Trends in Peak Flows of Selected Streams in Kansas

The possibility of a systematic change in flood potential led to an investigation of trends in the magnitude of annual peak flows in Kansas. Efficient design of highway bridges and other flood-plain structures depends on accurate understanding of flood characteristics. The Kendall's tau test was used to identify trends at 40 stream-gaging stations during the 40-year period 1958-97. Records from 13 (32 percent) of the stations showed significant trends at the 95-percent confidence level. Only three of the records (8 percent) analyzed had increasing trends, whereas 10 records (25 percent) had decreasing trends, all of which were for stations located in the western one-half of the State. An analysis of flow volume using mean annual discharge at 29 stations in Kansas resulted in 6 stations (21 percent) with significant trends in flow volumes. All six trends were decreasing and occurred in the western one-half of the State.

The Kendall's tau test also was used to identify peak-flow trends over the entire period of record for 54 stream-gaging stations in Kansas. Of the 23 records (43 percent) showing significant trends, 16 (30 percent) were decreasing, and 7 (13 percent) were increasing. The trend test then was applied to 30-year periods moving in 5-year increments to identify time periods within each station record when trends were occurring.

Systematic changes in precipitation patterns and long-term declines in ground-water levels in some stream basins may be contributing to peak-flow trends. To help explain the cause of the streamflow trends, the Kendall's tau test was applied to total annual precipitation and ground-water levels in Kansas. In western Kansas, the lack of precipitation and presence of decreasing trends in ground-water levels indicated that declining water tables are contributing to decreasing trends in peak streamflow. Declining water tables are caused by ground-water withdrawals and other factors such as construction of ponds and terraces.

Peak-flow records containing trends introduce statistical error into flood-frequency analysis. To examine the effect of trends on flood-frequency analysis, statistically significant trends were added systematically to four nontrending station records. Flood magnitudes estimated on the basis of each data series were compared. The added trends resulted in changes in the 100-year flood magnitudes of as much as 70 percent.

Kendall's tau (Kendall and Gibbons, 1990) served as the statistical basis for the trend analyses presented in this report. It is a nonparametric test that can be used to indicate the likelihood of an increasing or decreasing trend over time. A nonparametric test is one that does not require a known or assumed probability distribution for the variables in question. A parametric test, like linear regression, was not considered appropriate for this report because streamflow characteristics are not normally distributed. The Kendall's tau test is rank based and does not depend specifically on the magnitudes of the data values. It is effective for identifying trends in streamflow because extreme values and skewness in the data have little effect on the outcome (Helsel and Hirsch, 1992).

Using the Kendall's tau test, the rank of each peak-flow value is compared to the rank of the values following it in the series. If the second value is consistently higher than the first, the tau coefficient is positive. If the second value is consistently lower, the tau coefficient is negative. An equal number of negative and positive values would suggest that a trend does not exist. Therefore, the tau value is a measure of the correlation between the series and time. In this report, a trend was considered to be significant if the probability (p) value (probability that a true null hypothesis of no trend is erroneously rejected) was less than or equal to 0.05. This represents a 95-percent confidence level. The slope is a measure of the magnitude of the trend.

Past studies suggest that statistically significant trends in streamflow can be difficult to detect due to relatively short periods of record (Chiew and McMahon, 1993). Furthermore, Wahl (1998) showed that, although Kendall's tau test is relatively insensitive to the presence of individual outliers, a sequence of extreme occurrences near the beginning or the end of the period of record could have a significant effect on the outcome of the Kendall's tau test. Therefore, stream-gaging-station records used in this report were examined for multiyear sequences that were wetter or dryer than normal at either end of the period of record. Although several sequences were found, they were minor and did not appear to significantly alter the overall results of the trend analysis.

