The 1993 Midwest Extreme Precipitation in Historical and Probabilistic Perspective*

Transcription

1 The 1993 Midwest Extreme Precipitation in Historical and Probabilistic Perspective* Abstract Extreme rainfall amounts that resulted in severe flooding during the spring and summer of 1993 along the Missouri and Mississippi Rivers are examined from a historical and probabilistic viewpoint. Long-term average precipitation amounts and the departures of the 1993 summer rainfall from these averages are presented. Also, climatic regionalization and precipitation probabilities developed for the National Drought Atlas using L-moment techniques have been applied to the drainage area that contributed to the flooding. The exceedance probabilities of monthly and multiple-month observed precipitation amounts have been calculated. The results show that the three-month period May-July experienced unusually heavy rainfall when compared to prior years, and that July was particularly wet. Recurrence intervals for the rainfall events vary widely depending on the specific time period and locality, but the observed precipitation was an extreme event. 1. Introduction The 1993 flooding in the Midwest was reported extensively on daily television and radio news programs, in newspapers, and in magazines. We are all well aware of the widespread damage to agricultural lands, homes, businesses, and infrastructure (water supplies and transportation systems). We are also well aware of the acute disruption to almost every area of human endeavor and of the pain suffered by many in the path of the floods. This article helps answer the question, How rare was the precipitation that led to the flooding? The answer is important for the rebuilding process; new structures will be built and policies will be made that should take into account the risk of another flood of similar magnitude and consequence. Preliminary monthly precipitation amounts from + National Climatic Data Center, Asheville, North Carolina. IBM Thomas J. Watson Research Center, Yorktown Heights, New York. *Based on poster presented at the fall 1993 meeting of the American Geophysical Union. Corresponding author address: Dr. Nathaniel B. Guttman, National Climatic Data Center, Federal Building, Asheville, NC In final form 25 April American Meteorological Society # Bulletin of the American Meteorological Society ^ T ^ ^ d James R Wal,is# - April through July that were sent to the National Climatic Data Center from 273 sites in the Midwest and plains were examined. The sites correspond to those used in the development of the National Drought Atlas (U.S. Army Corps of Engineers 1994), which presents precipitation information in a probabilistic framework. For these sites, we looked at 1 2-, and 3month long-term averages, previous observed maximum precipitation amounts, departures of the 1993 rainfall from the long-term average and from the previous maxima, and the return periods of the 1993 observed rainfall. 2. Data Monthly precipitation totals recorded at the 273 sites were obtained from reports sent to the National Climatic Data Center by observers in the Cooperative Surface Observing Network. The data are preliminary in that they have not undergone complete quality assurance checks. They are, however, sufficient given the timeliness considerations of this study. The sites are a subset of the total in the network and were selected to match the long-term sites that were used in the preparation of the National Drought Atlas. The historical precipitation data for the sites come from the Historical Climatology Network (Karl et al. 1990) unadjusted dataset. These data have undergone extensive quality assurance checks and are intended to be used for detecting and monitoring longterm climatic changes on regional scales. Sites for which at least 60 years of record were available, no more than 10 percent of the data were missing, and not more than 12 consecutive months of data were missing were used in the computation of probabilities for the National Drought Atlas. The sites have been grouped into quasi-homogeneous collections of similar sites, referred to in this article as "regions." The grouping methodology is described by Guttman (1993). These regions are depicted on the figures by lines radiating from the centroid of a region to the location of sites within the region. No areal boundaries are shown, and no rigid 1785

