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  • View in gallery

    Quality measures for adaptive sensing: (a) revisit improvement factor I and (b) acquisition time A for cases I (dark line), II (gray line), and III (light gray–dashed line) as a function of storm-tracking occupancy O. Large O are desired to obtain large revisit improvement factors, but these do not necessarily lead to small acquisition times. A satisfactory range is indicated in (b) for case II where both I and A are improved with respect to the WSR-88D VCP 12.

  • View in gallery

    Flowchart for the TB scheduling algorithm. (left branch) The algorithm selects the tracking task with maximum nonnegative TB for the next tracking task execution; otherwise, (right branch) surveillance is scheduled. The TB for each tracking task is updated on every iteration.

  • View in gallery

    (top) Scheduling of two tracking tasks and surveillance task using the TB algorithm. Requested schedule for cells 1 (black block) and 2 (gray block) are shown on the first two rows. Requested U for cells 1 and 2 are 20 and 34 s, respectively. Actual schedule for cells 1 and 2 and surveillance is presented in the third row. The surveillance task is continuously executed while the TB of the tracking tasks is all negative. (bottom) Time balance evolution that is used to decide which tracking or surveillance task needs to be scheduled next.

  • View in gallery

    Reflectivity data of storm cells at 0.5° elevation angle in central Oklahoma on 22 Apr 2008. Four distinct regimes are identified: (a) cell 1, (b) cells 1 and 2, (c) cells 1, 2, and 3 and (d) cells 1 and 3 (cell 2 left 90° sector).

  • View in gallery

    Performance of the TB scheduling algorithm. (top) The task times for cells 1 (black line), 2 (light gray line), and 3 (gray solid line) and surveillance (black thin-dashed line) are denoted. The total task time of tracking and surveillance is represented (black thick-dotted line). (middle) The update times for each tracking task and surveillance are shown. Requested update times for each tracking task (black thick-dashed line) and surveillance (black thin-dashed line). Actual update times after TB scheduling for cells 1 (black solid thick line), 2 (light gray solid thick line), and 3 (gray solid thick line) are represented. In addition, the task time for WSR-88D (UC) is indicated (black solid thin line). (bottom) The occupancy for each tracking task and surveillance are provided. Total requested occupancy is represented (black thick-dashed line).

  • View in gallery

    Performance of the TB scheduling algorithm. (top) Envelop of time balance for tracking tasks 1 (black line), 2 (light gray line), and 3 (gray line) is indicated. (middle) Acquisition time A for all tasks. Theoretical (black dashed line) and estimated (black thin line with asterisks) acquisition times are denoted. In addition, acquisition time for WSR-88D is plotted (black solid line). (bottom) Total revisit improvement factor I. Theoretical (black dashed line), estimated (black thin line with asterisks), and conventional (black solid line) revisit improvement factors.

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Multifunction Phased-Array Radar: Time Balance Scheduler for Adaptive Weather Sensing

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  • 1 School of Electrical and Computer Engineering, and Atmospheric Radar Research Center, University of Oklahoma, Norman, Oklahoma
  • 2 School of Electrical and Computer Engineering, and Atmospheric Radar Research Center, and Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, and NOAA/OAR/National Severe Storms Laboratory, Norman, Oklahoma
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Abstract

Phased-array radars (PARs) have the capability of instantaneously and dynamically controlling beam position on a pulse-by-pulse basis, which allows a single radar to perform multiple functions, such as tracking multiple storms or weather and aviation surveillance. Moreover, these tasks can be carried out with different update times to achieve the goal of better characterizing and forecasting the storms of interest. However, these tasks usually compete for finite radar resources, and scheduling algorithms are often needed to address resource contention. To capitalize on the PAR capabilities, an algorithm based on the concept of time balance (TB) is developed for adaptive weather sensing. Two quality measures are introduced to quantify the gain of adaptive sensing relative to standard scanning patterns used by the Weather Surveillance Radar-1988 Doppler (WSR-88D). A simulation experiment is performed to demonstrate the advantages of adaptive sensing and to test and verify the performance of the TB scheduling algorithm. It is shown that the gain of adaptive sensing can be realized by the TB scheduler; that is, storms of interest can be revisited more frequently within a relatively short period time compared to conventional scanning.

Corresponding author address: Ricardo Reinoso-Rondinel, Room 5900, 120 David L. Boren Blvd., Atmospheric Radar Research Center, University of Oklahoma, Norman, OK 73072-7307. Email: rein3@ou.edu

Abstract

Phased-array radars (PARs) have the capability of instantaneously and dynamically controlling beam position on a pulse-by-pulse basis, which allows a single radar to perform multiple functions, such as tracking multiple storms or weather and aviation surveillance. Moreover, these tasks can be carried out with different update times to achieve the goal of better characterizing and forecasting the storms of interest. However, these tasks usually compete for finite radar resources, and scheduling algorithms are often needed to address resource contention. To capitalize on the PAR capabilities, an algorithm based on the concept of time balance (TB) is developed for adaptive weather sensing. Two quality measures are introduced to quantify the gain of adaptive sensing relative to standard scanning patterns used by the Weather Surveillance Radar-1988 Doppler (WSR-88D). A simulation experiment is performed to demonstrate the advantages of adaptive sensing and to test and verify the performance of the TB scheduling algorithm. It is shown that the gain of adaptive sensing can be realized by the TB scheduler; that is, storms of interest can be revisited more frequently within a relatively short period time compared to conventional scanning.

