Trends in floods and low flows in the United States: impact of spatial correlation
Introduction
Records of atmospheric concentrations of carbon dioxide indicate a dramatic increase since the beginning of the Industrial Revolution. It is generally believed that such an increase in CO2, a “green house” gas, could result in increased global mean temperatures. Bloomfield (1992) reported statistically significant rates of mean global temperature increase between 0.4 and 0.6°C per century. Results of general circulation model studies indicate that increased global temperatures could lead to regional increases in the amount and intensity of rainfall. This prediction has been verified for the North American continent by Vinnikov et al., 1990, Guttman et al., 1992, Groisman and Easterling, 1994, Karl and Knight, 1998, among others, who found increases in precipitation amount and intensity across the US and Canada in recent years. The sensitivity of streamflow to changes in precipitation, and other climate parameters, is well documented, hence it is informative to investigate whether streamflow records exhibit evidence of increasing trends which may be linked to climate change.
A number of recent studies in the US have investigated the presence of trends in streamflow data. The results of those studies vary widely depending on the spatial scale and location of the study area, with most of the significant trends occurring in the Midwest. Lettenmaier et al. (1994) detected strong increases in monthly streamflow across the United States during November through April for the period 1948 to 1988, with the largest trend magnitudes occurring in the north central region (Michigan, Illinois, Wisconsin and Minnesota). Hubbard et al. (1997) reported increases in annual runoff in 16 of 20 major hydrologic regions across the United States. Smith and Richman (1993) found increases in mean annual streamflow in Illinois ranging from 20 to 80% during the period from 1950 to 1987. Changnon and Kunkel (1995) found significant upward trends in floods in the northern Midwest during the period 1921–1985, and found a link between these trends and higher precipitation. Olsen et al. (1999) found large and statistically significant upward trends in flood flows over the last 100 years in the Upper Mississippi and Missouri rivers. Pupacko (1993) found a slight (non-significant) trend of increasing and more variable winter streamflow in the northern Sierra Nevada since the mid-1960s. Most recently, Lins and Slack (1999) reported increasing trends across the US in lower magnitude streamflow quantiles (annual minimum through the 70th quantile) but not at higher quantiles (90th quantile and annual maximum).
Of all the previously cited studies, Lettenmaier et al. (1994) performed the only trend study that accounted for the spatial correlation of flow records. The fact that most studies ignored the role of spatial correlation in the interpretation of their results belies the importance of such correlation in statistical analysis. However, this oversight is not without good cause since the assumption of independent observations is paramount to many trend tests.
The effect of spatial and/or temporal correlation among datasets on hypothesis testing is twofold. First, cross-correlation creates an overlap in the information contained in each datapoint. For example, if flood flows are spatially correlated (cross-correlated) and a trend is found at a site, one is more likely to find trends at nearby sites as well. From a statistical perspective, correlation reduces the effective sample size of the dataset. This results in a more “liberal” hypothesis test, meaning that, if correlation is ignored, the null hypothesis (of independence) will tend to be rejected more frequently than it should be. Second, the presence of correlation makes the analytical derivation of an exact probability distribution for the test statistic difficult, in which case an approximate distribution must be developed.
Olsen et al. (1998) argue that the major impact of non-stationary behavior of a random variable is manifested in the extremes. This impact has been observed in climate records by Karl and Knight (1998) who reported that the proportion of total precipitation within the US contributed by extreme events (upper 10% of daily precipitation amounts) has increased significantly since the early 1900s. Similar trends in streamflow extremes, if they exist, would directly impact the accuracy of hydrologic analysis and design. Many studies have investigated the existence of trends in flood flows but few have performed the same analysis at the opposite extreme, in low flows. Trends in one or both of these variables could be seen as potential evidence of climate change and its impact on the hydrologic cycle, which could eventually lead to shifts in the availability of water across the US. Such climate change impacts have reportedly been observed within the last few years (Trenberth, 1999). Infrastructural accommodation to such shifts would be both environmentally and economically costly. Therefore, proper statistical investigation of the existence of such trends is paramount. Violation of the assumption of spatial independence of datasets, as is commonplace, can result in misleading and erroneous interpretations of the climate and/or streamflow record. In light of this, the objectives of this study are:
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To investigate the existence of trends in flood and low flows in such a manner that the potential impact of climate change can be assessed and so that our results can be compared with previous studies.
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To evaluate the effect of spatial correlation of flow records on the interpretation of hypothesis test results by developing a hypothesis test that accounts for the spatial correlation of the data, thereby allowing comparisons with the results of analyses in which the spatial independence of flow records has been assumed.
Section snippets
Data
Analyses were performed on data contained in the Hydro-Climatic Data Network (HCDN), a dataset compiled by Slack et al. (1993) which is comprised of average streamflow values recorded on a daily, monthly and annual basis at 1571 gaging stations across the continental US (see Fig. 1a for locations of gaging stations). The HCDN contains streamflow records collected between 1874 and 1988, with an average station record length of approximately 48 years. The basins represented in the HCDN are
Trends in streamflow
Fig. 3, Fig. 4 graphically illustrate the results of the bootstrap trend tests for flood and low flows in the three geographical regions and in the nine superregions, respectively. No significant trends were found in the flood flow data at either spatial scale, however, trends in the low flow data were observed at both scales, even after accounting for the spatial and serial correlation of the flow series. At the larger spatial scale, significant upward trends were observed in the low flow data
Conclusions
Regional trends in flood flows and low flows across the US were evaluated using the regional average Kendall's S at two spatial scales (three geographic regions and nine smaller regions) and over two timeframes (the most recent 30 years and the most recent 50 years). Empirical cumulative density functions (cdfs) for were obtained using a bootstrap method which preserves the observed spatial covariance structure of the streamflows. Field significance was assessed by comparing the
Acknowledgements
Although the research described in this article has been funded in part by the United States Environmental Protection Agency (EPA) through STAR grant number R824992-01-0 to Tufts University and EPA grant number R825888 to the SUNY College of Environmental Science and Forestry, it has not been subjected to the Agency's required peer and policy review and therefore does not necessarily reflect the views of the Agency and no endorsement should be inferred.
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