2 assumptions are implied about the climatology in the area between sites. 3. Historical perspective The climatology of the flood area is portrayed by 1 2-, and 3-month averages and pre-1993 extremes for the months of April through July. Differences between the 1993 precipitation and the previous extremes and averages were calculated to illustrate the magnitude of the 1993 precipitation. Differences between the observed and average for the months of May through July are shown in Fig. 1, and differences from the previous extremes for the same months are shown in Fig. 2. Although a discussion for all four months follows, Figs. 1 and 2 do not portray April differences. As seen in the following discussion, the differences in April were not unusual. In April the entire study area except for sites in North Dakota and most of Kansas received higherthan-average precipitation. Amounts were less than 3 inches above average except mainly for sites in an area straddling the Minnesota-Iowa and WisconsinIllinois borders. In this latter area, reported amounts were between 3 and 6 inches above average. May was similar in that most locations received less than 3 inches above average. The area of higher precipitation, however, was oriented north-south from western Minnesota to eastern Oklahoma. In this area a few sites had between 3 and 6 inches more than the average precipitation, and some in northeastern Oklahoma received more than 6 inches above the average. In June the greatest departures of precipitation amounts from the averages occurred in a broad westeast band. Many sites in the area from South Dakota eastward to Wisconsin, southward to central Indiana, westward to the central Kansas-Nebraska border, and northward to the South Dakota-North Dakota border experienced precipitation that was more than 3 inches above average. More than 6 inches above average fell at sites from eastern South Dakota to the Iowa-Wisconsin border to northern Illinois. More than 6 inches above average fell at locations in northern Illinois and southern Wisconsin and also in northcentral Iowa and south-central Minnesota. Precipitation in July was heaviest, compared to the averages, in southeastern Nebraska, northern Kansas, northwestern Missouri, and southern Iowa. In this area, more than 12 inches above average was recorded at several sites, and more than 6 inches above average precipitation was recorded at almost all sites. A secondary area of heavy precipitation (more than 6 inches above average) was located in central North 1786 Dakota. Precipitation throughout the whole region was excessive, with most sites recording at least 3 and often 6 inches above average. Multiple-month precipitation, as one would expect based on the monthly patterns, was well above average throughout the Midwest. The magnitudes of the excessive amounts are graphically depicted in Fig. 1 and can also be appreciated by comparing the recorded precipitation with the previous long-term extremes (Fig. 2). Note that because of differing periods of record, comparison of extremes among the sites is not uniform. Some sites have 70 years of record, while others have over 120 years of record. Prior extremes at all sites, however, are based on at least 60 years of record. While the precipitation in April and May was above average, only a few new extremes were recorded. There were four new extremes in April (two in southern Minnesota, one in southern Wisconsin, and one in northeastern Illinois), and all were less than 2 inches above the previous extremes. In May only three new extremes (one each in southeastern South Dakota, eastern Nebraska, and northwestern Wisconsin) of similar magnitude to those in April were recorded. There were only two new 2-month (April-May) extremes. In June, several new extremes were recorded in an west-east band from eastern South Dakota eastward to northern Illinois. In July the new extremes were recorded mainly in a north-south band from North Dakota to Kansas. Excessive precipitation in the multiple-month periods is reflected by the extraordinary number of new extremes. 4. Probabilistic perspective Precipitation probabilities calculated for the National Drought Atlas were the basis for the probability assessment of the 1993 precipitation. Using gamma or Wakeby distributions that fit the historical regional precipitation, probabilities of observing the 1993 precipitation totals in each of the 1 -, 2-, and 3-month time periods from April through July were calculated. Return periods for each of the nine time periods were then calculated from these probabilities and portrayed on maps. The calculation of precipitation probabilities for the National Drought Atlas is described in Guttman et al. (1993). The approach is based on L moments (Hosking 1990), an alternative to the conventional moments. Moment-based methods have long been established in statistics for relating a probability distribution to an observed dataset. Conventional moments are Vol. 75, No. 10, October 1994

3 FIG. 1. Differences between the 1993 observed and the long-term, average precipitation for the months of May through July. Small x indicates missing data; small open square indicates that the 1993 precipitation was less than the average. Purple upward triangle, green downward triangle, orange circle, red right triangle, and red square indicate that the 1993 precipitation was 0-3,3-6,6-12,12-18, and >18 inches higher, respectively, than the average. Bulletin of the American Meteorological Society 1787

4 FIG. 2. Differences between the 1993 observed and the long-term, previous extreme precipitation for the months of May through July. Small x indicates missing data; small open square indicates that the 1993 precipitation was not a new extreme. Purple upward triangle, green downward triangle, orange circle, and red square indicate that the 1993 precipitation was 0-2,2-4,4-6, and >6 inches higher, respectively, than the old extreme Vol. 75, No. 10, October 1994

