1. Introduction
Convectively generated outflow boundaries, such as density currents and bores, have an important contribution to the dynamics of mesoscale convective systems (MCSs). The theoretical importance of density currents is well established due to their critical role in the MCS evolution (e.g., Rotunno et al. 1988; Weisman and Rotunno 2004). On the other hand, atmospheric bores are still less familiar to the meteorological community, but these disturbances have received considerable attention recently, including being a focus of the Plains Elevated Convection at Night field campaign (PECAN; Geerts et al. 2017). The increasing interest in bores is largely driven by their ability to initiate and maintain nocturnal MCSs (Carbone et al. 1990; Crook et al. 1990; Locatelli et al. 2002; Parker 2008; Blake et al. 2017; Parsons et al. 2018). Recent work has also shown that bores occur commonly in association with warm season nocturnal convection over the Great Plains (Haghi et al. 2017).
The dynamical significance of convective outflow boundaries has prompted the scientific community to create automated algorithms for identifying and tracking these features. The earliest algorithm developed for this purpose was entirely based on observational data and closely connected to the procurement plans for the Next Generation Weather Radar (NEXRAD) system (e.g., Crum and Alberty 1993). In particular, Uyeda and Zrnić (1986) as well as Smith et al. (1989) were the first to describe radar-based algorithms for gust front (density current) detection that relied on the velocity convergence along radials. Later enhancements to these algorithms included the addition of radar reflectivity in the Advanced Gust Front Algorithm (AGFA; Eilts et al. 1991) and the use of knowledge-based signal processing in the Machine Intelligent Gust Front Algorithm (MIGFA; Delanoy and Troxel 1993; Troxel et al. 1996; Smalley et al. 2005). Likewise, advances in computational resources have made it possible to identify and track convective outflow boundaries in high-resolution model outputs. Previous model-based algorithms have focused on detecting density currents by incorporating various physical parameters, such as temperature (Gentine et al. 2016), density potential temperature (Torri et al. 2015; Drager and van den Heever 2017), buoyancy (Tompkins 2001; Seigel 2014), wind (Langhans and Romps 2015), or a combination of several relevant parameters (Li et al. 2014).
Although the aforementioned methodologies have greatly enhanced our understanding of density current and gust front dynamics, they are somewhat restricted in their application, compared to the algorithm presented in this paper. On one hand, the approaches reviewed earlier on are not suitable for detecting multiple types of convective outflow boundaries. This limitation can be problematic with regard to typical nighttime environments in which density currents can trigger atmospheric bores upon their interaction with the stable boundary layer (White and Helfrich 2012). The frequent generation of bores during the nighttime hours (Haghi et al. 2017) and their important role in the maintenance of nocturnal MCSs (Parker 2008; Blake et al. 2017) necessitate the development of methods to detect and track bores as well as their parent density currents. The other limitation of earlier convective outflow algorithms is that they have been mostly applied in idealized modeling frameworks, which may make them inappropriate for real-time forecasting applications.
To understand the interplay between nocturnal outflow boundaries and convective systems in real-time high-resolution numerical weather prediction (NWP) models, this study presents a novel object-based algorithm that is capable of seamlessly identifying density currents and bores. The latter is achieved by employing a multivariate approach similar to the dryline identification algorithm of Clark et al. (2015). Rather than attempting to detect all convective outflow boundaries present in high-resolution model simulations, the objective of this algorithm is to isolate only those that provide sufficient lifting for the initiation and maintenance of nocturnal MCSs. The latter goal falls in line with the recent findings of Parker (2008), French and Parker (2010), and Parsons et al. (2018), who suggest that the primary lifting mechanism for nocturnal MCSs can change from a density current to an internal bore with the onset of nocturnal cooling.
Aside from the specific choice of identification parameters, the proposed algorithm differs from the previously discussed methods in terms of how it tracks the identified objects in time. Traditionally, object-tracking techniques rely on statistical methods to match objects from two different model time steps (Lakshmanan 2012). By contrast, the object tracker proposed in this study accounts for the dynamics of convective outflow boundaries in an explicit manner. As will be shown later in the paper, imposing dynamical constraints in the algorithm yields more robust tracking results, compared to an algorithm based on statistical considerations alone. It is also worth remarking that developing algorithms with due regard to the dynamical aspects of the tracked objects was a key recommendation of Davis et al. (2009b)—one of the first studies focusing on object-based identification and verification using NWP data.
In addition to the technical details behind the algorithm framework, this paper also highlights a spectrum of additional algorithm applications relevant for bore research and operational forecasting of nocturnal storms. Generally speaking, these algorithm applications can be utilized in two different ways. The first pertains to the verification of numerically simulated convective outflow boundaries. With the advance of convection-allowing NWP models, object-based verification techniques like the Method for Object-Based Diagnostic Evaluation (MODE; Davis et al. 2006a) have become a popular choice for validating the accuracy of localized and spatially inhomogeneous fields such as precipitation (e.g., Davis et al. 2009a; Johnson et al. 2011a,b; Johnson and Wang 2012, 2013; Johnson et al. 2013; Clark et al. 2014). Unfortunately, the majority of these object-based methods cannot be readily extended to verify bore forecasts. MODE, for instance, relies on the presence of continuous observational datasets in order to verify model forecasts, which is not feasible in the case of convective outflow boundaries.
Second, the algorithm applications proposed in this paper can be also used to obtain a better understanding of the underlying bore dynamics, as well as the role of bores in initiating and maintaining nocturnal MCSs. To examine the characteristics of numerically simulated bores, previous studies (e.g., Martin and Johnson 2008; Koch et al. 2008) had to first identify their location by subjectively examining the appropriate model output fields. While this is a reasonable approach in terms of single case studies, analyzing the dynamical properties of bores in large datasets spanning a large number of numerical simulations is considerably more time consuming and, additionally, prone to human errors.
