5. ConvectiveStratiform Separation
This section summarizes the work performed in this reporting period toward development of a realtime convectivestratiform 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 realtime convectivestratiform 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 firstyear 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 convectivestratiform separation. The secondary objective was to identify the candidate techniques that may
be used to objectively quantify the probability of a particular azimuthrange (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 convectivestratiform separation in the stormdynamical sense (see, e.g., Houze 1993, p197).
Rather, our interest is strictly reflectivitymorphological: separate all instantaneous and azran binspecific 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, convectivestratiform separation may also be used in application of regionspecific ZR parameters. This microphysical aspect of
convectivestratiform 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 databased convectivestratiform separation techniques. It is worth repeating their key findings here because they serve as our starting point:
 identifying stratiform precipitation by bright band signatures is severely limited,
 observation of bright band may, however, be used as a check on stratiform precipitation not being misidentified as convective,
 time continuity techniques (based on echotracking) are laborious and computationally expensive,
 use of the horizontal structure of precipitation field is simpler and more practical, and
 criteria for identifying convective precipitation include intensity, peakedness, and surrounding area.
From the viewpoint of WSR88D VPR correction, the biggest limitations of Steiner et al. (1995) are seen to be the following:
 separation is performed on Cartesiangridded reflectivity data at 3km altitude, and hence only out to ranges of about 140 km, and
 a more rigorous and objective set of criteria is probably needed to prevent intense bright band enhancement (easily exceeding 40 dBZ) from being misidentified as convective.
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):
 bright band is detected based on the second derivative of reflectivity with respect to range, and by imposing several conditions on the shape of the bright band profile and uniformity of the
height of the bright band peak, etc.,
 the height of the bright band must lie within ±1.5 km of the climatological freezing level,
 when bright band exists, rain is stratiform,
 when bright band is not detected and the maximum reflectivity exceeds the convective threshold, rain is convective, and
 the rest is classified as nonstratiform and nonconvective.
From the viewpoint of WSR88D 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
VPRuncorrected).
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 convectivestratiform 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:
 first identify convective cores and then perform checks on bright bandenhanced areas not being misidentified as convective cores,
 derive variables/attributes/indices/measures from the volumescan reflectivity data in their original polar format at the 1x1 km resolution and out to 230 km, and
 consider, at least initially, only those variables that may be objectively quantified in an azran binspecific manner (so that the probability of a particular azran bin belonging to the convective core may be estimated with a reasonably simple technique: see below).
5.3 Identification of Skillful Variables
In identifying variables that may possess significant skill in convectivestratiform separation, we assumed in this work that only the volumescan 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 volumescan reflectivity data. As also shown below, however, it is difficult to make an objective use of the resulting information in an azran binspecific 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:
 maximum apparent radar rain rate in the vertical, denoted as r_{x},
 local mean of r_{x}, denoted as m_{rx},
 local standard deviation of r_{x}, denoted as s_{rx},
 s_{rx}/m_{rx}, denoted as cv_{rx},
 local spatial correlation coefficient of r_{x} along the radial direction at the lag distance of 1 km,
denoted as r_{rx}(  1  _{ra}),
 local spatial correlation coefficient of r_{x} along the azimuthal direction at the lag distance of 1
km, denoted as r_{rx}(  1  _{az}),
 weighted (according to the sample size) average of r_{rx}( 1 _{az}) andr_{rx}( 1  _{ra})
 max{r_{rx}( 1  _{az}), r_{rx}( 1  _{ra})},
 min{r_{rx}( 1  _{az}), r_{rx}( 1 _{ra})},
 max{r_{rx}( 1  _{az})r_{rx}( 1 _{ra}),0},
 height of the top of the apparent convective core, denoted as h_{t},
 m_{ht},
 s_{ht},
 cv_{ht},
 r_{ht}( 1 _{ra}),
 r_{ht}( 1 _{az}),
 weighted average of r_{ht}( 1  _{az}) and r_{ht}( 1  _{ra}),
 max{r_{ht}( 1  _{az}),r_{ht}( 1< _{ra})},
 min{r_{ht}( 1 _{az}),r_{ht}( 1 _{ra})},
 max{r_{ht}( 1  _{az})r_{ht}( 1 _{ra}),0},
 height of the maximum reflectivity in the vertical, denoted h_{x},
 m_{hx,}
 s_{hx,}
 cv_{hx},
 weighted average of r_{hx}( 1  _{az}) and r_{hx}( 1 _{ra}),
 max{font face="Symbol">r_{hx}( 1 _{az}),r_{hx}( 1  _{ra})},
 min{r_{hx}( 1 _{az}),r_{hx}( 1 _{ra})},
 max{r_{hx}( 1 _{az})r_{hx}( 1 _{ra}),0}, and
 height of the bright band, and area of the bright band enhancement as estimated by a variant of Smith (1986) and Seo et al. (1997) (see below).