Corresponding author address: Ricardo Reinoso-Rondinel, Room 5900, 120 David L. Boren Blvd., Atmospheric Radar Research Center, University of Oklahoma, Norman, OK 73072-7307. Email: rein3@ou.edu

1. Introduction

Continuous technology upgrades on the Weather Surveillance Radar-1988 Doppler (WSR-88D) over the past two decades have considerably benefited both the research and operational communities (Crum et al. 1998; Serafin and Wilson 2000). After the installation of WSR-88D, Polger et al. (1994) have shown the significant improvement in the warning of severe weather. Moreover, the percentage of tornado warnings has increased from 35% to 60% and the mean lead time has improved from 5.3 to 9.5 min (Simmons and Sutter 2005). The WSR-88D surveys the atmosphere by mechanically rotating a reflector antenna 360° in azimuth at a predefined number of elevation angles. These conventional scanning patterns are known as volume coverage patterns (VCPs) and lead to update times of 4–6 min for convective storms in order to provide Doppler spectral moments with the required accuracy (ROC 2007). However, rapid updates are often desirable for a better understanding and a forecast of fast-evolving weather systems (e.g., Carbone et al. 1985; Steadham et al. 2002). For example, Rasmussen et al. (2000) suggested that update times of roughly 20–30 s are needed to resolve the processes in tornadogenesis. In addition, Wolfson and Meuse (1993) have shown that, in the terminal area, the lead time for microburst warning can increase from 2.2 to 5.2 min by reducing the update time from 3 to 1 min. Although fast updates can be achieved by increasing the antenna rotation rate, the accuracy of meteorological data is degraded because fewer samples are available for the same spatial sampling. Fast updates without compromising data quality can be achieved by novel techniques, such as range oversampling (Torres and Zrnić 2003; Torres et al. 2004) or beam multiplexing (BMX; Yu et al. 2007). Another approach is to only scan regions of high interest. For example, higher elevation angles can be skipped if no significant data are present (Steadham 2008; Wood and Chrisman 2009). In addition, the radar can adaptively scan regions of rapidly evolving weather with frequent updates, such as the X-band radar network developed by the research Center for Collaborative Adaptive Sensing of the Atmosphere (CASA; McLaughlin et al. 2009). It is advantageous for a radar to revisit the regions of interest more frequently and other regions less frequently, while adequate data quality is maintained. However, such flexibility is limited to conventional weather radars because of the inertia of mechanically rotated antennas.

Phased-array radar (PAR) technology was developed in the mid-1960s, primarily for military applications (Skolnik 2001). A PAR is capable of steering the beam electronically on a pulse-by-pulse basis. This beam agility makes PAR an ideal platform for performing multiple functions, such as surveillance, multitarget tracking, and weapon guidance, which were traditionally carried out by dedicated individual radars. However, all tasks are competing for radar time, and therefore an effective resource management is required for the success of a multifunction radar (e.g., Vannicola et al. 1993; Capraro et al. 2006; Haykin 2006; Gini and Rangaswamy 2008). The central part of resource management is the scheduler, by which these competing tasks can be arranged in a sequence without significant delays (e.g., Sabatini and Tarantino 1994; Miranda et al. 2006). The concept of time balance (TB) was developed and applied to PAR scheduling by Stafford (1990) and was later modified by Wray (1992) and Butler (1998). TB is an adaptive process used to schedule competing tasks by balancing the available radar time and the time demanded by each task. In this paper, the TB scheduling algorithm is extended for phased-array weather radar applications.

The PAR in the National Weather Radar Testbed (NWRT) in Norman, Oklahoma, has been available to research communities since September 2003 (Forsyth et al. 2005). This S-band PAR is able to electronically steer in both elevation and azimuth within a 45° cone-shaped volume. Benner et al. (2009) suggested that the PAR at the NWRT is a promising radar for adaptive sensing, with the goal of improving aviation weather services (e.g., convective thunderstorm forecasts, wind shear, modeling of the growth and decay of storms). Moreover, recent experiments have demonstrated that a better and more precise characterization of fast-evolving weather systems can be obtained with the fast updates provided by the NWRT PAR, compared to the WSR-88D (Zrnić et al. 2007; Heinselman et al. 2008).

In this work, two radar functions are considered for adaptive weather sensing: storm tracking and surveillance. For conventional radars with mechanically rotating antenna, the tracking of storm cells is typically carried out based on the detection from each volume scan. For example, the storm cell identification and tracking algorithm (SCIT) implemented on the WSR-88D is one of such approaches (Johnston et al. 1998). As a result, the tracking of storms and surveillance are performed using the same scanning strategy. In addition, the update time (revisit time) of different storm cells is the same and equal to the time for completing the VCP. On the other hand, a PAR system is flexible enough so that multiple storms can be revisited at different rates and the two functions of storm tracking and surveillance can be performed independently. Because the main purpose of surveillance is to ensure the detection of newly developed storms, it typically does not require the frequent revisits and long observation times as needed for tracking storms. As a result, PAR can adaptively provide fast updates on storms of interest for improved characterization and better forecasts. However, a scheduling algorithm is needed to arrange these tasks that might request different update times and execution times without significant delays.

The primary goal of this work is to develop a framework for a multifunction PAR weather radar to scan a number of regions of interest (i.e., storm cells) with different and fast update times without degrading data accuracy, while surveillance is still maintained to ensure the detection of newly developed storms. This paper is organized as follows. Two quality measures are first proposed and discussed in section 2 to quantify the trade-offs for adaptive weather sensing. In section 3, an algorithm based on TB is introduced to schedule surveillance and competing storm-tracking tasks for weather sensing. To demonstrate TB scheduling and its impact on the two quality measures, simulations based on interpolation of real WSR-88D data to a finer time scale are conducted in section 4. Finally, a summary and conclusions are presented in section 5.

