The U.S. Geological Survey (USGS) has a long history of working cooperatively with the South Carolina Department of Transportation to develop methods for estimating the magnitude and frequency of floods for rural and urban streams that have minimal to no regulation or tidal influence. As part of those previous investigations, flood-frequency estimates also have been generated for selected streamgages on regulated streams. This report assesses the effects of impoundments on flood-frequency characteristics by comparing annual exceedance probability (AEP) streamflows from pre- and post-regulated (before and after impoundment) periods at 18 long-term USGS streamgages, which is defined as a streamgage with 30 or more years of record, in Georgia, South Carolina, and North Carolina. For an assessment of how differences in such statistics can be influenced by period of record and hydrologic conditions captured in those records, which could be considered as natural variability, AEP streamflows at an additional 18 long-term USGS streamgages that represent unregulated conditions in those three States were computed and compared for the first and last half of those records.

Of the 18 long-term streamgages with pre- and post-regulated periods of record, 17 streamgages had both peak streamflows and daily mean streamflows available. To further assess how impoundments may influence a broader range of streamflow characteristics, The Nature Conservancy’s Indicators of Hydrologic Alteration software was used to compare selected streamflow characteristics generated from daily mean streamflows for pre- and post-regulated periods of record at 16 of those long-term streamgages. For comparison of the natural variability of such streamflow statistics, two periods of record (first half and last half) also were compared at 17 of the 18 long-term streamgages on unregulated streams. The remaining long-term streamgage on an unregulated stream included in this report had only annual peak streamflows and, therefore, was not included in the hydrologic alteration analysis.

In a separate USGS investigation completed in 2023, flood-frequency statistics for the 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent AEP streamflows (also known as the 2-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year recurrence interval streamflows, respectively) were computed for 72 streamgages on regulated streams in Georgia, South Carolina, and North Carolina. Of those 72 streamgages, 29 streamgages were found to be redundant, which is a situation where the drainage basin of one streamgage is contained inside another (nested) and the two basins are of similar size. For the remaining 43 streamgages, 39 had basins where 75 percent or more of the drainage area was above the Fall Line. Those 39 streamgages were included in this investigation to develop regional regression equations that can be used to estimate the flood-frequency statistics at ungaged locations on regulated streams in Georgia, South Carolina, and North Carolina in which 75 percent or more of the drainage basin is located above the Fall Line. The flood-frequency regression equations are functions of drainage area and maximum storage index computed for upstream reservoirs.

Musser, J.W., and Feaster, T.D., 2023, Tables and associated data for effects of impoundments on selected flood-frequency and daily mean streamflow characteristics in Georgia, South Carolina, and North Carolina: U.S. Geological Survey data release,

U.S. Geological Survey, 2019, USGS water data for the Nation: U.S. Geological Survey National Water Information System database,

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Photographs showing Hartwell Lake near Clemson, South Carolina; the reservoir was created by the impoundment of the Savannah River at the border of South Carolina and Georgia with the construction of the Hartwell Dam in the 1950s and 1960s (photographs by Toby Feaster, U.S. Geological Survey, May 29, 2023).

The authors acknowledge the longstanding partnership between the U.S. Geological Survey (USGS) and the South Carolina Department of Transportation (SCDOT). The foresight and leadership of engineers and management at the SCDOT have been vitally important to improving the understanding of water resources in South Carolina and the impacts that extreme events can have on highway infrastructure. The authors also would like to acknowledge Thomas Knight, SCDOT, for his support and guidance on this investigation.

The peak flow and daily mean flow data used in the analyses in this report were collected throughout Georgia, South Carolina, and North Carolina at streamgages operated in cooperation with a variety of Federal, State, and local agencies. The foresight of those cooperators in realizing the importance of long-term monitoring of streamflow is of paramount importance for investigations such as this. The authors also acknowledge the dedicated work of the USGS field-office staff in collecting, processing, and storing the peak flow and daily mean flow data necessary for the completion of this investigation.

Multiply | By | To obtain |

Length | ||
---|---|---|

mile (mi) | 1.609 | kilometer (km) |

Area | ||

square mile (mi^{2}) |
259.0 | hectare (ha) |

square mile (mi^{2}) |
2.590 | square kilometer (km^{2}) |

Volume | ||

acre-foot (acre-ft) | 1,233 | cubic meter (m^{3}) |

acre-foot (acre-ft) | 0.001233 | cubic hectometer (hm^{3}) |

Flow rate | ||

cubic foot per second (ft^{3}/s) |
0.02832 | cubic meter per second (m^{3}/s) |

annual exceedance probability

Bulletin 17C

expected moments algorithm

U.S. Environmental Protection Agency

generalized least squares

Indicators of Hydrologic Alteration

interquartile range

log-Pearson Type III

National Inventory of Dams

National Water Information System

ordinary least squares

probability percent

quartile

coefficient of determination

U.S. Geological Survey

variance inflation factor

Reliable estimates of the magnitude and frequency of floods are essential for flood insurance studies, floodplain management, and the design of transportation and water-conveyance structures such as roads, bridges, culverts, dams, and levees. Federal, State, regional, and local officials rely on such estimates to effectively plan and manage land use and water resources, protect lives and property in flood-prone areas, and determine flood insurance rates. The U.S. Geological Survey (USGS) and the South Carolina Department of Transportation have a long history of working cooperatively to develop techniques for estimating the magnitude and frequency of floods for rural and urban streams that have minimal to no regulation or tidal influence (

