1. Introduction
Hypothesis testing in nowcasting typically involves a mind-numbing crawl through hours of remotely sensed data and human identification of features in the dataset. This is then followed by a quasi-objective association of human-identified features to observed events. A consequence of such a labor-intensive method is that the simplest analyses often take years of effort.
For example, Davies (2004) studied the relationship between environmental sounding parameters and tornado potential in supercell thunderstorms, and 518 environmental soundings from January 2001 to July 2003 were culled from a numerical model to represent the near-storm environment in the inflow region of a nearby supercell. Supercells were identified by examining the text of associated tornado warning products issued by the National Weather Service (NWS) or from analyzing radar reflectivity signatures. From this dataset, statistics were developed to differentiate between tornadic and nontornadic supercell environments. The study examined just 10% of tornado events occurring in the time period. A more complete analysis could have been performed had there been an automated technique to extract the environmental parameters in the vicinity of candidate supercells.
As another example, Trapp et al. (2005) examined radar reflectivity images associated with 3828 tornadoes that occurred in 1998–2000 to determine the percentage of tornadoes that were spawned by quasi-linear convective systems (QLCS). Trapp et al. (2005) describe the process as “the labor-intensive categorization of a large number of events” into three broad categories: cell, QLCS, or other. Their categorizations were largely subjective in nature and reliant on the interpretation of the people examining the reflectivity imagery. Such long-term studies are undertaken less often than they should, because of the lack of a tool to analyze large amounts of data in an objective manner.
It would be far better if tasks like storm classification and attribute extraction in the vicinity of storms could be accomplished by reliable and accurate automated algorithms. The most straightforward approach to automated analysis would be to look within a small neighborhood (say 10 km) of an event of interest (say occurrence of a lightning flash) and see if certain values of a spatial gridded field (say the maximum radar reflectivity observed at 6 km or higher) are associated with the event. This does have the advantage of being able to rapidly accumulate large amounts of data with which to test a hypothesis (e.g., if a 45-dBZ echo is observed at 6-km height, a cloud-to-ground lightning strike will occur within the next 15 min). However, in reality, the cloud-to-ground lightning flash could occur anywhere from within an electrified cloud. The neighborhood would have to be so large that other, nearby storms would also get pulled in. It is because pixel-by-pixel verification does not work very well that researchers have resorted to hand creation of testing cases.
The objective of this paper is to describe a technique that makes it possible to extract features from large amounts of spatial data (typically remotely observed, although it could also be numerical model assimilated or forecast fields) and use the features to answer questions in an automated manner. Such automated analysis based on large datasets is referred to as data mining. Data mining is a multidisciplinary field that provides a number of tools that can be useful in meteorological research.
The rest of this section provides a brief introduction to data mining and provides the motivation for the technique described in this paper. The technique itself consists of three major steps, all of which are described in section 2. Two example uses of features extracted by using the technique of this paper are described in section 3. It should be emphasized that the point of this paper is not the results of the analyses themselves—even though they are quite interesting—but that analyses of this sort can be carried out quickly and objectively.
a. Data mining
Hand et al. (2001) define data mining as the analysis of often large observational datasets to find relationships and to summarize data. It comprises methods from applied statistics, pattern recognition, and computer science. The input to data mining techniques, such as neural networks or decision trees, is a set of “training patterns,” where each training pattern consists of multiple associated observations.1
Often, one of the observations is usually unavailable or hard to collect. The problem, then, is to estimate the normally unavailable observation using the commonly available ones. For example, there is a practical limit imposed by cost on the density of rain gauges. Radar and satellite observations are routinely available but do not provide exact measures of rainfall. Thus, data mining approaches such as neural networks (Hong et al. 2004) have been used to devise high-density rainfall estimates starting from remotely sensed measurements.
Another common use of data mining has been in quality control of datasets. A better, but usually unavailable, source of data can be used to devise models to determine the quality of routinely collected data using internal measures on the data itself. These models can then be applied in real time. Thus, hydrometeor classification by polarimetric radar was used to create a fuzzy logic system (Kessinger et al. 2003) operating on the texture of Weather Surveillance Radar-1988 Doppler (WSR-88D) reflectivity, velocity, and spectrum width fields to determine whether the echoes at each range gate corresponded to precipitation.