5 not always satisfactory in two major respects. They do not always impart easily interpreted information about the shape of a distribution (especially skewness and kurtosis), and estimates of parameters of distributions fitted by the moments are often less accurate than those obtained by other methods such as maximum likelihood. L moments are analogs of conventional moments, constructed so that they can be estimated by linear combinations of order statistics (hence the "L"). Theoretically, L moments are able to characterize a wider range of distributions than conventional moments. Practically, they are less subject to bias in estimation, and they approximate their asymptotic normal distribution more closely. The main advantage of L moments over conventional moments is that L moments suffer less from the effects of sampling variability; they are more robust to outliers in the data. A unified approach to the use of order statistics for the statistical analysis of univariate probability distributions, based on L moments, has been developed by Hosking (1990). Based on goodness-of-fit tests, the gamma distribution was chosen as a primary probability distribution from which to estimate return periods. It is not, however, acceptable for all time periods and regions. Two conditions preclude the use of the gamma. First, the goodness-of-fit measure finds it unacceptable, and second, precipitation within a region is heterogeneous. Forthis second condition, there is no reason to assume that a single distribution will give a good fit to every site's data within the heterogeneous area. The Wakeby five-parameter distribution was cho- FIG. 3. Recurrence intervals of the observed 1993 monthly precipitation for the months of April through July. Small x indicates missing data. Purple upward triangle, green downward triangle, orange circle, red right triangle, red square, and red circle indicate intervals of ,10-50,50-100, , , and >1000 years, respectively. Bulletin of the American Meteorological Society 1789

6 FIG. 4. Recurrence intervals of the observed 1993 multiple-month precipitation for the period April through July. Small x indicates missing data. Purple upward triangle, green downward triangle, orange circle, red right triangle, red square, and red circle indicate intervals of ,10-50,50-100, , , and >1000 years, respectively Vol. 75, No. 10, October 1994

7 sen as the single fitted distribution for a heterogeneous region. The Wakeby was also chosen as the distribution for a region where the gamma was unacceptable. It was chosen as the default distribution because it is robust to misspecification of the underlying distribution function for a region (Kotz et al. 1988; Hosking and Wallis 1993), and it can attain a wide range of distributional shapes with fixed lower bound that mimic many skew distributions, making it particularly useful for hydrologic studies (Hosking 1986). The 1-month return periods (Fig. 3) show that in April the observed precipitation could be expected to occur once in less than ten years at most sites in the study area. In north-central Iowa, southern Minnesota, southern Wisconsin, and northern Illinois, however, observed April precipitation could be expected to occur once in every ten to 50 years. In May, locations in a north-south-oriented band from South Dakota, west-central Minnesota, and Iowa southward to Oklahoma indicate return periods of 50 to 100 years. Rainfall was near normal at sites in Illinois, Indiana, and eastern Missouri. The highest return periods (50 to 100 years) in June were centered, as in April, at sites in north-central Iowa, southern Minnesota, southern Wisconsin, and northern Illinois. In July, return periods in excess of 100 years were calculated for sites in North Dakota, southern Nebraska, northeastern Kansas, northern Missouri, and southeastern Iowa. At several sites the return periods indicate that the observed July rainfall was exceptionally rare. Return FIG. 5. Stage and discharge for extreme flood events on the Mississippi River at St. Louis, Missouri. Solid line is the stagedischarge relation for the period Data, except for the 1993 event, are from Belt (1975). Bulletin of the American Meteorological Society periods in excess of 10 to 50 years were calculated for almost all the sites in the study area. Looking at 2-month precipitation (Fig. 4), the observed April-May rainfall at locations near the Missouri River, in north-central Iowa, and in southern Wisconsin could be expected to occur once in 50 to 100 years. The highest return periods for the MayJune precipitation occur in the same area, but the expected recurrence intervals are longer than those for April-May. The observed rainfall in June-July was very rare at sites in southern Nebraska, in North Dakota, along the Iowa-Minnesota border, in southern Wisconsin, and near the Mississippi River in south-central Iowa. The April-June rainfall could be expected to occur less often than once in every 100 years mainly at locations in an east-west band from south-central South Dakota through southern Wisconsin. The MayJuly rainfall was a rare event at sites in this same band as well as in a north-south band through the Dakotas, Nebraska, eastern Kansas, and western Missouri. 5. Concluding remarks Throughout April, May, June, and July, a succession of mesoscale convective storms inundated much of the Midwest and plains of the United States with above-average precipitation. The 3-month period MayJuly experienced unusually heavy rainfall when compared to prior years, as 43 out of 273 sites recorded new maxima. The month of July was particularly wet, with 50 sites recording new monthly maxima. Estimated recurrence intervals for these rainfall events vary widely depending on the specific period and locality. For the 3-month period May-July, 14 sites experienced precipitation estimated to occur once in more than 1000 years. At 7 more sites, the recurrence interval is between 500 and 1000 years, and at 30 other sites, between 100 and 500 years. In the very wet month of July, 18 sites experienced precipitation estimated to occur once in more than 1000 years; at 5 more sites, between 500 and 1000 years; and at 32 other sites, between 100 and 500 years. The results indicate that the observed precipitation was an extreme event. It is important to recognize that the calculated return periods are based on sample sizes that average about 90 years. Confidence in the long recurrence intervals (greater than about 200 years) is therefore low. The values can be used, however, in a qualitative and comparative sense. For example, a location with a calculated recurrence interval of 1000 years experienced a more extreme event than a place with an 1791