2. Quality measures for adaptive weather sensing

a. Radar tasks for adaptive weather sensing

In this work, a single stationary face PAR is considered. The complexities associated with a rotating PAR were considered by Butler (1998) in the context of military applications and are not discussed here. Adaptive weather sensing consists of tracking multiple storms and surveillance. Each tracking task is defined by task time (T) and update time (U). In addition, the occupancy (O) is defined as the ratio of task time and update time (TU−1; see Manners 1990) and indicates the amount of radar resources inquired by a given task. The task time is the sum of the dwell times for scanning the identified storm in 3D, which is determined by the product of the number of beams, number of pulses, and the pulse repetition time (PRT). It is assumed that the information about the size and location of the storm is provided by a storm identification and tracking algorithm. For example, tracking algorithms that can identify, track, and forecast individual 3D storm cells are given by Crane (1979), Rosenfeld (1987), and Johnston et al. (1998). The update time defines the time period between two consecutive tasks and is assumed to be provided by users. For example, the user can assign high occupancies (i.e., a faster update time for a given task time) to important and potentially hazardous storms and low occupancies to the other storms. Setting the optimal update time for different storm types is a challenging and ongoing research topic. For example, the impact of update times on storm characterization has been evaluated using the NWRT PAR (Heinselman et al. 2008). The surveillance task consists of scanning the regions where no storms are observed. To fully utilize radar resources, the surveillance task is designed to take place whenever no tracking tasks are scheduled. Additionally, this work considers the case where the tracking tasks cannot be interrupted, but the surveillance task can be decomposed into smaller task fragments to be interlaced within tracking tasks. In general, it is desirable that the total occupancy for all tracking and surveillance tasks adds up to 100% so that the radar resources are fully allocated. That is,
i1520-0426-27-11-1854-e1
where OT is the total tracking task occupancy, Oi = TiUi−1 is the occupancy for each tracking task i, N is the number of storms for tracking, and OS is the occupancy for the surveillance task (Sabatini and Tarantino 1994). The task time for the surveillance task (TS) is the total time needed to scan nonstorm regions. The update time for surveillance (US) is obtained from OS = TSUS−1, where OS = 100% − OT. If OT exceeds 100% (OS = 0%), the radar is said to be “overloaded.” This condition should be avoided because the surveillance task may be delayed significantly and the radar may miss any newly formed storms. A detailed discussion of the overloaded case is presented in section 4. Equation (1) can be rewritten in the following form in terms of task times and update times:
i1520-0426-27-11-1854-e2
where Um is the maximum of {U1, U2, … , UN, US}. If we assume that neither Ti nor TS change over Um, Eq. (2) indicates that over the time period Um, the number of executions for tracking task i and surveillance are UmUi−1 and UmUS−1, respectively. Note that so far the discussions are focused on the scheduling requirements of tasks and not on any particular algorithm used to generate the schedule. However, it is desirable that the occupancy requested by these tasks can be fulfilled over Um after they are properly scheduled and executed. A detailed description of the scheduling algorithm is provided in section 3.

In this work, the design criteria for adaptive sensing are to maintain the same data accuracy as the WSR-88D conventional scans (VCPs) in the region of storms and to allow a relaxed requirement (e.g., the standard deviation of reflectivity estimate is doubled) in the surveillance (nonstorm) region. For the purpose of discussions, conventional scanning with WSR-88D is artificially limited to the same 90° sector as the PAR. Further, it is assumed that PAR and WSR-88D scan a given storm using the same PRTs, number of pulses, and angular sampling. In general, with these assumptions, the data accuracy of the PAR would be reduced as the beam is steered off broadside resulting from scan losses (Barton 1988; Billeter 1989). However, scan losses for distributed weather targets are partially compensated by the increased beamwidth, and storms of interest typically exhibit relatively high signal-to-noise ratios (SNRs). Thus, this effect can be neglected so that the data quality is still preserved. Two quality measures are proposed and discussed in the next section to quantify the improved performance offered by PAR adaptive sensing from volume coverage pattern (VCP) scans.

b. Revisit improvement factor

For the WSR-88D, the update time is denoted by UC, which is the same for all storms. Over the time period of Um, all of the storms are revisited UmUC−1 times. On the other hand, for PAR with adaptive sensing, the number of revisits for the ith storm is provided by UmUi−1. Thus, the revisit improvement factor for the ith storm is defined by Ii = UCUi−1, which represents the gain of revisits using PAR adaptive sensing over conventional scans during the same period, while the data quality and spatial sampling are maintained. Moreover, the total revisit improvement factor (I) for N storms is defined by the ratio of the total number of revisits using adaptive scanning over the one with conventional scanning during Um, and can be obtained using the following equation:
i1520-0426-27-11-1854-e3
It is apparent that the total revisit improvement factor is the average of the improvement factors for N storms. The revisit improvement factor depends on the number of cells, their update times, and task times. One should be cautious when interpreting the total revisit improvement factor because values less than one could still represent significant improvement over conventional scanning for the most important tracking tasks.

The revisit improvement factor as a function of tracking occupancy is exemplified in Fig. 1a using a single storm for three different cases. The angular coverage at 0.5° elevation is 18°, 36°, and 72° for cases I, II, and III, respectively, which corresponds to 20%, 40%, and 80% of the 90° sector. If the data accuracy of the WSR-88D’s VCP 12 at an elevation of 0.5° is to be achieved, the task time for the three cases are 1.5827, 3.0573, and 6.1146 s, respectively.