A common thread to both the rainfall and quality-control studies mentioned is that the input features to the data mining system are statistics in a local neighborhood of every observation point. Such a data mining approach is limited to estimating spatially smooth fields such as rainfall. If the grid contains discontinuities (such as when a satellite image includes both ground and cloud tops), statistics computed in rectangular subgrids of the image will be unreliable, because they will include pixels from both sides of the discontinuity.
If the requirement is to identify characteristics of storms, the approach of using neighborhood statistics does not work, because the pattern instances in such a case should not be geographic points or pixels but the storms themselves. Correspondingly, the features used in the data mining technique have to correspond to attributes of the storms, not just the neighborhood of pixels. For example, to determine whether a given storm is tornadic, candidate circulations were identified from radar velocity measurements using the mesocyclone detection algorithm of Stumpf et al. (1998). Properties of the circulation were then used to train a neural network to identify tornadic storms (Marzban and Stumpf 1996). Similarly, to predict the hail potential of a storm, storms were identified using the stormcell identification and tracking algorithm of Johnson et al. (1998). Properties of the storm such as cell base, height, and near-storm environmental parameters were used to devise a neural network to nowcast hail (Marzban and Witt 2001).
The tornado and hail examples illustrate the crux of the problem. For each problem to be addressed through data mining, completely separate identification algorithm and attribute-extraction techniques were required. A general-purpose method that enables identification of storms and extraction of features from any suitable spatial field would be a significant advance. It should be noted that different applications would have different definitions of what constitutes a storm (data thresholds, minimum sizes, and presmoothing) and would require different attributes to be extracted from different spatial grids, but this does not imply that a general-purpose algorithm to extract such attributes cannot be devised. The availability of a general-purpose method would enable data mining to be applied routinely on a number of meteorological datasets and permit objective answers to questions that require automated analysis of large amounts of data.
Data mining in meteorology, then, often requires, as inputs, neighborhood features as well as attributes of storms at different scales, corresponding to the phenomena of interest. Neighborhood features are straightforward to compute. However, a general-purpose technique to extract storm attributes is needed in order to use extracted features to answer research questions on large amounts of data. This paper describes such a general-purpose technique for extracting storm properties from spatial grids.
2. Method
The technique consists of three steps: 1) identify storms from spatial grids; 2) estimate the motion of these storms; and 3) use the spatial extent of the storms and their movement to extract geometric, spatial, and temporal properties of the storms. These steps are described in detail in this section. The extracted properties can be used to answer different types of research questions. Two such questions are presented in section 3.
a. Identifying storms
Extracting storm attributes requires a general-purpose definition of a storm that is amenable to automated storm identification. Lakshmanan et al. (2009) define a storm in weather imagery as a region of high intensity separated from other areas of high intensity. A storm in their formalism consists of a group of pixels that meet a size criterion (“saliency”; Najman and Schmitt 1996), whose intensity values are greater than a value criterion (“minimum”) and whose region of support “foothills” is determined by the highest intensity within the group. The “intensity” depends on the weather data in question: reflectivity from weather radar, flash density from cloud-to-ground lightning observations, or infrared temperature from weather satellites may all be used.
The neighbors Nxy of a pixel x, y are the set of pixels within some spatial distance of that pixel. Through experiment, we found that setting this distance threshold to be 0.4
This technique of storm identification differs from the approach presented by Lakshmanan et al. (2009, 2003). Unlike in Lakshmanan et al. (2009), multiscale segmentation is possible. Also, pixels that are not spatially connected can belong to the same cluster (see Fig. 1c). In the multiscale approach of Lakshmanan et al. (2003), clusters were combined based on intercluster distances (i.e., clusters a and b would be combined if ‖μa − μb‖ was below some user-specified threshold). Here, clusters are combined to meet a size threshold. Storms identified through a size-based saliency definition correspond better to intuitive understanding of storm structures in remotely sensed imagery (Lakshmanan et al. 2009).
b. Motion estimation
There are, broadly, two approaches to estimating movement from spatial grids. A hybrid of the two basic approaches is followed in this paper.
