Observing Z-R Relationships in Indianapolis, Indiana - Elizabeth Dahl

This lab investigates a mid-latitude cyclone that affected the Midwest on October 23, 2009. We will be focusing on the storm's effects on Indianapolis, Indiana. The area experienced a wide swath of light precipitation throughout the night, similar to other affected cities in the region. 

A sounding of the closest available city, Wilmington, Ohio, is shown in Figure 1. There is no CAPE, signaling the fact that this event was not convective in nature. The surface is also relatively dry and the atmosphere becomes even drier around 850mb. At 600mb, the atmosphere becomes incredibly moist and it continues to look like that up to higher altitudes. This sounding appears a bit more dry than would be expected for a mid-latitude cyclone, but it is also important to note that the Indianapolis office does not have sounding data available, and this was the closest location. However, this is still helpful in identifying how the storm may have evolved by the time it reached a more eastward location.

Figure 1: Sounding from Wilmington, Ohio on October 23, 2009 at 00Z. From the University of Wyoming.

To better understand the rainfall event, we can look at the measured reflectivity. Figure 2 shows the 0.5 degree reflectivity recorded from the Indianapolis radar. Throughout the area, there is wide-ranging light precipitation with reflectivities between 5 and 30 dBZ. There are some small areas with a reflectivity of above 40 dBZ, but they are not very large. The precipitation appears to be fairly uniform as the system moves to the northeast. The combination of light rains over a large area lead me to believe that this event is likely stratiform precipitation.

Figure 2: 0.5 degree reflectivity on October 23, 2009 from 03:02 - 03:36 Z in Indianapolis.

Looking at the event's radial velocity, shown in Figure 3, we see that there are southwesterly winds for the most part. Wind speeds range from 10 to 40 knots over the area. There is also a ring around the radar with no data. This could possibly be the result of interfering radar returns and transmissions causing the radar to not be able to "see" data in that particular area. However, it is interesting that this only appears in the radial velocity image and not in Figure 2.

Figure 3: Radial velocity on October 23, 2009 from 03:02 - 03:36 Z in Indianapolis.

To determine the rain rate, we first try the Marshall-Palmer relationship where a=200 and b=1.6. Figure 4 depicts the Marshall-Palmer relationship rain rate over Indianapolis. Overall, there is a low rain rate of 3 mm/hr or less. There are some anomalous areas of high rain rate to the southwest of the radar, with rain rates reaching almost 14 mm/hr. This seems to be extremely high and likely would not match ground observations. 

Figure 4: Marshall-Palmer relationship rain rate from 03:02 - 03:36 Z on October 23, 2009 in Indianapolis.

Rather than look at the Marshall-Palmer relationship to determine rain rate, it could be more accurate to try another Z-R relationship. Figure 5 depicts the East-Cool Stratiform relationship rain rate using values of a=130 and b=2. The rain rate appears to be more uniform with most values still under 3 mm/hr. There is an anomalous area of high rain rates to the southwest of the radar, similar to Figure 4, but they appear for a much shorter time span, suggesting that this relationship could be more accurate. This relationship should also be more accurate because it is specific to stratiform rain events east of the continental divide, all of which matches this event. This relationship is also best used for wintertime precipitation, which is likely to be more accurate for this precipitation that takes place in October (although October is technically in meteorological autumn).

Figure 5: East-Cool Stratiform relationship rain rate from 03:02 - 03:36 Z on October 23, 2009 in Indianapolis.

To determine the accuracy of each of the Z-R relationships, we will now compare those rain rates to observed rainfall rates from Weather Underground. Figure 6 shows the Marshall-Palmer rain rate during the event. The accumulated precipitation totals to 0.089 inches. Figure 7 shows the East-Cool Stratiform rain rate, which totals to 0.076 inches. This value is slightly lower than the Marshall-Palmer relationship, but is only off by fractions of an inch. Figure 8 shows the actual recorded precipitation, which is 0 inches for the times in the Z-R relationship plots. Both relationships do not match the recorded values from Weather Underground, however, they are both extremely low, so Weather Underground could just be rounding down the values.

Figure 6: Marshall-Palmer relationship rain rate in Indianapolis from 03:02 - 03:36 Z on October 23, 2009.

Figure 7: East-Cool Stratiform relationship rain rate in Indianapolis from 03:02 - 03:36 Z on October 23, 2009.

Figure 8: Observed rain totals in Indianapolis on October 22-23, 2009. From Weather Underground.

The modeled rainfall values and observed values could both have errors. The Marshall-Palmer and East-Cool Stratiform relationships are models, so it's difficult to say that they might match exactly what was happening at the surface in Indianapolis. Additionally, the atmospheric conditions change which relationship will be the most accurate. Given the time of year and type of precipitation, the E-CS relationship is likely more accurate between that and M-P. 

The ground rain gauge can also have problems associated with it. The rain gauge measures precipitation only in one tiny, specific area. This means that the rain gauge could have recorded no precipitation accumulation, but a location five feet away could have measured some amount of accumulation. Additionally, depending on what the weather conditions were, heavy winds could blow the rain, causing ground measurements to not be entirely accurate. Rain gauges also have the issue of simple human error, causing the recorded amounts to be inaccurate. 

Overall, I believe that the E-CS relationship is likely the most accurate measurement of rainfall accumulation in this scenario because it is not subjected to human errors like the rain gauge. This model relationship also utilizes conditions that are similar to those experienced during this event. The type of precipitation and time of year can make a big difference in how a model interprets rainfall data, and this relationship most accurately accounts for those variables in this scenario.