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Baseflow plays an important role in maintaining streamflow. Seventeen gauged watersheds and their characteristics were used to develop regression models for annual baseflow and baseflow index (BFI) estimation in Michigan. Baseflow was estimated from daily streamflow records using the two-parameter recursive digital filter method for baseflow separation of the Web-based Hydrograph Analysis Tool (WHAT) program. Three equations (two for annual baseflow and one for BFI estimation) were developed and validated. Results indicated that observed average annual baseflow ranged from 162 to 345 mm, and BFI varied from 0.45 to 0.80 during 1967–2011. The average BFI value during the study period was 0.71, suggesting that about 70% of long-term streamflow in the studied watersheds were likely supported by baseflow. The regression models estimated baseﬂow and BFI with relative errors (RE) varying from −29% to 48% and from −14% to 19%, respectively. In absence of reliable information to determine groundwater discharge in streams and rivers, these equations can be used to estimate BFI and annual baseﬂow in Michigan.

Baseflow is a very important component of streamflow generated from groundwater inflow or discharge. Baseflow is generally derived from available streamflow records using hydrograph separation techniques such as graphical methods [

Although these programs are widely used and accepted in hydrologic studies [

Regression models relate baseflow and BFI to watershed characteristics in ungauged sites. The most common watershed characteristics that influence baseflow and streamflow variations reported in the scientific literature include topography, relief, climate, rainfall, evapotranspiration, slope, basin drainage area, geologic and hydrogeologic variables, soils infiltration rate, baseflow factor, and land cover [

Research in Michigan and the Great Lakes [

The modeling approach applied in this study consists of [

Developing a database to compile hydrologic and physiographic characteristics of the studied watersheds;

Partitioningbaseflow from daily streamflow records using the Web-based Hydrograph Analysis Tool;

Developing regression equations for baseflow and BFI estimation using multiple regression analysis;

Validating the regression equations with data from different watersheds in Michigan.

This study was conducted with a group of watersheds in Michigan. Seventeen gauging stations with data from 1967–2011 with no effects of regulation and diversion on streamflow were selected based on the 2011 USGS water report [

Michigan is located in the Great Lakes region of the United States (^{2} and form the largest watershed within Michigan. In the UP, most rivers flow southward into Lake Michigan and its various bays. About one-fifth of the state is covered by forest and the principal agricultural region is located in the southern half of the LP where farmlands account for about 50% of the total land area [

Gauging stations and delineated watersheds used for the study in Michigan.

The distribution of precipitation in Michigan depends on the season and location. The southwest of the LP and parts of the UP receive about 1020 mm of precipitation per year, including snowfall, while the northeast of LP receives only 660–760 mm of precipitation per year. In areas with plant cover, approximately 40% of rainfall is returned to the atmosphere through evapotranspiration, and 10% directly flow into streams [

Michigan watersheds used for model development and validation.

Gauging station ID | Station name and location | USGS drainage area (km^{2}) |
Delineated area (km^{2}) |
Relative error (%) |
---|---|---|---|---|

