This paper describes and evaluates a satellite rainfall estimation technique that combines infrared and lightning information to estimate precipitation in deep convective systems. The algorithm is developed and tested using seven years (2002–08) of TRMM measurements over the southern United States during the warm season. Lightning information is coupled with a modified IR-based convective–stratiform technique (CST) and produces a lightning-enhanced CST (CSTL). Both the CST and CSTL are then applied to the training (2002–04) and independent (2005–08) datasets. In general, this study shows significant improvement over the IR rainfall estimates (rain area, intensity, and volume) by adding lightning information. The CST and CSTL display critical skill in estimating warm‐season precipitation and the performance is very stable. The CST can generally identify the heavy (convective) and light rain regions, while CSTL further identifies convective areas that are missed by CST and removes convective cores that are incorrectly defined by CST. Specifically, the CSTL improves the convective cell detection by 5% and reduces the convective false alarm rate by more than 30%. Similarly, CSTL substantially improves the CST in the overall estimate of instantaneous rainfall rates. For example, when compared with passive microwave estimates, CSTL increases the correlation coefficient by 30%, reduces the bias by 50%, and reduces RMSE by 25%. Both CST and CSTL reproduce the rain area and volume fairly accurately over a region, although both techniques show some degree of overestimation relative to radar estimates.
The Geostationary Operational Environmental Satellite R series (GOES-R, to be launched in 2015; Gurka et al. 2006) will carry an Advanced Baseline Imager (Schmit et al. 2005) and the first-ever Geostationary Lightning Mapper (GLM; Christian 2008). GLM is modeled after the Tropical Rainfall Measuring Mission (TRMM) Lightning Imaging Sensor (Christian 1999). Geostationary satellite rainfall estimates (based mostly on infrared channels) are comparable or even superior to rain gauge observations, ground radar measurements, and orbital satellite passive microwave retrievals, in terms of high spatial and temporal resolution, continuous monitoring, and broad areal coverage (Vicente et al. 1998; Kuligowski 2002). However, infrared (IR)-based rainfall retrieval techniques are limited by the indirect and nonphysical relationships between cloud-top temperature and surface rainfall (Kidd et al. 2003; Joyce et al. 2004). Many studies suggest lightning information to be a complementary and additional (to the IR) factor in estimating convective system rainfall, because of its physical association with convection intensity and cloud microphysics (Tapia et al. 1998; Grecu et al. 2000; Morales and Anagnostou 2003; Chronis et al. 2004; Wang et al. 2012; Xu et al. 2013). Xu et al. (2013) have carefully examined relationships among lightning, convective rainfall, and clouds, on both the convective storm scale (10–1000 km) and satellite pixel scale (5–20 km) and provide a strong basis for applying lightning information in improving IR rainfall estimates. This current study builds on Xu et al. (2013) by using the lightning-rainfall relations from that paper to develop and test a lightning-enhanced IR rainfall estimation technique.
Most IR-based techniques employ empirical regressions to derive surface rainfall rates from cloud-top brightness temperatures (Tb; Arkin 1979; Negri and Adler 1981; Arkin and Meisner 1987; Griffith et al. 1978; Scofield 1987; Adler and Negri 1988; Goodman et al. 1994; Kuligowski 2002). Although some IR techniques consider additional factors (e.g., cloud growth and cloud-top structure; Adler and Negri 1988; Vicente et al. 1998), combine multiple spectral channels (Sorooshian et al. 2000; Ba and Gruber 2001; Kuligowski 2002), or add microwave calibrators (Kuligowski 2002), they are still highly limited by the ambiguous relationship between cloud-top temperature and surface rainfall. As a result, IR techniques frequently underestimate rainfall at the early stage of convection and overestimate rainfall after the system matures, falsely treating thick cirrus clouds or cloud anvils as active convection, and miss convective cores under large uniform cold cloud shields or sheared cloud tops (Adler and Negri 1988; Vicente et al. 1998; Xu et al. 2013). Lightning information may help to resolve these issues to some extent. In fact, there are close relationships between lightning activity and convective precipitation (Soula and Chauzy 2001; Seity et al. 2001; Sheridan et al. 1997; Petersen and Rutledge 1998; Soriano et al. 2001; Xu et al. 2010, 2013; Wang et al. 2012). Xu et al. (2013) explicitly illustrate that lightning information can be an aid to identify convective cores and remove false alarms of heavy rainfall, at least on the convective storm scale.
Previous rainfall retrieval studies have demonstrated lightning information as having a great potential in improving the estimation of convective rainfall (Tapia et al. 1998; Grecu et al. 2000; Morales and Anagnostou 2003; Chronis et al. 2004). Tapia et al. (1998) designed a simple model using the mean rainfall–lightning ratio (RLR) in Florida to derive rainfall rate from cloud-to-ground (CG) lightning flash rates. This technique is limited by the fact that RLR can vary by a factor of 100 at any given location and by a factor of 1000 between different locations or rainfall regimes (Zipser 1994; Petersen and Rutledge 1998). Grecu et al. (2000) combine both CG lightning and IR information for rainfall estimation. They use lightning clusters to identify convective areas and assign rainfall rate based on a regression relationship between convective rainfall and lightning flash rate–IR brightness temperature. Morales and Anagnostou (2003) and Chronis et al. (2004) combine lightning and IR measurements on the basis of cloud features (e.g., the 255-K isotherm) in a more comprehensive way. All of these IR–lightning combined techniques indicate the value of the lightning information but use ground-based lightning information, which is limited to CG lightning, and are based on relatively small samples in developing and testing the algorithm. This study employs total lightning information and is based on large samples. There are several benefits of using total lightning data versus using CG-only data. First of all, intracloud flashes (ICs) have been reported to be an excellent surrogate for convective vigor and strengthening updraft within severe continental storms (MacGorman et al. 1989; Lang and Rutledge 2002; Wiens et al. 2005; Fierro et al. 2006; Schultz et al. 2011), while CG information has been found to be mostly indicative of reflectivity core descent, and hence the collapse of an updraft (Reap and MacGorman 1989; MacGorman and Nielsen 1991; Carey and Rutledge 2000; Lang et al. 2000). Typically, IC flash amplitude and peak current are on average about an order of magnitude smaller than typical CG return strokes, making them essentially “undetectable” by most ground-based global very low frequency systems except for intense in-cloud discharges such as narrow bipolar events (Jacobson et al. 1999; Suszcynsky and Heavner 2003; Jacobson and Heavner 2005). Furthermore, the IC:CG ratio has been shown to vary from 2:1 in average thunderstorms to as much as 10:1 in severe convective cells (MacGorman et al. 1989; Boccippio et al. 2001) or more than 100:1 in some tornadic supercells (McCaul et al. 2002); thus, ICs cover a larger area and so provide better information on storm coverage than CGs.
