standard deviation and gradient) and that derived from albedo images can further distinguish between cloud-patch types presented in Fig. 4. For example, the mean brightness temperature and reflectance associated with C1 (low-level young convective) and Sl2 (low-level thick stratus) cloud patches have similar values. However, additional textural information such as the standard deviation and gradient, which are generally different, allow for better differentiation between the two cloud-patch types.

c. Cloud-patch classification

Cloud classification techniques using satellite imagery can be divided into supervised and unsupervised. Supervised classification techniques require expert analyst to label sufficient number of training cloud classes before classification is performed. Unsupervised classification does not require expert interference, and classes are obtained based on the utilization of cloud features using a suite of distance and/or similarity metrics. However, to label each class of clouds, an expert analyst is involved through a labor intensive, tedious, and error-prone procedure for both supervised and unsupervised classification techniques. In this study, however, cloud classification is used as an interface between input cloud patches and rain-rate estimation phase. Therefore, with the ultimate objective of automated estimation of rain intensity using unsupervised classification of cloud patches, labeling of the classified patches becomes unnecessary.

The popular unsupervised K-means technique was employed to separately classify the VIS-based (albedo) and IR-based (temperature) cloud patches into 125 predetermined groups (clusters), using the features listed in Table 1. A desirable aspect of the K-means technique, in addition to its simplicity and efficiency, is its rapid convergence. Briefly, K means tries to locate a predefined number of clusters in the input-feature space D in manners that minimizes the cost, which is the sum of the squared Euclidean distance from every point in D to its nearest cluster center. The classic cost (or error) function is described as
i1558-8432-49-5-1015-e1
where x is a point representing an input-feature vector, ck is the center of cluster pk, and n is the number of clusters. Algorithmically, the technique consists of the following steps:
  1. Randomly locate n cluster centers into the input-feature space (initial centroids);
  2. Assign each input-feature vector to the nearest center;
  3. Update the cluster centers as the mean value of the input-feature vectors for each cluster; and
  4. Repeat steps 2 and 3 until the cluster centers do not change.
Although K means have been proven as an effective clustering tool, the performance of the final solution depends largely on the initial set of clusters. The K means are likely to converge to some local optimum, preventing the algorithm from optimizing the objective function [Eq. (1)]. To alleviate this problem, K means were run 5 times with different initial cluster centers to reduce the chance of centers being attracted to local optimums. More information about the K-means technique is available in literature (e.g., Duda and Hart 1973; MacQueen 1967; Everitt 1993; Qiu and Tamhane 2007).

d. Rain-rate estimation

Classification of cloud patches into number of distinct groups makes it possible to establish an individual relationship between grid-scale cloud-top information and observed rain rate within each class of cloud patches. This is an important feature of the algorithm because the distribution of perceptible water content in a cloud is likely to vary not only among different cloud systems but also within the same cloud type at different stages of its life cycle (Cotton and Anthes 1989; Hong et al. 2004). The coldest part of a mature convective cloud system often yields intensive rainfall, whereas a stratus type of cloud may or may not supply any rainfall even at comparable temperatures. Although a fairly good relationship between cloud-top temperature and rain rate is often obtained for deep convective systems (Vicente et al. 1998), in many cases a vast area of anvil cirrus is associated with such a convective system and uncertainties increase in the Tb–rain-rate relationship. Therefore, establishing a Tb–rain-rate relationship within this system may result in false assignment of intense rain rate to the cold anvils with no rain.

Arguably, including a measure of cloud thickness such as albedo information may help to distinguish anvils from convective cores; with extension within each cloud-patch group, albedo and IR data can supplement each other to improve rain-rate estimation. In this study, the relationship between rain-rate and bispectral data was established using the PERSIANN-MSA technique. More specifically, within each cloud-patch group, visible and infrared input features (here, albedo and Tb values for each grid box) are extracted and classified into a number of distinct subgroups; then, for each subgroup, rain-rate values are identified by utilizing the histogram matching method. In this study, 75 distinct subgroups were selected to ensure statistically significant sample size within each subgroup. However, instead of the SOFM classification used in PERSIANN-MSA, the K-means technique was once more incorporated in the present work. The replacement of SOFM with K means facilitates an automated and efficient implementation of PERSIANN-MSA to each of the individual 125 classified cloud-patch clusters described in section 3c. As a result, for each of the 125 cloud-patch types, a unique rain-rate estimator was obtained to identify gridbox rain intensity after being associated to their corresponding subgroup. As will be described in the next section, the supplementary role of albedo information is investigated through derivation of rain intensity as well as through albedo-based cloud segmentation and classification.

