1. The Influence of Basin Size on Effective Flash Flood Guidance
David Slayter
Cooperative Institute for Mesoscale Meteorological Studies (CIMMS) University of Oklahoma

2. Motivation
Flash floods are a significant threat to lives and property across the U.S.
The 30-year average for annual flood deaths in the U.S. is 143 (NOAA Office of Meteorology)
There were 128 flash floods in Arizona reported during 1998 and 1999.
In Arizona, during 1998, the National Climatic and Data Center reported four deaths occurred from flash flooding and, during 1999, 5 injuries and approximately $13 million in property damage.
Flash floods are a significant threat to lives and property in the U.S.
According to NOAA, the 30-year average for annual flood related deaths in the U.S. is 143.
In this study, which uses Arizona as the study area, there were 128 flash floods in 1998 and From these there were 4 deaths in 1998 and 5 injuries and $13 million in property damage in 1999, so the rationale for forecasting of flash flood threats is clear.

3. Motivation
Implementation of AMBER (Areal Mean Basin Estimated Rainfall) functionality in AWIPS Flash Flood Monitoring and Prediction (FFMP).
FFMP version 2.0 now uses the resolution of the Digital Hybrid Reflectivity (DHR) product on a 1° x 1 km polar grid.
With DHR, rainfall accumulation is at the volume scan level.
FFMP uses two square mile basins developed at NSSL. (
The National Weather Service has implemented flash flood forecasting capabilities into the AWIPS software. The Flash Flood Monitoring and Prediction software, based on the AMBER algorithm originally developed by Davis and Jendrowski, has provided an opportunity to assess the threat of flash flooding from radar-based precipitation estimates.
With FFMP version 2, using Digital Hybrid Scan Reflectivity, there is near real-time opportunity to assess rainfall intensity and accumulation at the volume scan level.
The two square mile basins used in FFMP, delineated by researchers at the National Severe Storms Laboratory, will be used to assess, at the basin level, rainfall accumulations and intensity.

4. Objective RESEARCH QUESTION:
Are the two square mile threshold basins the most suitable basin size for FFMP in central Arizona?
OBJECTIVE:
Using various basin sizes, assess which size best represents flash flood warnings in AMBER when compared to known flash floods.
A question remains however, Are the two square mile accumulation threshold basins the most suitable basin size for Flash Flood Monitoring and Prediction in Arizona?
This research study used various basin sizes to assess which size best represents flash flood warnings in AMBER when compared to known flash flood events.

5. Data Sources Flash Flood Events
Forty-nine NCDC-reported flash floods occurring under KIWA or KFSX during 1998 and 1999.
These flash floods occurred during the summer months (July through early September).
NEXRAD
Archived Level II NEXRAD data from KIWA and KFSX.
DHR generated using WATADS version 10.2.
Basins
One-arc-second (~ 30-meter) National Elevation Dataset DEMs.
For data sources, this research used 49 National Climatic Data Center-reported flash flood events that occurred under the Phoenix or Flagstaff radars during 1998 and 1999.
All of these events occurred during the summer months of July through early September, the North American Monsoon season in Arizona and were associated with 28 cases of archived Level 2 NEXRAD data from the Phoenix and Flagstaff radars.
From this data Digital Hybrid Scan Reflectivity data was created using the WSR-88D Algorithm Testing and Display System.
The basins were delineated using one-arc-second DEMs of the National Elevation Dataset, the same DEMs used to create the two square mile basins delineated for FFMP version 2.

6. Location of Flash Floods, Flash Flood “Areas”, and WSR-88D Installations
This graphic shows the 230-km coverage of the Phoenix and Flagstaff radars, which comprise the study area, with the flash flood locations and areas of more widespread flash flooding represented by the triangles and magenta polygons.