Streams are impounded for a variety of reasons such as flood control, water supply, irrigation, and hydroelectric power generation (^{2}) would generally affect peak streamflows by less than 10 percent and, therefore, used that level of usable storage as a limiting value for assuming that flood-frequency statistics were not substantially influenced by upstream regulation. Along with other assessment tools, the guidance from

The purpose of this investigation was to assess the effects of impoundments on selected streamflow characteristics across the contiguous hydrologic regions in Georgia, South Carolina, and North Carolina as defined by

The study area includes all of Georgia, South Carolina, and North Carolina, covering an area of about 142,500 square miles (mi^{2}) within seven U.S. Environmental Protection Agency (EPA) level III ecoregions—Southwestern Appalachians, Ridge and Valley, Blue Ridge, Piedmont, Southeastern Plains, Middle Atlantic Coastal Plain, and Southern Coastal Plain (

Study area and ecoregions in Georgia, South Carolina, and North Carolina and the surrounding States. Level III ecoregions are from

The Southwestern Appalachians ecoregion is composed of open, low mountains. The eastern boundary of this ecoregion, along the more abrupt escarpment where it meets the Ridge and Valley ecoregion, is relatively smooth and only slightly notched by small, eastward-flowing streams. The Ridge and Valley ecoregion is composed of roughly parallel ridges and valleys that have a variety of widths, heights, and geologic materials. Springs and caves are relatively numerous in this ecoregion, and present-day forests cover about 50 percent of the ecoregion. The Blue Ridge ecoregion varies from narrow ridges to hilly plateaus to more massive mountainous areas. The mostly forested slopes; high-gradient, cool, clear streams; and rugged terrain overlie primarily metamorphic rocks, with minor areas of igneous and sedimentary geology. The Piedmont ecoregion is composed of a transitional area between the mostly mountainous ecoregions of the Appalachian Mountains to the northwest and the relatively flat Coastal Plain to the southeast. The Piedmont ecoregion is a complex mosaic of metamorphic and igneous rocks of Precambrian and Paleozoic age, with moderately dissected irregular plains and some hills. The soils tend to be finer textured than in the Coastal Plain ecoregions to the south. Once largely cultivated, much of this ecoregion has reverted to pine and hardwood forests, with increasing conversion to urban and suburban land cover (

The Southeastern Plains ecoregion is composed of irregular plains featuring a mixture of cropland, pasture, woodland, and forest. The sand, silt, and clay geology of this ecoregion contrasts with the older rocks of the Piedmont ecoregion. Elevations and relief are greater than in the Southern Coastal Plain ecoregion but generally are less than in much of the Piedmont ecoregion. Streams in this area have relatively low gradient and sandy bottoms. The Southern Coastal Plain ecoregion consists of mostly flat plains, but it is a heterogeneous ecoregion containing barrier islands, coastal lagoons, marshes, and swampy lowlands along the Gulf of Mexico and Atlantic coasts. This ecoregion is lower in elevation with less relief and wetter soils than the Southeastern Plains ecoregion. The Middle Atlantic Coastal Plain ecoregion consists of low-elevation flat plains and includes many swamps, marshes, and estuaries. The low terraces, marshes, dunes, barrier islands, and beaches are underlain by unconsolidated sediments. Poorly drained soils are common, and the ecoregion has a mix of coarse and finer textured soils compared to the mostly coarse soils in the majority of the Southeastern Plains ecoregion. The Middle Atlantic Coastal Plain ecoregion typically is lower, flatter, and more poorly drained than the Southern Coastal Plain ecoregion (

Most of the flood-frequency statistics included in this report for streamgages having pre- and post-regulated periods of record were previously published in a USGS data release by

The hydrologic regions used in

Study area, hydrologic regions, and locations of U.S. Geological Survey streamgages with unregulated or regulated streamflow conditions and with long-term periods of record compared for the flood-frequency analyses for Georgia, South Carolina, and North Carolina (hydrologic regions from

Of the 72 streamgages on regulated streams from

Flood-frequency estimates for the streamgages included in this report were completed using recommendations from “Guidelines for Determining Flood Flow Frequency—Bulletin 17C” (

For streamgages on unregulated streams, there can be a relatively large uncertainty in the skew of the annual peak streamflows (

Because the regional skew is estimated from unregulated rural streamflow data, it is not recommended that it be used when doing a flood-frequency analysis for regulated peak streamflows. For the regulated flood-frequency estimates included in this report, the analysis employed B17C methods by using the skew from the streamgage peak streamflows, also referred to as the “station skew.”

