## StreamStats in Iowa

Version 3 of Iowa StreamStats incorporates regression equations that can be used State-wide obtain estimates of (1) low-flow statistics (the annual 1-, 7-, and 30-day mean low flows for a recurrence interval of 10 years, the annual 30-day mean low flow for a recurrence interval of 5 years, the seasonal (October 1 through December 31, and April 1 to June 30) 1- and 7-, and 30-day mean low flows for a recurrence interval of 10 years, and the harmonic mean), (2) flow duration statistics (0.01-, 0.05-, 0.10-, 0.15-, 0.20-, 0.30-, 0.40-, 0.50-, 0.60-, 0.70-, 0.80-, 0.85-, 0.90-, 0.95-, and 0.99-exceedance probabilities), and (3) peak-flow statistics (50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities, which are equivalent to annual flood-frequency recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years, respectively). In addition, Iowa StreamStats can be used to estimate the probability of zero flow for the above-mentioned low-flow statistics for stream in the Southern Region of the State. The regression equations for estimating seasonal low flows have not yet been added to beta version 4. The reports below document the regression equations available in StreamStats for Iowa, the methods used to develop the equations and to measure the basin characteristics used in the equations, references to GIS data layers used in the analysis, and the errors associated with the estimates obtained from the equations. Users should familiarize themselves with the reports before using StreamStats to obtain estimates of streamflow statistics for ungaged sites.

- Eash, D.A., Barnes, K.K., and O’Shea, P.S., 2016, Methods for estimating selected spring and fall low-flow frequency statistics for ungaged stream sites in Iowa_ based on data through June 2014: U.S. Geological Survey Scientific Investigations Report 2016–5111, 32 p.
- Eash, D.A., and Barnes, K.K., 2012, Methods for estimating selected low-flow frequency statistics and harmonic mean flows for streams in Iowa: U.S. Geological Survey Scientific Investigations Report 2012–5171, 94 p.
- Eash, D.A., Barnes, K.K., and Veilleux, A.G., 2013, Methods for estimating annual exceedance-probability discharges for streams in Iowa, based on data through water year 2010: U.S. Geological Survey Scientific Investigations Report 2013–5086, 63 p.
- Linhart, S.M., Nania, J.F., Sanders, C.L., Jr., and Archfield, S.A., 2012, Computing daily mean streamflow at ungaged locations in Iowa by using the Flow Anywhere and Flow Duration Curve Transfer statistical methods: U.S. Geological Survey Scientific Investigations Report 2012–5232, 50 p.

Click on this link to obtain general information on the Iowa application, as well as specific sources and computation methods for basin characteristics.

# WARNINGS:

**Discharge-reporting limit for low-flow and flow-duration equation estimates:** Because of the uncertainty in measuring and estimating flows below 0.1 ft^{3}/s, the censoring threshold used to develop the low-flow and flow-duration left-censored regression equations was set at 0.1 ft^{3}/s. Thus, selected low-flow and flow-duration estimates calculated from left-censored regression equations that are 0.1 ft^{3}/s, or lower, should be reported as less than 0.1 ft^{3}/s. To maintain a consistent prediction-discharge-reporting limit for Iowa, any low-flow or flow-duration estimates for ungaged locations that are lower than 0.1 ft^{3}/s also should be reported as less than 0.1 ft^{3}/s.

**Use of zero-probability regression equations for the southern low-flow region:** The zero-probability (logistic) equations developed for the southern low-flow region should be used first to determine the probability of a specific low-flow frequency statistic equaling zero flow for an ungaged site in this region before the low-flow frequency statistic is estimated using the GLS regression equation. If the resulting probability (P_{zero}) is greater or equal to 0.5, then the value for that low-flow frequency statistic is estimated to be zero flow and the appropriate GLS regression equation should not be used. If the resulting probability is less than 0.5, then the appropriate GLS regression equation should be used to estimate the value of the low-flow frequency statistic. For example, if the probability estimate (P_{zero}) for M7D10Y from the zero-probability equation is 0.55, the estimate for M7D10Y is zero flow; if the probability estimate (P_{zero}) is 0.45, an estimate for M7D10Y should be calculated from the appropriate GLS regression equation.