The optical flow approach estimates movement on rectangular subgrids of the image by maximizing the cross correlation between a subgrid at a previous time and a translated version of the subgrid. For example, Tuttle and Gall (1999) utilized an optical flow approach to estimate winds in tropical cyclones. Such methods suffer from two major flaws: the extracted wind fields tend to be chaotic because of the approach’s reliance on the maximum, a statistically noisy operation, and because of the “aperture” problem. The aperture problem refers to the impossibility of following the movement of entities in a direction parallel to their length when estimating movement using subgrids that are smaller than the entity (Barron et al. 1994). The first problem (of chaotic motion fields) can be ameliorated by smoothing the image and imposing a maximum deviation from a global motion vector, as done by Wolfson et al. (1999). Another way to address the problem of noisy motion fields without imposing a global direction is to use a variational optimization approach and to remove echoes that correspond to unpredictable scales, as in Turner et al. (2004). The second problem, of aperture, remains endemic to optical flow approaches.
The second approach to estimating movement from spatial grids relies on associating storms between frames to determine the movement of each storm. For example, Johnson et al. (1998) describe a method of identifying storms and using heuristics to associate them across time, whereas Dixon and Wiener (1993) uses a global cost function to minimize association errors. However, association is fraught with problems, because storms grow, evolve, decay, merge, and split; each of these is a potential source of association error. Practical algorithms for association involve numerous heuristics. Applying the algorithms unchanged to a variety of remotely sensed fields can involve difficult choices, so the resulting parameters often perform better on one type of imagery than others. Also, in practice, motion estimates from storm association may perform poorly in situations such as changes in storm movement or stormcell splits and merges because of the technique’s reliance on the position of centroids, which are greatly affected by storm evolution. However, operational methods of storm tracking all employ association because of one huge benefit: the ability to track storm properties. Optical flow approaches are based on subgrids and therefore do not provide the ability to identify or track storm attributes over time.
One way to obtain high-quality motion estimates, retain the ability to associate motion with storm entities, and avoid association error is to employ a hybrid technique, such as that of Lakshmanan et al. (2003). Storms are identified in the current frame and associated, not with storms in the previous frame, but with the image in the previous frame. Thus, movement is associated not on rectangular subgrids but on subgrids that have the shape and size of the current cluster. Even if a storm has merged or split between the two frames, the motion estimate will correspond to the parts of image in the previous frame that the current cluster correspond to. As long as storms do not grow or evolve too dramatically in the intervening time period, this cluster-to-image matching side steps association errors and provides high-quality motion estimates, because the motion estimate corresponds to a relatively large group of pixels (see Figs. 1e,f). Motion estimates are estimated over the entire area of interest by interpolating spatially between the motion estimates corresponding to each storm. Motion estimates are also smoothed temporally over time by using a constant-acceleration Kalman filter. This yields a motion estimate over the entire domain.
c. Extracting properties
Once clusters have been identified and their motion have been estimated, geometric, spatial and temporal properties of the clusters can be extracted.
1) Geometric properties
The number of pixels in each identified cluster is indicative of the size of the cluster. Depending on the map projection used, that can be converted either exactly or approximately into a size in square kilometers.
2) Spatial properties
In addition to the properties of the clusters themselves (geometric properties), it may be useful to extract properties of the clusters that correspond to their location on the earth. For example, it may be desirable to obtain the number of people who live in the area covered by the cluster at a particular point in time. As long as such information is available as a spatial grid, this cluster-specific information can be readily extracted.
Spatial grids, such as remotely sensed observations or population density, should be remapped to the extent of the clustered grid, so that data are available for each pixel within a cluster. Geospatial information, such as watch or warning polygons, can be converted to a spatial grid where the grid value reflects whether the pixel is within the polygon. Then, the pixels x, y belonging to each cluster can be used to estimate spatial properties.
It is not necessary to use the max operation; other scalar statistical properties, such as mean, variance, minimum, median, and 90th percentile, can be similarly computed. Nonscalar properties, such as probability distribution functions, can be estimated by accumulating the frequency of occurrence of values within quantization bands.
Derived properties may also be estimated from spatial grids. For example, the severe hail index (SHI; Witt et al. 1998) may be used to determine if the radar data at a grid point corresponds to stratiform precipitation or to convection. The fraction of the cluster that is convective can be estimated by finding the ratio of pixels that have SHI above a certain threshold to the size of the cluster. The number of people who live in the area covered by the cluster at a particular point in time (i.e., the number of people affected by the storm) can be obtained by numerically integrating the population density associated with each of the pixels within the cluster.
