JULY 1, 1993

NATIONAL CLIMATIC DATA CENTER

RESEARCH CUSTOMER SERVICE GROUP

TECHNICAL REPORT 93-02

1992-1993 WINTER PRECIPITATION

IN SOUTHWEST ARIZONA

NATHANIEL GUTTMAN

NATIONAL CLIMATIC DATA CENTER

JUNG JIN LEE

SOONGSIL UNIVERSITY

JAMES WALLIS

IBM WATSON RESEARCH CENTER
1992-1993 WINTER PRECIPITATION IN SOUTHWEST ARIZONA

Nathaniel B. Guttman

National Climatic Data Center

Asheville, NC

Jung Jin Lee

Department of Statistics

SoongSil University

Seoul, Korea

James R. Wallis

IBM Watson Research Center

Yorktown Heights, NY

 In December 1992 a period of wetness began in southern Arizona. According to the

Weekly Climate Bulletin (Climate Analysis Center, 1992,1993), heavy precipitation inundated

parts of Arizona in December; more than 400 percent of normal December

precipitation fell in the southwestern part of the State. Heavy

precipitation continued to fall during the next two months causing extensive flooding along the

Gila River. This article summarizes the flood damage and the probabilities of observing the

heavy rainfall.

 Monthly storm data reports sent from the Phoenix Weather Service Forecast Office to the

National Climatic Data Center indicate flooding along the Santa Cruz and San Pedro Rivers

on the 29th of December. From January 7-20, roads, bridges, homes, businesses and

farmland suffered considerable flood damage from Graham County westward to Yuma County

as rivers and streams swelled. Several thousand people were isolated in their homes as flood

waters cut off roads. The January Storm Data Report indicates that the combination of a

northward-displaced subtropical jet stream, with its abundant moisture supply and associated

low pressure disturbances, and a southward-displaced polar jet stream, with its storm track, led

to the abnormally wet period from just after Christmas to mid-January. In February, severe

flooding was reported in several areas as water rose in the Painted Rock Reservoir; water

accumulating behind the dam produced the largest lake in the state. After exceeding the 2.5

million acre-feet capacity of the reservoir, water began spilling over the dam and damaging

homes, crops, farmland, roads, and bridges. About 3,500 residents were evacuated, and the

National Guard responded to the flooding with various relief efforts including helicopter

support operations.

 Press reports and summaries prepared by both the United States and Arizona

Departments of Agriculture indicate flood damage in excess of $50 million. In addition to loss

of a substantial part of the lettuce crop and the subsequent market volatility (Arizona normally

supplies about 70 percent of the country's lettuce in March), there has been extensive damage

to agricultural structures, irrigation and pumping systems, and farmland. The effects of the

flooding are expected to disrupt agriculture in the area for several months to come.

 Given the extensive damage resulting from this extremely wet period, a question arises as

to what is the probability of occurrence of rainfall of this magnitude? This question is similar to

one which prompted the development of a National Drought Atlas.
 Sponsored by the U.S. Army Corps of Engineers, under the direction of Dr. Gene Willeke,

Miami (Ohio) University, a National Drought Atlas is being prepared jointly by the National

Climatic Data Center, U.S. Geological Survey, and IBM Watson Research Center to give

water managers probabilistic information for use in making water-related decisions during

periods of drought. Distribution in both paper and electronic form is expected to begin in

October 1993. A component of the Atlas is a probability analysis of total precipitation

occurring over 1, 2, and 3 months with the durations beginning in each calendar month.

Because water managers want to know the probability that reservoirs drawn down during

droughts will refill in the next n months, the Atlas also includes the probabilities of extremely

wet periods.

 The Atlas results were applied to the Phoenix area to estimate the rarity of the monthly

precipitation that occurred from December 1992 through February 1993. The probability

estimates are presented as an example of available information that could be useful to

decision makers who manage water resources during times of stress.

 Probability distributions describing 1-, 2-, and 3-month precipitation totals for 111 regions

within the contiguous United States were determined from L-moments (Guttman et al, 1993).