The revisit improvement factor for the three cases is denoted by black, gray, and light gray lines, respectively. Note that the horizontal solid line I = 1 indicates that the number of updates on the storm is equal for both conventional and adaptive scans. For a fixed task time, larger tracking occupancies lead to faster update times, and hence a larger revisit improvement factor is obtained. In addition, for the same occupancy, a larger storm requires more task time and, therefore, the revisit improvement factor is reduced. For example, if the tracking occupancy is 80%, the storm cell for case I can be updated 4 times more frequently than the storm for case III.

c. Acquisition time

If a radar dedicates too much time to one or a few of the tasks, other tasks may be significantly delayed. Thus, a parameter that indicates how long the radar takes to perform multiple storms tracking and surveillance tasks is critical in the context of adaptive sensing. In this work, acquisition time (A) is defined as the minimum time needed to execute each task at least once. For example, if the radar is dedicated to tracking storms (i.e., the total tracking occupancy is high), then the acquisition time will be determined by the completion of the surveillance task. In other words, within the acquisition time, tracking tasks may be executed multiple times. For this case, the acquisition time can be derived by multiplying (1) by US
i1520-0426-27-11-1854-e4
where Uk is the maximum update time for all tracking tasks Uk = max{U1, U2, … , UN}. It is evident that in the time US, the surveillance task was executed exactly once and the ith tracking task was executed USUi−1 times, where USUi−1 ≥ 1. If the maximum update time for tracking is either equal to or larger than the update time for surveillance, then the acquisition time is defined when the tracking task k is complete. In other words, over the period of A the tracking task k will be executed only once. For this case, the acquisition time is derived by multiplying (1) by Uk as
i1520-0426-27-11-1854-e5
It is clear that, task k was executed exactly once and the other tasks were executed at least once, because UkUi−1 > 1(ik) and UkUS−1 ≥ 1. Combining both cases, the acquisition time is determined using the following equation:
i1520-0426-27-11-1854-e6
In other words, the task with the longest update time determines the acquisition time. Figure 1b shows the theoretical acquisition time as a function of tracking occupancy for the same three cases in Fig. 1a. The solid horizontal line represents the acquisition time for VCP 12 at 0.5°, which is also the revisit time for the storm. The dependence of the acquisition time on the tracking occupancy exhibits an interesting feature. On the far right side of Fig. 1b, it can be observed that the acquisition time increases rapidly with tracking occupancy. This occurs under the first condition depicted in Eq. (4): When the tracking occupancy increases, the time that is available for surveillance decreases and, therefore, the update time for surveillance increases, resulting a longer acquisition time. The extreme case is when the tracking occupancy is 100%; the acquisition time is infinity because surveillance cannot be performed. On the other hand, if we follow one of the curves with decreasing tracking occupancy, say case II, the update time for surveillance US decreases as expected. Until it is equal to the tracking update time at approximately O = 88%, US will continue decreasing. Beyond that, the acquisition time is determined by the tracking update time. A further decrease of O leads to longer tracking update times and acquisition times.

The trade-off between the two quality measures can be understood by comparing Figs. 1a,b. First of all, it should be noted that a large tracking occupancy is desirable for achieving a high revisit improvement factor but not necessarily for reducing the acquisition time. Second, an interval of tracking occupancy can be determined where, compared with conventional scanning, more frequent visits (I > 1) and shorter acquisition times can be achieved simultaneously. Such an interval for case II is exemplified in Fig. 1b and it is labeled as a “satisfactory range.” This satisfactory range could be used to establish optimum requirements for adaptive sensing. For instance, case II shows a satisfactory range that goes from 40% to 95% approximately. Thus, a user can utilize such information to choose a tracking occupancy (update time) that would result in improvement over conventional scanning. As an example, if the acquisition time needs to be minimized, then a tracking occupancy of 85% is suitable. On the other hand, if more frequent observations are desired without degrading the acquisition time, then 95% is the most favorable. However, it is not guaranteed that such a satisfactory range can be always obtained. For example, if the surveillance task time is increased, that would result in a larger acquisition time. Thus, the acquisition time curve for case II would move up and a satisfactory range may not be possible to obtain. As another example, if we consider a storm cell that is slightly bigger than case III, then a satisfactory range may not exist. In these cases, the user may decide what tracking occupancy should be assigned to a tracking task such that neither quality measures are significantly degraded. Note that the satisfactory range represents an improvement of both the number of revisits and the acquisition time gained by the adaptive scanning strategy before the observations. However, an algorithm is needed to schedule multiple tracking and surveillance tasks in such a manner so that these improvements can be actually achieved.

3. Time balance scheduling algorithm

The concept of TB was introduced for military applications by Stafford (1990), and a detailed analysis of TB scheduling for tracking multiple point targets was provided in Butler (1998). In this work, the TB scheduling algorithm is extended to adaptive weather sensing using PAR for tracking multiple storms. In the TB algorithm, each tracking task is associated with a time balance variable (TB), which varies when the task is being scheduled and executed. At any given time, a positive time balance indicates that the task is late for execution. Thus, the TB algorithm selects the task with maximum TB to be scheduled next. The surveillance task does not have a TB associated with it, and it is scheduled when the TB for all of the tracking tasks are negative. In other words, surveillance runs when all of the tracking tasks are being executed on time and radar resources are still available. For this algorithm, the surveillance region is divided into a number of fragments (smaller groups of beam positions). The time needed to scan the fragment is defined as the task fragment time (TF). Only one fragment at a time is scheduled so that surveillance can be interlaced within the tracking tasks. The surveillance task is completed when all of the fragments are scheduled.

