Observing Z-R Relationships in Detroit - Claire Mundi

This blog post will analyze a mid-latitude cyclone that extended across most of the continental United States on October 23, 2009 from the perspective of the Detroit, Michigan radar (KDTX). In this region of the northern US, this location saw a large swath of light precipitation. Figure 1 shows the radar reflectivity from the hour of the storm analyzed (from about 03Z to 04Z). Most of the reflectivity values are relatively low, ranging from about 5 dBZ to 30 dBZ, indicative of light rain.

Figure 1. Radar reflectivity (0.5° elevation angle) around Detroit, Michigan on October 23, 2009 showing the effects of the mid-latitude cyclone.

Figure 2 shows reflectivity values as viewed from the southwest corner of Figure 1. Since the increased reflectivity values are slightly higher in altitude, this storm likely consists of mostly stratiform precipitation. A strong convective core does not seem to be present during this event.

Figure 2. 3D Radar sweep looking at the 0.5° elevation reflectivity values of this storm from the southwest at 03:33:33Z.

This assumption of stratiform precipitation is then further confirmed when looking at the sounding taken a few hours before these radar images (Figure 3). From this sounding the Convective Available Potential Energy (CAPE) is zero, leading to a lack of convective motion within this event.

Figure 3. Sounding from 0Z on October 23, 2009 from the White Lake station near Detroit, MI. There is a CAPE value of zero.

Additionally, from the above sounding, there are very moist conditions present at the surface. To begin looking at precipitation characteristics of this event, rain rates were calculated using the Marshall-Palmer relationship (Z= 200 R^1.6). The overall distribution of rain rate values are shown in Figure 4. The rain rates are at their highest (about 1.5 mm/hr) along the southwest edge of the storm, and the rain rates are lowest (less than 0.2 mm/hr) around the outer edge of the storm, consistent with the regions of highest and lowest reflectivity shown in Figure 1.

Figure 4. Precipitation rates calculated using the Marshall-Palmer relationship. The location of the Detroit airport is marked in white.

The time series of how the rain rate changes at the Detroit airport is shown in Figure 5. By multiplying the rain rate by the time step between observations and summing over all time steps, the total amount of rain within this time series is about 0.14 mm or 0.0054 inches.

Figure 5. Time series of rain rates calculated using the Marshall-Palmer Z-R relationship at the Detroit airport. The total rainfall calculated from this approach over the hour analyzed was about 0.14 mm.

This total rainfall is less than the ground observations shown in Figure 6. The observed precipitation that fell at this time was about 0.01 inches, and results from the Marshall-Palmer relationship were about half that value.
 

Figure 6. Ground observations of precipitation (top) and wind (bottom) from Detroit Airport Station. At 9PM (3Z), the observed precipitation was about 0.01 inches (Weather Underground).

To try and obtain a slightly more accurate rainfall estimation, the East-Cool Stratiform relationship was applied (Z= 130 R^2.0). This relationship was selected based on the type of event identified at the beginning of this blog post. Additionally, this relationship is optimal for winter precipitation east of the continental divide, which likely still applies to this mid-autumn event. The general distribution of precipitation rates is shown in Figure 7. In comparison with the results using the Marshall-Palmer relationship, the same region of high precipitation rates is evident along the southwest edge of the storm. However, around the outer edge of the storm, the precipitation rate using the East-Cool Stratiform relationship is much higher, with typical values around 0.4 mm/hr as opposed to 0.2 mm/hr for the Marshall-Palmer relationship (referring back to Figure 4, where the storm is outlined in light blue values).

Figure 7. Precipitation rates calculated using the East-Cool Stratiform relationship. The location of the Detroit airport is marked in white.

Again, the time series of how the rain rate changes at the Detroit airport is shown in Figure 8.  The total rainfall calculated from this approach over the hour analyzed was about 0.28 mm or 0.011 inches.

Figure 8. Time series of rain rates calculated using the East-Cool Stratiform Relationship at the Detroit airport. The total amount of rain within this time series is about 0.28 mm.

This total rainfall calculation is more in line with the ground observations yielding a similar value of about 0.01 inches, about double the amount of the result derived using the Marshall-Palmer relationship. 

However, it is still somewhat unclear which of the three methods (Marshall-Palmer relationship, East-Cool Stratiform relationship, or ground measurements) provides the most accurate result. Figure 6, in addition to precipitation measurements, also shows surface wind values. At around 9PM, the winds were about 15 mph. These winds may be strong enough to have caused inaccurate precipitation readings if these measurements were collected using a tipping-bucket gauge, thus leading to an overestimation of the total rainfall. In that case, the Marshall-Palmer relationship could have been more accurate than the East-Cool Stratiform. One other note about the ground measurements is that the measurements were only reported with an accuracy on the order of 10^-2. Therefore, the actual precipitation may have varied from the reported value, and could have been a slightly lower value closer to the Marshall-Palmer-derived value, or a slightly higher value like the value derived using the East-Cool Stratiform relationship (both of which round to 0.01 inches).

In terms of errors in the radar estimates, the location selected near the Detroit airport is within a region of very light precipitation (on the lower end of the rainfall rate range) for the selected time frame. It is possible that a given relationship could be more accurate for larger raindrops and increased rainfall rates and less accurate for smaller rainfall rates. Testing a different location closer to the center of this event would confirm how well these relationships hold (and match ground observations) for increased rainfall rates.