This study aims to develop and evaluate an IR–lightning combined rainfall estimation algorithm using spaceborne lightning and IR measurements from the Tropical Rainfall Measuring Mission for potential application with GOES-R measurements. In general, we couple lightning information into our modified IR-based convective–stratiform technique (CST; Adler and Negri 1988) and develop a lightning-enhanced CST (CSTL) algorithm. A new version of the CST is developed based on statistics derived from three warm seasons (2002–04) of TRMM measurements. The CST defines convective and stratiform precipitation types and assigns rain rate as a function of IR Tb. In the CSTL, lightning information is coupled into the technique to correct the convective areas that are missed or falsely defined by CST. Different from the CST, the CSTL assigns rainfall rates as a function of both IR and lightning density for convective areas. Finally, CST and CSTL estimates are evaluated for both dependent (2002–04) and independent (2005–08) periods using TRMM rainfall retrievals as validation. In this study, lightning information truly stands for total lightning data. The TRMM Lightning Imaging Sensor has a nadir detection efficiency of 70%–90%, a false alarm rate of <10%, and geolocation accuracy of ~5 km in detecting total lightning flashes.
2. Data and methodology
a. TRMM dataset
This study applies three years (2002–04) of TRMM measurements to develop and tune an IR–lightning combined rainfall algorithm. We then use both the training (2002–04) and an independent (2005–08) dataset of TRMM rainfall retrievals to evaluate this particular technique. To be fairly evaluated by the independent data (4 yr), both datasets are selected to be after the TRMM orbit altitude boost in 2001. Our interests in this study focus on the warm‐season (May–August) precipitation over the southern continental United States (25°–35°N, 80°–120°W). The dataset is further constrained by the criterion of at least five lightning flashes within an 800 km × 800 km box centered at a TRMM overpass. By this method, a total of 1427 and 2009 TRMM snapshots (800 km × 800 km) are selected from the warm seasons of 2002–04 and 2005–08, respectively. The algorithm is then applied to these 800 km × 800 km TRMM snapshots. Sample sizes of measurements from different sensors are listed in Table 1.
The TRMM version‐7 dataset is used in this study. TRMM measurements are from four instruments (Kummerow et al. 1998), including the precipitation radar (PR), TRMM Microwave Imager (TMI), Lightning Image Sensor (LIS; Christian 1999), and Visible and IR Scanner (VIRS). The PR provides three-dimensional storm information of hydrometeors (radar reflectivity) at approximately 5-km horizontal and 250-m vertical resolution. In this study, we mainly use PR-based convective/stratiform rainfall separation (2A23; Kozu et al. 2001; Awaka et al. 2009) and rainfall rates (2A25) (Iguchi et al. 2000, 2009). In addition, rainfall estimates from TMI (2A12; Kummerow et al. 2001; Gopalan et al. 2010) are also used.
The VIRS is a five-channel imaging spectroradiometer scanning the earth through a 720-km swath with 2.11–3.02-km footprints (Kummerow et al. 1998). This study applies brightness temperatures from the 10.8-μm window channel to develop the IR-based rainfall estimation technique. The LIS is an optical sensor, which detects total lightning (intracloud and cloud-to-ground lightning). LIS monitors total lightning activity in a 600 × 600 km2 area during a period between 40 and 90 s with a footprint of ~5 km and temporal resolution of 2 ms (Christian 1999). The LIS algorithm separates lightning events (resolution at 5 km and 2 ms) with strong irradiance from the background and defines lightning flashes as clusters of adjacent events that occur within 330 ms. LIS detects 70%–90% of all lightning flashes within its field of view (FOV). The GOES-R GLM is modeled after TRMM LIS and is thus very similar to LIS, except that GLM is a staring sensor with a broad FOV (13 000 × 13 000 km2). GLM’s scheduled resolution will range between 8 and 12 km over the United States with detection efficiency for total lightning flashes of approximately 70%–90%.
b. Algorithm characteristics
Two major steps are involved in this algorithm development: the first step is to develop an IR-only rainfall estimation technique while the second step is to couple lightning information into that IR-based algorithm. The convective–stratiform technique (Adler and Negri 1988) is an IR-based rainfall estimation technique that has been applied to geostationary data. Because the CST already separately estimates convective core rainfall and anvil stratiform rainfall, it is a good candidate for the base algorithm, since the lightning information is meant to improve only the convective rain estimation. The flowchart of the algorithms is given in Fig. 1. First of all, we apply a version of the IR-based CST, with parameters determined from three years of TRMM VIRS IR data and PR and TMI rain retrievals. The CST convective portion (second column in Fig. 1) includes finding local minima in the Tb field (Tmin), conducting a slope test (Tb difference between the Tmin and surrounding points) on identified Tmin for final decision of location of convective cores, defining the convective area (as a function of Tmin and centered on the Tmin location), and assigning the convective rain rate (also as a function of Tmin over the convective area).