7. Limitations Radar Limitations
Blockage of lower-tilt radar scans by terrain and subsequent over-sampling.
Terrain-based hybrid scans used to accommodate for this.
Uncertainty resulting from the Z-R relationship.
Flash Floods
Reporting of only flash floods affecting a population versus those that occur unnoticed.
Using radar-estimated precipitation is exactly that, estimated. There are several limitations that most are acutely aware of but that must be kept in mind:
The blockage of lower-tilt radar scans by terrain is a significant problem in the Intermountain West. To accommodate for this, the terrain-based hybrid scans were used for generation of the DHR products so that blockage effects can be limited. However, this can result in adjacent basins using radar tilts that are looking at different portions of the same storm. This may result in different reflectivity readings and therefore different precipitation estimations.
Inherent uncertainty resulting from the Z-R relationship. In this study, the same Z-R equation as used operationally for the Phoenix and Flagstaff radars was used in this study.
Perhaps the most significant source of uncertainty is the reporting of flash flood events. Flash floods may occur in areas where no one notices them. Since this study used flash floods as reported to the National Climatic Data Center there can be a built-in bias on the results.

8. Methodology
The flash flood events used were selected based on availability of NEXRAD data covering the time frame of the flash flood and the six hours prior to the event.
Basins were delineated at accumulation thresholds of 2 mi2, 10 mi2, 100 mi2 and for the extent of the combined KIWA / KFSX radar umbrella.
Because of the necessity of using DHR data in AMBER, the flash flood events used in the study were selected based on available NEXRAD data that covered the time frame of the reported flash flood event and at least six hours prior to the event to allow for enough potential accumulation for assessment of the 6-hour FFG.
Then the basins were delineated on the NED at accumulation thresholds of 2, 10, and 100 square miles for the extent of the combined areas of the Phoenix and Flagstaff radars. The accumulation thresholds are the minimum flow accumulation for delineated basins, however, the actual basin sizes delineated at the 2 square mile threshold can range from very small basins less than one square mile to 10 square miles.

9. Methodology
Baseline 1, 3, and 6-hour FFG for Arizona supplied by the Colorado Basin River Forecast Center (CBRFC).
FFG values used in this study are uncorrected for antecedent soil moisture conditions.
According to CBRFC the FFGs may vary +/- 0.5 inch depending on soil moisture conditions.
AMBER/GIS (authored by Paul Jendrowski) used to determine accumulation warnings.
Flash Flood Guidance levels provided by the Colorado Basin River Forecast Center were used to compare rainfall accumulation to threat levels of accumulation. One major assumption that had to be made was that these baseline FFGs, since not adjusted for soil moisture conditions, would be representative since adjusted FFGs were not available. Operationally, the FFGs may vary by about half an inch in either direction from those used in this study.
The most recent version of AMBER was used, along with the DHR products, to determine accumulation warnings.

10. Methodology Arizona FFGs and Forecast Areas
This graphic shows Arizona forecast zones separated into six regions based on the unique 1, 3, and 6-hour Flash Flood Guidance.
The red outline is the combined 230-km radar coverage area of the Phoenix and Flagstaff radars, which overlap a portion of a New Mexico forecast zone.

11. Methodology Hypothesis
H0: There is no difference between the occurrence of AMBER warnings between 2, 10, and 100 sq mile basins.
HA: There is a significant difference between the occurrence of AMBER warnings between 2, 10, and 100 sq mile basins.
The null hypothesis tested was that there are no differences between the occurrence of AMBER warnings in 2, 10, and 100 square mile basins, with the alternative being that there are significant differences between them.

12. Methodology
AMBER warnings were compared to reported flash floods to assess the degree of association.
There were no 100 mi2 basins in this analysis that had a flash flood warning.
Three flash floods cases defined in this analysis:
Case 1: Rainfall >= FFG and FF occurred.
Case 2: Rainfall >= FFG and no FF occurred.
Case 3: Rainfall < FFG and FF occurred.
These cases were analyzed by basin size.
To test this hypothesis, AMBER warnings were compared to reported flash floods to assess the degree of association with known flash flood events. However, there were no flash flood warnings issued by AMBER using 100 square mile basins and current Flash Flood Guidance so these were removed from further analysis.
The reason for this is the large size of the 100 mi2 basins averages out locally heavy precipitation across the area of the basin.
To assess the occurrence of basin warnings versus flash floods, three cases were established:
Case 1 events are occurrences where basin rainfall was greater than a flash flood guidance and a flash flood occurred;
Case 2 events are occurrences where basin rainfall was greater than a flash flood guidance and no flash flood occurred, and;
Case 3 events are occurrences where rainfall was less than a flash flood guidance and a flash flood occurred.
The 2, 10, and 100 square mile basins were analyzed separately.