4. Case study and results

a. Scenario development

As shown in Table 3, four rain estimation scenarios were developed and the performance of each scenario was evaluated against reference radar rain rate. The first three scenarios are abbreviated by first indicating the data used in the cloud-patch segmentation (IR or VIS) followed by the data used for gridbox-scale classification and rain-rate estimation (IR, or IRandVIS) separated by a slash. The following are brief descriptions of the four scenarios:

  1. Scenario 1 (IR/IR) relies on temperature-only data for both cloud segmentation and rain-rate estimation and is calculated to serve as a reference for comparison of the other bispectral scenarios. Therefore, IR/IR somewhat resembles that of PERSIANN-CCS.
  2. Scenario 2 (IR/IRandVIS) shares the IR-based cloud patches of IR/IR but uses combined albedo and infrared data, with the key objective of improving the identification of cold no-rain cirrus clouds.
  3. Scenario 3 (VIS/IRandVIS) is similar to IR/IRandVIS in the rain estimation phase but uses cloud patches that are segmented and classified based on albedo image, which allows the inclusion of thick warm cloud patches with possible rainfall.
  4. Scenario 4 is a combination scenario (CMB). CMB is developed as an alternative solution to combine VIS/IRandVIS and IR/IRandVIS while attempting to reconcile the two different groups of cloud patches. In other words, the combination was simply obtained by averaging the two bispectral rain-rate estimation fields. Although this approach may alleviate some difficulties associated with preserving a continuous precipitation field, the linkage between computed rain rate and cloud patches is no longer apparent, complicating the post analysis of the results.

b. Statistical evaluation of scenarios

As described in section 2, the dataset is divided into two groups: the first group (odd days) is used for algorithm development and training, whereas the second group (even days) is used for evaluation and comparison. Using the evaluation dataset, high-resolution (0.04° × 0.04° latitude–longitude) rain estimate fields are generated over the study area for all of the four scenarios listed in Table 3. To have common grid boxes for cross comparison of VIS/IR and IR-only scenarios, only those grid boxes with SZA < 60° (daylight time) are collected and used for statistical analysis. It must be mentioned that, in this study, the daytime hours are limited to only 6 h between 0900 and 1500 local solar time (LST) so that 3- and 6-hourly rain rates can be generated and compared. Two groups of statistical indices are utilized to evaluate the results. The categorical indices, from the contingency table, are computed from the binary (0/1 or yes/no) definition of rainfall events as determined by a 0.1 mm h−1 threshold above which a rain event would be considered to have occurred. The calculated indices are equitable threat score (ETS), probability of detection (POD), false-alarm ratio (FAR), and areal bias (BIASa). The second group of statistical indices, quantitative indices, is based on gridbox rain-rate values, which include correlation coefficient (CORR), root-mean-square error (RMSe, and quantitative bias (BIASq). Note that BIASa represents the ratio of satellite-derived rain area over the observed rain area, whereas BIASq represents the ratio using rain volume. Descriptions of the aforementioned statistics are provided in appendix B. Table 4 provides overall 3-h evaluation of the scenarios against radar at a range of spatial resolutions: 0.04°, 0.08°, 0.12°, and 0.24° (latitude–longitude). For each of the statistical indices, except BIASa and BIASq, a performance gain metric is reported, facilitating evaluation of albedo-included scenarios (VIS/IRandVIS, IR/IRandVIS, and CMB) against the reference IR-only scenario (IR/IR). For each statistical index S, the performance gain metric of a given scenario is defined as
i1558-8432-49-5-1015-e2
Whether this index is considered as gain or loss depends on whether an increase or decrease of the value of performance measure is better or worse. For example, consider FAR and POD; the former is said to have gained if Eq. (2) yielded a negative number and the latter gains when Eq. (2) produces a positive value.