Lightning information is then combined with the IR-based CST to develop a lightning-enhanced CST (third column in Fig. 1). Lightning information is used to confirm or eliminate IR-based convective cores from Tmin features that already passed the slope test, identify convective areas from lightning flash rate features, even if no IR Tmin is collocated with the lightning, and assign convective rain rate (as a function of both Tmin and lightning flash density). Stratiform rain areas are determined by a background or mode Tb (Tmode) in the anvil, which is close in value to the tropopause temperature (Adler and Negri 1988). Therefore, the stratiform rain areas are similar for both CST and CSTL (first column in Fig. 1). In the order of defining raining areas, convective core areas take precedence over stratiform areas. Any convective area defined by the IR data that fails to pass the lightning test will go through the stratiform test again. Therefore, if an IR-defined convective core is eliminated by the lightning test but reaches the stratiform threshold, it will be reassigned as stratiform. Otherwise, the IR-based convective core area will be assigned as a no-rain area. Finally, the stratiform areas are assigned a median stratiform rain rate (~2.5 mm h−1) calculated from the training dataset. It should be noted that all the functions used in CST and CSTL are empirically defined and tuned by the training dataset used in this study.
c. Functions and parameters applied in the algorithm
First of all, the CST identifies local minima (Tmin) of Tb. These Tmin points are considered as the center points of potential convective cores. Certain empirical relationships are derived from the training dataset and used as part of the CST and CSTL. These functions include the slope test and relations between convective area and Tmin, convective rain rate and Tmin, stratiform rain rate and Tb, and convective rain rate and lightning. They are specifically defined as follows:
A slope function is defined as a function that linearly discriminates convective and nonconvective cores through linear discriminant analysis (Fig. 2a). A slope is defined as the difference between the local minimum of Tb (Tmin) and the mean Tb of the surrounding pixels within a 10-km radius [similar to Adler and Negri (1988)]. Convective cores are defined as Tmin cores that have at least two PR-defined convective pixels located within 10-km radius, while nonconvective cores have no PR convective pixels within that distance.
Convective area and rain rate over that area are further connected to Tmin, and finally derived from the regression of Tmin (Figs. 3a,b). The convective area is derived as the total number of PR convective pixels that are within a 25-km radius of the Tmin location (Fig. 3a). On the other hand, the convective rain rate of each pixel within the convective core area is derived from the relationship between PR maximum rain rate of the convective core and Tmin (Fig. 3b).
The stratiform rainfall area is defined by the background anvil stratiform threshold temperature (or Tmode) of the mature convective systems in the image (Adler and Negri 1988). Tmode has been used previously by Adler et al. (1985) as a background Tb and an indicator of the thick portion of mature anvils where precipitation is present. Tmode is calculated for each Tmin with slope is less than or equal to 4 K, since most Tmin reaching this slope criterion are mature thunderstorms found embedded in extensive cirrus background (Adler et al. 1985). Specifically, here this background Tb, or Tmode, is defined as the weighted mean of Tb surrounding ~80 km of the Tmin: Tmode = E[W(i) × Tb(i)], where E[⋅] is the expected value and the weight W(i) is the number of IR pixels at Tb(i). The 80-km surrounding area is selected because this area is large enough to obtain a stable statistic, yet small enough to be representative of a particular Tmin point. The final Tmode within the satellite image is derived from the average of all Tmin mode temperatures. The same Tmode temperature is applied to all pixels within a single IR image. Pixels with Tb at and below the Tmode value that have not been assigned a convective rain rate are given a fixed stratiform rain rate. Using the training dataset this value is derived from the PR data as 2.5 mm h−1. Figure 3c shows that the distribution of PR rain rate in these stratiform areas as a function of VIRS Tb is nearly constant, indicating the significance of applying the constant rain rate value over a range of Tb.
For locations with lightning flashes, the convective rain rate is derived from lightning flash density. Based on Xu et al. (2013), there is no clear regression relationship between lightning and the PR-defined rain rate, probably related to location differences between the surface radar echo and lightning locations at fine spatial resolution. This might also be due to efficient autoconversion and/or coalescence (warm rain) processes in storm cells under certain environments. On the other hand, the close correlation between lightning flash density and TMI rain rate is probably due to both the microwave measurements and the lightning occurrence having a physical connection to mixed-phase precipitation microphysics, but with only indirect connections to surface precipitation. Therefore, the TMI rain‐rate estimate is used here to connect with lightning. The passive microwave (TMI) rain cores are better collocated with locations of lightning flash density cores. The rain rate–lightning function is derived from the mean TMI rain rate and lightning flash density within a 10-km radius (Fig. 3d).
All constants in the above empirical functions are based on sensitivity tests, validation, and statistics. For example, multiple tests have been done for choosing a window (including 25-, 50-, 75-, and 100-km radius) to define convective core area. These tests have been applied to the 3-yr training dataset and evaluated by the PR convective area. The validation results show that the 25-km radius window is the best window for this purpose. A 10-km area for lightning area is also chosen in this way. Sensitivity tests have also been done for using a specific lightning density for the restriction of convective core. In this study, a density of two flashes per minute within 10-km radius ends up to be the best proxy. Sensitivity tests show that a five flashes per minute criterion would eliminate 50% of the convective cores and would not allow the algorithm to correctly represent the convective core population or area. We recognize that a true convective core, especially a wide convective core, might be separated into multiple “convective cores” in the CST algorithm. This might make the criterion of lightning density lower for identifying convective cores. Similarly, Xu et al. (2013) showed that the threshold of two flashes per minute restricts 90% of the precipitation cores to be convective cores (having convective elements).