Thus, spatial properties of the jth cluster can be extracted by computing scalar statistical properties over all the pixels xi, yiεclusterj on spatial grids that have been remapped to the extent and resolution of the clustered grid.
3) Temporal properties
A leading indicator for many phenomena is the rate of increase or decrease of a spatial property. For example, cloud-top cooling rates measured from satellite observations are an important indicator of convection. An increase in the aspect ratio of an area of high reflectivity coupled with a decrease in midaltitude rotation may indicate that a storm is undergoing evolution from an isolated cell to a linear system. Temporal properties can be estimated from a time sequence of spatial grids in two ways: one that relies on cluster association between frames of the sequence and another that does not.
It should be noted that this technique relies only on the clustering of the current field, not on the clustering of the previous frame. The assumption, instead, is that the pixels xi, yi that are part of clusterj will have moved with the same speed and direction from the previous frame. Therefore, this technique handles morphological operations such as splits and mergers well, because it does not require clustering of the previous frame; instead, just the corresponding part(s) of the previous grid are used. However, this technique assumes that there has not been significant spatial growth or decay of the storm between the time frames. If, for example, there has been decay, then δMESH,clusterj will reflect only the changes within the core of the storm (because the cluster at t0 will be smaller than the entity in t−1). On the other hand, if there has been growth, then statistics are computed over a slightly larger area. Depending on the scalar statistic and how it is distributed within the storm, this may not matter. For example, the impact is negligible for the maximum expected hail size criterion, because the maximum values tend to be in the core of the storm and not at the periphery.
The cluster-to-image matching method is more tolerant of unstable clustering results (i.e., poor storm identification or tracking). However, there are three limitations. First, as noted earlier, sizeable changes in storm size will cause problems. Second, if different parts of the cluster move in different directions, then the motion estimate will be wrong. Third, estimating changes in geometric properties, such as size or aspect ratio, has to be performed using the cluster association technique, because the second technique does not rely on the clustering result on earlier frames of sequence.
3. Example uses
Section 2 described the technique of identifying storms from geospatial images and extracting geometric, spatial, and temporal attributes of those storms in a fully automated manner. The technique, when applied to large collections of imagery, yields a pattern (a set of attributes) for each identified storm. These patterns can be used as inputs to standard statistical or data mining techniques. The utility of such an approach to answer a broad range of questions is illustrated in this section.
a. Forecaster skill
Is it more difficult to issue tornado warnings when the tornadoes are associated with short-lived pulse storms compared to tornadoes associated with supercells that have a much longer life? Intuitively, the answer to the question seems to be that it should, because pulse storms ought to be more unpredictable. Yet, the truth of such a statement would imply that many of the performance statistics employed by the NWS to evaluate the continuing improvement of forecast offices are problematic; year-over-year comparisons of the critical skill index (CSI; Donaldson et al. 1975) would be heavily influenced by the type of storms within the county warning area of a given NWS forecast office during the given time periods. Similarly, interoffice comparisons and rankings of forecast offices would be questionable practices. Before making such a charge, though, it is important to prove that it is indeed the case that tornadoes are systematically easier or harder to predict, depending on the type of storms they are associated with.
To show that tornadoes associated with supercells are easier to predict, it is necessary to compute the CSI achieved by NWS forecasters on a large number of supercell storms. One would then compute the CSI on pulse storms and check whether the difference in CSIs (if any) was statistically significant. To achieve statistical significance, it is expected that hundreds of tornado warnings would have be evaluated. This would mean that many hundreds of storms would have to be classified into supercells versus pulse storms. Doing this by hand would be prohibitively time consuming and expensive. An automated technique to do this is required to answer the question of forecaster skill in a practical manner. At the scale of storm cells, no automated storm-type algorithm exists.
The data mining approach of this paper was employed to address this question. The storm attributes were provided as input to a machine intelligent engine that would output the type of storm. The engine was trained based on human classification of a small subset of the complete collection of data. The first step in training was to manually associate a storm type with each identified storm by analyzing 72 multiradar images from six days and drawing polygons (see Fig. 2) representing areas where all the storms belonged to a certain type (unorganized, pulse storms, quasi-linear convective line, or supercells).
The polygons were mapped on to a spatial grid of the same extent and resolution as the multiradar reflectivity composite used for clustering and storm identification. Each pixel within the polygon was assigned a category corresponding to the storm type associated with the polygon.
