# Arkansas

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Arkansas StreamStats incorporates statewide regression equations for estimating instantaneous peak flows with annual exceedance probabilities of 50, 20, 10, 4, 2, 1, and 0.2 percent. These peak flows have recurrence intervals of 2, 5, 10, 25, 50, 100, and 500 years, respectively. Arkansas StreamStats also incorporates regional regression equations that are applicable to the western 2/3 of Arkansas for estimating low-flow frequency statistics, including annual 7-day, 2-year and 10-year low flows, monthly 7-day, 10-year low flows for the individual months of November through March, and 7-day, 10-year low flows for the combined months of November and December, November through April, January and February, and March and April. In addition, equations are available for this same area for estimating the probability of zero flow in streams at times of the annual 7-day low flow, the November 7-day, 10-year flow, and 7-day, 10-year flows for November to December, and November to April. The reports below document the regression equations, the methods used to develop them and to measure the basin characteristics used in the equations, and the errors associated with the estimates obtained from the equations. Users should familiarize themselves with these reports before using StreamStats to obtain estimates of flows for ungaged sites in drainage basins.

- Hodge, Scott A.; Tasker, Gary D., 1995, Magnitude and frequency of floods in Arkansas: U.S. Geological Survey Water Resources Investigations Report 95-4224, 52 p.
- Funkhouser, Jaysson E.; Eng, Ken; Moix, Matthew W., 2008, Low-Flow Characteristics and Regionalization of Low-Flow Characteristics for Selected Streams in Arkansas: U.S. Geological Survey Scientific Investigations Report 2008-5065, 162 p.

# Interactive Map

## Erroneous Drainage Area

On July 21, 2014, an error was found and corrected in the computed drainage area for the Black River in the vicinity of Pocahontas, Arkansas. The error began on the main stem of the Black River, at the outlet of HUC 11010007; latitude 36.253033, longitude -90.912041. Drainage area computations upstream from that point were not affected.

## Notes on computing basin characteristics:

When using the *Basin Characteristics* tool, if a value for basin shape (BSHAPE) is desired, then a two-step process is required. First, use the tool to compute either the adjusted or the unadjusted 10-85 stream slope, and then use it again to compute BSHAPE.

## Notes on peak-flow estimates:

Basin characteristics used as explanatory variables in the peak-flow regression equations by Hodge and Tasker (1995) were determined by manual methods. Methods used in StreamStats to compute stream slope, basin length, and basin shape, initially resulted in values that were biased in comparison to the values for streamgages that were published by Hodge and Tasker (1995), and the biased basin characteristics were causing bias in the resulting peak-flow estimates. Relations between the StreamStats and published values for these basin characteristics were determined and used to adjust the StreamStats values in an attempt to remove bias. Bias was adequately removed for regions A, B, and C, but peak-flow estimates for region D still are biased high, with average bias of 4.3, 5.8, 6.7, 7.6, 8.2, 8.7, and 9.9 percent for the 50, 20, 10, 4, 2, 1, and 0.2 percent exceedance probabilities, respectively. Also, after adjusting the basin characteristics for bias, individual differences between flow estimates provided by StreamStats and those determined using the published basin characteristics were sometimes large, with some differences of as large as 40 percent. As a result, StreamStats users should expect that the errors associated with the peak-flow estimates provided by StreamStats are larger than the published standard errors of prediction, which are shown in the StreamStats outputs for user-selected sites.

## Interpretation of zero flow-probability estimates:

At the bottom of the outputs for ungaged sites that are produced by the *Estimate Flows Using Regression Equations* tool are four estimates of the probabilities that minimum 7-day flow will be zero. The statistic labeled PROB_7DAY is an estimate of the probability that the annual minimum 7-day flow for any given climatic year (April 1 to March 31) will be zero. The likelihood that the minimum 7-day low flow will be zero for a particular recurrence interval (T) can be determined by comparing the estimated probability from the StreamStats output to the reciprocal of the recurrence interval (1/T). For example, to determine if the annual 7-day, 10-year flow is zero, divide one (1) by the recurrence interval (10) to obtain a probability of 0.1, and then compare that probability (0.1) to the probability for PROB_7DAY in the StreamStats output. If the probability given by StreamStats exceeds 0.1, then assume the annual 7-day 10-year low flow is zero; otherwise use the estimate labeled as M7D10Y in the StreamStats output as the estimate. Likewise, if value of PROB_7DAY in the StreamStats output exceeds 0.5, then assume that the annual 7-day, 2-year flow is zero; otherwise, use the estimate labeled as M7D2Y in the StreamStats output as the estimate. For the other estimates of the probability of zero flow, labeled PROB7D11, PROB7D1104, and PROB7D1112, if the estimates of the probability of zero flow exceed 0.1, then the flow estimate for the corresponding flow statistic should be considered zero; otherwise, use the values given for the corresponding statistics, M7D10Y11, M7D10Y1104, M7D10Y1112, respectively.

## Notes on low-flow and zero flow-probability estimates:

Annual, spring, or winter tau is used as an explanatory variable in all zero-flow probability equations and many of the low-flow frequency equations for Arkansas, including equations for M7D2Y, M7D10Y, M7D10Y11, M7D10Y12 in low-flow regions 2 and 3, the equation for M7D10Y0304 in low-flow region 2, and equations for M7D10Y1104 and M7D10Y1112 in low-flow region 3. Tau is the base-flow recession constant, measured in days, which characterizes the rate at which the flow in a stream recedes after a streamflow peak. Methods used by StreamStats to compute annual, spring, and winter tau for user-selected sites differ from the methods that were used to determine tau values for the streamgages that were included in the regression analyses. As a result, individual differences between the estimates provided by StreamStats for the affected streamflow statistics and those determined using the published basin characteristics were sometimes large. The largest percent differences generally were associated with the smallest flow estimates, with some differences of greater than 250 percent. StreamStats users should expect that the errors associated with the estimates for the affected statistics are larger than the published standard errors of prediction, which are shown in the StreamStats outputs for user-selected sites.

Arkansas StreamStats was developed in cooperation with the Arkansas State Highway and Transportation Department, the Arkansas Natural Resources Commission, the Natural Resources Conservation Service, the U.S. Forest Service, and the U.S. Army Corps of Engineers - Little Rock District.

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