There are two reasons that TMI rain rates are used to derive the relationships between rain rate and lightning in item 4 above. First, our main goal of using lightning is to improve the IR rain estimates up to the accuracy of microwave estimates, as lightning measurements have close relationships with the microwave measurements. If this goal is fulfilled, the IR rain estimates already have benchmark improvements. Second, when the TMI rain rates are used for the lightning–rainfall regression, then it will also be easy to do the validation/calibration by microwave estimates in the future. This is also straightforward, since calibration by passive microwave measurements is proposed for the final version of CSTL that will be applied to GOES-R data.
d. Evaluation methods and definitions
Dependent (2002–04) and independent (2005–08) TRMM PR and TMI estimates are used to evaluate the characteristics and accuracy of the CST and CSTL techniques. Functions and coefficients used in the algorithm are derived from the dependent data. The algorithm is then applied back to the dependent data and further to the independent data. The CST and CSTL are evaluated in terms of convective–stratiform rain identification, instantaneous rain‐rate estimates, and total rain volume. Accuracy statistics of correlation coefficient (CC), bias, and root-mean-square error (RMSE) are calculated. This study also examines contingency score parameters including the probability of detection (POD), false alarm rate (FAR), and critical success index (CSI). Specifically, the success–failure parameters are defined as POD = Nsuccess/(Nsuccess + Nfailure), FAR = Nfalse alarm/(Nsuccess + Nfalse alarm), and CSI = Nsuccess/(Nsuccess + Nfailure + Nfalse alarm).
3. Details of the CST and CSTL algorithms
a. IR-based convective/stratiform technique
The basic idea of the CST is that cloud top above the convective core is usually colder than the surrounding clouds as convective updraft develops and pushes more ice particles to the upper level (Zipser 1977; Houze 1989). As a result, local minima of brightness temperatures (Tmin) can represent the location of convective cores (and therefore heavy precipitation regions) better than assigning rain rate as a function of brightness temperatures through a regression method (the colder the brightness temperature is, the heavier is the rain rate). The CST algorithm first searches for local Tmin cores. Tmin cores are then examined by the slope test. If a Tmin core passes the slope test, it is identified as a convective core.
A function used for the slope test is first defined using the statistics of the training dataset. The slope parameter is defined as the difference between the mean of the Tb values surrounding the Tmin location and the Tmin value itself. This slope value is then compared to whether or not the PR has convective rain identified at that location. The slope function is then defined as a function that linearly discriminates the PR-defined convective and nonconvective Tmin features (cloud) based on VIRS and PR measurements (Fig. 2a). Specifically, this predefined slope function is Y = 0.85(X − 210), where Y is slope and X is Tmin.
If the measured slope value of a Tmin core is larger than the corresponding value in the slope function (Fig. 2a) and absolutely greater than 2 K, then it passes the slope test and is accepted as a location of a convective core; otherwise it fails. Given the sensor sensitivity, noise of the IR brightness field, and oscillation of cloud-top field due to factors such as turbulence, a 2-K gradient seems to be a reasonable lower value. Furthermore, some sensitivity tests have been done for this selection, and 2 K works out to be the lowest required gradient for a convective core using the CST technique. As shown in Fig. 2a, convective and nonconvective (relative to PR) Tmin features generally fall into two groups. These two groups are mainly discriminated at the temperature of 210 K for low-slope Tmin cores (<6 K) and at the temperature of 220 K for high-gradient (>12 K) Tmin cores. The performance of the slope function defined here is quite stable when applied to different years or months in either the training or independent dataset (Fig. 2b), with both the POD and FAR identification of convective cores being relatively invariant month by month. In addition, the detection of convective cores is significantly high (POD = 0.6–0.8), while the false alarm is at a reasonable level (FAR = 0.3–0.5). However, the technique obviously misses some convective cores and allows room for additional information to improve the detection algorithm.
Convective cores (Tmin features passing the slope test) are further assigned convective rain area (Fig. 3a) and rain rate (Fig. 3b) as a function of their Tmin values. These functions are derived from the median values of convective area and convective rain rate of PR estimates as a function of Tmin, respectively. In the original CST (Adler and Negri 1988), similar functions (slope, convective area–Tmin, and rain rate–Tmin) were derived from one-dimensional cloud model results. In the CST stratiform rain areas are determined as those with Tb values lower than the mode or background brightness temperature, which has been shown to be coincident with the outline of stratiform rainfall and approximately equal to the tropopause temperature (Adler and Negri 1988). The stratiform rain rate is assigned as the median stratiform rainfall rate (2.5 mm h−1) derived from the PR rain estimates in the training dataset (Fig. 3c). As shown in Figs. 3a–c, convective rain area and rain rate have strong relationships with Tmin, but the stratiform rain rate is independent of Tb. These relationships also indicate the importance of separating convective and stratiform precipitation, even for IR-based techniques.