The set of patterns corresponding to all the storms from the 72 images where storm-type polygons were manually drawn were then presented to the automated decision tree algorithm of Quinlan (1993) as implemented by Witten and Frank (2005). It was found that 30% of the training patterns were reserved for pruning the created decision tree (to limit overfitting). Part of the resulting decision tree is shown in Fig. 3. The full decision tree (as Java source code) is available online at http://cimms.ou.edu/~lakshman/aicompetition/. On an independent test set of 72 more images, the decision tree had a multicategory true skill statistic (Wilks 1995) of 0.58. More sophisticated data mining techniques yielded only marginal improvements over the plain decision tree (Lakshmanan et al. 2008) but lose the easy understandability of the machine model that a decision tree provides.
The trained decision tree was then used to classify all identified storms on 12 outbreak days over the entire continental United States. Every tornado warning issued by the NWS on those days was associated with the closest storm to the start of the polygon and thus to the storm type of that storm. Forecast skill was then computed conditioned on the type of storm.
In the case of tornado warnings, there was a significant (95% confidence) difference in skill between supercells and pulse storms, as shown in Fig. 4. The significant difference in skill held for all pairs of storm types except between convective lines and supercells. A data mining approach was thus used to show that tornado warning skill varies by storm type. For more results from this study, including lead time and the skill associated with thunderstorm warnings, see Guillot et al. (2008).
b. Lightning prediction
As another illustration of the utility of the attribute-extraction technique described in this paper, consider the problem of predicting cloud-to-ground lightning activity. A data mining approach may involve finding leading indicators of lightning and then using those to predict the onset of lightning activity. For example, Hondl and Eilts (1994) found that radar reflectivity at −10°C was an indicator of lightning. Watson et al. (1995) suggested the use of vertically integrated liquid (VIL; Greene and Clark 1972) as a predictor.
One advantage of cloud-to-ground lightning is that it is a hazard that is observed in real time. There is no similar real-time source of information on other severe weather hazards such as hail. Thus, it is possible to consider creating a data mining approach to predict cloud-to-ground lightning. If a system can be trained on input spatial grids of reflectivity and VIL at t−30min to predict the cloud-to-ground lightning activity that is observed at t0, it should be possible to use that system on the set of input spatial grids at t0 to predict the lightning activity at t30min. This approach was undertaken by Lakshmanan and Stumpf (2005) and found to not work very well.
There are two reasons why the approach of using spatial grids directly did not work very well. First, storms move. VIL at xi, yi, t−30min was an indicator of lightning activity not at xi, yi, t0 but at xi + uiδt, yi + υiδt, t0, where ui, υi is the motion of the storm at xi, yi. If that was the only problem, then the target lightning field at t0 could be advected backward before training the engine using inputs and outputs at xi, yi. A second problem is that, although reflectivity at −10°C was a leading indicator, it was a leading indicator of lightning somewhere within the storm, not necessarily at the location of the convective top. In other words, lightning activity was not limited to the core of the storm, but it often occurred in the anvil region where the radar reflectivity is not as high.
At coarse spatial resolutions, neither of these drawbacks applies. A pixel-by-pixel input–output mapping has been successfully employed at a 22-km resolution to train a neural network (Burrows et al. 2005). However, at the approximately 1-km resolution that we would like to address, a straightforward input to output mapping at every grid point will not work. Instead, it is necessary to consider storms as entities and train the model with storm properties, not just pixel values. This, of course, is exactly what the attribute-extraction technique described in this paper provides.
Cloud-to-ground strike locations from the National Lightning Detection Network (NLDN) were averaged in space (3-km radius) and time (15 min) to create a lightning density grid; that is, the value of the grid at any point was an exponentially weighted number of strikes within 15 min and 3 km of the point with farther away flashes receiving less weight.
The t30min lightning density grid was advected backward 30 min and used as one of the inputs to the attribute-extraction algorithm. Clustering was performed on a multiradar reflectivity composite image over the continental United States (Lakshmanan et al. 2006) at a scale (minimum size threshold) of 200 km2. Cluster attributes were extracted using spatial grids of VIL, reflectivity isotherms, current lightning density (the full list of attributes are listed in Table 2), and the t30min lightning density that was advected backward 30 min.