Most of the flood-frequency statistics included in this report for streamgages having pre- and post-regulated periods of record were previously published in a USGS data release by

For the 18 streamgages with both pre- and post-regulated periods (table 1 from

is the original value, and

is the value it changed to.

For this comparison,

Flood-frequency curves of the annual exceedance probability streamflows for the pre- and post-regulated periods at 18 U.S. Geological Survey streamgages with long-term periods of record in Georgia, South Carolina, and North Carolina (streamflow data from

The flood-frequency statistics computed for streamgages on unregulated streams are strongly influenced by period of record and hydrologic conditions captured in that record. This natural variability also will influence streamflow statistics computed at streamgages on regulated streams but with the added complexity of the influence from the regulation, which may enhance or even offset the natural variability in those data. Although the USGS typically designates streamgage records with 30 or more years as long term (

To get a sense of how flood-frequency statistics have varied at unregulated USGS streamgages in Georgia, South Carolina, and North Carolina, the percentage change in the flood-frequency estimates for the 10-, 1-, and 0.2-percent AEP streamflows was computed for 18 streamgages monitoring unregulated streams by separating the record into two periods: first half of the record and last half of the record (

Annual exceedance probability flood-frequency curves from two periods (the first half and the last half) of long-term periods of record at 18 U.S. Geological Survey streamgages monitoring unregulated streams in Georgia, South Carolina, and North Carolina (streamflow data from

To further explore the percentage change between the 10-, 1-, and 0.2-percent AEP streamflows for the two periods from the 18 USGS streamgages with pre- and post-regulated periods of record (tables 1 and 3 from

Distribution of the percentage change in the 10-, 1-, and 0.2-percent annual exceedance probability (AEP) streamflows for 18 U.S. Geological Survey streamgages that have both pre- and post-regulated long-term periods of record and for two long-term periods of record (the first half and the last half) at 18 U.S. Geological Survey streamgages monitoring unregulated streams in Georgia, South Carolina, and North Carolina (streamflow data from

In general, the boxplots of the percentage change in the 10-, 1-, and 0.2-percent AEP streamflows for the two periods from the 18 streamgages monitoring unregulated streams show a variability that tends to be more balanced between positive and negative changes as compared to the pre- and post-regulated AEP streamflows (

To determine the effects of impoundments on a broader range of streamflow characteristics, The Nature Conservancy’s IHA software (

The IHA software (^{2}), and 02335000 Chattahoochee River near Norcross, Ga., had the highest (2,183 acre-ft/mi^{2}). As compared to 03513000, which shows only minor differences between the pre- and post-regulated periods, the effects of regulation on the high and low streamflows at 02335000 are substantial, showing how regulation decreased the annual 1-day maximum streamflows and increased the annual 7-day minimum streamflows (

Annual

Annual

The percentage change in the mean annual streamflow from the pre- to post-regulated period ranged from −21.8 to 9.7 percent with a median of −0.9 percent and a mean of −1.4 percent (table 5 from

The percentage change in the low pulse count from the pre- to post-regulated period ranged from −93.5 to 400 percent with a median of 20.0 percent and a mean of 64.6 percent (table 5 from

To assess natural variability in selected daily mean streamflow characteristics based on period of record, the IHA software (

The percentage change in the mean annual streamflow ranged from −19.0 to 28.3 percent with a median of −3.7 percent and a mean of −2.4 percent (table 6 from

The percentage change in the low pulse count from the two periods at the streamgages monitoring unregulated streams ranged from −22.2 to 28.6 percent with a median of 0.0 percent and a mean of 1.0 percent indicating a relatively normal distribution (table 6 from

Boxplots of the percentage change in daily mean streamflow characteristics for pre- and post-regulated periods at the 16 USGS streamgages (table 5 from

The distribution of the percentage change in the mean annual, 1-day maximum (max), and 1- and 7-day minimum (min) streamflows for 16 U.S. Geological Survey streamgages that have both pre- and post-regulated long-term periods of record and for two long-term periods of record (the first half and the last half) at 17 U.S. Geological Survey streamgages monitoring unregulated streams in Georgia, South Carolina, and North Carolina (streamflow data from

The boxplot for the percentage change in the 1-day maximum streamflows for the pre- and post-regulated periods was mostly in the negative range with the median and mean values being −24.4 and −28.2 percent, respectively (

Comparisons of the boxplots of the percentage change in the 1- and 7-day minimum streamflows for the pre- and post-regulated streamflows and the two periods of unregulated streamflows show that the percentage change of the pre- and post-regulated streamflows had a larger variability with the mean values both being positive, thereby suggesting (as previously noted) that, on average, the low streamflows for the post-regulated period tended to be higher than those for the unregulated periods (

For the low and high pulse counts and durations, boxplots were generated for the actual values instead of the percentage change (