04040500 | Sturgeon River near Sidnaw | 442.9 | 429.8 | 3.0 |

04043050 | Trap Rock River near Lake Linden | 72.5 | 77.1 | 6.3 |

04045500 | Tahquamenon River near Paradise | 2046.1 | 1960.6 | 4.2 |

04057510 | Sturgeon River near Nahma Junction | 474 | 475.4 | 0.3 |

04096405 | St. Joseph River at Burlington | 533.5 | 530.7 | 0.5 |

04105700 | Augusta Creek Near Augusta | 100.8 | 95.2 | 5.5 |

04108800 | Macatawa River at State Road near Zeeland | 170.4 | 172.9 | 1.5 |

04117500 | Thornapple River near Hastings | 997.1 | 1063.4 | 6.7 |

04122500 | Pere Marquette River at Scottville | 1763.8 | 1787.7 | 1.4 |

04127997 | Sturgeon River at Wolverine | 497.3 | 454.7 | 8.6 |

04161580 | Stony Creek near Romeo | 66.3 | 61.7 | 6.9 |

04164000 | Clinton River near Fraser | 1150 | 1188.3 | 3.3 |

04059500 | Ford River near Hyde | 1165.5 | 1156.8 | 0.8 |

04105000 | Battle Creek at Battle Creek | 624.2 | 710 | 13.7 |

04108600 | Rabbit River near Hopkins | 184.9 | 174.9 | 5.4 |

04124000 | Manistee River near Sherman | 2219.6 | 2241.9 | 1.0 |

04166100 | River Rouge at Southfield | 227.7 | 225.3 | 1.0 |

Baseflow was separated from long-term streamflow records using the Web-based Hydrograph Analysis Tool (WHAT) [_{max}. The filter parameter describes the rate at which the streamflow decreases with time following a recharge event and can be derived by recession analysis. The BFI_{max} is the maximum baseflow index which can be modeled by the recursive digital filter algorithm [_{b,t}, Q_{b,t−1} is baseflow at time step t and t−1; Q_{s,t} is the total streamflow at time step t; a is the filter parameter. Baseflow for the first time step, Q_{b,t-1}, was assumed 50% of streamflow in Equation (1). Eckhardt [_{max} [in Equation (1)] based on various aquifer types such as perennial streams with porous aquifers, ephemeral streams with porous aquifers and perennial streams with hard rock aquifers. In this study, the 17 watersheds selected were considered perennial streams with porous aquifers based on hydrologic and geological characteristics of the studied watersheds [_{max} and filter parameter values of 0.80 and 0.98 describing watersheds with perennial streams and porous aquifers were used as implemented in WHAT.

Baseflow is generally influenced by watershed characteristics such as watershed physiographic features, distribution of water storage, evapotranspiration, geomorphology, land use, and soil types [

Multiple linear regression was used to develop equations for estimating annual baseflow and BFI in the following form:
_{b} is the predicted annual baseflow (m^{3}) or BFI; b_{0} is the regression constant; b_{1}, b_{2}, b_{3}, …, b_{n} are regression coefficients; X_{1}, X_{2}, X_{3}, …, X_{n} are watershed characteristics. The log-transformation of Equation (2) is written as:

The models developed were evaluated using Relative Error (RE), R^{2} and Nash-Sutcliffe coefficient (E_{NS}) shown respectively as [_{b(obs)}(i) is the observed baseflow or BFI which was separated from the daily streamflow record; Q_{b(pred)}(i) is the predicted baseflow or BFI; _{b(obs)} is the mean of Q_{b(obs)}, and n is the total number of years. These statistics are widely used to evaluate the performance of hydrologic and water quality models [^{2} greater than 0.5 could be considered acceptable. Moriasi _{NS} was greater than 0.50. Ramanarayanan _{NS} were greater than 0.5 and 0.4, respectively. It appears that acceptable model performance based on statistical measures is project specific requirements [

Abbreviation and unit of all watershed characteristics for multiple regressions.

Watershed characteristics | Symbol | Unit |
---|---|---|

Basin drainage area | BDA | km^{2} |

Average basin slope | ABS | % |

Average basin relief | ABH | m |

Total stream length | TSL | km |

Wetland cover | WLC | % |

Developed land cover | DLC | % |

Forest land cover | FLC | % |

Grass land cover | GLC | % |

Agricultural land cover | ALC | % |

Annual precipitation | AP | mm |

Annual temperature | AT | °C |

Annual evapotranspiration | AE | mm |

Glacial drift transmissivity | GDT | m^{2}/day |

Water table depth | WTD | m |

Coarse-texture sediment surficial geology | CSG | % |

Till surficial geology | TSG | % |

Hydrologic soil group (A-D) | HSG(A-D) | % |

Baseflow index | BFI | No unit |

Annual baseflow | Q_{b} |
m^{3} |

Sources of datasets for all watershed characteristics.

Notation | Sources of datasets |
---|---|

BDA, ABS, ABH, TSL | National Hydrography Datasets [ |

WLC, DLC, FLC, GLC, ALC | National Land Cover Data [ |

AP, AT | PRISM Climate Group [ |

AE | |

GDT, WTD | Michigan Geographic Data Library [ |

CSG, TSG | Map Database for Surficial Materials in the Conterminous US [ |

HSG(A-D) | Soil Survey Geographic database [ |

BFI | Baseflow separation with WHAT [ |

Prior to model development, the Spearman correlation test was used to determine the correlation among baseflow, BFI and watershed characteristics. The correlation analysis showed that BFI, BDA and HSGA were independent variables (from each other) but related to baseflow, while BFI was affected by WLC and WTD (

After the independent variables were selected, regression models were developed in SAS (at a significance level of 5%) using “proc reg” procedure [^{2} and adjusted R^{2} values. Then, p-values of individual explanatory variables were examined for significance. If two independent variables have similar significance, the simplest (

Correlation analysis of variables as used for the development of regression models.