The results shown in Table 4 demonstrate that including albedo results in significant improvement in both categorical and quantitative statistical indices in all different spatial scales. For the 0.04° bispectral scenarios R/IRandVIS, VIS/IRandVIS, and CMB, CORR gains are 20.1%, 17.6%, and 26% and ETS gains are 40.5%, 62.6%, and 65.9%, respectively. ETS scores allow for equitable cross comparison (Schaefer 1990) and are less sensitive to being “played” by systematic overestimation or underestimation. Theoretically and as discussed in the introduction, thick clouds contain both convective and stratiform rain areas. Therefore, unlike IR-based cloud-patch scenarios (IR/IR and IR/IRandVIS), VIS/IRandVIS should contain almost all of the rain areas and account for both temperature and albedo in discerning gridbox rain-rate estimates. This explains why VIS/IRandVIS outperforms both IR/IR and IR/IRandVIS scenarios in delineating rain areas. Although IR/IR and IR/IRandVIS share the same cloud patches, IR/IRandVIS shows considerable improvements in POD, FAR, and ETS. However, IR/IRandVIS is associated with lower BIASa, meaning that the rain area observed by IR/IRandVIS is smaller than that of IR/IR. This can be attributed to the two-stage estimation procedure. First, during the IR-based cloud segmentation, warm rains are excluded. In the subsequent step (rain estimation from gridbox classification), thin cold clouds are not mistakenly recognized as rain area. In other words, IR/IRandVIS prevents assigning large false rains to remaining cold grid boxes, which results in obtaining the lowest FAR among all other scenarios. Note that IR/IRandVIS also shows higher POD than IR/IR because of higher correct detection of rain grid boxes in IR/IRandVIS. IR/IRandVIS also outperforms IR/IR by demonstrating higher CORR (20.1%–34.5% gain) and lower RMSE (from −6.5% to −12.9%; reduction in value is gain) and comparable BIASq across all different spatial resolutions. As shown in Table 4, although CMB does not show considerable improvement over VIS/IRandVIS for rain detection purpose, it brings about almost the best quantitative statistics among all other scenarios in different space scales. Analysis of a number of individual storm events suggests that CMB helps to moderate overestimated rain rates obtained from either thick cirrus clouds or relatively warm patches with extremely high albedo.

Table 5 presents the statistical measurements for 6-h rain rates. The results are consistent with the 3-h statistics reported in Table 4, confirming that VIS/IRandVIS and CMB are effective scenarios across different temporal and spatial resolutions. CMB consistently shows the best gains for ETS, CORR, and RMSE with the value of 49.5%, 27.6%, and −13.1%, respectively, at 6-h 0.24° resolution. IR/IRandVIS shows the best gain for FAR with maximum gain of −52.2% (negative sign represents FAR reduction) across different resolutions. All scenarios, however, underestimate both areal extent and volume of rainfall when compared to ground-based radar observations. Part of this underestimation can be attributed to early removal of warm (Tb > 253 K) or dim (albedo < 0.4) grid boxes during cloud segmentation stage, as explained in section 3a and shown in Fig. 1.

Figure 5 provides a cross comparison of the statistical indices of all four scenarios using 30-day evaluation of 6-h (0900–1500 LST), 0.04° resolution rain estimates over the whole study area. The categorical and quantitative statistical indices are shown in the left- and right-side columns of Fig. 5, respectively. Although VIS/IRandVIS and CMB show very similar rain detection skills, both significantly and consistently exhibit higher ETS, POD, and BIASa skills compared to IR/IRandVIS and IR/IR scenarios. As shown in Fig. 4e, IR/IRandVIS shows the best FAR and consistently performs better than IR/IR in terms of ETS and POD. However, given that a perfect BIASa score is 1, IR/IRandVIS displays the worst BIASa value among all other scenarios. It is important to recognize that a perfect BIASa score does not necessarily guarantee a perfect match of rain/no-rain pixels between observed and predicted fields. Figure 5b implies that CMB has the best correlation with radar rain rates, followed by VIS/IRandVIS. Unlike CMB, VIS/IRandVIS does not show consistently superior RMSE (Fig. 5d) among all other cases. However, comparison of VIS/IRandVIS with CMB suggests that both scenarios perform almost comparably. The poorest CORR and RMSE are both attributed to IR/IR, followed by IR/IRandVIS. This indicates that the IR/IR scenario can be significantly improved by incorporating albedo information to cloud-patch segmentation/classification phase, rain-rate estimation phase, or both. Figure 5f shows that none of the scenarios consistently outperforms all others with respect to bias. IR/IRandVIS shows overall lowest BIASq, whereas VIS/IRandVIS presents overall larger BIASq than other scenarios.