Figure 4 shows an example of the CST applied to a young thunderstorm complex from the step of finding local Tb minima (Fig. 4a) to assigning convective/stratiform areas (Fig. 4c) and to deriving rain‐rate estimates (Fig. 4d). Generally, the CST can catch the convective cores and define the heavy precipitation (convective) areas very well for young convective cells (when compared with radar; Fig. 4b). In such new developing systems, cloud-top overshooting is very evident, and the convective area is closely related to the minimum cloud-top temperature. However, as the convective storm develops and becomes mature, the relationships between IR Tb and rain rate in the CST (and most IR techniques) become more complicated (Fig. 5). As shown by the example in Fig. 5c and previous studies (Adler and Negri 1988; Xu et al. 2013), the CST may incorrectly identify cold cloud debris of mesoscale convective storms (MCS) or thick cirrus as convective areas and define too many convective cores in the broad, cold Tb field. Some of the Tmin cores might result from the oscillation of the Tb field due to forced tropospheric mesoscale gravity waves generated by overshooting tops (Fovell et al. 1992) rather than true overshooting cloud tops. As shown in the next section, this situation could be corrected through combining lightning information with the CST.
b. Lightning-enhanced CST
The IR-based CST, described in the last section, is combined with lightning measurements to develop the CSTL. The use of lightning information is based on the lightning–cloud–rainfall relationships quantified by Xu et al. (2013). Xu et al. (2013) showed that the lightning information is useful in aiding the identification of convective cores in thick anvils missed by the IR technique, eliminating misidentified convective cores in cold cloud debris or thick cirrus, and improving convective rainfall volume estimates. In addition, the effective lightning flash area also has a very good correlation with the convective rainfall area (Grecu et al. 2000; Xu et al. 2013).
In the lightning-enhanced algorithm, lightning information is incorporated into the CST after Tmin cores are identified and pass the slope test (Fig. 1) using just IR data. In the CSTL, Tmin cores that pass the CST slope test are further tested and must have at least two lightning flashes (in a 1-min period) within 10-km radius of the Tmin to remain as convective cores. Areas of these convective cores are derived from the area-Tmin function (Fig. 3a). In addition, lightning-associated areas (areas within a 10-km radius of lightning flash centers) are also considered as convective areas, since lightning flash areas are highly correlated to convective area (Xu et al. 2013). No areas survive as being convective after failing these two kinds of lightning test. The lightning clusters add an increment to the IR convective cores (with more than two flashes) rather than dominating the numbers. Grecu et al. (2000) showed that lightning clusters only defined 50% of the true convective area. In most cases lightning clusters are much smaller than the IR-defined convective cores. For example, even for a convective core having 10 lightning flashes, these lightning flashes might overlap over a relatively smaller area than the large convective core. On the other hand, lightning-defined areas help to redefine real convective areas missed by CST in the situation when CST is misled by large uniform cold cloud cover over the convective core. Although stratiform or anvil lightning flashes do occur, they are only a very small fraction of the total lighting and most of them are related to a convective core nearby (more details in section 5b).
The Tmin-based convective areas (with nearby lightning) plus those 10-km areas with lightning (even with no IR Tmin) together make up the estimated convective rain areas. The example in Fig. 5 shows obvious improvement (CSTL over CST) as compared to the passive microwave (Fig. 5b) in identifying convective areas through the use of the lightning information. The lightning information helps to remove convective regions incorrectly defined by the CST (Fig. 5d). This incorrect definition might be due to cold temperatures and Tmin features appearing due to fluctuations and oscillations in thick anvil cirrus (Xu et al. 2013). Since we need an overall large view of the case, TMI retrievals instead of PR are shown here. There is some difference even between PR and TMI as seen from the heavy precipitation areas in Fig. 6. Based on Fig. 6, CSTL (or TMI) catches most convective precipitation (e.g., >10 mm h−1) that has been detected by the PR, except for the narrow line over the most western part of the system. In comparison with PR, CST still generates much more convective precipitation.
After defining convective areas, convective rain rate is assigned as a function of Tmin and lightning flash density. For convective areas without lightning occurrence, rain rate is derived from the rain rate–Tmin function as shown in Fig. 3b. In addition, rain rate is also derived as a function of lightning flash density in convective areas having lightning flashes (Fig. 3d). The final estimates of instantaneous rainfall are degraded to 10- or 20-km resolution (Fig. 6). As shown in the example, both CST and CSTL generally reproduce the distribution of heavy and light (stratiform) rain even under the large cold cloud shield. CST artificially overestimates the rainfall in some no-rain or very light rain regions (Fig. 6a) where CST falsely defines convective features (Fig. 5c). In contrast, the CSTL helps to solve this problem (Figs. 5d and 6d) and produces more accurate rain‐rate patterns. As also shown in this example, CSTL estimates even catch those extremely heavy (>30 mm h−1) precipitation locations, especially when they are compared with TMI estimations. On the other hand, CST and CSTL also show skill in identifying the light rain (stratiform) area or delineating the rain and no-rain boundary in this mature MCS as shown in Figs. 5 and 6.
4. Evaluations of CST and CSTL rain estimates
This section evaluates CST and CSTL rain estimates by using TRMM PR and TMI rain retrievals dependently (using the TRMM 2002–04 training set) and independently (using 2005–08 TRMM data). Both the dependent and independent datasets include over a million PR- and TMI-defined precipitation pixels (Table 1). To fully evaluate the modified CST and the value of incorporating lightning information, the CST and CSTL estimates are compared with PR and TMI estimations on the basis of convective–stratiform separation, instantaneous rainfall rates, and total rainfall volume. Ground-based rain rates are not used for validation in this study for two major reasons: 1) the current version of the algorithm is a prototype and is for testing the value of adding lightning data (ground-based measurements will be included in later validation of products) and 2) time–space matching is easy and accurate when all measurements are on the same platform (TRMM satellite), whereas matching to ground-based measurements would be much more difficult.