Variables | Q_{b} |
BFI | BDA | HSGA | AP | WLC | WTD |
---|---|---|---|---|---|---|---|

Q_{b} |
1.00 | ||||||

BFI | 0.48 | 1.00 | |||||

BDA | 0.97 | 0.39 | 1.00 | ||||

HSGA | 0.50 | 0.39 | 0.42 | 1.00 | |||

AP | 0.01 | −0.01 | −0.09 | −0.19 | 1.00 | ||

WLC | 0.30 | 0.52 | 0.26 | 0.24 | −0.15 | 1.00 | |

WTD | 0.28 | 0.54 | 0.15 | 0.50 | 0.05 | 0.03 | 1.00 |

Average annual baseflow and BFI ranged from 162 to 345 mm/yr and 0.45–0.80 in the studied watersheds for the period of 1967–2011 (

Average annual baseflow for 17 watersheds in Michigan.

Gauging station ID | Total streamflow (mm/yr) | Baseflow (mm/yr) | BFI |
---|---|---|---|

04040500 | 416 | 273 | 0.66 |

04043050 | 529 | 345 | 0.66 |

04045500 | 395 | 289 | 0.73 |

04057510 | 348 | 255 | 0.74 |

04059500 | 278 | 187 | 0.68 |

04096405 | 319 | 243 | 0.76 |

04105000 | 335 | 241 | 0.72 |

04105700 | 394 | 308 | 0.78 |

04108600 | 307 | 213 | 0.70 |

04108800 | 406 | 182 | 0.45 |

04117500 | 328 | 230 | 0.71 |

04122500 | 396 | 313 | 0.79 |

04124000 | 428 | 342 | 0.80 |

04127997 | 402 | 320 | 0.80 |

04161580 | 237 | 162 | 0.69 |

04164000 | 340 | 238 | 0.70 |

04166100 | 307 | 185 | 0.61 |

In the LP, baseflow varied from 162 mm/yr for Stony Creek (04161580) to 342 mm/yr for Manistee River (04124000) and the corresponding total streamflow ranged from 237 to 428 mm/yr during the study period (

The average BFI value of 0.71 for the studied watersheds suggests that about 70% of long-term total streamflow in the studied watersheds could possibly be the contribution of groundwater discharge. Holtschlag and Nicholas [

Twelve out of 17 watersheds were used for model development and the remaining five watersheds were used for model validation (1967–2011). The regression equations developed for estimating annual baseflow and BFI are shown in

Regression equations for estimating annual baseflow and baseflow index in Michigan.

Model description | Equation | R^{2} |
P value |
---|---|---|---|

Model 1 | 0.96 | <0.0001 | |

Model 2 | 0.96 | <0.0001 | |

Model 3 | 0.55 | 0.0264 |

In _{b(pred)} is the predicted baseflow (m^{3}); BFI is baseflow index; BDA is basin drainage area (km^{2}); HSGA is hydrologic soil group A (%); AP is annual precipitation (mm); BFI_{(pred)} is the predicted BFI; WLC is wetland cover (%); WTD is water table depth (m).

Both Model 1 and Model 2 were developed for baseflow estimation, and Model 3 was developed to estimate BFI. The significant explanatory variables to estimate baseflow in this study include basin drainage area (BDA), precipitation (AP), hydrologic soil group A (HSGA) and baseflow index (BFI) (

For BFI estimation, the significant explanatory variables in the present study include wetland cover (WLC) and water table depth (WTD) (

Watershed characteristics like precipitation, land cover, slope and soils have also been used in previous studies to estimate BFI (e.g., [

The evaluation of the two baseflow equations (Model 1 and Model 2) in the 12 watersheds used for model development shows that the RE between predicted and observed annual baseflow for Model 1 and Model 2 vary from −26% to 45% and from −29% to 48%, respectively (^{2 } values range from 0.17 to 0.57, and E_{NS} values vary between −2.95 and 0.39 for Model 1 and Model 2, indicating that Model 1 performed slightly better than Model 2 (

It should be noted that the RE values in Stony Creek watershed (04161580) are higher, simultaneously, for Model 1 (39%) and Model 2 (48%) compared to the other studied watersheds, and the corresponding E_{NS} values are −0.86 and −1.49, respectively (_{NS} values appeared to be negative for watersheds with high RE between predicted and observed baseflow (_{NS} values for Model 1 are slightly better than that of Model 2 for these three watersheds. The negative E_{NS} values indicated that there were large deviations between the predicted and observed annual baseflow, suggesting that the models have limited predictive power when used for baseflow estimation in these three watersheds (

Relative Error (%), R^{2} and E_{NS} in watersheds used for model development.