c. Event-scale analysis

To exemplify the analysis of the four described scenarios at event scale, a rain event at 1615 UTC 24 August 2006 over Arizona is shown in Fig. 6. Instantaneous maps of IR brightness temperature and albedo (Figs. 6a,b) in conjunction with radar rain-rate map (Fig. 6c) show the presence of a mesoscale convective system in the center of the image, coupled with some warm rainfall at the top-right corner of the studied area. Figure 6d shows cloud patches segmented through implementation of the ITT approach on the IR brightness temperature image. Albedo-based cloud patches are also shown in Fig. 6g, which were obtained by applying ITT approach to the smoothed albedo field (Fig. 6e). Rain-rate maps of IR/IR, IR/IRandVIS, and VIS/IRandVIS scenarios are shown in Figs. 6f,h,i below their corresponding cloud-patch maps. Finally, the estimated rain-rate map from CMB is displayed in Fig. 6j. Color-scale bars for the IR brightness temperature, albedo, and rain-rate maps are collected in the center of the right-side column.

As shown in Fig. 6d, the implementation of IR-based cloud segmentation screens out all grid boxes with Tb > 253 K that may include rainfall (see zone A in Figs. 6a,c). This results in relatively poor performance of IR/IRandVIS and IR/IR scenarios in terms of their ability to capture the observed rain areal extent. Visual comparison of IR/IRandVIS (Fig. 6h), IR/IR (Fig. 6f), and radar rain-rate (Fig. 6c) maps in addition to the suite of evaluation statistics (reported in Table 6) indicate that IR/IRandVIS substantially performs better than IR/IR in terms of locating rain areas. Relative to IR/IR, more than 30% gain in ETS, 29% gain in POD, and a noticeable improvement in BIASa are obtained by using bispectral information in the rain estimation phase (IR/IRandVIS), although FAR does not show any significant gain. Albedo-based segmentation (VIS/IRandVIS), on the other hand, substantially scores better than IR/IRandVIS and IR/IR with more than 41% and 53% gains in ETS and POD, respectively. VIS/IRandVIS also extends the detected rain area to a size comparable to that of the ground radar observation (BIASa = 0.89). However, by detecting larger rain areas, the albedo-based segmentation resulted in higher FAR than Tb-based approached, with almost 25% loss in skill compared to IR/IR. As expected, most of the rain area is captured by VIS/IRandVIS; thus, the combination of VIS/IRandVIS and IR/IRandVIS does not show significant change in rain detection scores. Although FAR for CMB is increased to some extent (29% loss relative to IR/IR), with about 49% gain in ETS, 64% gain in POD, and BIASa = 0.96, it can be argued that the combined alternative serves as the best rain detector.

Figure 6 and Table 6 also demonstrate that CMB results in the best quantitative statistical indices with 25.3% gain in CORR, 8.7% gain in RMSE, and a fairly reasonable capture of the total volume of rainfall (BIASq = 1.05). Although VIS/IRandVIS and IR/IRandVIS do not show any significant improvement in RMSE, both present substantial gains in CORR and capturing the rainfall volume. The improved volumetric bias (BIASq) for VIS/IRandVIS (1.18) and IR/IRandVIS (0.91), compared to the traditional Tb-only approach (0.65), indicates that overall albedo is also effective in supplementing infrared-only data to capture a more realistic total amount in addition to distribution and areal extent of the rainfall.

5. Discussion

The method presented in this paper benefits from infrared and visible data not only for the purpose of cloud segmentation and classification but also to generate more accurate rainfall rates using a combination of the two. The bispectral rain rate is obtained using PERSIANN-MSA; therefore, it is extensible to multispectral data. In other words, within each cloud patch, it is possible to extract multispectral information for each grid box and apply PERSIANN-MSA to extend the histogram matching technique to multiple dimensions. As shown in Behrangi et al. (2009a), multispectral information, which is increasingly becoming available, can supplement infrared-only data during both daytime and nighttime.

