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5. Convective-Stratiform Separation
This section summarizes the work performed in this reporting period toward development of a real-time convective-stratiform separation algorithm in support of VPR correction (Seo et al. 2000). 5.1 Introduction In Seo et al. (2000), a need has been identified for development of a real-time convective-stratiform separation algorithm so that VPR correction (Seo et al. 2000) may be performed at all times regardless of the type of the storm on hand. In this section, we summarize the first-year effort toward developing such an algorithm. The primary objective of this year's work was to identify the variables/attributes/indices/measures that possess significant skill in convective-stratiform separation. The secondary objective was to identify the candidate techniques that may be used to objectively quantify the probability of a particular azimuth-range (azran) bin belonging to the convective core. Before proceeding further, it must be pointed out here that, even though we freely use the terms "convective" and "stratiform" throughout this section, we are not necessarily interested in convective-stratiform separation in the storm-dynamical sense (see, e.g., Houze 1993, p197). Rather, our interest is strictly reflectivity-morphological: separate all instantaneous and azran bin-specific VPRs in the rain area into "convective" and "stratiform" groups such that VPR correction yields the largest margin of improvement in estimation of surface rainfall. It must also be noted here that, in addition to supporting VPR correction, convective-stratiform separation may also be used in application of region-specific Z-R parameters. This microphysical aspect of convective-stratiform separation (see, e.g., Houze 1993, p1999), however, cannot be effectively dealt with without VPR correction, and hence is not considered in this work. 5.2 Literature Review Steiner et al. (1995) offers probably the most extensive review of the radar data-based convective-stratiform separation techniques. It is worth repeating their key findings here because they serve as our starting point:
From the viewpoint of WSR-88D VPR correction, the biggest limitations of Steiner et al. (1995) are seen to be the following:
TRMM (the Tropical Rainfall Measuring Mission) PR (the Precipitation Radar) employs two different methods to classify rain type; the vertical profile method and the horizontal pattern method of Steiner et al. (1995). Below, we reproduce the summary of the vertical profile method (http://trmm.gsfc.nasa.gov/2a23.html):
From the viewpoint of WSR-88D VPR correction, use of the climatological freezing level is clearly inadequate. Also, because bright band can be reliably identified only when enhancement is intense, a large area of mild bright band enhancement may go largely undetected (and hence VPR-uncorrected). It is somewhat puzzling to note that not much attention has been given in the literature to using standard spatial statistics (e.g., those used in the Radar Echo Classifier, Kessinger et al. 1998) in convective-stratiform separation. It may be that the computational burden has been a discouraging factor. As will be seen, such statistics are extensively explored in this work. In light of the above observations, the approach taken in this work is the following:
5.3 Identification of Skillful Variables In identifying variables that may possess significant skill in convective-stratiform separation, we assumed in this work that only the volume-scan reflectivity data are available. It is acknowledged that the height of the freezing level may also be available from sounding, surface observations and/or model output. As illustrated below, such an information may indeed be used to guide estimation of bright band height from the volume-scan reflectivity data. As also shown below, however, it is difficult to make an objective use of the resulting information in an azran bin-specific manner. For this reason, we did not explicitly require in this work that the freezing level be known from an external source. The following variables (at each 1°x1 km azran bin and mapped onto the 230x360 base tilt) are considered in this work:
The motivation for the maximum apparent radar rain rate in the vertical, rx, is to detect the presence of convective core (reflectivity>40dBZ, an adaptable parameter) regardless of the stage of development of the convection (see, e.g., Houze 1993, p198). Examination of many volume scans at KINX (Tulsa, OK) and KHGX (Houston, TX) indicates that identification of convective core based on the magnitude of rx works well, as long as there is no bright band enhancement. The motivation for the spatial statistics of the maximum apparent radar rain rate in the vertical, rx, the height of the top of the apparent convective core, ht, and the height of the maximum reflectivity, hx, is to detect the stratiform region and, in particular, the area of bright band enhancement. The spatial correlation coefficients are examined in two directions (i.e., azimuthal and radial) under the presumption that, e.g., rx might be better correlated in the azimuthal direction than in the radial in the area of bright band enhancement. The local statistics for the ij-th azran bin are calculated over an area that is i azimuthal bins wide and j radial bins long. The initial sensitivity analysis indicates that a reasonable choice for i and j may be between 5 and 7 for