13. Methodology
Case 2 events are those basins where estimated precipitation exceeded an FFG but no flash flood was reported.
The extent of time examined for these basins is based on the extent of the same storm event as reported flash floods.
Case 2 basins result from the number of basins that “flashed” during the same storm event as a reported flash flood but no flash flood was reported.

14. Example of 2, 10, and 100 sq mile basins
Example of 2, 10, and 100 sq mile basins. Flash flood reported in Washington Park on 7/11/99 15:40 MST
The graphic at the upper right shows basins delineated for one of the flash flood events. The red triangle is the site of the reported flash flood in the Washington Park area just below the Mogollon Rim on the East Verde River. The magenta line is the outline of a 100 sq mile basin, the green lines the extent of 10 sq mile basins, and orange the 2 sq mile delineated basins.
The bottom left graphic shows the AMBER-generated precipitation accumulations for the 6 hours prior to the flash flood. For this event, the dark green basins had estimated precipitation between 1.5 and 2 inches and the lightest green being less than a half inch of precipitation. None of these basins exceeded FFG, yet the description of the event notes that a five-foot wave of water rushed down the river and carried a woman 100 yards downstream.
The dots that curve across the basin are the radar bins for the Flagstaff radar.

15. 1, 3 and 6-hour ABR/FFG for Washington Park flash flood
FF reported 2240 UTC
This graphic shows the AMBER basin accumulation for a basin from the flash flood event on the previous slide. The three horizontal lines at the top are the 1, 3, and 6-hour flash flood guidance values, and the cyan curve is the 1-hour average basin rainfall accumulation and the pink and green curves the 3 and 6-hour average basin rainfall curves, respectively.
The red curve is the basin rate of accumulation in inches per hour, which is a measure of the intensity of rainfall falling in the basin measured for each volume scan.
The flash flood occurred at 10:40 pm UTC, at which time the basin stopped receiving significant rainfall. Notice however that this basin, which received the most precipitation of the basins upstream of the reported flash flood, did not exceed any flash flood guidance value. This is true of the other basins upstream of the reported flash flood. Yet the description of the event notes that a five-foot wave of water rushed down the river and carried a woman 100 yards downstream.

16. Analysis
Corrections were made to counts of basins with FFG warnings at the two and 10 mi2 thresholds for a FF:
# observed 2 mi2 basins (obs) = ((FF2 / FFT) * FF2)
# observed 10 mi2 basins (obs) = ((FF10 / FFT) * FF10)
# expected 2 mi2 basins (exp) = (obs) * 0.2
# expected 10 mi2 basins (exp) = (obs) * 0.8
where FF2,10 = the number of basins exceeding an FFG at a particular basin size;
FFT = the number of basins exceeding an FFG for both the two and 10 sq mi basins.
There were several flash floods where the same location had flash flood warnings at both the 2 and 10 square mile scale. So as not to “double-count” these occurrences and provide for equitable contribution to a flash flood from basins from different scales, a correction was made so that the number of basins with observed warnings was proportional to the total basin warnings from both scales. The expected number of basins with warnings would be the above results multiplied by the scale of each basin.

17. Results
Hypothesis
To test the differences between the three basin sizes, the number of basins >= FFG for each flash flood event were totaled.
The number of observed basins >= FFG was modified in cases where multiple basins at each scale were found.
These observed and expected numbers were included as part of a chi-square test between the two categories. Given the number of observed warnings and expected, the chi-square variable at one degree of freedom and 95% confidence far surpassed the critical chi-square value of 3.84, showing us that there are significant differences between the warnings produced from each scale.
314.39
2 =
0.699
3.345
4.181
10 sq mi
19.636
98.181
2 sq mi
(Obs–Exp)2
Expected
Observed
Scale

18. Results Hypothesis Chi-square test
There is a 95% probability that the chi-square random variable would be less than 3.84 for validation of the null hypothesis.
314.39
2 =
0.699
3.345
4.181
10 sq mi
19.636
98.181
2 sq mi
(Obs–Exp)2
Expected
Observed
Scale
These observed and expected numbers were included as part of a chi-square test between the two categories. Given the number of observed warnings and expected, the chi-square variable at one degree of freedom and 95% confidence far surpassed the critical chi-square value of 3.84, showing us that there are significant differences between the warnings produced from each scale.