8 interval of 100 years, but both could be considered to have experienced a rare event. The degree of extremeness among sites can be qualitatively assessed by comparing the appropriate calculated recurrence intervals. Translation of return periods of precipitation into return periods of flood discharge and stage should be made with caution. Not all flood events on the upper Mississippi are caused directly by precipitation many may arise from snowmelt. Furthermore, man-made changes in the Mississippi's channel have caused flood events of given discharge to result in increasingly higher flood stages over the years (Belt 1975; Myers and White 1993). This tendency is illustrated in Fig. 5 for the Mississippi River at St. Louis, Missouri. Extreme floods in the period up to 1927 lie close to the extrapolation of the stage-discharge relation for given by Belt (1975). Later extreme floods lie well above this curve, with the 1993 event having a particularly high stage for its discharge. References Belt, C. B., Jr., 1975: The 1973 flood and man's constriction of the Mississippi River. Science, 189, Guttman, N. B., 1993: The use of L-moments in the determination of regional precipitation climates. J. Climate, 6, , J. R. M. Hosking, and J. R. Wallis, 1993: Regional precipitation quantile values for the continental U.S. computed from L-moments. J. Climate, 6, Hosking, J. R. M., 1986: The Wakeby distribution. Research Rep. RC 12302, IBM Watson Research Center, 21 pp. [Available from Distribution Services F-11 Stormytown, P.O. Box 218, Yorktown Heights, NY ], 1990: L-moments: Analysis and estimation of distributions using linear combinations of order statistics. J. Roy. Statist. Soc. B, 52, , and J. R. Wallis, 1993: Some statistics useful in regional frequency analysis. Water Resour. Res., 29, Karl, T. R., C. N. Williams Jr., F. T. Quinlan, and T. A. Boden, 1990: United States Historical Climatology Network (HCN) serial temperature and precipitation data. ORNL/CDIAC-30, NDP-019/R1, Carbon Dioxide Information Analysis Center, Oak Ridge National Lab., Oak Ridge, TN, 374 pp. Kotz, S., N. L. Johnson, and C. B. Read, Eds., 1988: Wakeby distributions. Encyclopedia of Statistics,Vol. 9., Wiley, Myers, M. F., and G. White, 1993: The challenge of the Mississippi flood. Environment, 35,6-9, U.S. Army Corps of Engineers, 1994: National Drought Atlas, in press. With the development of meteorological science and the continual refinement of the technologies used in its practical application, the need to produce a new edition of the International Meteorological Vocabulary (IMV) became evident (the original edition was published in 1966). This volume is made up of a multilingual list of over 3500 terms arranged in English alphabetical order, accompanied by definitions in each of the languages (English, French, Russian, and Spanish) and an index for each language. This new edition has been augmented with numerous concepts relating to new meteorological knowledge, techniques, and concerns. It should help to standardize the terminology used in this field, facilitate communication between specialists speaking different languages, and aid translators in their work. WMO No. 182, 784 pp., softbound, color-coded index, $95 (including postage and handling). Please send prepaid orders to: WMO W Publications Center, American Meteorological Society, 45 Beacon St., w 1 x Boston, MA (Orders from U.S. and Canada only.) ~ <1 International Meteorological Vocabulary 1792 Vol. 75, No. 10, October 1994