both. Because we are using the same choice of i regardless of the slant range, the averaging area at a close range is necessarily much smaller than that at a far range. This dependence of statistics on the averaging area (i.e., on the slant range) will have to be examined further. Likewise, because the arc length of the azran bin is range-dependent, sample spatial correlation coefficients along the azimuthal direction can only be calculated at different lag distances. To convert the sample spatial correlation coefficients at varying spatial lag distances to those at 1 km, it is assumed in this work that the correlation function is negative exponential (with no nugget effect). This assumption will also have to be investigated further. To screen the variables listed above, we used the following two cases extensively; the squall line of May 8-9, 1995, at KINX, and the extreme rainfall event of Oct 17-18, 1994, at KHGX. The overriding motivation for the use of these cases was that they are rather difficult examples of the separation problem and that we know where the true areas of convective cores and stratiform region are: the squall line allows a clear-cut visual separation of convective and stratiform areas and, in the Houston case, we know from the radar-gage analysis (Seo et al. 1996) where bright band enhancement is present (though difficult to tell visually). Based on various types of visual and statistical analyses using Splus (MathSoft 1998), we identified the following three as the most skillful; rx, min{rrx(| 1 |az,)rrx(| 1 |ra)}, and min{rrx(| 1 | az),rrx(| 1 |ra}. For notational brevity, we denote min{rrx(| 1 |az,)rrx(| 1 |ra)} and min{rht(| 1 | az),rht(| 1< |ra)} as rrx and rht, respectively. The particular skill that each of these variables brings to convective-stratiform separation may be best illustrated through the following examples. 5.4 Example 1 This is an archetypical southern-plains squall line with clear-cut convective front and trailing stratiform region. Fig 1 shows the field of rx. Note the concentric arcs in the stratiform region due to bright band enhancement. Figs 2 and 3 show the fields of rx>15 and <15 (mm/hr), respectively. They represent the convective core (Fig 2) and the apparent non-convective core (Fig 3) regions after the initial separation using rx. Note that this simple screening works well in the convective core. It fails, however, in the stratiform region because of intense bright band enhancement. Fig 4 shows the field of rrx. Note that the stratiform region is characterized by larger values of rrx, particularly at far ranges due in part to beam widening. Figs 5 and 6 show the fields of rrx>0.96 and <0.96, respectively. They represent the stratiform (Fig 5) and the apparent non-stratiform (Fig 6) regions. It may appear that the stratiform region could have been better identified with a smaller threshold value of rrx. Further examination, however, suggests that the threshold has to be chosen rather conservatively because smaller threshold values of rrx tend to result in the identified stratiform region intruding on the (true) convective cores. Comparison between Figs 2 and 5 indicates that the area of bright band enhancement in Fig 2 can be negated by the rrx screening only partially. To screen out the area of bright band enhancement at close ranges, we turn to rhx. Fig 7 shows the field of hx. Note that the convective core is characterized by highly variable hx whereas the stratiform/bright band-enhanced region is characterized by rather uniform hx. Fig 8 shows the field of rht. Figs 9 and 10 show the fields of rht>0.99 and <0.99, respectively. They represent the stratiform/bright band (Fig 9) and the apparent non-stratiform/non-bright band (Fig 10) regions. E Figs 11 through 14 illustrate how each of the three variables, rx, rrx, and rht, contributes to isolation of the convective core. Fig 11 - the rx threshold is applied: a large area of intense bright band enhancement is misidentified as convective Fig 12 - the rrx threshold is additionally applied: bright band enhancement at mid - to far ranges is now correctly identified as stratiform, but that at close range is still misidentified as convective Fig 13 - the rht threshold is additionally applied: bright band enhancement at the close range is now correctly identified as stratiform, but the convective core at the farthest range at the top of the radar umbrella is now misidentified as stratiform Fig 14 - convective-stratiform separation after applying all three thresholds It may be argued that the rrx screening does not contribute much, and that screening based only on rx and rht may be just as effective. On the other hand, rht is a measure that is significantly more range-dependent than rrx due to the sparsity of the sampling interval of the radar beams in the vertical, and hence is subject to large uncertainties. As such, exclusive reliance on rht for identification of stratiform region/area of bright band enhancement should probably be avoided. To assess the range dependence of these measures and their skill, further investigation is needed. We now turn our attention to the question of what may be gained in convective-stratiform separation if the height of the freezing level is available from an external source. Fig 15 shows the locations of the "couplets" corresponding to Fig 1. The couplet locations in the figure mark the azran bins in the volume-scan reflectivity data projected onto the base tilt for