David B. Reed and Ethan A. Jolly
LMRFC Slidell, Louisiana
El Niño! Much has been written about the effects of El Niño and the associated weather that is expected across the United States. Concerns over the effects of El Niño are heightened because this year's El Niño is approaching the strength of the 1982/83 El Niño, the strongest measured this century. At LMRFC, we are often asked if we expect serious flooding similar to 1982/83 because of the effects of this climatological phenomenon. Is serious flooding more likely during an El Niño year? This brief study is an attempt to begin to answer this question.
For this study, the mean and variance of the instantaneous maximum discharges in cubic feet per second (cfs) for a water year (defined as October 1 through September 31) were computed for nine locations in the LMRFC's area of responsibility. We used standard t and F tests to determine if there is a statistical difference in discharge for El Niño years compared to non-El Niño years. The t test compares the statistical difference in the means for the two groups whereas the F test compares the difference in variability.
2. Site Selection and Data Processing
We chose nine river gages distributed over the LMRFC's Hydrologic Service Area (HSA) (Figure 1) to be representative of our HSA which includes approximately 220,000 square miles in the southeast US. More gaging sites were selected along the Gulf Coast where statistics indicate El Niño has the greatest effect in the LMRFC area.
Cairo, IL (CIRI2), at the confluence of the Ohio and Mississippi Rivers was chosen for its good representation of discharge for the Ohio River Valley and upper Mississippi River Valley. Results should be indicative of flows in the lower Mississippi River.
Other points included the French Broad River at Asheville, NC (AVLN7), the Pascagoula River at Merrill, MS (MRRM6), the Pearl River at Pearl River, LA (PERL1), the Black River at Pocahontas, AR (POCA4), the White Oak Creek at Talco, TX (WOCT2), the Calcasieu River near Kinder, LA (KDRL1), the Bogue Chitto River at Franklinton, LA (FRNL1), and the Amite River near Denham Springs, LA (DENL1). Locations and drainage areas for these points are indicated on Figure 1.
For water years 1950 through 1997, peak discharge data were obtained from the US Geological Survey's web site (http://h2o.usgs.gov/swr/). Discharge was chosen rather than stage because discharge is a better representation of the hydrologic response of a basin. This is due to the logarithmic properties of a rating curve as the stage increases as well as physical changes in the stream bed from year to year. For CIRI2, the U.S. Army Corps of Engineers measures stage and publishes the data for calendar years. For this reason, calendar year stages were used in the analysis of CIRI2.
El Niño events were defined as warm events on the Climate Prediction Center (CPC) home page
(http://nic.fb4.noaa.gov). The following years were assumed to be El Niño events: 51/52, 53/54, 57/58, 65/66, 69/70, 72/73, 76/77, 82/83, 86/87, 91/92, and 94/95. During these events, the effects of El Niño are felt during the winter and spring of the second year. For the rest of the analysis, we will refer to El Niño years as the second year of these events, although the usual convention is to use the first year.
3. Statistics Computed
Assuming a normal distribution, a t test was used to determine if the means of peak stages or flows during an El Niño year and those during a year that was not an El Niño year were similar. The value for t is computed as:
t= ( XN - XE ) / S
where XN is the mean or average of the peak discharges for the non El Niño years, XE is the mean of the peak discharges for years where El Niño occurred, and S is the variance of the population of the sampling distribution (XN - XE). The critical t value for a 90% probability with 46 (37+11-2) degrees of freedom is 1.68. If the t statistic was between -1.68 and +1.68, we would conclude there is no statistical difference in the two groups.
An F test was then used to determine if the standard deviation or variance was equal for these two groups. This test will indicate whether the peaks during El Niño years are more variable than the other years. If there is greater variability, we might assume more extreme events (i.e., flooding or drought) during an El Niño year. The value for F was computed with the following equation:
where s2N is the variance of the peak discharges for non El Niño years and s2E is the variance of the peak discharges during years that are El Niño years. For a 90% confidence, the confidence interval for the F statistic ranged from 0.373 to 2.12.
Statistics for stages for the calendar year for CIRI2 are shown in Table 1. Although the average peak stage during the El Niño years is less than that during the remainder of the years, the difference is not statistically significant even at a 90% confidence interval. During the winter and early spring of an El Niño year, the Ohio Valley normally receives below normal rainfall. Since the Ohio River is the primary contributor of flows for the lower Mississippi River at CIRI2, flows during El Niño years are expected to be less than other years.
Table 1. Statistics for peak stages at CIRI2 for El Niño years vs. non El Niño years
|Gage||Years with El Niño||Years without El Niño||t statistic||f statistic|
|Mean Stage (ft)||Std.Dev (ft)||Mean Stage (ft)||Std.Dev (ft)|
Table 2 shows that, for all gaging sites except MRRM6, the average peak discharge during El Niño years is greater than during other years. Due to the natural variability in peak discharges, no statistical conclusions can be drawn between discharges during El Niño years as compared to other years.
Table 2. Statistics for average peak discharges for all other locations
|Gage||Years with El Niño||Years without El Niño||t statistic||f statistic|
|Mean Discharge (Kcfs)||Std.Dev (Kcfs)||Mean Discharge (Kcfs)||Std.Dev (Kcfs)|
The F statistics indicate that there is no difference in the variability of the peak discharges between El Niño and non El Niño years for all locations except FRNL1 and DENL1. For half of the stations, the variability is greater during years when there is no El Niño.
The drainage areas of FRNL1 and DENL1 are close to the Gulf of Mexico, the area where above normal rainfall is expected during El Niño years. Although the means of the two sets of years are not statistically different, the peaks during El Niño are variable. We may conclude that extreme events are more likely during an El Niño year for small basins along the Gulf Coast. However, KDRL1 is also a small basin along the Gulf Coast and this basin exhibits more variability during years that are not El Niño years.
We have come to some surprising conclusions from this limited analysis. There is no statistical difference between peak flows in the LMRFC's HSA area during El Niño and non El Niño years. Does this mean that major flooding is more likely to occur because of El Niño? No. What it does indicate is that there is no statistical difference in the probability of major flooding this El Niño year compared to other years.
5. Limitations of this Study
This study has been very limited and should be used with caution. Since the full period of record for these stations was not used, using additional years might alter the results. Another way of testing would be to look at the peaks that occurred in the winter and spring since this is the time of year where El Niño has its greatest impact.
Haan, Charles T. Statistical Methods in Hydrology. 3rd ed. Ames: Iowa State UP, 1982.
Neter, John and William Wasserman. Applied Linear Statistical Models. Homewood: Richard D. Irwin, Inc., 1974.