The distribution of

The distribution of

For the pre- and post-regulated periods at the 16 streamgages, the median values for the high pulse count were similar, but the post-regulated distribution of high pulse count had much greater variability (

Flow-duration curves are cumulative frequency curves that show the percentage of time during which specified streamflows were equaled or exceeded during the period of record analyzed (

Flow-duration curve comparisons for pre- and post-regulated long-term periods of record at 17 U.S. Geological Survey streamgages in Georgia, South Carolina, and North Carolina (streamflow data from

To gain an understanding of how flow-duration curves may differ based on period of record, a comparison of two periods at the 17 streamgages monitoring unregulated streams also was made (table 2 from

Flow-duration curve comparisons for two long-term periods of record (the first half and the last half) at 17 U.S. Geological Survey streamgages monitoring unregulated streams in Georgia, South Carolina, and North Carolina (streamflow data from

Regional regression analyses were used to develop a set of flood-frequency equations that can be used to estimate selected AEP streamflows at ungaged locations on regulated streams. The multiple linear regression analyses used standard USGS methods (

The general model for an ordinary least squares (OLS) regression analysis is of the form

is the response variable, which is the flood magnitude at a selected percent AEP;

are explanatory (independent) variables; and

are regression coefficients.

If the response and explanatory variables are logarithmically transformed, the regression model has the following line form:

The initial set of streamgages included in the analyses was the 72 streamgages on regulated streams for which AEP streamflows were computed by

Because there were not enough regulated streamgages in the regression analysis to properly represent basins draining predominately from below the Fall Line, the regression equations are applicable for only basins draining predominantly (75 percent or more) from above the Fall Line. It also should be noted that the 39 streamgages included in the regression analysis are considered rural streamgages for the purpose of this investigation.

For the exploratory regression analysis, OLS regression techniques were used to determine the best regression models for all combinations of basin characteristics and testing of the two hydrologic regions above the Fall Line (

Multicollinearity, which is a situation where two or more independent variables are highly correlated with strong linear dependence, was also assessed by the variance inflation factor (VIF). A VIF greater than 10 indicates highly correlated explanatory variables and warrants additional investigation (

As part of the update of rural flood-frequency regional regression equations for Georgia, South Carolina, and North Carolina,

Maximum storage, in acre-feet, which is defined as the total storage space in a reservoir below the maximum attainable water-surface elevation;

Maximum storage index, in acre-feet per square mile, which was computed as the cumulative maximum storage from reservoirs upstream from the USGS streamgage divided by the drainage area at the streamgage;

Surface area, in acres, of the reservoir at its normal retention level;

Distance, in miles, from the streamgage to the first upstream reservoir; and

Distance, in miles, from the streamgage to the last upstream reservoir.

The maximum storage and surface area were obtained from the

All-possible-subsets regression methods were tested using the candidate explanatory variables related to impoundments along with drainage area, percentage of hydrologic regions 1 and 2, and a cross product of drainage area and percentage of hydrologic region 2, which was statistically significant in the rural regression equations from ^{2}), and (5) ease of measurement of explanatory variables. Based on the OLS assessments of various groupings of explanatory variables and the criteria noted previously, a regression model including drainage area and maximum storage index was selected using only streamgages for which the basin drained 75 percent or more from above the Fall Line.

Generalized least squares (GLS) regression methods, as described by

For both the OLS and GLS regression analyses, regression diagnostics were computed and reviewed to assess potential problems with the regression models. Along with reviewing the residuals in terms of being randomly distributed around zero and assessing the geographic distribution, regression diagnostics also were reviewed to assess high leverage and high influence. The leverage metric measures how unusual the values of independent variables at one streamgage are compared to the values of the same variables at all other streamgages. The influence metric indicates whether the data at a streamgage had a high influence on the estimated regression metric values (

State | Number of streamgages included in regression analyses |

Georgia | 11 |

North Carolina | 24 |

South Carolina | 4 |

The final regression equations for estimating peak streamflows at the selected AEPs are listed in

Comparisons of the observed and predicted

[DA, drainage area in square miles; MSI, maximum storage index in acre-feet per square mile]

Annual exceedance probability (percent) | Recurrence interval (years) | Regression equation |

50 | 2 | 838×DA^{0.696}×MSI^{−0.350} |

20 | 5 | 2,050×DA^{0.650}×MSI^{−0.370} |

10 | 10 | 3,050×DA^{0.632}×MSI^{−0.378} |

4 | 25 | 4,400×DA^{0.619}×MSI^{−0.322} |

2 | 50 | 5,380×DA^{0.613}×MSI^{−0.384} |

1 | 100 | 6,320×DA^{0.609}×MSI^{−0.384} |

0.5 | 200 | 7,210×DA^{0.607}×MSI^{−0.383} |

0.2 | 500 | 8,320×DA^{0.606}×MSI^{−0.381} |

Regression equations are statistical models that must be interpreted and applied within the limits of the data and with the understanding that the results are best-fit estimates with an associated scatter or variance. Uncertainty, or error, in the model (that is, differences between the predicted and observed values) can be examined to determine parameters that describe the accuracy of a regression equation, which depends on both the model error and the time-sampling error. Model error measures the ability of a set of explanatory variables to estimate the values of peak-streamflow characteristics calculated from the streamgage records used to develop the equation. The model error depends on the number and predictive power of the explanatory variables in a regression equation. Time-sampling error measures the ability of a finite number of streamgages with a finite number of recorded annual peak streamflows to describe the true characteristics of the entire peak-streamflow record for a streamgage. The time-sampling error depends on the number and record length of streamgages used in the analysis and decreases as the number of streamgages and record lengths increase. A measure of the uncertainty in a regression equation estimate for a site, _{p,i}_{p,i}