The motivation for the maximum apparent radar rain rate in the vertical, r_{x}, 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 r_{x} 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, r_{x}, the height of the top of the apparent convective core, h_{t}, and the height of the maximum reflectivity, h_{x}, 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., r_{x} might be better correlated in the azimuthal
direction than in the radial in the area of bright band enhancement.
The local statistics for the ijth 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 rangedependent, 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 89, 1995, at KINX, and the extreme rainfall event of Oct 1718, 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 clearcut visual separation of convective and stratiform areas
and, in the Houston case, we know from the radargage 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; r_{x}, min{r_{rx}( 1 _{az},)r_{rx}( 1 _{ra})}, and min{r_{rx}( 1  _{az}),r_{rx}( 1 _{ra}}. For notational brevity, we denote min{r_{rx}( 1 _{az},)r_{rx}( 1 _{ra})} and
min{r_{ht}( 1  _{az}),r_{ht}( 1< _{ra})} as r_{rx} and r_{ht}, respectively. The particular skill that each of these variables brings to convectivestratiform separation may be best illustrated through the following examples.
5.4 Example 1
This is an archetypical southernplains squall line with clearcut convective front and trailing stratiform region. Fig 1 shows the field of r_{x}. Note the concentric arcs in the stratiform region
due to bright band enhancement. Figs 2 and 3 show the fields of r_{x}>15 and <15 (mm/hr), respectively. They represent the convective core (Fig 2) and the apparent nonconvective core
(Fig 3) regions after the initial separation using r_{x}. 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 r_{rx}. Note that the stratiform region is characterized by larger values
of r_{rx}, particularly at far ranges due in part to beam widening. Figs 5 and 6 show the fields of
r_{rx}>0.96 and <0.96, respectively. They represent the stratiform (Fig 5) and the apparent nonstratiform (Fig 6) regions. It may appear that the stratiform region could have been better identified with a smaller threshold value of r_{rx}. Further examination, however, suggests that the threshold has to be chosen rather conservatively because smaller threshold values of r_{rx} 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 r_{rx} screening only partially. To screen out the area of bright band enhancement at close ranges, we turn to r_{hx}. Fig 7 shows the field of h_{x}. Note that the convective core is characterized by highly variable h_{x} whereas the stratiform/bright bandenhanced region is characterized by rather uniform h_{x}. Fig 8 shows the field of r_{ht}. Figs 9 and 10
show the fields of r_{ht}>0.99 and <0.99, respectively. They represent the stratiform/bright band
(Fig 9) and the apparent nonstratiform/nonbright band (Fig 10) regions.
E
Figs 11 through 14 illustrate how each of the three variables, r_{x}, r_{rx}, and r_{ht}, contributes to isolation of the convective core.
Fig 11  the r_{x} threshold is applied: a large area of intense bright band enhancement is
misidentified as convective
Fig 12  the r_{rx} 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 r_{ht} 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  convectivestratiform separation after applying all three thresholds
It may be argued that the r_{rx} screening does not contribute much, and that screening based
only on r_{x} and r_{ht} may be just as effective. On the other hand, r_{ht} is a measure that is significantly
more rangedependent than r_{rx} 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 r_{ht} 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 convectivestratiform 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 volumescan 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 convectivestratiform 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
externallyprovided freezing level can be useful.
5.5 Example 2
The second example comes from the extreme rainfall event at KHGX occurred in Oct 1718,1994 (NWS 1995). Fig 19 shows a field of r_{x} in the middle of the event. It is convective everywhere except at the farthest ranges in the northestern sector, where based on the gageradar 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 r_{rx} corresponding to Fig 19. Note that the r_{rx} values are larger in the area of bright band enhancement. Fig 21 shows the field of r_{ht}. 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 r_{rx} and r_{ht}. Figs 22 through 25 are completely analogous to Figs 11 through 14, respectively. Considering that there was no casespecific 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 convectivestratiform separation. In practice, however, such a "binary decisionbased" 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 binarymapped).
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 r_{x}=r_{x},r >r_{rx}=>r_{rx},>r_{ht}=>r_{ht}], 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 r_{x}, r_{rx}, and r_{ht} may be accounted for (e.g.,
r_{ht} 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;
 neural network,
 fuzzy logic,
 optimal linear estimation (in particular, techniques based on indicator variable transformation),
 Bayesian estimation (probably following variable transformation into multivariate normal), and
 direct empirical estimation of the conditional probability.