Although incorporating the visible channel is promising, there are issues that need to be considered. First, snow on the ground may pose a limitation during the cloud-patch-type identification and rain-rate estimation steps because it can be confused with thick clouds. Second, the albedo normalization process used in this study is simple, and it assumes that the reflected radiation field is isotropic; thus, it is subject to errors. In addition, normalization performance using the inverse cosine of SZA deteriorates during the early morning and late afternoon periods, as discussed in Behrangi et al. (2009b), which limits the applicability of the method to grid boxes where SZA < 60°, as used in this study. A more rigorous approach of directly retrieving the cloud microphysical properties from reflected solar radiation such as that presented in Nakajima and King (1990) and Nakajima et al. (1991) can be investigated. Third, cloud reflectance is only available during daylight hours, albeit for longer duration during Northern Hemisphere summertime. As such, bispectral algorithms are limited to a few hours in many regions of the world. Finally, despite the fact that visible data are almost globally available from constellation of GEO satellites, no serious attempt has been made to collect and process the data for users outside operational agencies as is the case of IR (∼11 μm) data that were made available, at global scale, to the research community through the efforts of the Climate Prediction Center (CPC; Janowiak et al. 2001).

Despite some of the arguments in the literature against incorporating visible channel into the operational precipitation algorithms, one should note that, depending on location and time of year, significant amount of rainfall events may occur during the daylight period. In many regions of the world, rainfall volume and intensity peaks during daytime and even in some cases during morning and early afternoon (Hong et al. 2005; Sorooshian et al. 2002; Tian et al. 2007; Yang and Slingo 2001). However, there remains a question as to whether the visible–infrared rain estimates can serve different scientific communities. On one hand, climatologists are more interested in the quantitative and algorithmic consistency of the final precipitation product for both daytime and nighttime hours to investigate long-term rainfall trends. Accordingly, multispectral precipitation products that use VIS bands are not necessarily adequate for the development of long-term precipitation climatology. Operational hydrologists and flood forecasters, on the other hand, are very interested in improving the accuracy of real-time rain-rate estimates and the ability to accurately identify the areal extent of precipitation at any time. As such, it is likely that they will welcome any improvement, whether it is at daytime, nighttime, or both.

6. Summary and conclusions

In this paper, two of our previously developed algorithms, the cloud-patch-based PERSIANN-CCS and the gridbox-based PERSIANN-MSA, were integrated. The objective of this integrated method is to facilitate the incorporation of multispectral information into the cloud segmentation–classification and rain estimation phases of PERSIANN-CCS when coupled with the multispectral technique of PERSIANN-MSA.

A bispectral experiment was performed in which one reference infrared-only and three different bispectral (visible–infrared) rain estimation scenarios were compared. The goal of this comparison was to address existing drawbacks of infrared-only techniques, which are related to their inability to (i) estimate warm rainfall and (ii) screen out no-rain thin cirrus clouds. The first shortcoming may result in significant underestimation of the total volume of rainfall, whereas the later may terminate assigning rain to places with no rain. The proposed approach combines the benefit of multispectral strategies and the ability of cloud-patch-based algorithms to consider the association of gridbox rain rates to their corresponding cloud synoptic type.

Of the four scenarios, the baseline infrared-only scenario (IR/IR) resembles that of the PERSIANN-CCS technique, in which a fixed threshold 253 K is used to isolate rain areas, segment clouds into number of distinct cloud patches, classify the patches into a number of groups, and subsequently estimate rain rate by establishing an IR brightness temperature–rain-rate relationship for each cloud-patch class using observed rain rate. This fixed temperature threshold was shown to prevent IR-only algorithms from capturing warm rainfalls. To couple infrared data with albedo during daytime, three scenarios were investigated. In the first scenario, a bispectral approach was developed that employs a temperature-based cloud segmentation scheme with threshold 253 K (as in PERSIANN-CCS) followed by a bispectral rain-rate estimation from each individual cloud-patch class (based on PERSIANN-MSA). This approach was termed IR/IRandVIS. The second bispectral scenario (VIS/IRandVIS) also uses bispectral data for rain-rate estimation but segments cloud patches using a smoothed image of cloud albedo. Finally, the third bispectral scenario (CMB) is obtained by combining IR/IRandVIS and VIS/IRandVIS using arithmetic averaging.