is the model error variance, in log units; and

is the time-sampling mean square error for site

Assuming that the explanatory variables for the streamgages in a regression analysis are representative of all streamgages in the region, the average accuracy of prediction for a regression equation can be determined by computing the average variance of prediction,

A more traditional measure of the accuracy of P-percent AEP streamflow regression equations is the standard error of prediction, _{p}

is the average standard error of prediction, in percent.

The _{p,ave}_{p,ave}

A measure of the proportion of the variation in the response variable explained by the explanatory variables in OLS regressions is the coefficient of determination, ^{2} (^{2} is ^{2} described by ^{2} metric, ^{2} is based on the variability in the response variable explained by the regression after removing the effect of the time-sampling error. The ^{2} is computed using the following formula:^{2}

is the model error variance from a GLS regression with

is the model error variance from a GLS regression with no explanatory variables.

Annual exceedance probability (percent) | ^{2} (percent) |
Average variance of prediction (log units) | Average standard error of prediction (percent) |

50 | 92.6 | 0.0281 | 40.0 |

20 | 91.4 | 0.0296 | 41.2 |

10 | 90.1 | 0.0327 | 43.5 |

4 | 88.1 | 0.0385 | 47.6 |

2 | 86.3 | 0.0442 | 51.4 |

1 | 84.1 | 0.0519 | 56.3 |

0.5 | 81.8 | 0.0605 | 61.5 |

0.2 | 77.9 | 0.0758 | 70.3 |

Users of the regression models may be interested in a measure of uncertainty at a particular site as opposed to the uncertainty statistics based on streamgage data used to generate the regression models. One such measure of uncertainty at a particular ungaged site is the confidence interval of a prediction, or prediction interval. The prediction interval is the range that likely contains the streamflow characteristic for a new observation not included in the development of the regression equations.

is the streamflow characteristic for the ungaged site, and

is the confidence or prediction interval computed as

is the normal critical value at a particular alpha level α, which equals 0.05 for a 95-percent prediction interval, divided by 2 and is equal to 1.96 for an α of 0.05; and

is the standard error of prediction and is computed as

is the model error variance;

is a row vector of variables

is the covariance matrix for the regression coefficients; and

is the transpose of _{i}

[AEP, annual exceedance probability; ^{2}, model error variance;

AEP (percent) | ^{2} |
||||

Intercept | DA | MSI | |||

50 | 0.0258 | Intercept | 0.0473 | −0.00388 | −0.0133 |

DA | −0.00388 | 0.00124 | 0.000143 | ||

MSI | −0.0133 | 0.000143 | 0.00484 | ||

20 | 0.0273 | Intercept | 0.0507 | −0.00421 | −0.0142 |

DA | −0.00421 | 0.00134 | 0.000164 | ||

MSI | −0.0142 | 0.000164 | 0.00517 | ||

10 | 0.0301 | Intercept | 0.0571 | −0.00480 | −0.0160 |

DA | −0.00480 | 0.00152 | 0.000194 | ||

MSI | −0.0160 | 0.000194 | 0.00578 | ||

4 | 0.0355 | Intercept | 0.0686 | −0.00584 | −0.0191 |

DA | −0.00584 | 0.00183 | 0.000247 | ||

MSI | −0.0191 | 0.000247 | 0.00690 | ||

2 | 0.0414 | Intercept | 0.0795 | −0.00680 | −0.0220 |

DA | −0.00680 | 0.00213 | 0.000296 | ||

MSI | −0.0220 | 0.000296 | 0.00796 | ||

1 | 0.0487 | Intercept | 0.0938 | −0.00804 | −0.0260 |

DA | −0.00804 | 0.00251 | 0.000357 | ||

MSI | −0.0260 | 0.000357 | 0.00938 | ||

0.5 | 0.0574 | Intercept | 0.109 | −0.00939 | −0.0303 |

DA | −0.00939 | 0.00293 | 0.000423 | ||

MSI | −0.0303 | 0.000423 | 0.0109 | ||

0.2 | 0.0717 | Intercept | 0.136 | −0.0117 | −0.0379 |

DA | −0.0117 | 0.00364 | 0.000533 | ||

MSI | −0.0379 | 0.000533 | 0.0137 |

The following limitations should be recognized when using the final regional regression equations for regulated rural basins in Georgia, South Carolina, and North Carolina:

The regulated flood-frequency analyses computed at the USGS streamgages by

The methods are applicable to regulated rural basins draining 75 percent or more from above the Fall Line.