Gauging station ID | Model 1 | Model 2 | Model 3 | ||||
---|---|---|---|---|---|---|---|

RE | R^{2} |
E_{NS} |
RE | R^{2} |
E_{NS} |
RE | |

04040500 | −14 | 0.57 | 0.02 | −11 | 0.57 | 0.13 | 14 |

04043050 | −22 | 0.25 | −1.34 | −29 | 0.24 | −2.35 | 7 |

04045500 | −7 | 0.52 | 0.26 | −13 | 0.51 | −0.29 | 8 |

04057510 | 22 | 0.43 | -0.40 | 5 | 0.43 | 0.39 | 2 |

04096405 | 3 | 0.38 | 0.35 | 27 | 0.38 | −0.54 | −14 |

04105700 | −26 | 0.17 | −2.95 | −4 | 0.17 | 0.00 | −2 |

04108800 | 45 | 0.52 | −1.49 | 3 | 0.52 | 0.38 | 19 |

04117500 | 3 | 0.42 | 0.39 | 26 | 0.42 | −0.65 | −8 |

04122500 | 2 | 0.30 | 0.15 | −4 | 0.30 | 0.16 | −7 |

04127997 | −10 | 0.21 | −1.12 | −17 | 0.20 | −2.95 | −2 |

04161580 | 39 | 0.22 | −0.86 | 48 | 0.22 | −1.49 | 1 |

04164000 | 7 | 0.40 | 0.30 | 9 | 0.39 | 0.25 | −13 |

The RE between predicted and observed (calculated with WHAT) BFI ranges from −14% to 19% (

Predicted and observed average annual baseflow in watersheds used for model development (values on the bars represent average annual baseflow in the studied watersheds).

Predicted and observed BFI in watersheds used for model development.

The three regression models (Model 1, 2, and 3) were validated with five watersheds during the 1967–2011 study period. The predicted BFI values (calculated with Model 3) were applied to evaluate Model 2 in this study. Results showed that Model 1 performed slightly better than Model 2 for 3 [

Predicted

The models developed in this study mostly overestimated baseflow in the watersheds used for model validation, except in Manistee River watershed (04124000), where most predicted baseflow are smaller than observed baseflow (

The models developed in this study did not seem to predict annual baseflow with high accuracy in the watersheds used for model validation. This could be explained by factors such as lake effects and snow melt that were not explicitly considered in model development. Limitations in the predictive capacity of the models could also be due to the fact that all baseflows in a watershed do not necessarily originate from areas within the watershed boundary.

Regression equations for estimating baseflow and BFI in Michigan were developed in this study. Seventeen watersheds were delineated to summarize various hydrophysiographic and geologic characteristics using ArcGIS. Baseflow was partitioned from daily streamflow records from 1967–2011 using the two-parameter recursive digital filter method. Twelve watersheds were used to develop two regression models for baseflow estimation and one model for BFI estimation. The remaining five watersheds were used for model validation.

Results indicate that average annual baseflow and BFI vary from 146 to 345 mm and 0.45–0.80, respectively. The average BFI value is 0.71 across Michigan, suggesting that about 70% streamflow in the studied watersheds might be derived from groundwater discharge. The significant explanatory variables to estimate annual baseflow include basin drainage area, precipitation, hydrologic soil group A, and baseflow index. For BFI estimation, the significant independent variables are wetland cover and water table depth. Overall, Model 1 performed slightly better than Model 2 due to the presence of HSGA as an explanatory variable in Model 1. The BFI equation (

This study was supported by the Chinese Scholarship Council (CSC) and the Department of Agricultural and Biological Engineering in Purdue University. The authors would like to thank Larry Theller for his help in GIS data processing and two anonymous reviewers for their constructive comments and suggestions to improve the manuscript.

The authors declare no conflict of interest.