which, for each azimuthal angle, the peak reflectivity (a proxy for the bright band peak in the vertical) is observed at approximately the same height between any two adjacent tilts (for details see Smith 1986, Seo et al. 1997). In the figure, the concentric clusters are associated with the bright band peaks observed in the lowest (located at the farthest range) to the highest (located at the closest range) tilts. The elongated cluster in the southeastern sector is associated with the convective core (misidentified as bright band by the couplet analysis). Fig 16 shows the distribution of the height of the couplets from all azimuthal angles. Visually, it is easy to tell that the tight horizontal cluster along the altitude of approximately 3.5 km is associated with the bright band, and that the loose clusters above and below the bright band height are associated with the convective front. The two solid horizontal lines in the figure are the break points produced from a cluster analysis, in which the data points in the figure are asked to be grouped into three cluster. Visually, it is easy to tell that it is the middle cluster which is associated with the bright band. By simply calculating the mean and standard deviation of the data points in the middle cluster, one may obtain a very good estimate of the height of the bright band and a measure of uncertainty associated with it, as shown in Fig 17 by the solid and dashed lines, respectively. Following such an analysis, it is then possible to screen out the misidentified couplets (i.e., those that are associated with the convective front), and produce an estimate of the area of intense bright band enhancement (by what amounts to "connecting the dots" of surviving couplet points in Fig 15), as shown in Fig 18. Note that Fig 18 compares well visually with the area of intense bright band enhancement seen in Fig 1, suggesting that such a map may serve as an additional screening criterion in convective-stratiform separation. Experience suggests, however, that in an automatic mode it is rather difficult to ascertain which cluster is associated with the bright band and which are not (note that the skill level for this discrimination has to be extremely high, probably close to perfection, for the technique to be operationally viable). The problem is much more difficult if the area of intense bright band enhancement is relatively small. It is in this area of pointing to the right cluster that the externally-provided freezing level can be useful. 5.5 Example 2 The second example comes from the extreme rainfall event at KHGX occurred in Oct 17-18,1994 (NWS 1995). Fig 19 shows a field of rx in the middle of the event. It is convective everywhere except at the farthest ranges in the northestern sector, where based on the gage-radar analysis (Seo et al. 1996) we known that bright band enhancement is present. To assess robustness of the screening criteria, we used in this example exactly the same adaptable parameter and threshold values as those used in Example 1. Fig 20 shows the field of rrx corresponding to Fig 19. Note that the rrx values are larger in the area of bright band enhancement. Fig 21 shows the field of rht. The spotty nature of the field is due in part to the relatively high (i.e., for this event) cutoff of 40 dBZ used to determine the convective core in calculation of rrx and rht. Figs 22 through 25 are completely analogous to Figs 11 through 14, respectively. Considering that there was no case-specific tuning of any kind, the results are encouraging. 5.6 Objective Quantification of Prob[the bin0convective] In the two examples given above, we limited ourselves, for the sake of demonstration, to simply applying the thresholds to arrive at the final field of convective-stratiform separation. In practice, however, such a "binary decision-based" approach is not very desirable because a single set of thresholds cannot possibly work consistently and reliably for all sites, for all seasons, and regardless of the radar calibration accuracy. For this reason, for the separation algorithm to be operationally viable it is necessary that the likelihood of a paricular azran bin belonging to the convective core be objectively quantified on a continuous scale (rather than binary-mapped). One such commonly used scale is the probability measure, which we will adopt here also. The objective then is to estimate the conditional probability, Prob[the azran bin0convective |rx=rx,r >rrx=>rrx,>rht=>rht], where the bold signifies that it is a random variable. Though not explicitly denoted as such, the above probability will also have to be conditioned on the slant range so that range dependence of the skill in rx, rrx, and rht may be accounted for (e.g., rht at close and far ranges is much less informative than that at the mid range because of the cone of silence and the sparse sampling of the radar beams in the vertical, respectively). To estimate the conditional probability, we may consider a number of different techniques;