a. Convective and stratiform identification
As mentioned previously, cloud-top Tb–rainfall and lightning–rainfall relationships are totally different in the convective and stratiform regions. One of the advantages of CST and CSTL is that they define convective and stratiform precipitation type before assigning specific rain rates. Figure 7 shows their POD, FAR, and CSI in identifying convective-type rainfall (with reference to PR-based identification). All comparisons are done at 10-km resolution; the contingent performance scores are even higher for the 20-km resolution. In general, both the CST and CSTL show significant accuracy in identifying convective rain features and the level of accuracy is invariant between dependent and independent estimates. First of all, the CST already has substantial ability (POD = 0.7) to determine convective precipitation regions even before lightning information is used (Fig. 7a). This is reasonable, since overshooting cloud tops and associated minimum Tb features (defined as convective areas in CST) often correspond to heavy precipitation near the surface. Lightning information slightly improves (0.05 or 8% increase in POD) the convective detection after it is incorporated into CST. The combination of both IR and lightning should be superior to IR-only or lightning-only methods (Grecu et al. 2000). In addition, the improvement by using total lightning versus CG is quite obvious. For example, Grecu et al. (2000) reported that CG lightning cluster method detects only 36% (POD) of the convective areas. Therefore, only using CG lightning area as a convective proxy could largely underestimate the convective areas. The relatively small increase in POD from CST to CSTL is due to the relatively few, but probably important, convective features that are missed just using IR under a dense anvil cirrus deck. In fact, the most important role of lightning information seems to be to screen out convective areas incorrectly defined by CST (Fig. 7b). Specifically, lightning data help to reduce the false alarms in convective rain by about 30% (i.e., the FAR drops from 0.5 for CST to 0.35 in CSTL). Because of the increase of convective detection and false alarm decrease, CSTL improves its CSI over that of CST by about 25% (Fig. 7c). These statistics clearly support our hypothesis that lightning information can be used to identify convective cores (areas) that are missed by CST and remove CST false alarms on convective cores (areas). These results are critical in understanding how the lightning information can improve convective system rain estimation.
Figure 8 shows convective areas defined by CST and CSTL versus those derived from PR (general statistics are in red text). Each point in the figure is the total convective area over the 800 × 800 km2 TRMM sector image, with a number of individual convective features contributing to the total area for that image. In general, both CST (CC = 0.86) and CSTL (CC = 0.92) show great skill in representing convective features over a region. The CST has a fairly small overall bias (15%) but does generate larger (up to 100%) convective precipitation areas than the corresponding PR estimates for large precipitating system (Figs. 8a,b). This area overestimation at high values is due to the high convective false alarm rate of CST at the latter stage of storms such as MCSs when cold and complicated cloud debris mislead the IR-based technique searching for Tmin features. This is a common issue for IR-only rainfall estimation techniques. Since lightning information helps to lower the convective identification FAR in the CST (Fig. 7), the CSTL produces more accurate estimates of convective area (Figs. 8c,d). For example, CSTL lowers the overall bias on independent PR convective area estimation from 16% to −2%, while reducing the RMSE from 0.95 to 0.66 (×104 km2). Both the CST and CSTL display very small changes in statistics between the dependent and independent periods (2002–04 vs 2005–08) in deriving convective area. The correlation coefficient between CST (or CSTL) and PR estimates of convective area is very high (0.86–0.92). The addition of the lightning information, however, does improve the bias and RMSE of the identification of the convective areas (statistics shown in Fig. 8).
The stratiform area is estimated primarily from the IR data using a thresholding technique in both the CST and CSTL. Figure 9 shows that IR techniques in this study have significant skill in estimating stratiform rain area (CC = 0.78–0.82). However, both CST and CSTL estimates have a somewhat larger scatter and higher bias in the identification of stratiform areas than convective areas. This reflects the difficulty of defining light rain boundaries with IR information. The lightning information improves the stratiform area estimation (e.g., reduces the bias by 15%–20%), although the scatter (as seen in CC and RMSE values) is not significantly affected by the lightning information. The bias reduction is due primarily to improving the convective area estimation (e.g., by eliminating false convective signatures), and thereby in turn improving the remaining stratiform area definition. As expected, the primary impact of the inclusion of (total) lightning data in this algorithm lies in improving estimations in convective areas, not stratiform areas.
b. Estimates of instantaneous rainfall rates
Figures 10 and 11 display the CST and CSTL rain estimates in comparison with PR–TMI estimates at 20-km resolution in May 2002 (dependent) and May 2007 (independent). Only two months are displayed to restrict the number of points, with each point representing a 20-km pixel. As shown in Figs. 10 and 11, the CSTL persistently produces better instantaneous estimates than CST whether applied to the dependent data or the independent data. Both the CST and CSTL estimates are closer (better correlations and lower bias) to estimates based on passive microwave (TMI) than to radar (PR) retrievals. This might be due to the fact that IR (or IR plus lightning) or the passive microwave method indirectly retrieves near surface precipitation, while radar directly measures the precipitation hydrometeors. In particular, the CST overestimates light rain but underestimates extreme precipitation (Figs. 10a,b and 11a,b). In fact, most IR-only techniques tend to underestimate precipitation at the early storm stage and overestimate rainfall at the decaying stage of the storm (Kidd et al. 2003; Joyce et al. 2004). After lightning information is applied, the CSTL significantly improves this issue (Figs. 10c,d and 11c,d). This might result from the fact that lightning may help raise the rain intensity estimate at the early stage of an MCS after lightning onset. In addition, lightning could further correct the convective area and lower the rain intensity during the decaying period when lightning occurrence is only occasional. Passive microwave rain retrievals over land (such as from TMI) are closely tied to ice scattering signatures at the microwave frequencies (Wang et al. 2012). The presence of ice is also highly correlated to occurrence of lightning (Takahashi 1978; Wiens et al. 2005; Fierro et al. 2006). Thus the estimation of rainfall via microwave techniques (over land) and via the use of total lightning information should show similar results. Indeed the best correlations are in Figs. 10d and 11d, where the CSTL is compared to the passive microwave (TMI) rain information.