The algorithm framework and the attendant algorithm applications in this study are illustrated through a forecast experiment based on the 6 July 2015 PECAN case study. Using the Weather Research and Forecasting (WRF) Model (Powers et al. 2017), 40 ensemble members with a horizontal grid spacing of 1 km are run between 0300 and 0900 UTC. These high-resolution forecast members are initialized with a Gridpoint Statistical Interpolation (GSI)-based convection-allowing ensemble data assimilation system (Johnson et al. 2015; Johnson and Wang 2017; Wang and Wang 2017) after assimilating both radar and conventional data over a time window of 3 and 12 h, respectively.
The rest of the paper is organized as follows. Sections 2 and 3 introduce the identification and tracking components of the algorithm. Section 4 describes several algorithm tools and their application to the 6 July 2015 case study. Finally, section 5 summarizes the main aspects of the algorithm, outlines some of its limitations, and suggests possible ways to overcome those in future work.
2. Identification of convective outflow boundaries
a. Concept
As elucidated in section 1, the novelty of this algorithm comes from the unified description of density currents and bores, which is made possible by taking into account the dynamical similarities between these two convective outflow boundaries. Specifically, it is well known that (i) density currents and bores are characterized by high values of vertical velocity along their leading edge, and (ii) their passage leads to a sudden jump in pressure near the surface. The pressure rise in density currents is mostly hydrostatic in nature and arises due to the horizontal advection of cold air behind them, but it also contains a nonhydrostatic component associated with the deceleration of the density current relative inflow. This is to be contrasted with the pressure increase in a bore, which is caused by the net upward displacement and subsequent adiabatic cooling of near-surface stable air. The identification component of the algorithm parameterizes these effects through the 1-km above ground level (AGL) vertical velocity 
Workflow for the identification component of the algorithm. The variables 
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-18-0116.1
Parameter values for the identification and tracking components of the object-based algorithm. The identification thresholds refer to the smoothed and/or filtered model identification fields.
The workflow associated with the identification component of the algorithm is further illustrated through the 1-km horizontal grid spacing simulation of the 6 July 2015 case study (Fig. 2), the details of which are summarized in section 1. In particular, the information contained within the 
Illustrating the identification component of the algorithm. The 15-min changes in the (a) mean sea level pressure 
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-18-0116.1
Additional evidence for the discriminating capabilities of the algorithm is provided in Fig. 3. The first column of this figure shows the algorithm output for two consecutive times, during which the tracked object splits into two additional objects, and the southern one changes its morphology from a density current to a bore. The objectively determined outflow classification results (Figs. 3a,c) verify successfully against the vertical cross sections for the corresponding forecast lead times (Figs. 3b,d). More specifically, the vertical cross section from Fig. 3b shows classical density current signatures, such as an enhanced prefrontal updraft and a sudden drop in the virtual potential temperature (
Example of classifying convective outflow objects for two different forecast times: (top) 0400 UTC and (bottom) 0630 UTC. (a),(c) Location of the identified objects. The color shading corresponds to the object morphology as determined by the identification component of the algorithm: blue represents density currents (DC), red is bores (B), and gray marks those parts of the convective outflow objects whose morphology cannot be determined unambiguously (CO). The final shape of the objects is additionally modified with the medial axis transform. (b),(d) Cross sections are taken along the line segment 
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-18-0116.1
b. Implementation
All variables used in the identification component of the algorithm are modified in order to yield meaningful identification results. As far as the 
It is worth mentioning that the DCT filter may be not as effective during the first hour or two of model integration when the spurious gravity wave activity is prolific and spans a larger spectrum of wavelengths. To address this issue, the algorithm has the option to substitute the 
Last, we discuss the application of morphological image processing techniques within the identification component of the object-based algorithm. These techniques aim to address the discontinuous nature of the convective outflow objects produced as a result of merging the 
c. Grid spacing considerations
Apart from the need to choose appropriate model parameters, the identification of convective outflow boundaries in the algorithm is ultimately dependent on the ability of NWP models to correctly represent their dynamical characteristics (e.g., surface warming, pressure rise). Past studies (Koch et al. 2008; Martin and Johnson 2008; Johnson et al. 2017) along with additional analyses based on the 6 July 2015 simulations (see Fig. S1 in the online supplemental material) have concluded that the adequate representation of atmospheric bores in NWP models requires a horizontal grid spacing of less than 4 km. This, in turn, implies that the object-based algorithm should be used only in conjunction with data from higher-resolution convection-permitting NWP models. With a view of making our algorithm applicable to a broader range of model configurations, the remainder of this section discusses how changes in the horizontal resolution of convection-allowing models impact its identification capabilities. In particular, we comment on the key modifications required to successfully adapt the algorithm to a coarser 3-km model output, which is more typical of currently operational convection-allowing NWP systems such as the High-Resolution Rapid Refresh model (HRRR; Smith et al. 2008).