These moments are linear combinations of order statistics (Hosking, 1990). The L-moment

technique depends upon homogeneity within a region. It is assumed that data observed at all

locations in a region are random representations of a physical process that is operating

everywhere in the region. Weighted, average, regional, dimensionless quantile functions were

computed from distributions found to be acceptable by goodness-of-fit tests. Site-specific

quantile estimates are obtained by multiplying the site mean (scale factor) by the regional

quantile function. Figure 1 shows the 111 regions that resulted from the cluster analysis of

1,119 precipitation sites (Guttman, 1993). Figure 2 is an enlargement of the Arizona portion of

Fig. 1 and shows the location of the principal dams in the area, the two Atlas precipitation

regions (71 and 72), and the seven sites within the Gila River drainage area that were used in

the Atlas precipitation analysis. The primary difference between regions 71 and 72 is that in

region 71, average annual precipitation is less than 12 inches, and in region 72, average

annual precipitation is more than 12 inches.

 The historical precipitation data used to construct the regions and to derive the probabilities

were taken from 1,119 of the National Climatic Data Center's 1,219-station Historical

Climatological Network (Karl et al., 1990) with monthly data through 1989. Record lengths are

at least 60 years and average about 85 years. Other than record length, the criteria for

selecting the stations are that no more than ten percent of the monthly data are missing, and

that no more than twelve consecutive months of data are missing. Since all available data

meeting the selection criteria are used, record lengths are not constant among stations.

 Probability estimates of the winter precipitation that occurred at the 7 sites in Arizona were

computed from the Atlas information. Observed December 1992, January and February 1993

monthly precipitation amounts for the sites were extracted from preliminary forms sent to the

National Climatic Data Center. The winter wetness is assessed relative to the observed

record (probabilistic climatology).

 Longterm average 1-, 2- and 3-month precipitation totals during the winter months for the 7

sites are shown on Table 1, and the observed amounts from December 1992 through

February 1993 are shown on Table 2. Comparing these two tables, it is obvious that rainfall

far exceeded the longterm average at each site during each month. Precipitation in

January 1993 was particularly excessive. The December-January 2-month totals were more

than 3 times the longterm average. The January-February as well as the December-February

totals were more than 4 times the longterm average.
 Table 3 shows the probability of exceeding the observed totals. The inverse of the listed

probabilities is the mean return period of the observed precipitation. Looking at the individual

months, the December totals may be expected to occur once every 15 to 20 years at all sites

except Buckeye. The December rainfall at this site can be expected to occur once in 125

years. January was even more unusual; 5 out of the 7 sites reported values that yield

recurrence intervals more extreme than 1,000 year events. February precipitation was quite

variable but less severe than January; the return periods ranged from 14 years at Mesa to 125

years at Wickenburg. The 2-month December-January totals were once in more than 250-year

events at all sites except Sacaton and Wickenburg. At Sacaton, the 2-month rainfall could be

expected to occur about once every 33 years, while at Wickenburg, the expectation is about

once every 90 years. The January-February totals, as well as the 3-month

December-February totals, were exceptionally high; they could be expected to occur once in

more than a 1,000 years.

 Confidence in estimates of return periods of hundreds of years based on sample sizes of

fewer than 100 is low. As a guide to estimates that have higher confidence, Tables 4 and 5

show the .95 confidence interval, obtained by simulation, of precipitation that can be expected

to occur on the average of once every 50 and 100 years. Intervals for longer return periods

are likely to be too broad to be useful except for very general comparisons similar to those in

the previous paragraph.

 Despite low confidence that can be placed on very small estimated probabilities, the

precipitation that fell from December 1992 through February 1993 could be considered to be

an extremely rare event. A similar but not as severe an event occurred from January through

April 1905 (Weather Bureau, 1905). In the region from Phoenix to Tucson, January

precipitation was about 2 inches. February rainfall totals were more than 4 inches at most

locations, with Buckeye receiving a record 6.46 inches. During March and April, the monthly

totals were generally between 2 and 3 inches. The 1905 event was the most extreme

previously recorded event, but it was significantly less intense than in January-February 1993

(and certainly in December 1992-February 1993).