A neural network was trained using spatial (1-km resolution every 5 min) grids over the continental United States on six days between April and September 2008: 10 April, 14 May, 13 June, 1 July, 20 August, and 11 September.2 The output of the neural network is a number between 0 and 1 that, because of our choice of neural network architecture, is the probability of the storm producing lightning 30 min later. This output was thresholded to yield a binary outcome: lightning or no lightning. The variation of the skill of the neural network and steady-state technique on an independent test set at different thresholds is shown in Fig. 5. If the output of the trained neural network is thresholded at 0.41, then the algorithm has its maximum critical success index (CSI; Donaldson et al. 1975) of 0.79 when predicting lightning activity 30 min ahead. By way of contrast, simply advecting the current lightning density field (and thresholding the forecast field at zero, where the steady-state technique’s skill is maximum) attains a CSI of 0.69. Other skill scores at the same thresholds are shown in Table 3.
The difference in the probability of detection (POD) between the data mining technique of this paper and the simple steady-state forecast is on the order of 0.2 (0.91 versus 0.71: see Table 3). By definition, the steady-state forecast consists of already occurring lightning activity. Therefore, the increase of 0.2 in POD has to be due to successfully predicted lightning initiation. However, the price of this increase in POD is a corresponding increase in the false alarm rate (of about 0.1). On balance, though, the technique demonstrates improvements in CSI of 0.1 and in Heidke skill score (HSS; Heidke 1926) of 0.04. Thus, the technique is able to predict the initiation of lightning with skill.
In real time, the neural network is employed to predict the lightning activity associated with a storm. This probability is distributed within the extent of the storm and then advected forward in time to yield the probability of cloud-to-ground lightning at a particular point 30 min in the future. Example output from the algorithm is shown in Fig. 6. Note that the algorithm is able to successfully predict initiation of lightning in the storm in the south-central part of the domain.
4. Discussion
This paper described a technique of automatically extracting geometric, spatial and temporal attributes of storms. The technique is comprised of three steps. The first step is clustering a geospatial grid using an expectation-minimization criterion that balances the needs of self-similarity and spatial contiguity within and between clusters. The clustering can be controlled in a general-purpose manner through a saliency criterion based on size. The second step is estimating motion using a hybrid technique that relies on the best match between the clusters in one frame and the image itself in the previous frame. Spatial and temporal smoothness of the motion estimates are achieved by interpolation and Kalman filtering. The third step is using the pixels that belong to the cluster to fit the cluster to an ellipse to extract geometric properties. Spatial properties can be extracted by computing scalar statistics on appropriately remapped spatial grids over the pixels that belong to the cluster. Temporal properties can be computed in one of two ways depending on whether association errors or growth/decay is more likely in the time period of interest.
The technique when applied to large collections of imagery yields a pattern (i.e., a set of attributes) for each identified storm. These patterns can be used as inputs to standard statistical or data mining techniques. The utility of such an approach was illustrated by considering two problems: forecaster skill in issuing tornado warnings and the creation of a real-time, high-resolution lightning prediction algorithm.
Object identification is also now an active area of research in model verification (Marzban and Sandgathe 2006; Davis et al. 2006). However, the challenge in that area is quite different and cannot be addressed by the technique of this paper. In object-based model verification, objects are identified in both model forecasts and observed fields and an attempt is made to associate observed objects with forecast objects (and vice versa) based on their properties. The method of this paper deals with objects identified on one spatial field and properties of that object extracted from other spatial fields. In doing so, an implicit assumption is made that the extracted object is aligned in all the fields, an assumption that holds on observed data but emphatically (given the skill of present-day models) does not hold for observed data versus model forecasts.
The technique described in this paper allows for the extraction of properties at different scales. However, it is not yet known how to select the size parameter that determines the scale. For example, would the lightning prediction have been improved if the size threshold had been set to 150 km2 instead of 200 km2? Currently, this can be determined only through experimentation. An objective scale selection criterion would be an improvement.
The lightning prediction algorithm is ongoing work, presented to illustrate the utility of being able to rapidly build automated algorithms by training on copious amounts of data. The authors are continuing to collect data and will retrain the system on a year’s worth of geospatial grids (the current training set was limited to the warm season only). At that time, it is expected that testing will be expanded to a larger dataset. Also, it is expected that other forecast time periods (besides the 30 min used in this illustration) will be of interest. A clustering saliency of 200 km2 was arbitrarily chosen here; it is to be expected that a different clustering saliency may provide superior skill and that different forecast time periods will require different saliencies.