It is well known that coarser-resolution model simulations tend to have a smoothing effect on the underlying model fields, which can, in turn, have downstream impacts on the number and/or extent of objects identified by the algorithm. Nonetheless, the application of a Gaussian filter implicitly circumvents this problem as it smooths the identification variables from different model resolutions to the same spatial scale. This statement is supported both by Table 2 and Figs. S2a and S2b, which show that the median and interquartile range (IQR) values associated with the smoothed identification variables are nearly identical on the 1- and 3-km model domains (i.e., their ratio is 
Dependence of the algorithm’s identification component on the horizontal resolution of convection-allowing NWP models. The second and third columns show the median and IQR ratios of the coarser 3-km identification variables to the original 1-km ones. To obtain these ratios, the median and IQR values from one of the ensemble members are averaged throughout the 6-h model integration period used in the 6 Jul 2015 case study. The fourth column shows the scaling factor 
3. Tracking convective outflow boundaries
a. Concept
The concept behind the object tracker is presented in Fig. 4. This schematic shows how a convective outflow boundary might evolve in a typical nighttime environment and also highlights the key processes that the object tracker is expected to handle. Suppose that the leftmost object in Fig. 4 is one of the many objects identified by the algorithm at some initial time 
A schematic showing the concept behind the tracking component of the algorithm as well as the typical evolution of a convective outflow boundary in the nighttime environment starting from an analysis time 
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-18-0116.1
b. Implementation
Association of objects from two neighboring image frames is a challenging problem, particularly in cases of object splitting, merging, or rapid evolution (all of which are common for convective outflow boundaries). Past work on multiobject tracking has examined several techniques with a varying degree of complexity (Lakshmanan 2012). Those methods range from a simple minimization of object distances (greedy approach; Dijkstra 1959) to Kalman filter applications (Kalman 1960). Nevertheless, the aforementioned tracking techniques are prone to errors, especially when the identified objects undergo rapid structural changes. To address these problems, Lakshmanan et al. (2003) developed a hybrid tracking approach that exhibits superior performance over the aforementioned methods. In this work, we use a variation of the hybrid tracking approach to formulate our object tracker.
The components of the object tracker are summarized by the block diagram in Fig. 5 and further illustrated in Fig. 6 through a representative case scenario, in which a target object (black shading) splits into two smaller objects (1 and 2; gray shading) at the current model time step. In addition to these two objects, the binary field in Fig. 6 contains an additional third object (3), which is not physically related to the target object. Ideally, the tracking component of the algorithm should only associate objects 1 and 2 with the target object. Within the framework of the object tracker, this is achieved through a sequential application of three different constraints, the technical details of which are explained in the remainder of this section.
Workflow for the tracking component of the algorithm that illustrates the association procedure between a target object identified in a previous image frame (
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-18-0116.1
(a) Application of the object tracker to a splitting case scenario. The black and gray color shading shows the position of the target and candidate objects, respectively. Their centroids are marked with a blue dot and used to estimate the candidate object’s motion vector 
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-18-0116.1
Unlike other approaches, the tracker presented in this paper prioritizes the dynamics of convective outflow boundaries by adding two dynamical constraints as part of the object association procedure. The first one makes use of the pressure gradient force [PGF; 
Association between a target and a candidate object occurs only if the following three conditions are met simultaneously: 
The addition of dynamical constraints in the object tracker is beneficial for several reasons. First, the simultaneous fulfillment of three different conditions relaxes the prescribed threshold values used for object association (Table 1). Tracking objects only with the aid of template matching [e.g., the hybrid tracking approach of Lakshmanan et al. (2003)] would have required a significantly higher value of 
Another benefit of incorporating dynamical constraints in the algorithm’s tracker is to make the search area (i.e., the area within which target and candidate objects are associated) flow dependent (dynamic). This idea is illustrated in the schematic from Fig. 7, where all three candidate objects are perfectly correlated with the target object (
A schematic illustration highlighting the benefits of using dynamical constraints in the object tracker. The black-filled shape represents a target object from a previous image frame, while the three gray-filled shapes (numbered 1, 2 and 3) are candidate objects identified in the current image frame. The black arrow indicates the direction of the PGF 
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-18-0116.1
The use of dynamical constraints is also important when candidate objects are perfectly correlated with the target object (i.e., 
4. Applications of the object-based algorithm
The intention of this section is to discuss the development of specific algorithm tools relevant for both research and operational forecasting applications. Special emphasis is placed on using the algorithm in conjunction with convection-allowing ensemble prediction systems.
a. Theoretical prediction of bores based on environmental profiles from NWP models
One application of the object-based algorithm is to use hydraulic and linear wave theories in order to determine whether a density current can trigger a bore and whether this bore will be maintained in the nighttime environment. Predicting the development and longevity of bores is needed due to their potential role in modifying convective instability and initiating deep convection (Carbone et al. 1990; Karyampudi et al. 1995; Koch and Clark 1999; Locatelli et al. 2002; Wilson and Roberts 2006). During the PECAN field campaign, such theoretical predictions were made by manually picking two environmental profiles on both sides of a numerically simulated density current (Haghi et al. 2015; Geerts et al. 2017). Despite the encouraging results from such a forecasting approach, its application is highly subjective and time consuming. In the context of ensemble prediction systems where information from multiple ensemble members is integrated to provide probabilistic bore forecasts, an automated objective method is much more desirable. As a result, the algorithm introduced in sections 2 and 3 is extended to objectively determine whether the nighttime environment can support convectively generated bores using environmental profiles from NWP models.