 More than half the sites in each of the two regions that were used to compute the regional

quantiles included observations from the 1905 event. However, of the seven sites used in the

current analysis, only data from Buckeye and Roosevelt include the 1905 precipitation. The

possibility therefore exists that the data used are not representative of the historical events at

all sites in the two regions. However, even if the 1905 event had been measured at all sites, it

is probable that the regional quantiles would have changed little and would still indicate that the

1992-1993 winter precipitation was a very rare occurrence. If it is accepted that the winter

precipitation was indeed an extremely rare event, i.e., the observed precipitation could be

expected to occur once in more than a few hundred years, then the question could be asked,

"What is the effect the probabilistic knowledge could have on water managers' decisions?"

 Operationally, water management decisions are generally based on current conditions and

on the forecasts issued by the National Weather Service. Taken into consideration are, for

example, current streamflows, potential increase in streamflows from snowmelt and/or

precipitation, reservoir capacity, dam outflow channel capacity, and projected losses from

varying degrees of flooding. Historical probabilities of the occurrence of extreme precipitation

are not major factors in making decisions to contain water in reservoirs or to release water

into downstream channels.

 The historical record is important, however, in planning for extreme events. In the

aftermath of the floods, one might ask, "Should we have built larger dams or other structures

that would have prevented damage from the winter rains?" Descriptions of prior events, such
as the one that occurred in 1905, enhance the background knowledge necessary to minimize

damage from unusual events. They also subjectively influence the degree of risk that decision

makers are willing to take.

 It is a well established principle in water resources planning that the damage from large, but

rare, events must be weighed against the higher costs (financial, environmental and social) of

larger preventive projects. Structures necessary for the economic well-being of an area, such

as roads, bridges, buildings, irrigation systems, drainage facilities, dams, etc., are designed

and built to withstand unusual events that are expected to occur with a quantified frequency.

The U.S. Army Corps of Engineers, for example, generally recommends project sizes that

reasonably maximize the net national economic benefits. The Corps recognizes a residual

risk as the consequence of large events times the probability of the events (U.S. Army Corps

of Engineers, 1992). In theory, this deterministic approach leads to a rational dam size

because one can demonstrate that it is cheaper to pay for damages from large, rare events

than to build the more costly project that would prevent the damages.

 The information presented herein is intended for decision makers and builders who will be

redesigning and reconstructing the facilities that were damaged or destroyed by the Gila River

flooding. The historical probabilistic estimates should be used to refine the probability

estimates of larger events when assessing plans to build new structures and systems.

REFERENCES

Climate Analysis Center, Weekly Climate Bull., Washington, DC, No. 92/41-93/9, 1992-1993.

Guttman, N.B., The use of L-moments in the determination of regional precipitation climates,

J. Climate, in press, 1993.

Guttman, N.B., J.R.M. Hosking and J.R. Wallis, Regional precipitation quantile values for the

continental U.S. computed from L-moments, J. Climate, in press, 1993.

Hosking, J.R.M., L-moments: analysis and estimation of distributions using linear

combinations of order statistics, J. Royal Statist. Soc. B, 52, 105-124, 1990.

Karl, T.R, C.N. Williams, Jr., F.T. Quinlan and T.A. Boden, United States Historical

Climatology Network (HCN) serial temperature and precipitation data,

ORNL/CDIAC-30,NPD-019/R1, Carbon Dioxide Information Analysis Center, Oak Ridge Natl.

Lab., Oak Ridge, TN, 374 pp., 1990.

U.S. Army Corps of Engineers, Guidelines for risk and uncertainty analysis in water resources

planning, volume 1, IWR Report 92-R- 1, Inst. for Water Resources, Ft. Belvoir, VA, 10-12,

1992.

Weather Bureau, Reports from January-April 1905, Arizona Section of the Weather and Crop

Service, Phoenix, 8 pp., 1905.
Figure Legends

1. Precipitation regions. Lines radiating from the centroid of a region end at the location of

the sites within the region.

2. Enlargement of figure 1 showing study locations, dams, and county boundaries.

Superimposed are the centroids of regions 71 and 72 and lines radiating to the locations of

region sites (truncated at the enlargement boundary).
Table 1. Longterm average precipitation (inches).