19. Results Hypothesis Testing
To test the hypothesis that there are significant differences between the basin sizes to detect flash floods, the results were tested against “a binomial distribution” at each scale.
The results show that, comparing flash floods greater than a flash flood guidance against those less than flash flood guidance, the two square mile basins show an average of approximately 35% probability of association of an exceeded FFG with a reported flash flood. Accounting for the 95% range of potential values, this number could range from 21 to 48%.
The 10 square mile basins show an even lesser degree of association between flash floods and flash flood guidance. Again, comparing the flash floods with precipitation greater than an FFG to those less and an FFG, the probability of association is approximately 16% with and lower and upper confidence level of 6 to 27%, respectively.
Comparing flash floods with rainfall greater than FFG to those basins exceeding FFG without a reported flash flood,
The study of Case 1 events to Case 2 events involves the comparison of all cases where basins exceeded a flash flood guidance with the difference being the occurrence of a flash flood.
Case 1: Rainfall >= FFG and FF occurred.
Case 2: Rainfall >= FFG and no FF occurred.
Case 3: Rainfall < FFG and FF occurred.

20. Results POD / FAR / CSI 2 sq miles 10 sq miles 17 626 32 8 112 41
Flood Observed?
YES NO
>= FFG 17
626
< FFG 32
POD = Case 1 / (Case 1 + Case 3) = 35%
FAR = Case 2 / (Case 1 + Case 2) = 97%
CSI = Case 1 / (Case 1 + Case 2 + Case 3) = 3%
POD = 16%
FAR = 93%
CSI = 5%
10 sq miles
Flood Observed?
YES NO
>= FFG 8
112
< FFG 41
A probabilty of detection, false alarm rate, and critical success index were performed on the cases. The data shows that, at the two square mile scale, the probability of detection was 35% and when the number of Case 2 events are examined, a false alarm rate of 97% with similarly poor results for the critical success index.
At the 10 square mile scale, the probability of detection is even less at 16%.
Considering the large number of Case 2 FFG warnings where no flash floods were observed, the false alarm rate and critical success numbers may be poorer than warranted because flash floods may have actually occurred in some of these basins but they did not affect a population.
We must also remember that the FFGs used are uncorrected for soil moisture conditions, so there could be some variance in these results.
Observed FF
YES NO
>= FFG
Case 1
Case 2
< FFG
Case 3
Case 1: Rainfall >= FFG and FF occurred.
Case 2: Rainfall >= FFG and no FF occurred.
Case 3: Rainfall < FFG and FF occurred.

21. Conclusions
With a POD of 35%, two square mile basins detected flash floods much better than 10 square mile basins (POD = 16%).
The range of probability of association between FFG and reported flash floods for two square mile basins, at a 95% confidence level, is 21% to 48%.
With a probability of detection of 35%, using the current, uncorrected FFGs in Arizona, the basins delineated at the two square mile threshold were significantly better than those at the 10 square mile threshold.
Incorporating a standard error measurement at the 95% confidence level shows that the worst and best case probability of detecting a flash flood at the 2 square mile scale ranges from 21 to 48%.

22. Conclusions
Ten and 100 square mile basins are too large to be effectively used for flash flood warnings using current FFGs.
POD for 10 square mile basins of 16%
No 100 square mile basins had an accumulation > an FFG.
Using AMBER and current FFGs, the basins delineated at the 2 square mile threshold are the best hope for prediction of flash floods.
The ten and 100 square mile basins are too large to be effectively used for flash flood warnings using the current FFGs since the probability of detection of 16% for the 10 square mile basins is too poor for use and since no 100 square mile basins in this analysis had average basin rainfall exceeding flash flood guidance.

23. Recommendations
Improve Flash Flood Guidance to the basin level, incorporating basin physiographic characteristics.
Research is currently underway to associate the physiographic characteristics of basins used in this study to show statistical differences between basins where flash floods were reported or unreported.
Considering the improvement in precipitation estimates, the next step may be a near real-time assessment of soil conditions and updating of FFG.
A distributed model?

24. Questions & Comments