The method for extracting environmental profiles of meteorological variables on both sides of a density current will be referred to as a four-dimensional (4D) distance minimization and is schematically portrayed in Fig. 8a. The key variable in this method is the user-defined reference point 
The 4D distance minimization of convective outflow objects with respect to a user-defined reference point. (a) The minimization procedure for an idealized example in which a convective outflow boundary propagates in the positive x direction at a constant speed 
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-18-0116.1
The 4D minimization procedure is typically applied throughout the entire time period for which the algorithm is run, such as in the example from Fig. 8b. The time series showing the minimal distances for different time steps suggests that the objects from most of the ensemble members pass over the user-selected reference point 
An example of a probabilistic bore prediction using theoretical considerations is shown in Fig. 9 and refers to a specific choice of 
Theoretical bore predictions performed over a reference point 
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-18-0116.1
The second part of the probabilistic bore prediction utilizes linear wave theory and estimates whether the environmental conditions are favorable for maintaining the convectively generated atmospheric bore. In particular, the algorithm calculates the ensemble distribution of the Scorer parameter 
b. Analysis of object attributes based on explicitly resolved convective outflow boundaries
The ability of convection-allowing NWP models to explicitly simulate convective outflow boundaries provides a unique opportunity for the object-based algorithm to extract dynamically relevant density current and bore attributes. One of them is the propagation speed 
Evaluating the propagation speed 
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-18-0116.1
There are at least two advantages of calculating 
The procedure for estimating 
Evaluating the effective bore amplitude 
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-18-0116.1
It is worth remarking that the definition of 
Analogous to the estimation of the propagation speed 
Repeating the outlined procedure for the entire ensemble of 36 quality-controlled members provides the ensemble distribution of bore amplitudes in Fig. 11b. For this specific choice of 
c. Object-based probabilities of explicitly resolved convective outflow boundaries
Apart from its ability to objectively analyze the characteristics of explicitly resolved convective outflow boundaries, the algorithm presented herein can also provide probabilistic information regarding their representation in convection-allowing ensemble prediction systems. Given that each member in the ensemble forecast is associated with two distinct binary fields corresponding to the location of the simulated density currents and bores, object-based probabilities can be generated by simply calculating the relative frequency of the aforementioned binary fields over different model grid points. An example application of the outlined procedure is shown in Fig. 12 and illustrates how the object-based probabilities that are linked to the largest convective outflow object identified close to the model initialization time (0315 UTC; refer to Figs. 12a,c) evolve after more than 3 h of model integration (Figs. 12b,d). Note that the object-based probabilities evaluated with respect to the other target objects are not shown in Fig. 12 for clarity.
Object-based (a),(b) density current and (c),(d) bore probabilities computed with respect to the largest convective outflow boundary in the 1-km ensemble forecasts of the 6 Jul 2015 case study. (left) The first set of probabilities is generated for 0315 UTC and coincides with the time when the largest convective outflow object is initialized by the algorithm. (right) The second set of probabilities is plotted for 0630 UTC or after the algorithm has tracked the largest convective outflow boundary for 3 h 15 min. Probability fields are additionally smoothed with a Gaussian kernel (
Citation: Monthly Weather Review 146, 12; 10.1175/MWR-D-18-0116.1
The sequence of images in Fig. 12 suggests that the largest convective outflow boundary initialized in our numerical simulations is expected to move east-southeast and that the main lifting mechanism associated with this particular boundary is very likely to change from a density current to a bore in the later forecast hours. Although a similar evolution is also evident in the deterministic forecast from Fig. 3, the algorithm-derived probabilities in this example contain additional information that could be potentially useful to operational forecasters. For instance, Figs. 12b and 12d reveal that the bore (density current) probabilities in the southern portion of the tracked outflow boundary are higher (lower), compared to its northern parts. Given a hypothetical scenario in which the ensemble members predict the development of convection in the vicinity of the highest bore probabilities, operational forecasters would have an additional physical insight about the forcing mechanism behind the model-simulated convection. If the radar and surface observations collected later on do (or do not) confirm the presence of a bore, these operational forecasters will have strong evidence that the NWP products used as part of their analysis are accurate (inaccurate) and would be able to adjust their forecasts accordingly. This idealized example suggests that the ability of the object-based algorithm to discriminate between density currents and bores could serve as useful guidance for the operational forecasting of nocturnal convection.
It is important to add that the object-based probabilities calculated with respect to the initial target objects are not the only means of utilizing the ensemble information contained in convection-allowing NWP models. In particular, density current and bore probabilities can be produced by independently considering all objects identified at a given model time step. However, since the latter approach does not make use of the algorithm’s tracker, operational forecasters would be unable to follow the evolution of convective outflow boundaries that are of particular interest to them. By contrast, the object-based probabilities in the example from Fig. 12 do not only add a temporal component to the algorithm’s output, but are also quite relevant in the context of short-range and rapidly updating NWP systems (e.g., the HRRR; Smith et al. 2008), wherein convective outflow boundaries are commonly present in the model’s initial conditions.
5. Conclusions and discussion
This study describes the development of an object-based algorithm for the automatic identification and tracking of convectively generated outflow boundaries. While object-based techniques to analyze density currents have been developed previously (Li et al. 2014; Drager and van den Heever 2017), a unique aspect of this algorithm is its ability to simultaneously account for both density currents and atmospheric bores. The detection of these morphologically different convective outflow boundaries is possible only after combining several model fields. Although the use of multiple identification variables is not a new concept (e.g., Clark et al. 2015), the specific parameter choice made in this algorithm is fundamentally different from past studies and is designed to target only those convective outflow boundaries that provide sufficient lifting for the initiation and maintenance of nocturnal MCSs. It is important to note that some of the identification variables are challenging to use without additional preprocessing steps. In particular, the spatial inhomogeneity of vertical velocity (
Another novel feature of the proposed algorithm is its object tracker. Following the suggestion of Davis et al. (2009b), the object tracker is formulated to explicitly account for the dynamics of convective outflow boundaries. The inclusion of the pressure gradient force direction 
To address the growing interest in atmospheric bores among researchers and operational forecasts (e.g., during the PECAN field campaign; Geerts et al. 2017), the second objective of the paper was to describe several algorithm applications relevant to the analysis and prediction of bores in NWP models. These applications were shown in the context of a convection-allowing ensemble forecast experiment from 6 July 2015. To the authors’ best knowledge, this is the first time a dedicated methodology for describing the ensemble distribution of specific bore parameters is presented. Such ensemble estimates are expected to provide valuable information for assessing the predictability of the studied phenomenon.