A flowchart of the TB scheduling algorithm for weather sensing is presented in Fig. 2.

The first step is to acquire information about the storms from the tracking algorithm. This information consists of the number of storm cells and their location and size. The update time for the storms and the fragment time for the surveillance task can be specified either by users or from empirical values in a knowledge-based system. The second step is to set the time balance variable of any new tracking tasks to zero, if they are present. The TB for all the tracking tasks are evaluated in step 3. If one of the tracking tasks has nonnegative TB, step 4 will be reached, where the task with the maximum TB (e.g., task i) will be selected. In step 5, the TB of task i, TB(i), will be decreased by its update time (Ui), while the TB for the rest of the tasks are kept the same. In step 6, task i is scheduled. On the other hand, if in step 3 the TB for all tracking tasks are negative, indicating that all tasks are on time, a fragment of surveillance is scheduled in step 8. After the period of execution of any task, the TB of all tracking tasks is increased. In other words, the TB of each task is increased by the task time (or fragment time in the case of surveillance) of the scheduled task when this task is completed, that is, step 7 (or step 9 in the case of surveillance). This procedure is repeated until there are no more tasks to be scheduled.

An example of scheduling two tracking tasks and surveillance is provided in Fig. 3.

The requested schedules for the two tracking tasks are depicted on the top two panels. The task time for tracking storm cells 1 and 2 is T1 = 10 s and T2 = 14 s, and the requested update time for the two cells is U1 = 20 s and U2 = 35 s, respectively. As a result, the occupancy for the two tracking tasks is 50% and 40%, respectively. The surveillance task is done in fragments of 1 s. As described previously, the TB algorithm is designed to determine the order of the tracking tasks so that no task will be significantly delayed. Initially, at t = 0, the TB for the two tracking tasks are zero (step 2). Any of the tracking tasks can be selected to initialize the schedule, and task 1 is selected (step 4). As a result, the TB for task 1 is decreased by U1 (step 5), as indicated by the black line in the bottom panel at t = 0. The TB of task 2 is unchanged and denoted by the gray line. After task 1 is executed (step 6), the TB for both tasks are increased with the task time of the scheduled task given by T1 = 10 s (step 7). At t = 10 s, the algorithm returns to step 1. Because there are no new tasks and TB(2) has a maximum of 10 s, task 2 is selected (step 4). Similarly, TB(2) is reduced by U2 to −25 s at t = 10 s and task 2 is executed. Subsequently, the TB for both tasks is increased by T2 at t = 24 s. These steps are iterated and the actual scheduled tasks are shown on the third panel from the top. The surveillance task is not scheduled until t = 34 s, where TB(1) = −1 s and TB(2) = −34 s (step 8). One fragment of surveillance is scheduled and the TB for both tracking tasks are increased by TF = 1 s (step 9). The white block in the third panel corresponds to scheduled surveillance task fragments. At t = 35 s, the algorithm returns to step 1 again and the scheduling decision repeats.

It is of interest to know whether the occupancy of the tracking tasks is achieved after TB scheduling. This can be determined by adding the task times of the scheduled tasks over a long period of time. For the first 100 s, the actual occupancy for the two tracking tasks is 50% and 42%, which are similar to the requested occupancies of 50% and 40%, respectively. Moreover, the difference between the requested and actual occupancies becomes smaller if the actual occupancy is estimated over a longer periods. This simple example shows that the TB algorithm can meet the requested update times when executing multiple storms and surveillance tasks. In the next section, we assess the performance of the TB scheduling algorithm using real weather observations.

4. Simulation experiment for PAR adaptive sensing

As mentioned before, only a single-face PAR is considered in this work and, therefore, the radar observation is limited to a 90° sector. In practice, the scene observed by the radar varies constantly due to storm evolution. For example, the size of the storms can change from time to time, new storms can be initiated from existing storms, and existing storms can either enter or leave the radar scene. Because the current PAR at NWRT is not able to implement the proposed scheduling algorithm in real time, reflectivity observed by an operational WSR-88D radar was used to simulate PAR observations for the purpose of verifying the feasibility of the TB scheduling algorithm in a realistic severe weather environment.

a. Simulation methodology

A case of multicell storms was observed by the KTLX radar in Twin Lakes, Oklahoma, on 22 April 2008. Two VCPs, 11 and 12 (Lee and Steadham 2004), were used from 0120 to 0140 UTC and from 0140 to 0300 UTC, respectively. A 90° azimuthal sector between 120° and 210° was selected. Additionally, the azimuthal sampling was assumed to be 1° for both radars. It should be noted that the beam broadening for the PAR off broadside is not considered, because it will not affect the scheduling algorithm or the two quality measures. At each elevation angle, the KTLX data were linearly interpolated in time to artificial, more frequent weather datasets at 15-s intervals. These interpolated KTLX reflectivities are assumed to be the high temporal resolution observations from the NWRT PAR. Subsequently, storm cell centroids were identified if the area enclosed by the 45-dBZ contour of reflectivity is larger than 10 km2. For each storm, a lower-reflectivity threshold of 35 dBZ was used to estimate its azimuthal extent at each elevation angle. As a result, the total number of beams for scanning each cell in 3D for the tracking tasks can be determined. If the total number of beams is smaller than 14, then the storm is no longer tracked and it becomes part of the surveillance task. The information about the size and location of the storms will be fed to the TB scheduling algorithm (step 1 in Fig. 2). Although a better identification algorithm like SCIT could improve the accuracy of beam positions, this simple identification is sufficient for the purpose of demonstrating the TB scheduling algorithm.

