Lab 4: Observing Z-R Relationships in McIDAS-V: Detroit, Michigan (Kassidy Lange)
Fitting the appropriate Z-R relationship to radar data
Here, Rain rate and Rain amount values are determined for the Marshall-Palmer, East-Cool Stratiform, and WSR-88D Z-R relationships to determine which Z-R relationship provides the best fit for the conditions observed over Detroit Michigan (KDTX) on October 23rd, 2009.
Rain rate values for Marshall-Palmer Z-R Relationship:
Time 1: 0.10 mm/hr
Time 2: 0.13 mm/hr
Time 3: 0.05 mm/hr
Time 4: 0.05 mm/hr
Time 5: 0.06 mm/hr
Time 6: 0.09 mm/hr
Time 7: 0.10 mm/hr
Time 8: 0.09 mm/hr
Time 9: 0.13 mm/hr
Rain amount values for Marshall-Palmer Z-R Relationship:
Time 1: 0.01 mm
Time 2: 0.0108 mm
Time 3: 0.005 mm
Time 4: 0.0042 mm
Time 5: 0.006 mm
Time 6: 0.009 mm
Time 7: 0.008 mm
Time 8: 0.009 mm
Time 9: 0.0195 mm
Total: 0.0815 mm
Ground-based Rainfall amount: 0.254 mm
Rain rate values for East-Cool Stratiform Z-R Relationship:
Time 1: 0.21 mm/hr
Time 2: 0.29 mm/hr
Time 3: 0.26 mm/hr
Time 4: 0.36 mm/hr
Time 5: 0.20 mm/hr
Time 6: 0.16 mm/hr
Time 7: 0.16 mm/hr
Time 8: 0.30 mm/hr
Time 9: 0.45 mm/hr
Rain amount values for East-Cool Stratiform Z-R Relationship:
Time 1: 0.021 mm
Time 2: 0.0243 mm
Time 3: 0.026 mm
Time 4: 0.03 mm
Time 5: 0.02 mm
Time 6: 0.016 mm
Time 7: 0.013 mm
Time 8: 0.03 mm
Time 9: 0.0675 mm
Total: 0.2478 mm
Rain rate values for WSR-88D Z-R Relationship:
Time 1: 0.06 mm/hr
Time 2: 0.09 mm/hr
Time 3: 0.07 mm/hr
Time 4: 0.12 mm/hr
Time 5: 0.05 mm/hr
Time 6: 0.04 mm/hr
Time 7: 0.04 mm/hr
Time 8: 0.10 mm/hr
Time 9: 0.18 mm/hr
Rain amount values for WSR-88D Z-R Relationship:
Time 1: 0.006 mm
Time 2: 0.0075 mm
Time 3: 0.007 mm
Time 4: 0.01 mm
Time 5: 0.005 mm
Time 6: 0.004 mm
Time 7: 0.0033 mm
Time 8: 0.01 mm
Time 9: 0.027 mm
Total: 0.0798 mm
Partner Discussion: How well did the Marshall-Palmer relationship do in estimating the observed rainfall at the surface? What other relationship should you try to see if you can get a better estimate?
In this case, the Marshall-Palmer is may not be the optimal Z-R relationship to use to estimate observed rainfall at the surface as the calculated rainfall rate appears to be slightly lower than the actual rainfall amount. I think it is worth looking into the East-Cool Stratiform relationship to determine observed rainfall over this area and maybe even the WSR-88D Z-R relationship may yield better results than the Marshall-Palmer relationship.
Partner Discussion: How does the rainfall rate of this Z-R relationship compare with the Marshall-Palmer relationship at estimating surface rainfall rate? Is there another relationship that you would like to try to fit to the data? If so, try out another relationship.
The East-Cool Stratiform Z-R relationship produces a rainfall value that is much closer to the actual rainfall amount compared to the Marshall-Palmer Z-R relationship outputs. To reaffirm the notion that this event should be characterized by a Z-R relationship suited to stratiform precipitation, It may be worth looking into the WSR-88D Z-R relationship to see if this relationship will yield the expected results or something closer to the ground-based observations.
Observing Z-R Relationships
On October 23, 2009, a mid-latitude cyclone dominated the weather patterns of the continental United States, with strong squall line thunderstorms in the South to large and broad regions of light precipitation around the comma head in the North. The area of interest for this analysis was over DTX White Lake in Detroit, Michigan. The time of interest for the reflectivity scans is from approximately 9pm. From the reflectivity maps and the sounding, the structure of the storm appears to be stratiform, in nature due to the fact that the precipitation does not penetrate very deep into the atmosphere. Taking a sounding from 00z (8pm), on October 23rd, 2009, temperatures and dew point values are almost identical from the surface all the way up to approximately 525 mb in the atmosphere indicating an extremely saturated layer which is a surefire indicator of precipitation in most cases.
Using the Marshall-Palmer relationship, the calculated rain rates followed a relatively consistent pattern over the hour with max values at 0.13 mm/hr and minimum values of 0.05 mm/hr. Rain rates never surpassed 0.5 mm/hr. Looking at the radar reflectivity scan for the Marshall-Palmer relationship, there are areas surrounding orange 45 dBZ values that seem anomalously high as these values exceed 70 dBZ. There is even an area in northwestern Ohio that appears to exceed 80 dBZ at the ninth timestep (9:50 pm).