The four-dimensional minimization procedure, which lies at the heart of the suggested algorithm tools, allows algorithm users to automatically sample convective outflow boundaries and perform various diagnostics pertinent to their own research objectives. The specification of user-defined verification (reference) points through the aforementioned minimization procedure obviates the need for a spatially continuous verification dataset, which is required in other object-based verification methods (e.g., MODE; Davis et al. 2006a). The postprocessing tools developed as part of this object-based algorithm represent a natural extension of previous PECAN efforts to forecast the development and maintenance of bores based on manual input from model-derived environmental profiles (Haghi et al. 2015; Geerts et al. 2017). Apart from completely automating the routines needed for the theoretical bore analysis, the ability of the algorithm to determine the likelihood of bore occurrence could prove especially beneficial to operational forecasters by guiding them where the initiation of nocturnal convection is more likely.
Despite the encouraging performance of the newly developed object-based algorithm, it is also important to point out some of its limitations. The algorithm weaknesses are largely associated with its identification component. Most evidently, the static threshold values used to define convective outflow boundaries in the model domain are global in nature and only valid over relatively short periods of time. Within this study, the aforementioned problem is addressed by introducing two different sets of threshold values dependent upon the forecast lead time and the magnitude of the spurious numerical noise. One way to improve the identification capabilities of the algorithm is to use adaptive thresholding methods (e.g., through utilizing image histograms; Tobias and Seara 2002). Alternatively, introducing more sophisticated techniques such as marker-controlled watershed segmentation (Soille 2003) could completely remove the need for prescribing threshold values. Past experience related to the development of methods for detecting and tracking convective outflow boundaries in radar data can be also helpful in bolstering the identification results of our object-based algorithm. For instance, Delanoy and Troxel (1993) show how tracking gust fronts and anticipating their location in future radar scans improves the overall identification results. Another potentially useful concept incorporated in the aforementioned study is the application of functional template correlation (FCT) filters (Delanoy et al. 1992). In particular, this type of matched filters can be designed to describe the topological characteristics of model-simulated convective outflow boundaries and, hence, reduce the number of spuriously identified objects.
Finally, it is hoped that this paper will serve as a foundation for future studies aiming at advancing the algorithm’s capabilities as well as developing other relevant algorithm applications. A particularly interesting line of research would be to determine whether the classification of convective outflow boundaries can be extended to more complex features such as solitons and deep tropospheric gravity waves. Future work should also take advantage of the algorithm’s capability to objectively analyze some of the dynamical aspects of convective outflow boundaries. In line with the observational study of Toms et al. (2017), the algorithm could offer a convenient framework to examine the temporal evolution of the wave trapping characteristics following a model-simulated bore. Such an analysis could lend important insights into the two-way interactions between atmospheric bores and the ambient environment in which they develop and maintain. Moreover, a data assimilation study utilizing the proposed algorithm to objectively evaluate the forecast impact of assimilating novel PECAN observations is already being carried out by the authors of this work and will be reported in an upcoming paper.
Acknowledgments
The work is primarily supported by NSF Award AGS-1359703. Computing resources were provided by the Yellowstone (ark:/85065/d7wd3xhc) and Cheyenne (https://doi.org/10.5065/D6RX99HX) machines at NCAR’s Computational and Information Systems Laboratory, sponsored by the NSF. The authors of this paper would like to thank Kevin Haghi for providing code routines for the theoretical bore calculations. Special acknowledgements go to Aaron Johnson and Samuel Degelia from the University of Oklahoma, who regularly participated in discussions regarding the object-based algorithm and provided valuable feedback.
REFERENCES
Ahmed, N., T. Natarajan, and K. R. Rao, 1974: Discrete cosine transform. IEEE Trans. Comput., 23C, 90–93, https://doi.org/10.1109/T-C.1974.223784.
Baer, F., and J. J. Tribbia, 1977: On complete filtering of gravity modes through nonlinear initialization. Mon. Wea. Rev., 105, 1536–1539, https://doi.org/10.1175/1520-0493(1977)105<1536:OCFOGM>2.0.CO;2.
Blake, B. T., D. B. Parsons, K. R. Haghi, and S. G. Castleberry, 2017: The structure, evolution, and dynamics of a nocturnal convective system simulated using the WRF-ARW Model. Mon. Wea. Rev., 145, 3179–3201, https://doi.org/10.1175/MWR-D-16-0360.1.
Brunelli, R., 2009: Template Matching Techniques in Computer Vision: Theory and Practice. Wiley, 348 pp.
Carbone, R. E., J. W. Conway, N. A. Crook, and M. W. Moncrieff, 1990: The generation and propagation of a nocturnal squall line. Part I: Observations and implications for mesoscale predictability. Mon. Wea. Rev., 118, 26–49, https://doi.org/10.1175/1520-0493(1990)118<0026:TGAPOA>2.0.CO;2.
Clark, A. J., R. G. Bullock, T. L. Jensen, M. Xue, and F. Kong, 2014: Application of object-based time-domain diagnostics for tracking precipitation systems in convection-allowing models. Wea. Forecasting, 29, 517–542, https://doi.org/10.1175/WAF-D-13-00098.1.
Clark, A. J., A. MacKenzie, A. McGovern, V. Lakshmanan, and R. A. Brown, 2015: An automated, multiparameter dryline identification algorithm. Wea. Forecasting, 30, 1781–1794, https://doi.org/10.1175/WAF-D-15-0070.1.
Crook, N. A., R. E. Carbone, M. W. Moncrieff, and J. W. Conway, 1990: The generation and propagation of a nocturnal squall line. Part II: Numerical simulations. Mon. Wea. Rev., 118, 50–66, https://doi.org/10.1175/1520-0493(1990)118<0050:TGAPOA>2.0.CO;2.
Crum, T. D., and R. L. Alberty, 1993: The WSR-88D and the WSR-88D operational support facility. Bull. Amer. Meteor. Soc., 74, 1669–1688, https://doi.org/10.1175/1520-0477(1993)074<1669:TWATWO>2.0.CO;2.