If the number of attributes can be kept to as small as three (e.g., rx, rrx, and rht), direct empirical estimation of the conditional probability may be the most desirable (completely data-driven, unbiasedness guaranteed). If the number of attributes is larger (say, several), optimal (linear or Bayesian) estimation may be preferred (they approximate multivariate statistics with a set of bivariate statistics). If the number of attributes is more than several, neural network or fuzzy logic may have to be used (explicit statistical modeling becomes very difficult). The choice of the technique depends additionally on answers to the following questions: 1) are the model parameters to be updated on line? (algorithmically desirable but operationally impractical: see below), and 2) is unbiasedness in probability critical? If the answer to the first question is "yes," neural network, fuzzy logic, and Bayesian estimation become more difficult to implement because they will require on-line training and/or parameter estimation. If the answer to the second question is "no," neural network and fuzzy logic become more attractive because, to produce only "reasonable" results, rigorous training and parameter estimation/updating may not be needed. In reality, the answer to the first question is probably "no" because, other than the human forecaster manually performing convective-stratiform separation on a volume-scan by volume-scan basis (clearly a very difficult task in the current operational environment), it will not be possible to generate the truth field on line. For this reason, it is particularly important that the technique of choice be parsimonious so that processing of long-term Level II data for parameter estimation (requiring manual convective-stratiform separation) may be avoided. The answer to the second question is probably "yes" because biasedness in probability results, e.g., in VPR correction being applied mistakenly to convective cores even though the adjustment factors are derived from the stratiform profile (an error of very damaging consequence). In this respect, the last three candidates are more appealing because they are by design unbiased estimators (this unbiasedness, however, is guaranteed only if the second-order statistics required can be accurately estimated, which in reality may or may not be met depending in particular on the sample size). Given the above observations and the fact that as simple a screening as applying three thresholds produces as encouraging a result as seen in Figs 11 through 14 and through 22 through 25, optimal linear estimation based on indicator (i.e., binary) variable transformation is seen to be an attractive compromise. In this approach, one may estimate the conditional probability, Prob[the bin0convective | rx=rx,rrx=rrx,rht=rht], via: Prob[the bin0convective | rx=rx,rrx=rrx,rht=rht], via: .E[Iconv| Irx=irx,Irrx=irrx,Irht=irht] =E[Iconv] + Slrxk (irx - E[Irxk]) + Slrrxl (irrx - E[Irrxl]) + Slrhtm (irht - E[Irhtm]) where
+1 if the bin of interest is in the (true) covective core
iconv=/
,0 otherwise
+1 if rx at the bin of interest exceeds the k-th threshold
irxk= /
,0 otherwise
+1 if rrx at the bin of interest exceeds the l-th threshold
irrxl=/
,0 otherwise
+1 if rht at the bin of interest exceeds the m-th threshold
irhtm=/
,0 otherwise
Note that, by definition, we have E[Iconv]=Prob[the bin0convective], E[Irxk]=Prob[rx>k-th threshold], E[Irrxl]=Prob[rrx>l-th threshold], and E[Irhtm]=Prob[rht>m-th threshold]. The weights, lrxk, lrrxl, lrand htm, are given by:
$Cov[Irx,Irx] Cov[Irx,Irrx] Cov[Irx,Irht]) -1 $Cov[Irx,Iconv])
(Lrx, Lrrx, Lrht)= &Cov[Irx,Irrx] Cov[Irrx,Irrx] Cov[Irrx,Irht]& &Cov[Irrx,Iconv]&
(Cov[Irht,Irx] Cov[Irht,Irrx] Cov[Irht,Irht]* (Cov[Irht,Iconv]*
where, e.g., Cov[Irxk,Irrxl] is given, by definition, by Prob[rx> k-th threshold,rrx> l-th threshold]-Prob[rx> k-th threshold]Prob[rrx> l-th threshold] (i.e., the centered bivariate probability). The indicator approach is intuitive, and can accommodate both off-line parameter estimation and on-line parameter updating. A known drawback, however, is that the estimate becomes biased near the tail ends of the distribution if the variables involved are highly skewed (as rx, rrx, and rht are). This, however, is probably not an issue in convective-stratiform separation because, for purposes of binary classification (i.e., either convective or stratiform), unbiasedness in probability is critical only near the median. 5.7 Conclusions and Recommendations
References Houze, R. A., Jr., 1993: Cloud dynamics. Academic Press, Inc. Kessinger, C., S. Ellis, J. Van Andel, D. Ferraro, and R. J. Keeler, 1998: NEXRAD data quality optimization, FY98 Annual Report. NCAR, Boulder, CO. MathSoft, 1998: S-PLUS5. MathSoft, Inc., Seattle, WA. NWS, 1995: Natural Disaster Survey Report, Southeast Texas tropical mid-latitude rainfall and flood event, October 1994. DOC/NOAA/NWS Southern Region, Jan 1995. Seo, D.-J., R. Fulton, J. Breidenbach, M. Taylor, and D. Miller, 1996: Final Report, Interagency MOU among the NEXRAD Program, WSR-88D OSF, and NWS/OH/HRL. HRL/OH/NWS, Silver Spring, MD. Seo, D.-J., R. Fulton, J. Breidenbach, 1997: Final Report, Interagency MOU among the NEXRAD Program, WSR-88D OSF, and NWS/OH/HRL. HRL/OH/NWS, Silver Spring, MD. Seo, D.-J., J. Breidenbach, R. Fulton, D. Miller, and T. O'Bannon, 2000: Real-time adjustment of range-dependent biases in WSR-88D rainfall estimates due to nonuniform vertical profile of reflectivity. J Hydrometeorol, 1(3), 222-240. Smith, C. J., 1986: the reduction of errors caused by bright bands in quantitative rainfall measurements made using radar. J. Atmos. Oceanic Technol., 3, 129-141. Steiner, M. R., R. A. Houze Jr., and S. E. Yuter, 1995: Climatological characterization of three- dimensional storm structure from operational radar and rain gauge data. J. Appl. Meteor., 34, 1978-2007. |
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