To achieve the same data quality, the number of pulses and PRT for tracking tasks was set to be the same as in the VCPs used by the WSR-88D. As mentioned in section 2a, PAR scan losses can be neglected for storm cells with high SNR. Task times for tracking were obtained as the product of the number of beam positions, number of pulses, and PRT. Nevertheless, it is worth mentioning that the PAR is not constrained to use the same waveforms as the WSR-88D. For example, BMX (Yu et al. 2007) and/or range oversampling (Torres and Zrnić 2003; Torres et al. 2004) could be used to further decrease the update time, but this is beyond the scope of this work. It is important to note that variations in the size of storms were assumed to be negligible over the task time period. For surveillance, a dwell time of 9.2 ms was used for all elevations. This is the same as the shortest dwell times used for detection in VCP 12 (i.e., the long-PRT pulses of the batch mode). In addition, the surveillance task was fragmented by elevation. Thus, the surveillance task fragment time may vary in elevation according to the vertical structure of the storms, and TS was obtained by the sum of TF over all of the elevations in the scanning strategy. The surveillance task was considered to be finished when the fragment corresponding to the last elevation angle was executed regardless if, during the acquisition time, fragments of the surveillance task at the lower elevations needed to be redefined due to storm evolution. This simplification can cause missed detections of newly developed storms under extreme cases of high tracking occupancies. This issue can be mitigated by the operator forcing surveillance or by carefully selecting the update time for the tracking tasks. During the experiment period, about 20% of the time the surveillance task would have had to have been redefined due to the storm motion of more than one beam.

The evolution and identification of multicell storms is exemplified in Fig. 4 for the lowest elevation of 0.5°.

At 0120 UTC, only a single cell was present on the right-hand side of the radar view; this is referred to as cell 1. The 35-dBZ contour line for cell 1 is shown and its azimuthal boundaries are depicted by two red lines. Later, at approximately 0125 UTC, cell 2 was split from cell 1 and continued developing. The reflectivity field of the two cells at 0136 UTC is shown in Fig. 4b, where the azimuthal boundaries of cell 2 are denoted by blue lines. At approximately 0140 UTC, cell 2 was further split to produce the third cell and both of them continued moving northeastward with different speeds. The three cells at 0200 UTC are presented in Fig. 4c. As shown in Fig. 4d, at 0217 UTC, cell 2 almost exited the 90° sector and cell 3 started weakening. Finally, only cell 1 remained after 0220 UTC and until the end of experiment. Notice that some storms were partially or totally overlapped during the period experiment. In this work, the TB algorithm handles each storm cell independently. TB could be modified to consider the condition of overlapped storms to further improve the performance of adaptive sensing by sharing the data among the tasks. However, this situation becomes more complex when the overlapped storms need to be scanned using different radar waveforms or when the spatial and temporal continuity of the data need to be preserved.

b. Evaluation of the TB scheduling algorithm

The task times for tracking of three storm cells and surveillance are provided on the top panel of Fig. 5 and are denoted by black, light gray, gray solid, and thin-dashed lines, respectively. The total task time is also included as a black thick-dotted line.

To investigate the impact of update times on the scheduling algorithm, four different periods were selected with different update time requirements. For each period, if more than one storm cell is present, the update times for all of tracking tasks are identical. Specifically, in period I (0120–0125 UTC), the requested update time for the only cell is 35 s; in period II (0125–0140 UTC), the requested update time for both cells is 40 s; in period III (0140–0215 UTC), the requested update time for all three cells increased to 45 s; and in period IV (0215–0300 UTC), an update time of 30 s was requested. Note that during the first 5 min in period IV, cells 1 and 3 were present, but after that only cell 1 remained. The requested occupancy for all the tracking and surveillance tasks can be determined from the corresponding task times and update times.

The performance of the TB algorithm is assessed by comparing the requested and actual executions of tasks. The requested update time in the four periods is denoted by a thick-dashed line in the middle panel of Fig. 5. The update time UC for the 90° sector of KTLX is represented by the black solid thin line. Note that UC is a constant and the reduction of UC at 0140 UTC is caused by the change of VCP from 11 (68 s) to 12 (58 s). The actual update time for a tracking task was determined by finding the time separation between the current and next execution of the same task. The results for cells 1, 2, and 3 are denoted by black, light gray, and gray solid thick lines, respectively. The update time for the surveillance task can be obtained from Eq. (1) and is indicated by a thin-dashed line. It is apparent that the requested update time is fully achieved after TB scheduling in periods I, II, and IV. However, during 0140–0155 UTC in period III, all three tracking tasks were not updated as fast as requested. From the scheduling point of view, they were delayed for execution. The reason is that within this period, the total task time is larger than the requested update time of 45 s. Moreover, between 0155 and 0205 UTC, the actual update time is shorter than the requested one. This is because all of the tracking tasks were executed late and, in order to reach the zero time balance, the scheduler forces faster updates than those requested. After 0205 UTC, the situation is balanced and the requested update times can be met again by TB scheduling.