Davis, C. A., B. G. Brown, and R. Bullock, 2006a: Object-based verification of precipitation forecasts. Part I: Methodology and application to mesoscale rain areas. Mon. Wea. Rev., 134, 1772–1784, https://doi.org/10.1175/MWR3145.1.
Davis, C. A., B. G. Brown, and R. Bullock, 2006b: Object-based verification of precipitation forecasts. Part II: Application to convective rain systems. Mon. Wea. Rev., 134, 1785–1795, https://doi.org/10.1175/MWR3146.1.
Davis, C. A., B. G. Brown, and R. Bullock, 2009a: Spatial and temporal object-based evaluation of numerical prediction forecasts. 23rd Conf. on Weather Analysis and Forecasting/19th Conf. on Numerical Weather Prediction, Omaha, NE, Amer. Meteor. Soc., 5A.4.
Davis, C. A., B. G. Brown, R. Bullock, and J. Halley-Gotway, 2009b: The method for object-based diagnostic evaluation (MODE) applied to numerical forecasts from the 2005 NSSL/SPC Spring Program. Wea. Forecasting, 24, 1252–1267, https://doi.org/10.1175/2009WAF2222241.1.
Delanoy, R. L., and S. W. Troxel, 1993: Machine intelligent gust front algorithm. MIT Tech. Rep. ATC-196, 96 pp., http://www.dtic.mil/dtic/tr/fulltext/u2/a273695.pdf.
Delanoy, R. L., J. G. Verly, and D. E. Dudgeon, 1992: Functional templates and their application to 3-D object recognition. ICASSP-92: 1992 IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, San Francisco, CA, IEEE, https://doi.org/10.1109/ICASSP.1992.226256.
Denis, B., J. Côté, and R. Laprise, 2002: Spectral decomposition of two-dimensional atmospheric fields on limited-area domains using the discrete cosine transform (DCT). Mon. Wea. Rev., 130, 1812–1829, https://doi.org/10.1175/1520-0493(2002)130<1812:SDOTDA>2.0.CO;2.
Dijkstra, E. W., 1959: A note on two problems in connection with graphs. Numer. Math., 1, 269–271, https://doi.org/10.1007/BF01386390.
Dougherty, E. R., 1992: An Introduction to Morphological Image Processing. SPIE Optical Engineering Press, 161 pp.
Dougherty, E. R., and R. A. Lotufo, 2003: Hands-On Morphological Image Processing. SPIE Optical Engineering Press, 290 pp.
Drager, A. J., and S. C. van den Heever, 2017: Characterizing convective cold pools. J. Adv. Model. Earth Syst., 9, 1091–1115, https://doi.org/10.1002/2016MS000788.
Eilts, M. D., S. Olson, G. J. Stumpf, L. G. Hermes, J. C. Abrevaya, K. Thomas, K. Hondl, and D. Klingle-Wilson, 1991: An improved gust front detection algorithm for the TDWR. Proc. Fourth Int. Conf. on the Aviation Weather System, Paris, France, Amer. Meteor. Soc., J37.
French, A. J., and M. D. Parker, 2010: The response of simulated nocturnal convective systems to a developing low-level jet. J. Atmos. Sci., 67, 3384–3408, https://doi.org/10.1175/2010JAS3329.1.
Geerts, B., and Coauthors, 2017: The 2015 Plains Elevated Convection at Night field project. Bull. Amer. Meteor. Soc., 98, 767–786, https://doi.org/10.1175/BAMS-D-15-00257.1.
Gentine, P., A. Garelli, S.-B. Park, J. Nie, G. Torri, and Z. Kuang, 2016: Role of surface heat fluxes underneath cold pools. Geophys. Res. Lett., 43, 874–883, https://doi.org/10.1002/2015GL067262.
Goff, R. C., 1976: Vertical structure of thunderstorm outflows. Mon. Wea. Rev., 104, 1429–1440, https://doi.org/10.1175/1520-0493(1976)104<1429:VSOTO>2.0.CO;2.
Haghi, K. R., D. B. Parsons, and B. T. Blake, 2015: Forecasting bores during PECAN 2015: A case study. 16th Conf. on Mesoscale Processes, Boston, MA, Amer. Meteor. Soc., 13.5, https://ams.confex.com/ams/16Meso/webprogram/Paper274581.html.
Haghi, K. R., D. B. Parsons, and A. Shapiro, 2017: Bores observed during IHOP_2002: The relationship of bores to the nocturnal environment. Mon. Wea. Rev., 145, 3929–3946, https://doi.org/10.1175/MWR-D-16-0415.1.
Johnson, A., and X. Wang, 2012: Verification and calibration of neighborhood and object-based probabilistic precipitation forecasts from a multimodel convection-allowing ensemble. Mon. Wea. Rev., 140, 3054–3077, https://doi.org/10.1175/MWR-D-11-00356.1.
Johnson, A., and X. Wang, 2013: Object-based evaluation of a storm-scale ensemble during the 2009 NOAA Hazardous Weather Testbed Spring Experiment. Mon. Wea. Rev., 141, 1079–1098, https://doi.org/10.1175/MWR-D-12-00140.1.
Johnson, A., and X. Wang, 2017: Design and implementation of a GSI-based convection-allowing ensemble data assimilation and forecast system for the PECAN field experiment. Part I: Optimal configurations for nocturnal convection prediction using retrospective cases. Wea. Forecasting, 32, 289–315, https://doi.org/10.1175/WAF-D-16-0102.1.