The results above are also consistent for different months (May–August) and for different years (see Fig. 12). Table 2 and Fig. 12 show the complete set of validation statistics (i.e., correlation coefficient, bias, and RMSE). In general, the CSTL improves the statistics over CST (Table 2), with the correlation coefficient increasing by more than 30% when evaluating by PR (CC increases from 0.36 to 0.49) or TMI (CC increases from 0.53 to 0.66) retrievals. CSTL reduces the bias over CST by 30% (50%) and RMSE by 20% (25%) when compared with PR (TMI) estimates. Furthermore, lightning information also helps to improve the POD and lowers the FAR. For example, in the validation by TMI estimates with rainfall rates > 5 mm h−1, CSTL increases the POD slightly (from 0.67 to 0.70) and greatly reduces the FAR (from 0.64 to 0.52) over CST. These statistics further support the conclusion in the earlier section that lightning does help to improve detection and eliminate false alarms in convective (or heavy) precipitation.
All results (Figs. 10–12 and Table 2) show that both the CST and CSTL have significant skill in instantaneous rainfall estimation and the CSTL has better statistical performance due to the addition of the lightning information. CST estimates show a correlation coefficient of 0.53, bias of 0.8 mm h−1, and RMSE of 6.5 mm h−1, when evaluated by comparing to passive microwave estimates (Table 2). Compared with several IR techniques at similar time and space scales reported by Kuligowski (2002), the performance score of CST falls into the best group. Lightning-enhanced CSTL shows even more accurate rainfall estimates, with a correlation coefficient of 0.66 and bias of only 0.4 mm h−1. These improvements on IR-only estimates by lightning information are comparable to previous studies (Grecu et al. 2000; Morales and Anagnostou 2003; Chronis et al. 2004), although this study focuses on a much larger dataset.
c. Total rainfall volume estimations
This section evaluates the overall performance of the CST and CSTL by considering both the precipitation area and intensity. Accurate estimates of the rainfall total (or volumetric rainfall) over a region are important for hydrological applications and even climate studies. Figure 13 shows the instantaneous rainfall volume estimations by CST and CSTL as a function of TRMM PR–TMI estimates in each 800 × 800 km2 box or image over the southern United States. Statistics (CC, bias, and RMSE) in Fig. 13 also summarize the performance of CST and CSTL in these rainfall volume estimates. Both the CST and CSTL generally perform well in representing the rainfall total over a region (CC = 0.71–0.92, bias from −8% to 38%). These results are very encouraging in terms of applying CST and CSTL to GOES-R satellites for continuous monitoring of rainfall over a large region. On the other hand, CST and CSTL both have significant positive biases when compared with PR (bias = 29%–38%). The CST and CSTL estimates, however, match the microwave estimations on rainfall total volume much better (bias from −8% to 13%). This difference is partly due to the use of the TMI rain rates to calibrate the convective part of the CST algorithm. The CSTL seems to further improve the CST estimates (reduce both the bias and RMSE by 30%–40%), especially for extremely large and rainy events (see improvement in scatter for high rain volume events), possibly through reducing the incorrect identification of convective rainfall area with lightning information. The statistics of precipitation volume in the independent samples are very similar to that of the dependent samples. For example, the CC (bias) of CST or CSTL evaluated by TMI has a 0.01 (1%) difference between the dependent and independent samples (results are similar to those shown in Fig. 13). All these statistics indicate that lightning information combined with an approach such as the CST provides the basis for making rain estimates close to that of passive microwave, at least over land for deep convective systems. This effort is certainly a goal worth pursuing.
5. Summary and discussion
This study develops and evaluates an IR–lightning combined rainfall estimation algorithm using TRMM measurements over the southern United States during seven warm seasons (2002–08). Three seasons of measurements are used to train the algorithm, while another four seasons of data are used for evaluation. The IR algorithm used is an update of the convective–stratiform technique of Adler and Negri (1988), which is well suited to the incorporation of lightning data because of its separation of convective system rainfall into convective cores (where lightning should be primarily located) and stratiform rainfall areas (where lightning can be present but is much less frequent). A lightning-enhanced CST algorithm is developed through incorporating lightning information into the modified IR-based technique (CST). Both CST and CSTL define convective and stratiform precipitation types and assign rain rate separately for convective and stratiform areas. In the CSTL, lightning information is used to identify convective cores (areas) that are missed by CST and remove CST-identified convective cores (areas) that are false. In addition, the CSTL defines convective rain rate as a function of both IR brightness temperature and lightning flash density.
Major results from this study include the following: 1) Both CST and CSTL show significant skill and stable performance in warm‐season rainfall estimates over the southern United States in different years. 2) The CST generally identifies the heavy (convective) and light rain regions, while CSTL dramatically removes (by 30%) convective rainfall areas that are incorrectly defined by CST and provides higher detection of convective rainfall areas (by 5%). 3) CST overestimates the convective rainfall area and CSTL exhibits improved skill in defining that convective area. 4) In terms of instantaneous rainfall, CST and CSTL estimates are much closer to microwave estimates than to PR estimates; CSTL improves results over CST in rain‐rate estimates by about 30% (i.e., CC increases from 0.53 to 0.66) and substantially reduces the bias (50%) and RMSE (25%). 5) CST generally represents the rainfall total (volume) well over a region (CC = 0.85), as compared with the passive microwave estimates, while the CSTL further improves the estimate of rainfall volume (CC = 0.92; bias reduces by 30%).