In addition to the peak-flow analysis, flow volume in Kansas was analyzed for trends using mean annual discharge for 29 stream-gaging stations. Mean annual discharge is the average of the individual daily mean discharge values. Fewer stream-gaging stations were studied in this part of the analysis than for the peak-flow analysis because some of the stations had only partial records of daily mean discharge. Regulated streams were not used in the peak-flow analysis because dams and diversions significantly altered peak flows on regulated streams. However, records from four regulated stream-gaging stations with large drainage basins were used in the analysis of flow volumes. Losses from lake evaporation and diversions were not accounted for in total annual flow volume at the regulated stations. Analyzing the flow volumes for the larger drainage basins may provide more reliable indicators of flow trends because they are less susceptible to localized flooding and human-related factors. Larger drainages also have a larger ground-water component that can make them slower to respond to changes in precipitation. Again, the 29 flow-volume stream-gaging stations were distributed evenly and were representative of conditions across Kansas.

Establishing that a statistically significant trend in streamflow occurred over the past 40 years does not indicate that the trend will continue into the future. In evaluating whether the trend is likely to continue, the cause of the trend needs to be determined. Trends in peak streamflow can be caused by a variety of factors, many of which are difficult to relate statistically to the trend due to lack of appropriate data.

The most direct potential cause of an increasing trend in peak flow is an increase in either the frequency, intensity, or amount of rainfall. Increased rainfall frequency may support higher average streamflows, which then are supplemented during intense storms, resulting in higher peak flow. Urbanization, particularly stream channelization and increasing paved surface areas, may result in higher downstream peak flows (Bedient and Huber, 1992). A substantial decrease in upstream water use, although not common, also could affect downstream peak flows.

Decreasing peak-flow trends also can be caused by changes in rainfall patterns, such as decreases in total rainfall or decreases in the intensity or frequency of rainfall. Construction of reservoirs, levees, and diversions may decrease peak flows. Increases in upstream water use are likely to contribute to decreasing streamflows. Ground-water depletion usually decreases streamflow, particularly over a long period of time, because it decreases base flow (ground-water contribution to streamflow). Average annual runoff in Kansas varies from 0.1 in. in the west to about 10 in. in the east (Sophocleous and Wilson, 2000). Terracing, particularly in western Kansas, could reduce available runoff, resulting in decreasing peak flows. In addition, changes in land use and farming practices can decrease streamflow. In the 1930s, the Federal government, primarily through the Soil Conservation Service, initiated a series of programs designed to reduce soil erosion. Land-management practices including contour farming, crop rotation, pasture improvement, highly erodible land repair, and construction of watershed dams all control soil erosion. These practices also reduce and delay surface runoff, which should result in a decrease in peak flows and flow volumes.

Total precipitation in the United States has increased by 10 percent during the 20th century from 1910 to 1995 (Karl and Knight, 1998). The increase in precipitation has been attributed in part to increasing global temperatures. As the mean surface temperatures of the Earth increase, more evaporation occurs. Warmer temperatures also allow the atmosphere to hold more water that subsequently falls as precipitation. In their analysis of precipitation trends, Karl and Knight (1998) showed a statistically significant increase in the number of annual precipitation occurrences in each of the nine regions covering the entire contiguous United States. The same analysis also revealed an increase in the intensity of excessive rainfall in all nine regions, which has an even greater effect on total precipitation than does increased frequency.

An increasing trend in flood intensities would be expected from increased precipitation. Runoff occurs when rainfall intensity exceeds the infiltration capacity of the soil, which is affected primarily by the existing soil-moisture conditions. The increasing trend in rainfall frequency may not increase flood intensity if the time interval between rainfall allows adequate evapotranspiration to deplete the soil moisture. However, an increase in the intensity of rainfall does result in increased runoff and floods of greater magnitude. Lins and Slack (1999) found that across the United States annual minimum and mean streamflows were increasing significantly but that annual maximum flows were neither increasing nor decreasing nationwide.