Johnson, A., X. Wang, F. Kong, and M. Xue, 2011a: Hierarchical cluster analysis of a convection-allowing ensemble during the Hazardous Weather Testbed 2009 Spring Experiment. Part I: Development of the object-oriented cluster analysis method for precipitation fields. Mon. Wea. Rev., 139, 3673–3693, https://doi.org/10.1175/MWR-D-11-00015.1.
Johnson, A., X. Wang, M. Xue, and F. Kong, 2011b: Hierarchical cluster analysis of a convection-allowing ensemble during the Hazardous Weather Testbed 2009 Spring Experiment. Part II: Ensemble clustering over the whole experiment period. Mon. Wea. Rev., 139, 3694–3710, https://doi.org/10.1175/MWR-D-11-00016.1.
Johnson, A., X. Wang, F. Kong, and M. Xue, 2013: Object-based evaluation of the impact of horizontal grid spacing on convection-allowing forecasts. Mon. Wea. Rev., 141, 3413–3425, https://doi.org/10.1175/MWR-D-13-00027.1.
Johnson, A., X. Wang, J. R. Carley, L. J. Wicker, and C. Karstens, 2015: A comparison of multiscale GSI-based EnKF and 3DVar data assimilation using radar and conventional observations for midlatitude convective-scale precipitation forecasts. Mon. Wea. Rev., 143, 3087–3108, https://doi.org/10.1175/MWR-D-14-00345.1.
Johnson, A., X. Wang, and S. Degelia, 2017: Design and implementation of a GSI-based convection-allowing ensemble-based data assimilation and forecast system for the PECAN field experiment. Part II: Overview and evaluation of a real-time System. Wea. Forecasting, 32, 1227–1251, https://doi.org/10.1175/WAF-D-16-0201.1.
Kalman, R. E., 1960: A new approach to linear filtering and prediction problems. J. Basic Eng., 82, 35–45, https://doi.org/10.1115/1.3662552.
Karyampudi, V. M., S. E. Koch, C. Chen, J. W. Rottman, and M. L. Kaplan, 1995: The influence of the Rocky Mountains on the 13–14 April 1986 severe weather outbreak. Part II: Evolution of a prefrontal bore and its role in triggering a squall line. Mon. Wea. Rev., 123, 1423–1446, https://doi.org/10.1175/1520-0493(1995)123<1423:TIOTRM>2.0.CO;2.
Koch, S. E., and W. L. Clark, 1999: A nonclassical cold front observed during COPS-91: Frontal structure and the process of severe storm initiation. J. Atmos. Sci., 56, 2862–2890, https://doi.org/10.1175/1520-0469(1999)056<2862:ANCFOD>2.0.CO;2.
Koch, S. E., P. B. Dorian, R. Ferrare, S. H. Melfi, W. C. Skillman, and D. Whiteman, 1991: Structure of an internal bore and dissipating gravity current as revealed by Raman lidar. Mon. Wea. Rev., 119, 857–887, https://doi.org/10.1175/1520-0493(1991)119<0857:SOAIBA>2.0.CO;2.
Koch, S. E., W. Feltz, F. Fabry, M. Pagowski, B. Geerts, K. M. Bedka, D. O. Miller, and J. W. Wilson, 2008: Turbulent mixing processes in atmospheric bores and solitary waves deduced from profiling systems and numerical simulation. Mon. Wea. Rev., 136, 1373–1400, https://doi.org/10.1175/2007MWR2252.1.
Lakshmanan, V., 2012: Automating the Analysis of Spatial Grids: A Practical Guide to Data Mining Geospatial Images for Human and Environmental Applications. Springer, 320 pp.
Lakshmanan, V., R. Rabin, and V. DeBrunner, 2003: Multiscale storm identification and forecast. J. Atmos. Res., 67–68, 367–380, https://doi.org/10.1016/S0169-8095(03)00068-1.
Langhans, W., and D. M. Romps, 2015: The origin of water vapor rings in tropical oceanic cold pools. Geophys. Res. Lett., 42, 7825–7834, https://doi.org/10.1002/2015GL065623.
Li, Z., P. Zuidema, and P. Zhu, 2014: Simulated convective invigoration processes at trade wind cumulus cold pool boundaries. J. Atmos. Sci., 71, 2823–2841, https://doi.org/10.1175/JAS-D-13-0184.1.
Locatelli, J. D., M. T. Stoelinga, and P. V. Hobbs, 2002: A new look at the super outbreak of tornadoes on 3–4 April 1974. Mon. Wea. Rev., 130, 1633–1651, https://doi.org/10.1175/1520-0493(2002)130<1633:ANLATS>2.0.CO;2.
Lynch, P., and X.-Y. Huang, 1992: Initialization of the HIRLAM model using a digital filter. Mon. Wea. Rev., 120, 1019–1034, https://doi.org/10.1175/1520-0493(1992)120<1019:IOTHMU>2.0.CO;2.
Martin, E. R., and R. H. Johnson, 2008: An observational and modeling study of an atmospheric internal bore during NAME 2004. Mon. Wea. Rev., 136, 4150–4167, https://doi.org/10.1175/2008MWR2486.1.
Parker, M. D., 2008: Response of simulated squall lines to low-level cooling. J. Atmos. Sci., 65, 1323–1341, https://doi.org/10.1175/2007JAS2507.1.
Parsons, D. B., K. R. Haghi, K. T. Halbert, B. Elmer, and J. Wang, 2018: The potential role of atmospheric bores and gravity waves in the initiation and maintenance of nocturnal convection over the southern Great Plains. J. Atmos. Sci., https://doi.org/10.1175/JAS-D-17-0172.1, in press.
Powers, J. G., and Coauthors, 2017: The Weather Research and Forecasting Model: Overview, system efforts, and future directions. Bull. Amer. Meteor. Soc., 98, 1717–1737, https://doi.org/10.1175/BAMS-D-15-00308.1.