Site Dec Jan Feb Dec-Jan Jan-Feb Dec-Feb

Wickenburg 1.24 1.18 1.07 2.46 2.26 3.52

Buckeye 0.87 0.81 0.71 1.70 1.53 2.43

Mesa 1.06 0.85 0.79 1.92 1.64 2.72

Sacaton 1.08 0.84 0.78 1.93 1.63 2.71

Childs 2.11 1.89 1.71 4.01 3.62 5.77

Roosevelt 2.00 1.87 1.79 3.84 3.66 5.57

Miami 2.30 2.08 1.76 4.41 3.84 6.17

Table 2. Observed precipitation (inches).

Site Dec Jan Feb Dec-Jan Jan-Feb Dec-Feb

Wickenburg 3.46 5.34 5.20 8.80 0.54 14.00

Buckeye 4.52 4.30 2.70 8.82 7.00 11.52

Mesa 3.18 5.81 2.19 8.99 8.00 11.18

Sacaton 3.28 2.29 1.59 5.57 3.88 7.16

Childs 5.97 9.77 4.80 15.74 14.57 20.54

Roosevelt 5.80 11.25 5.21 17.05 16.46 22.26

Miami 6.43 10.29 5.98 16.72 16.27 22.70

Table 3. Exceedance probabilities.

Site Dec Jan Feb Dec-Jan Jan-Feb Dec-Feb

Wickenburg .076 .001 .008 .011 < .001 .002

Buckeye .008 < .001 .022 .001 < .001 < .001

Mesa .061 < .001 .073 .002 < .001 .002

Sacaton .059 .023 .154 .030 .050 .079

Childs .052 < .001 .036 .003 .001 < .001

Roosevelt .048 < .001 .033 .001 < .001 < .001

Miami .054 < .001 .020 .004 < .001 < .001
Table 4. Precipitation range (.95 confidence) for 50-year return period.

Site Dec Jan Feb Dec-Jan Jan-Feb Dec-Feb

Wickenburg 4.21 3.40 3.43 6.95 4.85 8.83

5.22 4.22 4.30 8.47 7.07 10.65

Buckeye 2.95 2.34 2.28 4.81 3.97 6.10

3.66 2.90 2.86 5.87 4.80 7.36

Mesa 3.59 2.43 2.53 5.42 4.24 6.82

4.45 3.01 3.18 6.61 5.12 8.24

Sacaton 3.65 2.42 2.48 5.46 4.20 6.81

4.52 3.01 3.12 6.66 5.09 8.22

Childs 6.49 5.35 4.72 10.47 8.72 13.17

8.42 6.91 6.28 12.58 10.38 15.44

Roosevelt 6.14 5.31 4.94 10.03 8.81 12.71

7.97 6.85 6.57 12.05 10.49 14.90

Miami 7.08 5.92 4.86 11.51 9.25 14.07

9.19 7.63 6.46 13.83 11.01 16.50

Table 5. Precipitation range (.95 confidence) for 100-year return period.

Site Dec Jan Feb Dec-Jan Jan-Feb Dec-Feb

Wickenburg 4.87 3.69 3.82 7.87 6.44 9.88

 6.21 4.79 5.11 9.87 8.18 12.22

Buckeye 3.41 2.53 2.54 5.45 4.38 6.83

 4.35 3.29 3.39 6.83 5.55 8.44

Mesa 4.15 2.63 2.82 6.14 4.67 7.64

 5.30 3.42 3.77 7.70 5.93 9.45

Sacaton 4.42 2.63 2.76 6.18 4.64 7.62

 5.39 3.42 3.70 7.76 5.88 9.42

Childs 7.28 5.94 5.21 11.74 9.63 14.16

10.23 8.22 7.86 14.51 11.77 17.22

Roosevelt 6.89 5.90 5.45 11.25 9.74 13.67

 9.68 8.16 8.22 13.90 11.90 16.62

Miami 7.95 6.57 5.36 12.91 10.22 15.13

11.16 9.08 8.08 15.96 12.49 18.40
 Figure 1
 Figure 2