The Kendall's tau test was applied to total annual precipitation values for each of the 26 meteorological divisions of the National Weather Service in Kansas, Oklahoma, and Nebraska for 1958-97, the same 40-year period used for the peak-flow analysis described earlier in this report. The precipitation data were from the National Climatic Data Center's database (National Oceanic and Atmospheric Administration, 1998).

The Kendall's tau test was applied to winter water levels in 17 wells in Kansas for 1958-97. All the wells with water levels less than 50 ft below land surface for which annual data were available for the majority of the period were included. Wells with water levels less than 50 ft below land surface were used because they measure ground water that is likely to be more directly related to surface flow than water at greater depths. Water-level measurements used in the analysis were made during the winter months because less natural fluctuation normally occurs due to the fact that it is typically the driest season in Kansas. Also, water levels are more stable in winter because they have recovered from irrigation pumping during the previous summer. January measurements were used when available, and when unavailable, the closest February or December measurements were substituted. If no December, January, or February water level was available, the year was skipped. The water-level values used represented the altitude of the water table. A positive tau represented an increase in water-table altitude.

Flood-frequency analysis uses annual peak flows to estimate the probabilities for certain flood magnitudes when designing bridges, highways, and other flood-plain structures. Frequency analysis assumes that the data series is stationary; that is, the statistical parameters, such as mean, variance, and skewness coefficient, do not change over time. If significant trends exist in the peak-flow series, the data are not stationary, violating the assumptions of frequency analysis and introducing error into the statistical analysis. Whether the error is large enough to invalidate the frequency analysis results becomes the issue.

The effects of significant trends on flood-frequency analysis were investigated by adding hypothetical trends to four nontrending stream-gaging-station records and comparing estimated flood magnitudes. Flood-frequency analysis was carried out according to procedures outlined in Bulletin 17B of the Interagency Advisory Committee on Water Data (1982). The guidelines presented in Bulletin 17B were established to provide consistency in flood-frequency analysis done by Federal agencies. It uses annual peak-flow series to compute flood-frequency curves by fitting a Pearson type-III distribution to the logarithms of the peak flows. Special techniques are recommended for handling low outliers, zero-flow years, historic peaks, and other aspects of the procedure. As a general rule, frequency analysis is questioned when using a historical record less than 10 years in length and in estimating frequencies of floods greater than twice the length of record (Viessman and Lewis, 1996).

Flood risk changes over time. It appears that flood estimates for specific frequencies can change considerably on the basis of period of record used and on whether trends, either cyclic or monotonic, occur in the data. Flood-frequency analysis assumes that future peak-flow conditions will be similar to past conditions.

Determining the appropriate period of record to use when estimating flood recurrence intervals is perhaps a larger issue than previously thought. The traditional approach to flood-frequency estimation involves a tradeoff between bias and variance (National Research Council, 1999). Bias arises when long periods of record are used that include time periods when flood risk is different than during the current planning period. However, long periods of record result in better definition of the variance.

Climate variations may prove to be the most challenging aspect to estimating floods. Although human-related causes of peak-flow trends, such as changes in land and water use, can be projected into the future with reasonable accuracy, climate is much less predictable. As the National Research Council (1999, p. 67-68) explains in its recent study of the American River flood-frequency analysis:

"Non-stationarities pose a serious challenge to flood frequency and risk analysis, and flood control design and practices. If cyclical or regime-like variations arise due to the natural dynamics of the climate system, a relatively short historical record may not be representative of the succeeding design period. Furthermore, by the time one recognizes that the project operation period has been different from the period of record used for design, the climate system may be ready to switch regimes again. Thus it is unclear whether the full record, the first half of the record, the last half of the record or some other suitably selected portion is most useful for future decisions- ."

A general conclusion, then, is that more uncertainty exists in flood-frequency estimates than that suggested by conventional statistical analysis. Although a large amount of uncertainty is built into the frequency analysis, it is rarely considered in flood-plain decisionmaking processes. The National Research Council (1999) recommends that the existing static flood-risk framework, in which a single flood-frequency distribution is estimated from all available data and applied to an indefinite future period, be replaced with a more dynamic framework. A more appropriate approach would be to consider the length of the record, climatic factors, the length of the planning period, risk and uncertainty, and then follow up with periodic flood-frequency updates.