When using the East-Cool Stratiform relationship, the calculated rain rates followed a more variable pattern over the hour with a maximum value of 0.45 mm/hr at the ninth timestep (9:22 pm) and a minimum value of 0.16 mm/hr. The radar reflectivity for the East-Cool Stratiform Z-R relationship appears slightly similar to the WSR-88D relationship but appears to have slightly greater areas of blue (lower) dBZ values and fewer overall areas of pink and orange values (30-40 dBZ). The anomalously high dBZ values surrounding the 45 dBZ areas are still present in the East-Cool Stratiform Z-R relationship.
When the WSR-88D relationship was implemented, the calculated rain rates also followed a mostly consistent pattern with an exception at the 9th timestep (9:50pm) with a max value of 0.18 mm/hr compared to values that averaged around 0.07 mm/hr (minimum value of 0.04 mm/hr). The radar reflectivity scan for the WSR-88D Z-R relationship still appears to have anomalously high dBZ values surrounding the 45 dBZ areas similar to the Marshall-Palmer relationship but not at the same magnitude as the Marshall-Palmer relationship (less area covered overall by the higher dBZ values).
How does the Marshall-Palmer relationship of rainfall during the hour match with the ground observations?
The Marshall-Palmer relationship of rainfall during the recorded hour, provides an underestimation of the actual rainfall amount recorded from surface observations (calculated value using Marshall Palmer relationship of 0.0815 mm versus an observed value of approximately 0.254 mm from ground observations.)
What Z-R relationship did you choose and why?
Aside from the Marshall-Palmer relationship, the East-Cool Stratiform Z-R relationship was analyzed as well as the WSR-88D relationship. Due to the fact that the Marshall-Palmer relationship was insufficient to characterize this rainfall event, a Z-R relationship better suited to stratiform conditions was needed. The East-Cool Stratiform relationship was used first as it seemed like it would provide more accurate measurements (this assumption was made based off of the time of year, the given sounding, and radar reflectivity images). The East-Cool Stratiform Z-R Relationship provided a much more accurate calculated rainfall amount than the Marshall-Palmer relationship. Even so, it was worth looking into the WSR-88D relationship to see if an even more accurate measurement could be provided
How do these new estimates of rainfall during the hour match with the ground observations, and how do they compare to the Marshall-Palmer relationship?
The East-Cool Stratiform Z-R relationship was much more accurate in measuring the rainfall values in
this area providing a total of 0.2478 mm compared to the recorded 0.254 mm. The East-Cool Stratiform Z-R relationship provided a more reliable reading than when the
Marshall-Palmer relationship was used. Given these results, a Z-R relationship that is optimal for
areas of stratiform precipitation was needed. To test this hypothesis, a test was conducted for the WSR-88D Z-R relationship as well.
The WSR-88D relationship, much like the Marshall-Palmer relationship actually provided an
underestimation of the recorded rainfall over the area with a calculated value of 0.0798 mm compared to
the observed value of 0.254 mm. This calculated value is even more inaccurate than the
Marshall-Palmer relationship. The data gathered from the WSR-88D Z-R relationship reaffirms the notion that a Z-R relationship best suited for stratiform precipitation events is
required in this case
What sources of error could there be in your estimates?
One source of error that could have led to the underestimation of rainfall values using the
East-Cool Stratiform Z-R relationship, or even the other two relationships, could be that inaccurate
values of rain rate were read off the graph. This could be due to the fact that since the distribution
of rain rates was fairly spread out that it made the graph more difficult to interpret accurately. Additionally,
error in measurements could be the result of inaccurate placement of the probe. It is not a guarantee that
in each of the three datasets that the probe was placed exactly in the location of DTX. Finally, when
calculating rainfall values, exact time measurements of the time intervals were not used but were rounded
to the nearest minute for simplicity (6 minutes and 22 seconds were rounded down to 6 minutes). This could
have lead to slight errors in the calculation of rainfall values for all three datasets.
Which is a more accurate measurement: your remote estimation or the airport rain gauge, and why do you think so?
It is more likely that the remote estimation of rainfall values is more accurate than the amount
recorded by the airport. This is due to the fact that rain gauges are subject to many sources of error
including the structure of the rain gauge, the rain gauge's exposure to the environment, the nature of
the precipitation, and overall weather conditions. For example, a rain gauge could provide faulty
readings of rainfall accumulation if the gauge is susceptible to being tipped. Another instance of error
would be that the rain gauge is structured in a way that allows for rain splashes to escape the gauge
(if the precipitation is intense enough and the gauge is already filled with an amount of water, a
particularly large or intense water droplet could disturb the gauge enough that some of the water splashes
out. Finally, rain gauges are only accurate of the immediate area in which they are found. Incidentally,
if the rain gauge were placed on the opposite end of the airport, it may have gotten different
measurements of rainfall that previously recorded.
If you chose a third Z-R relationship, how does this relationship compare with the first two relationships used? Are the rainfall rates higher or lower and why?
A third Z-R relationship was already established. The third Z-R relationship (WSR-88D)
was overall the least accurate Z-R relationship used in this setting with an estimated rainfall amount of
0.0798 mm compared to the observed value of 0.254 mm versus the rainfall amounts estimated by the
Marshall-Palmer Z-R relationship(0.0815 mm) and the East-Cool Stratiform relationship (0.2478 mm). In
this relationship, the rainfall rates were slightly lower than estimated by the Marshall-Palmer and much
lower than the East-Cool Stratiform Z-Relationships. Since the East-Cool Stratiform Z-R relationship is
most commonly used to estimate rainfall in light stratiform rain conditions, it is expected that a greater
value of rainfall would be recorded than in the “standard” Marshall-Palmer and the WSR-88D
Z-R relationship (generally used for summer deep convection).
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