To understand why such delays occurred, the actual occupancy (i.e., after scheduling) of the three tasks are shown on the bottom panel of Fig. 5 with black, light gray, and gray solid thick lines, respectively. The actual occupancy for a tracking task was estimated by summing its task time within a window of size given by the estimated acquisition time. The actual occupancy was obtained after each scheduling decision was made. The actual occupancy for surveillance was determined in a similar manner and is denoted by a thin-dashed line. The total requested occupancy for both tracking and surveillance is denoted by a thick black-dashed line. It is clear that between 0140 and 0155 UTC, the total requested occupancy exceeds 100%; that is, the radar was overloaded. Simply speaking, the total requested resources are more than what is available from the radar. This has significant impact on the surveillance task because it is only scheduled when the radar has extra resources available (i.e., when all TB are negative). Hence, the surveillance task will not be executed until the overloading is relieved, and the radar may miss any newly formed storms.

The performance of the TB scheduling algorithm can also be investigated by defining the envelope of TB for each storm cell tracking task denoted by . For a tracking task, is defined as the value of TB every time task that is executed. Consider the example of scheduling two tracking tasks shown in Fig. 3. Task 1 is scheduled at 0, 24, 49, 60, 84, and 100 s; hence, is the line connecting the TB values at those times. Here, is shown on the top panel of Fig. 6, where the constant indicates the task is on time and, on the contrary, an increasing means that the task is late for execution.

When only cell 1 needs to be scheduled, its remains at zero, indicating that the task is scheduled on time because there are no other competing tracking tasks. The reason for cell 2 being executed with an initial delay of 10 s is that cell 1 had a slightly larger TB at the moment when cell 2 was added to the scheduler algorithm. Thus, cell 1 with T1 = 10 s was scheduled first. A similar situation happened when cell 3 began its execution, but now with a delay of around 30 s, which corresponds to the sum of T1 and T2 (top panel of Fig. 5). The overloading case between 0140 and 0155 UTC is manifested by the continuous increase of . Between 0155 and 0205 UTC, each decreases with time because tracking tasks are scheduled in time intervals that are smaller than those requested. Because all three TBs are positive, the TB algorithm “catches up” by constantly scheduling tracking tasks to promptly achieve a balanced state. After 0205 UTC, behaves normally again, as is expected for a nonoverloaded case.

The two quality measures—acquisition time and revisit improvement factor—for adaptive sensing after TB scheduling are provided on the middle and bottom panels of Fig. 6. The theoretical acquisition time and revisit improvement factor were computed using (6) and (3), respectively, and are depicted by thick-dashed lines. The estimated acquisition time was calculated by counting the minimum time in which all of the tasks were executed at least once. Similar to the calculation of the actual occupancy, the estimated revisit improvement factor for a tracking task was calculated by summing the task time over the estimated acquisition time. Both the estimated acquisition time and the revisit improvement factor are indicated by a thin line with asterisks. The acquisition time for KTLX is plotted in the middle panel of Fig. 6 with a black solid line. Note that the acquisition time for conventional scanning is the same as the update time. It is important to point out that for this experiment, the estimated acquisition time for the PAR is always smaller than the one with the WSR-88D under nonoverloading conditions. Moreover, the estimated revisit improvement factor is always larger than unity. These results indicate that, compared to conventional scanning, adaptive sensing has the potential to revisit the storms more frequently and complete all of the requested tasks in a relatively short period of time. Furthermore, the theoretical and estimated values for both acquisition time and revisit improvement factor agree extremely well, except for the period between 0140 and 0205 UTC when the overloading and “catch up” conditions occurred. This result verifies that the gain from adaptive sensing can be realized through the TB scheduling algorithm. It is shown that storms in this experiment can be revisited at an average rate of 1.5–2 times faster than the VCP scans, and the time to complete the requested tasks can be reduced from VCP scans by as much as 50%.

During the periods of overloading and catch up, the theoretical and estimated quality measures do not agree. During the overloading period, the occupancy of the surveillance task is 0%, and the theoretical A is infinity. The estimated A is extremely large because surveillance is not being executed until the beginning of the catch-up period. During both periods, the estimated I shows a continuous increment compared to the theoretical I. Such increment is caused by two factors: 1) a delay in all tracking tasks that would produce an actual update time that is smaller than the one requested (middle panel of Fig. 5), and 2) the window in which I was estimated becomes extremely large because of the inability to schedule surveillance fragments. Therefore, the estimated I becomes larger than the theoretical one during the overloading and catch-up periods. In general, overloading results in poor performance of the TB algorithm; the estimated acquisition time becomes larger than the conventional update time, and the revisit improvement factor becomes smaller than 1. Dealing with the overloading case is not the focus of this work; however, a recent work by Reinoso-Rondinel et al. (2010) proposed two approaches to handle this situation. In the first approach, the requested update times are adjusted proportionally so that the total tracking occupancy is less than 100%, and therefore the surveillance task continues to be executed. The second approach, based on Miranda et al. (2007), suggests the use of task prioritization in the TB algorithm such that the performance of tasks with lower priorities is allowed to be degraded, while the ones with higher priorities may still achieve the requested performance.

5. Summary and conclusions

For conventional radars, the trade-off between fast updates and high data quality for weather applications is inexorable. Phased-array radar systems have the potential to overcome such trade-offs and, consequently, lead to increased warning lead times and better understandings of fast-evolving weather phenomena. PAR is ideal for performing multiple tracking tasks and surveillance in an adaptive sensing paradigm. However, the problem of allocating radar resources for surveillance and competing storm-tracking tasks needs to be addressed. In this work, a TB scheduling algorithm was presented for this purpose. Two quality measures were introduced: revisit improvement factor and acquisition time. Both measurements were used to evaluate the performance of adaptive sensing relative to that of conventional scanning given the same data accuracy in storms.