The magnitude of the annual peak flow for some streams in Kansas appears to be changing. The Kendall's tau trend test was used to identify and evaluate peak-flow trends in Kansas and in two adjoining States, Oklahoma and Nebraska. Initially, the same 40-year period of record, 1957-98, was used in the analysis. Thirteen (32 percent) of the 40 stream-gaging stations in Kansas that were analyzed showed a significant trend in peak flow. Of the 13 trending station records, 10 indicated decreasing trends occurring in the western one-half of the State. The three increasing-trend stations were located in eastern Kansas.

A similar pattern occurred when station records from Oklahoma and Nebraska were included in the peak-flow analysis. When the same 40-year period of record was analyzed for peak-flow trends at 88 stream-gaging stations in the three-State area, 22 (25 percent) of the station records showed significant trends. Four station records showed increasing trends, and 18 records showed decreasing trends. Nearly all the stations with decreasing trends were located in western Kansas and southwestern Nebraska, whereas most of the stations with increasing trends were scattered across the eastern one-half of the area.

As the period of record is adjusted, so is the trend test result. The Kendall's tau test also was used to identify trends over the entire available period of record for 54 stations in Kansas with a record length of more than 38 years. Of the 54 stations used in this part of the analysis, 23 station records (43 percent) showed significant trends over their entire record. Sixteen station records (30 percent) had decreasing trends, and seven records (13 percent) had increasing trends. The trend test then was applied to 30-year periods moving in 5-year increments through the available period of record to identify time periods within each station record when peak-flow trends were occurring.

In addition to the peak-flow analysis, flow volume in Kansas was analyzed for trends using mean annual discharge for 29 stream-gaging stations. A regional pattern similar to the peak-flow analysis was apparent. Records from six stations showed a significant trend. All six trends were decreasing and occurred in the western one-half of Kansas.

To help evaluate possible causes of the streamflow trends, the Kendall's tau trend analysis was applied to total annual precipitation in the three-State area and to ground-water levels in Kansas. A significant trend in annual precipitation was detected for 3 of the 26 meteorological divisions analyzed in the three-State area. All three trends in precipitation were increasing and occurred in meteorological divisions located in south-central Oklahoma. One of three stream-gaging stations tested for trends in peak flow within the three trending meteorological divisions showed a significant increasing trend in peak flow.

Although the increasing trends may be caused by changes in precipitation patterns, decreasing streamflow in western Kansas and Nebraska probably are caused by factors other than precipitation. The Kendall's tau test was applied to water levels in 17 ground-water wells in Kansas. Water levels in 13 wells showed significant trends. Water levels in 10 wells, all located in central and western Kansas, indicated that the water table was declining. As the water table declines below streambed elevation, more rainfall is necessary to create flow and to attain peak flows comparable to those under previous conditions. Therefore, declining water tables caused largely by ground-water withdrawals are contributing to decreasing trends in peak streamflow in western Kansas. Decreasing peak streamflow also may be related to other factors such as construction of ponds and terraces.

Peak-flow data are used to estimate probabilities for certain flood magnitudes. Nonstationary data, such as the peak-flow records containing trends, introduce statistical error into the flood-frequency analysis. To examine the effect of trends on flood-frequency analysis, hypothetical trends were systematically added to four nontrending station records. For each record, flood-frequency analysis was conducted on both the unchanged record and the corresponding record with the added trend. The resulting estimated flood magnitudes were compared. The magnitude of the 100-year flood changed by as much as 70 percent. In some cases, flood-frequency estimates calculated using trending peak-flow records fell outside the wide confidence limits established by flood-frequency analysis using the unaltered series, indicating the potential importance of accounting for trends in the analysis.

 

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