Applying the equations outside the range of the explanatory variables used to develop the regional regression equations (

[mi^{2}, square mile; acre-ft/mi^{2}, acre-foot per square mile]

Basin characteristics | Minimum | Maximum |

Drainage area (mi^{2}) |
14.7 | 8,480 |

Maximum storage index (acre-ft/mi^{2}) |
102 | 2,410 |

The maximum storage for the individual reservoirs upstream from the streamgages included in the regulated rural regression analysis ranged from 185 acre-feet (acre-ft) to 3,820,000 acre-ft (

For the 10-, 1-, and 0.2-percent AEP streamflows, the at-site regulated flood-frequency estimates were compared with the regulated regression estimates by using the equations in

The distribution of the percentage change between the at-site regulated estimates and the regulated regression estimates and between the at-site regulated estimates and the unregulated regression estimates in the 10-, 1-, and 0.2-percent annual exceedance probability (AEP) streamflows at 39 U.S. Geological Survey streamgages in Georgia, South Carolina, and North Carolina (streamflow data from

The percentage change between the at-site regulated estimates and regulated regression estimates for the 10-percent AEP streamflows ranged from −62 to 126 percent with a median and mean of −2.9 and 10 percent, respectively (

For the 1-percent AEP streamflows, the percentage change between the at-site regulated estimates and the regulated regression estimates ranged from −67 to 182 percent with a median and mean of 6.6 and 12 percent, respectively (

For the 0.2-percent AEP streamflows, the percentage change between the at-site regulated estimates and the regulated regression estimates ranged from −82 to 229 percent with a median and mean of 5.8 and 15 percent, respectively (

Regulated regression flood-frequency curves and unregulated flood-frequency curves for basins draining 75 percent or more from hydrologic regions above the Fall Line in Georgia, South Carolina, and North Carolina for the

B17C (

B17C (

The variance from the EMA analyses at a streamgage is provided for each AEP estimate as part of the output in PeakFQ (table 13 from

Once the variances have been computed, the two independent streamflow estimates can be weighted using the following equation:

is the weighted estimate of peak streamflow for any P-percent AEP for a streamgage, in cubic feet per second;

is the variance of prediction at the streamgage derived from the applicable regional regression equations for the selected P-percent AEP, in log units, and can be obtained from the weighted least squares regression for streamflow frequency statistics program (

is the estimate of peak streamflow at the streamgage from the LPIII analysis for the selected P-percent AEP, in cubic feet per second;

is the variance of prediction at the streamgage from the LPIII analysis for the selected P-percent AEP (table 13 from

is the peak-streamflow estimate for the P-percent AEP at the streamgage derived from the applicable regional regression equations in

For the 63 streamgages in Georgia, South Carolina, and North Carolina that drained 75 percent or more from above the Fall Line (table 13 from

The variance of prediction values at the streamgage (table 13 from

The average variance of prediction (

Confidence intervals for the weighted estimate also can be computed (

An example of the application of the procedure described above is the following computation of the weighted 1-percent AEP streamflow for 02147020 Catawba River below Catawba, S.C. (map index number 348 in

Obtain the streamgage estimate of the 1-percent AEP streamflow based on the systematic flood peaks (table 13 from _{s}^{3}/s);

Obtain drainage area and maximum storage index (table 7 from ^{2} and maximum storage index = 326 acre-ft/mi^{2});

Compute the peak-streamflow estimate at the streamgage using the 1-percent AEP equation in _{r}_{(}_{s}_{)} = 6,320 × (3,540^{0.609}) × (326^{−0.384}) = 99,308 ft^{3}/s, which is rounded to the value 99,300 for _{r}_{(}_{s}_{)} for this streamgage [table 13 from

Obtain the variance of prediction for the LPIII streamgage estimate for the 1-percent AEP streamflow (table 13 from _{s}

Obtain the variance of prediction for the 1-percent AEP streamflow regression estimate (table 13 from _{r}_{(}_{s}_{)} = 0.0519);

Compute the weighted 1-percent AEP streamflow for the streamgage by using _{w}_{(}_{s}_{)} = ((0.0519) (log 156,000) + (0.0117) (log 99,300)) / (0.0117 + 0.0519) = 5.157, and the base 10 antilog _{w}_{(}_{s}_{)} = 143,549 ft^{3}/s, which is rounded to the value 144,000 ft^{3}/s for _{w}_{(}_{s}_{)} for this streamgage).

Compute the weighted 1-percent AEP variance for the streamgage by using _{w}_{(}_{s}_{)} = (0.0117 × 0.0519) / (0.0117 + 0.0519) = 0.00955); and

Compute the 95-percent confidence interval by using

With respect to step 2 for an ungaged location, the drainage area can be obtained using the USGS StreamStats application, which is available at ^{2}).