Using 3 months (June–August 2006) of high-resolution visible–infrared and radar rain-rate data over the eastern and central conterminous United States, the scenarios were trained utilizing odd-day data and subsequently evaluated with data from even days. The comparison included both categorical and quantitative statistical scores over a range of temporal and spatial resolution. The results indicate that overall CMB performs the best with respect to identifying rain area as well as accurate estimation of rain intensity. VIS/IRandVIS and IR/IRandVIS are second and third, with IR/IR (temperature only) yielding the least favorable performance measures. Improvement of CMB over VIS/IRandVIS is found marginal, which suggests that segmentation of clouds using their reflection intensity is effective in expanding rain areas to include warm rainfall prior to the rain-rate estimation phase. In addition, albedo information supplements infrared-only data to refine cloud-patch classes and establish more robust rain-rate estimates for each cloud-patch class.

Acknowledgments

Partial financial support is made available from NASA Earth and Space Science Fellowship (NESSF) Award (NNX08AU78H), NASA-NEWS (Grant NNX06AF93G), NOAA/NESDIS GOES-R Program Office (GPO), and NSF STC for Sustainability of Semi-Arid Hydrology and Riparian Areas (SAHRA; Grant EAR-9876800) programs. The authors thank Mr. Dan Braithwaite for his technical assistance.

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APPENDIX A

Cloud-Patch Feature Description

For a cloud patch P with gridbox brightness temperature T(x, y), albedo A(x, y), and total gridbox count N, the cloud-patch features listed in Table 1 are described as follows:

  1. Minimum temperature (Tmin):
    i1558-8432-49-5-1015-eqa1
  2. Maximum albedo (Amax):
    i1558-8432-49-5-1015-eqa2
  3. Mean temperature (Tmean):
    i1558-8432-49-5-1015-eqa3
  4. Mean albedo (Amean):
    i1558-8432-49-5-1015-eqa4
  5. Cloud-patch area (AREA):
    i1558-8432-49-5-1015-eqa5
  6. Slope parameter at Tmin (SMNT):, where Ωc5 is a window size of 5 × 5 grid boxes centered on grid box r (corresponding with Amax) and is the number of grid boxes within Ωc5. Note that SMNT is similar to the slope parameter calculated in CST (Adler and Negri 1988) to remove no-rain cirrus.
  7. Slope parameter at Amax (SMXA):, where Ωr5 is a window size of 5 × 5 grid boxes centered on grid box r (corresponding with Amax). is number of grid boxes within Ωr5.
  8. Standard deviation of cloud-patch temperature (STDT):
    i1558-8432-49-5-1015-eqa6
  9. Mean value of local standard deviations of cloud-patch temperature :
    i1558-8432-49-5-1015-eqa7
    where STDT5 is the standard deviation of cloud-top temperature within window size of 5 × 5 grid boxes centered on grid box i.
  10. Standard deviation of local standard deviations of cloud-patch temperature (STDT5):
    i1558-8432-49-5-1015-eqa8

APPENDIX B

Definition of Statistical Indices Used in this Study

a Categorical statistics using the contingency table (Fig. B1) and by identifying binary (0/1 or yes/no) rainfall events

  • Probability of detection (POD) = H/(H + M);
  • False-alarm ratio (FAR) = F/(H + F);
  • Areal bias (BIASa) = (H + F)/(H + M);
  • Equitable threat score (ETS) = (H − hitsrandom)/(H + M + F − hitsrandom); and
  • hitsrandom = [(H + M)(H + F)]/(H + M + F + Z).

b Qualitative statistics, which are obtained using observed (RRobs) and estimated (RRest) rain rates

where N is the total number of observed and estimated rain pairs.

Fig. 1.
Fig. 1.