Reiter, P., O. Gutjahr, L. Schefczyk, G. Heinemann, and M. Casper, 2018: Does applying quantile mapping to subsamples improve the bias correction of daily precipitation? Int. J. Climatol., 38, 1623–1633, https://doi.org/10.1002/joc.5283.
Rottman, J., and J. Simpson, 1989: The formation of internal bores in the atmosphere: A laboratory model. Quart. J. Roy. Meteor. Soc., 115, 941–963, https://doi.org/10.1002/qj.49711548809.
Rotunno, R., J. B. Klemp, and M. L. Weisman, 1988: A theory for strong, long-lived squall lines. J. Atmos. Sci., 45, 463–485, https://doi.org/10.1175/1520-0469(1988)045<0463:ATFSLL>2.0.CO;2.
Scorer, R. S., 1949: Theory of waves in the lee of mountains. Quart. J. Roy. Meteor. Soc., 75, 41–56, https://doi.org/10.1002/qj.49707532308.
Seigel, R. B., 2014: Shallow cumulus mixing and subcloud-layer responses to variations in aerosol loading. J. Atmos. Sci., 71, 2581–2603, https://doi.org/10.1175/JAS-D-13-0352.1.
Smalley, D. J., B. J. Bennett, and R. Frankel, 2005: MIGFA: The Machine Intelligent Gust Front Algorithm for NEXRAD. 32nd Conf. on Radar Meteorology/11th Conf. on Mesoscale Processes, Albuquerque, NM, Amer. Meteor. Soc., 8R.4, https://ams.confex.com/ams/32Rad11Meso/techprogram/paper_96098.htm.
Smith, S., A. Witt, M. D. Eilts, L. G. Hermes, D. Klingle-Wilson, S. Olson, and J. P. Stanford, 1989: Gust front detection algorithm for the terminal Doppler weather radar. Part I: Current status. Proc. Third Int. Conf. on the Aviation Weather System, Anaheim, CA, Amer. Meteor. Soc., 31–34.
Smith, T. L., S. G. Benjamin, J. M. Brown, S. Weygandt, T. Smirnova, and B. Schwartz, 2008: Convection forecasts from the hourly updated, 3-km High Resolution Rapid Refresh (HRRR) model. 24th Conf. on Severe Local Storms, Savannah, GA, Amer. Meteor. Soc., 11.1, https://ams.confex.com/ams/24SLS/techprogram/paper_142055.htm.
Soille, P., 2003: Morphological Image Analysis: Principles and Applications. Springer, 392 pp.
Tobias, O. J., and R. Seara, 2002: Image segmentation by histogram thresholding using fuzzy sets. IEEE Trans. Image Process., 11, 1457–1465, https://doi.org/10.1109/TIP.2002.806231.
Tompkins, A. M., 2001: Organization of tropical convection in low vertical wind shears: The role of water vapor. J. Atmos. Sci., 58, 529–545, https://doi.org/10.1175/1520-0469(2001)058<0529:OOTCIL>2.0.CO;2.
Toms, B. A., J. M. Tomaszewski, D. D. Turner, and S. E. Koch, 2017: Analysis of a lower-tropospheric gravity wave train using direct and remote sensing measurement systems. Mon. Wea. Rev., 145, 2791–2812, https://doi.org/10.1175/MWR-D-16-0216.1.
Torri, G., Z. Kuang, and Y. Tian, 2015: Mechanisms for convection triggering by cold pools. Geophys. Res. Lett., 42, 1943–1950, https://doi.org/10.1002/2015GL063227.
Troxel, S. W., R. L. Delanoy, J. P. Morgan, and W. L. Pughe, 1996: Machine intelligent gust front algorithm for the Terminal Doppler Weather Radar (TDWR) and Integrated Terminal Weather System (ITWS). AMS Workshop on Wind Shear and Wind Shear Alert Systems, Oklahoma City, OK, Amer. Meteor. Soc., 70–79.
Uyeda, H., and D. S. Zrnić, 1986: Automatic detection of gust fronts. J. Atmos. Oceanic Technol., 3, 36–50, https://doi.org/10.1175/1520-0426(1986)003<0036:ADOGF>2.0.CO;2.
Vickers, D., and L. Mahrt, 2004: Evaluating formulations of stable boundary layer height. J. Appl. Meteor., 43, 1736–1749, https://doi.org/10.1175/JAM2160.1.
Wang, X., D. Parrish, D. Kleist, and J. Whitaker, 2013: GSI 3DVar-based ensemble–variational hybrid data assimilation for NCEP Global Forecast System: Single-resolution experiments. Mon. Wea. Rev., 141, 4098–4117, https://doi.org/10.1175/MWR-D-12-00141.1.
Wang, Y., and X. Wang, 2017: Direct assimilation of radar reflectivity without tangent linear and adjoint of the nonlinear observation operator in the GSI-based EnVar system: Methodology and experiment with the 8 May 2003 Oklahoma City tornadic supercell. Mon. Wea. Rev., 145, 1447–1471, https://doi.org/10.1175/MWR-D-16-0231.1.
Weisman, M. L., and R. Rotunno, 2004: “A theory for strong long-lived squall lines” revisited. J. Atmos. Sci., 61, 361–382, https://doi.org/10.1175/1520-0469(2004)061<0361:ATFSLS>2.0.CO;2.
White, B. L., and K. R. Helfrich, 2012: A general description of a gravity current front propagating in a two-layer stratified fluid. J. Fluid Mech., 711, 545–575, https://doi.org/10.1017/jfm.2012.409.
Wilson, J. W., and R. D. Roberts, 2006: Summary of convective storm initiation and evolution during IHOP: Observational and modeling perspective. Mon. Wea. Rev., 134, 23–47, https://doi.org/10.1175/MWR3069.1.
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