_{w}_{(}_{u}_{)}, the weighted streamflow estimates for an upstream or downstream streamgage, _{w}_{(}_{s}_{)}, must first be determined by using _{w}_{(}_{u}_{)}, is then computed using the following equation:

is the weighted estimate of peak streamflow for the selected P-percent AEP at the ungaged site, in cubic feet per second;

is the absolute value of the difference between the drainage areas for the streamgage (_{s}_{u}

is the drainage area for the streamgage, in square miles;

are as previously defined in

is the peak-streamflow estimate derived from the applicable regional regression equations in

Use of

An example application of this procedure is the computation of the weighted 1-percent AEP streamflow for a hypothetical ungaged site on the Catawba River located downstream from USGS streamgage 02147020 Catawba River below Catawba, S.C., referred to in the previous section. The ungaged downstream location has a drainage area of 3,620 mi^{2}. Because there are no major impoundments between 02147020 and the downstream location, the maximum storage index at the downstream location can be computed from the maximum storage index at 02147020 times the ratio of the drainage area at 02147020 and the downstream location:

Calculate the value of _{w}_{(}_{s}_{)} for the streamgage (see step 6 of example in previous example application in section “Estimation for an Ungaged Site Near a Streamgage,” _{w}_{(}_{s}_{)} = 144,000 ft^{3}/s);

Obtain the drainage areas for both the gaged and ungaged sites (_{s}^{2} and _{u}^{2});

Determine the maximum storage index for the ungaged site (326 × (3,540/3,620) = 319 acre-ft/mi^{2});

Compute _{r}_{(}_{u}_{)} for the ungaged site by using the 1-percent AEP equation in _{r}_{(}_{u}_{)} = 6,320 × (3,620^{0.609}) × (319^{−0.384}) = 101,511 ft^{3}/s, which is rounded to 102,000 for _{r}_{(}_{u}_{)} for this ungaged site);

Compute _{r}_{(}_{s}_{)} for the streamgage by using the 1-percent AEP equation in _{r}_{(}_{s}_{)} = 99,300 ft^{3}/s);

Compute ^{2}; and

Compute the weighted estimate for the ungaged site, _{w}_{(}_{u}_{)}, by using _{w(u)}^{3}/s (rounded to 141,000 ft^{3}/s)).

For an ungaged site that is located between two streamgages on the same stream and whose drainage area is 75 percent or more from above the Fall Line, two streamflow estimates can be made using the methods and criteria outlined in this section. Hydrologic judgment may be necessary to determine which of the two estimates (or some interpolation thereof) is most appropriate. Other factors that might be considered when evaluating the two estimates include differences in the length of record for the two streamgages and the hydrologic conditions that existed during the data-collection period for each streamgage (for example, whether the time series represents a climatic period that was predominantly wet or dry).

Reliable estimates of the magnitude and frequency of floods are essential for flood insurance studies, floodplain management, and the design of transportation and water-conveyance structures such as roads, bridges, culverts, dams, and levees. Federal, State, regional, and local officials rely on such estimates to effectively plan and manage land use and water resources, protect lives and property in flood-prone areas, and determine flood insurance rates. The U.S. Geological Survey (USGS) and the South Carolina Department of Transportation have a long history of working cooperatively to develop techniques for estimating the magnitude and frequency of floods for rural and urban basins that have minimal to no regulation or tidal influence. The Federal guidelines for flood-frequency analyses at streamgaging stations (streamgages) were developed for basins where streamflows under flood conditions are not appreciably altered by regulation, basin changes, or long-term changes in the hydrologic system. However, under certain conditions, it may be appropriate to apply those techniques at streamgages on regulated streams. Over the years, flood-frequency analyses have been done at selected streamgages in Georgia, South Carolina, and North Carolina, but there has not been a comprehensive report assessing the effects of regulation from impoundments on streamflow until this investigation. The effect of an impoundment on downstream streamflows can vary widely based on the purpose and structure of the impoundment. The degree of regulation reflected at USGS streamgages located downstream from impoundments often is assessed more on a qualitative rather than quantitative basis. For humid areas of the United States, one USGS investigation determined that a usable storage of less than 103 acre-feet per square mile would generally affect peak streamflows by less than 10 percent.

The purpose of this investigation was to assess the effects of impoundments on peak streamflows and other selected streamflow characteristics. Streamgages from Georgia, South Carolina, and North Carolina with long-term periods of record (30 or more years) were included in the investigation. At 18 streamgages, annual exceedance probability (AEP) streamflows were compared for pre- and post-regulated (before and after impoundment) periods of record. For the 10-, 1- and 0.2-percent AEP streamflows, the average reduction in the streamflows from the pre- to post-regulated periods was about 31 percent. For the 10-percent AEP streamflows (10-year flood), the percentage change from the pre- to post-regulated periods ranged from 2.0 to 72.0 percent. For the 1-percent AEP streamflows (100-year flood), the percentage change from the pre- to post-regulated periods ranged from −78.0 to 22.4 percent. For the 0.2-percent AEP streamflows (500-year flood), the percentage change from the pre- to post-regulated periods ranged from −83.4 to 44.7 percent.