As another example of the type of data mining work that this algorithm enables, Bedka et al. (2009) track cloud-top cooling rates from high-resolution satellite imagery to predict the onset of convecting initiation, with the aim of improving the pixel-by-pixel technique of Mecikalski et al. (2008).
Acknowledgments
Funding for this research was provided under NOAA–OU Cooperative Agreement NA17RJ1227, Engineering Research Centers Program (NSF 0313747). The attribute-extraction algorithm described in this paper has been implemented within the Warning Decision Support System Integrated Information (WDSSII; Lakshmanan et al. 2007) as the w2segmotionll process (available online at http://www.wdssii.org).
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Multiscale hierarchical clustering to identify storms and estimate motion: (a) reflectivity composite field being clustered, where the data are over northwest Arkansas on 6 Jun 2008 and depict an area of approximately 75 km × 75 km; (b) storms identified at a 20 km2 saliency, where different storms are shaded differently; (c) storms identified at 200 km2 saliency; (d) storms identified at 200 km2 using the approach of Lakshmanan et al. (2009); (e) motion estimate at the 200-km2 scale; and (f) using the motion estimate to advect the current field forward by 30 min.
Citation: Journal of Atmospheric and Oceanic Technology 26, 11; 10.1175/2009JTECHA1257.1
(a) An expert drew polygons by hand around storms and labeled each polygon with the storm type of the storms contained within it. (b) The polygons drawn by the expert were converted into a spatial grid. The storm-type grid is treated as observed data and a storm type (supercell or pulse storm for the storms in this image) is associated with every cluster.
Citation: Journal of Atmospheric and Oceanic Technology 26, 11; 10.1175/2009JTECHA1257.1
Part of the decision tree learned from the training data. See Table 1 for more detail on the attributes, and see the text for an online link to the full tree.
Citation: Journal of Atmospheric and Oceanic Technology 26, 11; 10.1175/2009JTECHA1257.1
Tornado warning forecast skill by storm type, as evaluated using the data mining approach of this paper.
Citation: Journal of Atmospheric and Oceanic Technology 26, 11; 10.1175/2009JTECHA1257.1
Skill of steady-state method and trained neural network at predicting lightning activity 30 min into the future as the threshold on the output grids is varied to yield a binary yes/no decision. CSI, HSS, POD, and FAR are shown. The current lightning density field was advected to create the steady-state forecasts.
Citation: Journal of Atmospheric and Oceanic Technology 26, 11; 10.1175/2009JTECHA1257.1
The lightning prediction algorithm in real time on 28 Apr 2009 over East Texas: (a) lightning density at 1300 UTC; (b) reflectivity composite, the field on which storm identification is carried out; (c) identified storms, with different storms shaded differently; (d) reflectivity at −10°C, one of the spatial attributes considered; (e) predicted probability of lightning 30 min later; and (f) actual lightning density at 1330 UTC.
Citation: Journal of Atmospheric and Oceanic Technology 26, 11; 10.1175/2009JTECHA1257.1
Attributes extracted automatically to help answer the question of forecaster skill according to storm type.
Attributes extracted from clusters for the lightning prediction algorithm. “Cluster to image” refers to the second approach of estimating temporal properties described in section 2. The units of lightning density are flashes (fl) per square kilometer per second.
Skill of steady-state method and trained neural network at predicting lightning activity 30 min into the future. The neural network achieves its peak skill in CSI (see Fig. 5) at a threshold of 0.41, whereas the steady-state method achieves its peak skill at a threshold of zero. All the statistics correspond to those thresholds.
For example, hourly measurements of temperature and humidity at some location for a decade could form the training dataset. Each pattern would consist of the temperature and humidity measurements at a certain instant in time.
These days were selected because they had relatively widespread lightning activity and because we did not experience hardware or software problems when collecting the data on these days. The resulting patterns were randomly divided into three sets of 50%, 25%, and 25%, which were used for training, validation, and testing, respectively. A neural network with one hidden layer consisting of eight nodes was trained on the training set, with the validation set utilized for early stopping to limit overfitting. The transfer function of the output node was a sigmoid so that the neural network output is a true probability (Bishop 1995).