Effect of Tb and albedo thresholds on the capture of daytime rain area and rain volume during the summer of 2006 over central and eastern conterminous United States: The numbers next to the dashed threshold lines represent the percentages of missed–underestimated rain area and volume. The numbers are obtained after implementation of the two previously suggested thresholds of 253 K and 0.4 on a pool of high-resolution bispectral grid boxes with RR > 0.1 mm h−1. Corresponding RR data are obtained from ground radar observation: (a) relative frequency distributions of Tb under rain condition, (b) distribution of normalized rain volume with respect to the corresponding Tb value, (c) relative frequency distributions of albedo under rain condition, and (d) distribution of normalized rain volume with respect to the corresponding albedo value.

Citation: Journal of Applied Meteorology and Climatology 49, 5; 10.1175/2009JAMC2291.1

Fig. 2.
Fig. 2.

Schematic overview of the algorithm development–calibration and precipitation estimation steps.

Citation: Journal of Applied Meteorology and Climatology 49, 5; 10.1175/2009JAMC2291.1

Fig. 3.
Fig. 3.

Demonstration of cloud patches and different threshold layers for an event at 1915 UTC 6 Jul 2006: (a) map of IR Tb, (b) map of smoothed albedo, (c) IR temperature-based cloud patches, (d) albedo-based cloud patches, (e) IR temperature threshold layers, and (f) albedo threshold layers. Cloud-type labels in (a) and (b) are obtained through comparison with Fig. 4. The zones Pt and Pa, shown in (c) and (d) are examples of patches captured by one cloud-patch segmentation approach and not by the other.

Citation: Journal of Applied Meteorology and Climatology 49, 5; 10.1175/2009JAMC2291.1

Fig. 4.
Fig. 4.

Schematic representation of a simple cloud classification scheme using different layers of cloud temperature–height and reflectance.

Citation: Journal of Applied Meteorology and Climatology 49, 5; 10.1175/2009JAMC2291.1

Fig. 5.
Fig. 5.

Evaluation statistics for all four scenarios using 30 days of 6-h (0900–1500 LST) high-resolution (4 km) RR over the whole study area: (left) categorical statistics including (a) ETS, (c) POD, (e) FAR, and (g) BIASa and (right) quantitative statistics including (b) CORR, (d) RMSE, and (f) BIASq. Note that perfect score for both BIASa and BIASq is 1.

Citation: Journal of Applied Meteorology and Climatology 49, 5; 10.1175/2009JAMC2291.1

Fig. 6.
Fig. 6.

Visual assessment of performances of the studied scenarios using a rain event at 1615 UTC 24 Aug 2006 over Arizona: (a) IR Tb (K), (b) normalized albedo, (c) radar RR, (d) IR-based cloud patches, (e) smoothed albedo image prior to cloud segmentation, (f) RR estimate from scenario IR/IR, (g) albedo-based cloud segmentation, (h) RR estimate from scenario IR/IRandVIS, (i) RR estimate from scenario VIS/IRandVIS, and (j) RR estimate from scenario CMB. Note that columns are associated with (left) IR-based and (middle) albedo-based cloud patches.

Citation: Journal of Applied Meteorology and Climatology 49, 5; 10.1175/2009JAMC2291.1

i1558-8432-49-5-1015-fb01

Fig. B1. Visual representation of the contingency table.

Citation: Journal of Applied Meteorology and Climatology 49, 5; 10.1175/2009JAMC2291.1

Table 1.

Input features extracted for temperature- and albedo-based cloud patches.

Table 1.
Table 2.

Simple demonstration of how cloud-patch features can describe differences between cloud-patch types in various elevations and thicknesses, where H, L, and M represent high, middle, and low values, respectively, for the different cloud types (e.g., C1, C2, C3, Sh1, Sm1, etc.) described in Fig. 4.

Table 2.
Table 3.

Description of the developed scenarios used for evaluation and comparison.

Table 3.
Table 4.

Overall 3-h statistics in a range of space resolution: note that reduction in value of FAR and RMSE is gain.

Table 4.
Table 5.

Overall 6-h statistics in a range of space resolution: note that reduction in value of FAR and RMSE is gain.

Table 5.
Table 6.

Statistics for the event-scale case study at 1615 UTC 24 Aug 2006 over Arizona, as shown in Fig. 6: note that reduction in value of FAR and RMSE is gain.

Table 6.
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