Saturday, July 27, 2013

Biggerstaff Algorithm for Echo Classification

Introduction

I recently took a look at the Biggerstaff and Listemaa (2000) algorithm for echo classification, which is supposed to be an improved scheme from the Steiner et al. (1995) algorithm. To examine this algorithm, I use reflectivity observations from a scanning ARM C-band radar (C-SAPR), and apply the algorithm to this data. All data used in this post was recorded during the Midlatitude Continental Convective Clouds Experiment, or MC3E for short. Furthermore, I will be using gridded (or interpolated) C-SAPR data, on a Cartesian grid 100 x 100 x 17 km in \(x\), \(y\), and \(z\), with a resolution of 500 m for each dimension.

Methodology

This modified algorithm focuses on two estimates: the magnitude of horizontal reflectivity gradient \(\left(\left|\left|\nabla_h Z_e\right|\right|\right)\) at the working level, and the vertical lapse rate of reflectivity \(\left(\nabla_z Z_e\right)\). The vertical lapse rate of reflectivity is defined as the decrease in reflectivity with increasing height in a 3 km layer directly above the height of maximum reflectivity.

These two estimates are put through a thresholding, as described below:

  • \(\left|\left|\nabla_h Z_e\right|\right| \ge\) 3 dB km-1 \(\rightarrow\) grid point possibly convective
  • \(\left|\nabla_z Z_e\right| \le\) 3.5 dB km-1 \(\rightarrow\) grid point possibly convective

I say possibly in the above criteria because there are some other criteria involved in this algorithm (e.g. brightband fraction and a 2-D window filter). These other criteria are ignored in this post.

Since the vertical lapse rate is computed for a 3 km layer above the height of maximum reflectivity, I used the following equation for each column,

$$\nabla_z Z_e \approx \frac{Z_e|_{\text{max}} - Z_e|_{+3 \; \text{km}}}{3 \; \text{km}}$$.

Note with the above equation that we should expect a positive vertical reflectivity lapse rate to be computed, without taking the absolute value.

Finally, note that finite differences used in the gradient calculation were that of 1st and 2nd-order accurate centered, forward, and backward differences.

Results

To test this algorithm, I want to look at the results of both the magnitude of horizontal reflectivity gradient and the vertical lapse rate of reflectivity, and see if these estimated values reflect the expected values described in Biggerstaff and Listemaa (2000). In order to do this, I picked an observation time during the passage of a squall line which had well-defined anvil and stratiform regions.

Fig. 1. C-SAPR reflectivity at the working level (1.5 km) during 1040 UTC on May 20th 2011. Reflectivity values below 0 dBZ were masked.


The cross section of reflectivity shown in Fig. 1 shows a north-south squall line located in the middle of the analysis domain, which was moving west-east. There is an anvil region ahead of the squall line, as well as a trailing stratiform region. Since Fig. 1. is a cross section at 1.5 km altitude, the anvil region is largely not seen.

First I will show the results of the lapse rate calculation.

Fig. 2. Vertical reflectivity lapse rate within the 3 km layer above the height of maximum reflectivity for the same time as shown in Fig. 1.


Notice that the upper limit of the color bar in Fig. 2 is 3.5 dB km-1. From the criteria shown above, we expect all areas shown in red to possibly be stratiform, and the rest possibly convective. The minimum and maximum values computed were 0.02 and 30.3 dB km-1, respectively. The missing data seen around 97.5 W and 36.8 N is due to the cone of silence of the C-SAPR. Also, since the lapse rate was computed for each column, the anvil region has filled in because there is data above the working level.

Now let's look at the results of the gradient calculation.

Fig. 3. Magnitude of horizontal reflectivity gradient at the working level for the same time as shown in Fig. 1.

Here I have set the upper limit of the color bar to highlight areas of possible convection. Any areas shaded in red are possibly convection according to Biggerstaff and Listemaa (2000). The minimum and maximum values computed were 0.001 and 14.1 dB km-1, respectively. Since this calculation is at the working level, the anvil region is once again not available.

Discussion

A first look at the results shows that most areas will not be well classified using these two criteria alone. By any standard the current implementation of the lapse rate estimation does a very poor job at highlighting both convective and stratiform grid points. The gradient criterion does not appear to fair much better, and is severely affected by poor attenuation correction (the ray-like features in Fig. 3). The gradient criterion does do a good job at classifying the leading edge of the squall line as convective, since the precipitation mass in this region would likely be a direct result of convective updrafts.

Further analysis and discussion with colleagues is in order here!

References

Biggerstaff, M. I., and S. A. Listemaa, 2000: An Improved Scheme for Convective/Stratiform Echo Classification Using Radar Reflectivity. J. Appl. Meteor., 39, 2129-2150

Steiner, M., and 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