The use of lightning shows significant improvement over IR-based rainfall estimates as also shown in previous studies (Grecu et al. 2000; Morales and Anagnostou 2003; Chronis et al. 2004). As mentioned previously, most IR-based techniques employ empirical regressions to derive surface rainfall rate from cloud-top brightness temperatures. However, the relationship between cloud-top Tb and surface rain rate is subject to great variability. Precipitating systems with efficient warm rain processes are great examples, whose surface rain rates are high but updrafts are too weak to transport ice particles to the upper troposphere; therefore the cloud tops are warm. On the storm scale, the Tb–rain rate relationship changes at different stages of the storm life cycle and in different parts of the storm. If the same Tb–rain rate relationship is applied throughout the storm life cycle, IR techniques could frequently underestimate rainfall at early stages when the system is dominated in terms of area by convective cores at high rain rates and overestimate rainfall at later stage, when the system is mostly stratiform by area. Similarly, the IR technique would overestimate stratiform precipitation and underestimate convective rainfall volume when the same Tb–rain rate function is derived from the whole precipitation area. The CST IR approach takes these variations into account, with the result that a CST pixel with the same Tb could have different rain rates depending on whether it is defined as convective or stratiform. In addition, most IR techniques could falsely treat thick cirrus clouds or cloud anvils as active convection, and miss convective cores under large uniform cold cloud shields or sheared cloud tops. The CST itself will improve things in this regard, but lightning information can help significantly more to solve these issues, as lightning provides indirect information about convective intensity and microphysics. The CST approach of separating the convective estimation from the stratiform estimation is well suited for the inclusion of lightning information since the lightning will help in only the estimation in areas of convective cores. For example, many IR-only techniques might have high false alarm rates in heavy precipitation due to overestimation in areas of stratiform precipitation under extremely cold cloud shields. This false alarm rate could be lowered significantly by certain techniques (still based on only IR), but at the great expense of detection possibility (e.g., Fig. 2 in Kuligowski 2002). However, the lightning information will help to solve this dilemma as shown in this study.
The general performance of the lightning-enhanced IR technique is comparable to previous studies in using IR–lightning or lightning-only data for rainfall estimation (Tapia et al. 1998; Grecu et al. 2000; Morales and Anagnostou 2003; Chronis et al. 2004). For example, most IR–lightning-derived instantaneous rainfall estimates (including this study) show correlation coefficients of 0.5–0.6 and RMSE of 2.0–3.0 mm h−1 when evaluating by microwave or radar estimates at a resolution of 20–30 km. However, this study shows a few advances. Tapia et al. (1998) use only the rainfall–lightning ratio to derive rainfall rate from cloud-to-ground lightning flash rates. This technique is limited by the fact that RLR can vary by a factor of 100 at any given location and by a factor of 1000 between different locations or rainfall regimes (Zipser 1994; Petersen and Rutledge 1998). Grecu et al. (2000) defined CG lightning clusters as convective cores and combined lightning and IR information for rainfall estimation. In practice, lightning clusters significantly underestimate convective area. Morales and Anagnostou (2003) and Chronis et al. (2004) combined lightning and IR measurements on the basis of cloud features (e.g., 255-K isotherm) in a more comprehensive way. However, these IR–lightning combined techniques are limited due to the relatively small samples in developing and testing the algorithm (e.g., only up to three months of satellite overpasses) and the use of only CG lightning information. CG lightning is only a fraction of the total lightning and the fraction is subjected to change both regionally and seasonally. There are several benefits of using total lightning data versus using CG-only data as mentioned in the introduction section.
There are, of course, limitations in the lightning-enhanced rainfall estimation technique developed in this study. First of all, lightning information in our technique is only connected to identifying convective areas and in estimating convective rain intensity, but lightning does occur in the stratiform or anvil cloud region of convective systems. However, lightning flashes initiating in stratiform or anvil areas are less than 10% of the total lightning (Dye et al. 2007; Peterson and Liu 2011; Wang et al. 2012). Moreover, these occurrences are still mainly associated with convective cores because most anvil discharges arise from charged ice particles being advected from the convective cores (Dye et al. 2007; Peterson and Liu 2011). Screening layers forming atop positively charged anvil clouds within MCS were shown to potentially lead to IC discharges. Even considering this, there is a very low fraction of lightning flashes that are not associated with convective cores. A second concern is that the lightning-enhanced technique is based on the warm‐season and continental precipitation regime where lightning occurrence and frequency is higher than the cool season, oceanic, and monsoon regimes (Williams and Stanfill 2002; Zipser et al. 2006; Xu and Zipser 2012). Under certain CCN concentration and thermodynamic environments, a given storm cell can be characterized by efficient autoconversion–coalescence processes producing large rain rate at the surface, while an ice mass aloft will be depleted by these processes, leading to a dearth in lightning activity. The IR-based rain estimation approach and even the IR–lightning approach are very much empirical, depending on a training dataset of some sort. For use in various regimes, for example, the CST and CSTL could be appropriately tuned. Both the IR–rain and lightning–rain relations would be a function of regime. This is a subject for future development. This study serves as the test for the CSTL algorithm and concentrates more on deep convection over the southern United States. The CSTL developed here is not necessarily the final algorithm for GOES-R. This algorithm could be tuned for other regions and regimes if necessary. For example, it could be evaluated and tuned for a specific region using information such as microwave rain estimates whenever microwave measurements are available. The final version of the algorithm would definitely involve calibration by microwave rain estimates during a specific time window such as every 24 h. Furthermore, for the regions or seasons where/when lightning activity is very rare, the CSTL would revert to the CST automatically.
In terms of practical application, the approaches described and tested in this paper seem well matched with the data from the forthcoming GOES-R satellite with its IR and lightning information. This approach, or others like it, seemed poised to take rain estimation from geosynchronous satellite information into a new era of improved results.
This research was supported by the National Oceanic and Atmospheric Administration (NOAA) Geostationary Operational Environmental Satellite R-Series Program (GOES-R) Risk Reduction (GOES-R3) program. We acknowledge Mr. Andrew Negri in the University of Maryland and Dr. Robert Kuligowski at NOAA for providing science discussions.