To get a sense of how flood-frequency statistics can vary based on analyzing different periods of record, the 10-, 1-, and 0.2-percent AEP streamflows were compared for two periods of record at 18 USGS streamgages monitoring unregulated streams. For the three AEP streamflow statistics, the average change was a reduction of 8.6, 6.4, and 5.0 percent, respectively. The ranges of change in the three AEP streamflow statistics from minimum to maximum percentage change were −38.9 to 30.1, −48.1 to 57.0, and −53.6 to 69.0 percent, respectively. These results provide some indication of the natural variability in the AEP streamflows at specific streamgage locations based on length of record and hydrologic conditions captured in those records. As compared to the percentage change from the pre- and post-regulated periods of record, the range of percentage changes between the two periods at the unregulated streamgages tends to be more balanced between the positive and negative percentage changes with average percentage changes that are much smaller than the average for the pre- and post-regulated AEP streamflow statistics.

To assess the effects of impoundments on a broader range of streamflow statistics, The Nature Conservancy’s Indicators of Hydrologic Alteration (IHA) software was used to assess a limited number of streamflow characteristics computed from daily mean streamflows. The IHA software was used to compare mean annual streamflow, 1-day maximum streamflow, 1- and 7-day minimum streamflows, low pulse count and duration, and high pulse count and duration for pre- and post-regulated periods of record at 16 streamgages. The length of records analyzed for the pre-regulated period ranged from 34 to 80 years. The length of records analyzed for the post-regulated period ranged from 39 to 68 years. The mean annual streamflows were relatively consistent for the pre- and post-regulated periods of record with the average percentage change being −1.4 percent with a range of −21.8 to 9.7 percent. The average change between the pre- and post-regulated 1-day maximum streamflows was −28.2 percent, which was close to the average reduction in the AEP streamflows. The average change in the 1- and 7-day minimum streamflows was an increase of 29.7 and 24.1 percent, respectively. These findings reflect conditions that are often found to occur from regulation; on average, the low streamflows increased and the high streamflows decreased.

To assess the natural variability in selected daily mean streamflow characteristics based on period of record and hydrologic conditions captured in those records, the IHA software was used to analyze long-term periods at 17 streamgages monitoring unregulated streams. The length of records in the two periods ranged from 39 to 60 years. The average percentage change in the mean annual streamflow for the two periods was −2.4 percent, which was similar to the percentage change in the mean annual streamflows the pre- and post-regulated periods of record. However, a comparison of boxplots showed that the variability in the mean annual streamflows was much less from the streamgages with pre- and post-regulated periods as compared to the two periods of record analyzed at the streamgages monitoring unregulated streams. The average percentage change in the 1-day maximum streamflows for the two periods of record was −7.3 percent. For the 1- and 7-day minimum streamflows, the average change between the two unregulated periods analyzed at the 17 streamgages was −19.5 and −21.4 percent, respectively. These results may reflect historical drought periods that have occurred in the Southeast over the last couple of decades or other influences in the basins.

In a separate USGS investigation completed in 2023, flood-frequency statistics were computed for 72 streamgages monitoring regulated streams in Georgia, South Carolina, and North Carolina. Of those 72 streamgages, 29 were found to be redundant, which is a situation where the drainage basin of one streamgage is contained inside another (nested) and the two basins are of similar size. For the remaining 43 streamgages, 39 had basins that drained 75 percent or more from above the Fall Line. Those 39 streamgages were used in this investigation to develop regression equations for the 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent AEP streamflows. The independent variables in the equations were drainage area and maximum storage index from upstream reservoirs. The pseudo coefficient of determination statistics, which is based on the variability in the AEP streamflows explained by the regression equation after removing the time-sampling error, ranged from 77.9 to 92.6 percent. The average standard error of prediction, which is a measure of the average uncertainty of the regression equations when predicting flood estimates at ungaged locations, ranged from 40.0 to 70.3 percent. There were not enough streamgages monitoring regulated streams available to allow for development of similar equations in the Coastal Plain portion of the study area (below the Fall Line).

The at-site regulated flood-frequency estimates for the 10-, 1-, and 0.2-percent AEP streamflows were compared with the regulated regression and unregulated regression estimates for the 39 streamgages included in the regulated regression analysis. Boxplots of percentage change showed that the regulated regression estimates match the at-site regulated flood-frequency estimates better than do the unregulated flood-frequency estimates. The median and mean percentage change showed that the unregulated flood-frequency estimates tend to overestimate the at-site regulated flood-frequency estimates and have greater variability than do the percentage change from the regulated regression estimates. These comparisons suggest that in most instances when estimating flood-frequency statistics at an ungaged regulated location, using the regulated flood-frequency regression equations instead of the unregulated flood-frequency regression equations will provide a more accurate estimate.

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