If the number of attributes can be kept to as small as three (e.g., r_{x}, r_{rx}, and r_{ht}), direct empirical estimation of the conditional probability may be the most desirable (completely datadriven, 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 online 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 convectivestratiform separation on a volumescan by volumescan 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 longterm Level II data for parameter
estimation (requiring manual convectivestratiform 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 secondorder 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  r_{x}=r_{x},r_{rx}=r_{rx},r_{ht}=r_{ht}], via:
Prob[the bin0convective  r_{x}=r_{x},r_{rx}=r_{rx},r_{ht}=r_{ht}], via:
.E[I_{conv} I_{rx}=i_{rx},I_{rrx}=i_{rrx},I_{rht}=i_{rht}]
=E[I_{conv}] + Sl_{rxk} (i_{rx}  E[I_{rxk}]) + Sl_{r}_{rxl} (i_{rrx}  E[I_{rrxl}]) + Sl_{r}_{htm} (i_{rht}  E[I_{rhtm}])
where
+1 if the bin of interest is in the (true) covective core
i_{conv}=/
,0 otherwise
+1 if r_{x} at the bin of interest exceeds the kth threshold
i_{rxk}= /
,0 otherwise
+1 if r_{rx} at the bin of interest exceeds the lth threshold
i_{rrxl}=/
,0 otherwise
+1 if r_{ht} at the bin of interest exceeds the mth threshold
i_{rhtm}=/
,0 otherwise
Note that, by definition, we have E[I_{conv}]=Prob[the bin0convective], E[I_{rxk}]=Prob[r_{x}>kth
threshold], E[I_{rrxl}]=Prob[r_{rx}>lth threshold], and E[I_{rhtm}]=Prob[r_{ht}>mth threshold]. The weights,
l_{rxk}, l_{r}_{rxl}, l_{r}and _{htm}, are given by:
$Cov[I_{rx},I_{rx}] Cov[I_{rx},I_{rrx}] Cov[I_{rx},I_{rht}]) 1 $Cov[I_{rx},I_{conv}])
(L_{rx}, L_{r}_{rx}, L_{r}_{ht})= &Cov[I_{rx},I_{rrx}] Cov[I_{rrx},I_{rrx}] Cov[I_{rrx},I_{rht}]& &Cov[I_{rrx},I_{conv}]&
(Cov[I_{rht},I_{rx}] Cov[I_{rht},I_{rrx}] Cov[I_{rht},I_{rht}]* (Cov[I_{rht},I_{conv}]*
where, e.g., Cov[I_{rxk},I_{rrxl}] is given, by definition, by Prob[r_{x}> kth threshold,r_{rx}> lth threshold]Prob[r_{x}> kth threshold]Prob[r_{rx}> lth threshold] (i.e., the centered bivariate probability).
The indicator approach is intuitive, and can accommodate both offline parameter estimation and online 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 r_{x}, r_{rx}, and r_{ht} are). This, however, is probably not an issue in convectivestratiform 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
 Three variables have been identified as particularly skillful in convectivestratiform separation; the maximum apparent rain rate in the vertical, the local spatial correlation coefficient of the maximum apparent rain rate in the vertical, and the local spatial correlation coefficient of the height of the top of the apparent convective core.
 The initial results, obtained by simple application of the three thresholds, are very encouraging. It suggests that optimal linear estimation based on indicator variable transformation is wellsuited for probabilistic quantification of convectivestratiform separation. It is proposed that such a procedure be prototyped and evaluated.
 The variables examined and identified as promising in this work need to be further tested against a wide spectrum of precipitation events. Also, the search for other potentially skillful variables needs to continue.
 Generation of validation data sets remains a critical outstanding issue. Manual massgeneration (eventually at the WFO's?) based on visual examination of volumescan reflectivity data is not only laborintensive but will also require a graphical user interface (GUI) tool (WATADS?). A user operations concept needs to be developed for VPR correction (including convectivestratiform separation) to address such issues.
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: SPLUS5. MathSoft, Inc., Seattle, WA.
NWS, 1995: Natural Disaster Survey Report, Southeast Texas tropical midlatitude 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, WSR88D 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, WSR88D 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: Realtime adjustment of
rangedependent biases in WSR88D rainfall estimates due to nonuniform vertical profile of
reflectivity. J Hydrometeorol, 1(3), 222240.
Smith, C. J., 1986: the reduction of errors caused by bright bands in quantitative rainfall
measurements made using radar. J. Atmos. Oceanic Technol., 3, 129141.
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,
19782007.