**Computing basin shape:** 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 basin length or the 10-85 slope, and then use it again to compute BSHAPE.

**Use of drainage-area only equations for peak-flow region 1:** Peak-flow regression equations used in the StreamStats *Estimate Flows Using Regression Equations* tool for region 1 appear in table 9 of Eash and others (2013). Those equations require the measurement of the sum of stream lengths in the basin in order to calculate the basin characteristic CCM (constant of channel maintenance). The sum of stream lengths in the basin is measured using 1:24,000-scale streams. For small basins in peak-flow region 1, no 1:24,000-scale streams may be present and the value measured for the sum of stream lengths in the basin will equal zero. In these cases, then drainage-area only equations from table 15 in Eash and others (2013) will be used. A header in the *StreamStats Ungaged Site Report* will note the use of the drainage-area only equations by stating: "Sum of stream lengths in basin in miles = 0.000."

The drainage-area only equations from table 15 in Eash and others (2013) will also be used for computing peak-flow estimates for region 1 when CCM > 3.87, which is the maximum value for CCM used to develop the region 1 peak-flow equations. Errors for basins with CCM values greater than 3.87 are unknown and use of the drainage-area only equations with the *Estimate Flows Using Regression Equations* tool will report the uncertainty of the estimates for ungaged basins when the area in square miles is within the range of values that were used to develop the regression equations.

**Selected sites with drainage area in multiple hydrologic regions:** Eash and others (2013) identified three peak-flow regions for which separate regression equations were developed for estimating peak-flow statistics in Iowa. StreamStats provides estimates based on the regression equations for each peak-flow region that is within the drainage area and final weighted estimates, with weights corresponding to the proportion of the drainage area that is in each peak-flow region. Because the Des Moines Lobe basin characteristic is a weighting factor that decreases peak-flow estimates for region 2 relative to the percentage of drainage area within the Des Moines Lobe landform region, use of the area-averaged peak-flow estimates may underestimate flows. If the value for the Des Moines Lobe basin characteristic is greater or equal to 10 percent for peak-flow region 2, the preferred peak-flow estimates are those determined using only the regression equations for the peak-flow region in which the selected site is located. The Basin Characteristics tool can be used to determine the peak-flow region number for the region in which the selected site is located.

**Errors associated with estimated streamflow statistics for ungaged sites:** StreamStats outputs from the *Estimate Flows Using Regression Equations* tool report the uncertainty of the estimates for ungaged basins when basin characteristics for selected sites are within the ranges of the basin characteristics for streamgages that were used to develop the regression equations. Errors for basins with basin characteristics that are beyond these bounds are unknown. The applicable ranges of the basin characteristics are provided in the outputs and messages are provided when basin characteristics are outside of the applicable ranges. See the Streamflow Statistics Definitions page on the StreamStats home page for explanations of the statistics used as indicators of uncertainty.

Iowa StreamStats does not provide error indicators for estimates of the 99-percent duration flow. The average standard errors of prediction are given for other flow-duration percentiles, but it was not possible to compute this statistic for the 99-percent duration flow equation because a different method was used to develop the equation. Instead, the average standard error of estimate was computed, which was 97.7 percent. As StreamStats programming allows the display of only one type of standard error statistic for all equations within a hydrologic region, the error statistic for the 99-percent duration flow is not shown in StreamStats outputs.

A “jagging” phenomenon can sometimes be encountered with the estimates from flow-duration regression statistics when a discharge estimate for a particular exceedance probability is greater than the discharge estimate for the next successively lower exceedance probability. For example, an estimate for the 0.15-exceedance probability may be greater than the estimate for the 0.10-exceedance probability. Jagging can occur when the basin characteristics that are included as explanatory variables in the regression equations change between adjacent exceedance probabilities, and is a result of the inherent uncertainty in the estimates obtained from the individual regression equations. This phenomenon occurred for approximately 20 percent of the streamgages used to develop the flow-duration regression equations. See Linhart and others (2012) for more information about this error.

StreamStats for Iowa was developed in cooperation with the Iowa Department of Transportation and the Iowa Department of Natural Resources.