Reflectivity data taken from KTLX were used to simulate high-temporal-resolution PAR data in order to test the TB scheduling algorithm. Actual update times (occupancies) and estimates of acquisition time and revisit improvement factor were calculated after scheduling to evaluate the gain of adaptive sensing and to assess the performance of the TB scheduling algorithm. For the nonoverloading cases, the results have demonstrated that adaptive weather sensing for PAR based on TB can provide more frequent revisits on storms than VCPs used by WSR-88D, while the same data quality and spatial sampling are maintained. The TB scheduling algorithm is capable of scheduling multiple tracking tasks and satisfying requested update times (occupancies). Consequently, the theoretical revisit improvement factor and acquisition time can be achieved. However, this is not the case when an overloading situation arises (i.e., when the total requested occupancy is higher than 100%) and it becomes impossible to meet the requested update times not only for the TB algorithm, but for any scheduling algorithm without any trade-offs.

A scheduling algorithm is one of the most important components in a multifunction PAR system. Such algorithm and knowledge of both quality measures may prove to be key in balancing the execution of competing radar tasks and enhancing the number of revisits and acquisition time gained by adaptive sensing compared to conventional scanning. Still, under some weather scenarios conventional scanning may be preferable (e.g., a large storm covering the entire 90° sector). In such situations, the user can intervene and create a single tracking task that covers the entire volume as part of adaptive sensing, a versatility that is easily obtained with PAR. It is foreseen that in an adaptive weather sensing context, such as the one presented in this work, users of weather products will benefit from better data interpretation leading to significant improvements on weather warnings and forecasts.

Acknowledgments

This work was primarily supported by NOAA/NSSL under Cooperative Agreement NA17RJ1227. Part of this work was supported by DOD, EPSCoR Grant N00014-06-1-0590.

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Fig. 1.
Fig. 1.

Quality measures for adaptive sensing: (a) revisit improvement factor I and (b) acquisition time A for cases I (dark line), II (gray line), and III (light gray–dashed line) as a function of storm-tracking occupancy O. Large O are desired to obtain large revisit improvement factors, but these do not necessarily lead to small acquisition times. A satisfactory range is indicated in (b) for case II where both I and A are improved with respect to the WSR-88D VCP 12.

Citation: Journal of Atmospheric and Oceanic Technology 27, 11; 10.1175/2010JTECHA1420.1

Fig. 2.
Fig. 2.

Flowchart for the TB scheduling algorithm. (left branch) The algorithm selects the tracking task with maximum nonnegative TB for the next tracking task execution; otherwise, (right branch) surveillance is scheduled. The TB for each tracking task is updated on every iteration.

Citation: Journal of Atmospheric and Oceanic Technology 27, 11; 10.1175/2010JTECHA1420.1

Fig. 3.
Fig. 3.

(top) Scheduling of two tracking tasks and surveillance task using the TB algorithm. Requested schedule for cells 1 (black block) and 2 (gray block) are shown on the first two rows. Requested U for cells 1 and 2 are 20 and 34 s, respectively. Actual schedule for cells 1 and 2 and surveillance is presented in the third row. The surveillance task is continuously executed while the TB of the tracking tasks is all negative. (bottom) Time balance evolution that is used to decide which tracking or surveillance task needs to be scheduled next.

Citation: Journal of Atmospheric and Oceanic Technology 27, 11; 10.1175/2010JTECHA1420.1

Fig. 4.
Fig. 4.

Reflectivity data of storm cells at 0.5° elevation angle in central Oklahoma on 22 Apr 2008. Four distinct regimes are identified: (a) cell 1, (b) cells 1 and 2, (c) cells 1, 2, and 3 and (d) cells 1 and 3 (cell 2 left 90° sector).

Citation: Journal of Atmospheric and Oceanic Technology 27, 11; 10.1175/2010JTECHA1420.1

Fig. 5.
Fig. 5.

Performance of the TB scheduling algorithm. (top) The task times for cells 1 (black line), 2 (light gray line), and 3 (gray solid line) and surveillance (black thin-dashed line) are denoted. The total task time of tracking and surveillance is represented (black thick-dotted line). (middle) The update times for each tracking task and surveillance are shown. Requested update times for each tracking task (black thick-dashed line) and surveillance (black thin-dashed line). Actual update times after TB scheduling for cells 1 (black solid thick line), 2 (light gray solid thick line), and 3 (gray solid thick line) are represented. In addition, the task time for WSR-88D (UC) is indicated (black solid thin line). (bottom) The occupancy for each tracking task and surveillance are provided. Total requested occupancy is represented (black thick-dashed line).

Citation: Journal of Atmospheric and Oceanic Technology 27, 11; 10.1175/2010JTECHA1420.1

Fig. 6.
Fig. 6.

Performance of the TB scheduling algorithm. (top) Envelop of time balance for tracking tasks 1 (black line), 2 (light gray line), and 3 (gray line) is indicated. (middle) Acquisition time A for all tasks. Theoretical (black dashed line) and estimated (black thin line with asterisks) acquisition times are denoted. In addition, acquisition time for WSR-88D is plotted (black solid line). (bottom) Total revisit improvement factor I. Theoretical (black dashed line), estimated (black thin line with asterisks), and conventional (black solid line) revisit improvement factors.

Citation: Journal of Atmospheric and Oceanic Technology 27, 11; 10.1175/2010JTECHA1420.1

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