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Water-Table Fluctuation (WTF) Method

Recharge to Surficial Aquifers in Minnesota based on the WTF Method

Figure 1. Location of measurement sites for the water-table fluctuation (WTF) method (modified from Delin and others, 2006)
Figure 1. Location of measurement sites for the water-table fluctuation (WTF) method (modified from Delin and others, 2006)

Ground-water recharge was estimated across Minnesota using a variety of methods as part of a recent U.S. Geological Survey (USGS) Groundwater Resources Program recharge study ( Delin and others, 2006). One of the methods employed utilized water-table fluctuations. Water-level data used in the water-table fluctuation (WTF) method were collected from a variety of sites across Minnesota (Fig. 1). The USGS has conducted intensive, long-term research at five sites that yielded 1 to 10 years of continuous (meaning collected at intervals no longer than 1 day) ground-water-level data for 29 wells: Bemidji – 8 wells (1993-2003); Princeton – 4 wells (1992-95); Williams Lake – 9 wells (1998-2003), Des Moines River – 4 wells (1999-2001); Glacial Ridge – 4 wells (2003). Because wells were closely spaced at these sites, results in this paper are generally presented as an average for each site. Additional water-level data were obtained from the Minnesota Department of Resources (MDNR) observation well network (T. Gullett, Minnesota Department of Resources, written commun., 2003). Only wells with at least a weekly water-level measurement interval throughout a given year were used. Thirty-four MDNR wells at 31 sites met these criteria, with most of the data collected before 1980. Where data were available only in analog form, one value from every fifth day was entered manually into a database. The fact that the water-level data from the various WTF sites represent different time periods imposes a bias on recharges estimates toward the climate of that respective time period.

Average recharge estimated using the MRC approach to the WTF method was 30% greater than recharge estimates made using the graphical approach and 63% greater than recharge estimates made using the RISE program approach (Table 1). This was expected because the MRC approach by design accounts for all recharge, no matter how short in duration or magnitude, and also accounts for the projected recession curve. Conversely, the graphical approach may not account for the smaller recharge volumes and the RISE program approach ignores the projected recession curve.

Figure 2. Inverse correlation between unsaturated-zone (UZ) thickness and recharge estimated using the water-table fluctuation (WTF) method. As the unsaturated-zone thickness decreases, the recharge rate based on the WTF method increases. The data are graphical WTF recharge estimates for all continuously measured wells at the Bemidji, Williams Lake, and Glacial Ridge sites for 2003.
Figure 2. Inverse correlation between unsaturated-zone (UZ) thickness and recharge estimated using the water-table fluctuation (WTF) method. As the unsaturated-zone thickness decreases, the recharge rate based on the WTF method increases. The data are graphical WTF recharge estimates for all continuously measured wells at the Bemidji, Williams Lake, and Glacial Ridge sites for 2003.

There is a relation between unsaturated-zone thickness and estimates of recharge that were based on the WTF method. The data in Figure 2 represent WTF recharge estimates that were based on the graphical approach used in the WTF method for all continuous-measurement wells at the Bemidji, Williams Lake, and Glacial Ridge sites for 2003. A similar relation is evident for other years as well as for the graphical and MRC approaches. There is no relation between recharge estimates and unsaturated-zone thickness for thicknesses greater than about 3.5 m. At shallower depths to the water table, however, the WTF-estimated recharge rate increases. One possible reason for this increase in recharge rate may be that it takes proportionately less time for water to travel through a thinner unsaturated zone, thus bringing the water to the saturated zone before it can be transpired by plants. Another is that the effective Sy decreases with proximity to the water table due to increased water content ( Childs, 1960). Without taking this phenomenon into consideration Sy is overestimated. It should be noted that although a shallow water table at Williams Lake and Glacial Ridge indicates a greater recharge rate, it also implies a greater groundwater ET rate. The relatively shallow depth to the water table is thought to be the cause for some of the anomalously large WTF recharge rates estimated for the Des Moines River site (Fig. 3).

Figure 3. Temporal variability of recharge using the RISE, master recession curve (MRC), and graphical approaches to the water-table fluctuation (WTF) method for selected continuously measured locations at the Williams Lake, Bemidji, Princeton, and Des Moines River sites in Minnesota.
Figure 3. Temporal variability of recharge using the RISE, master recession curve (MRC), and graphical approaches to the water-table fluctuation (WTF) method for selected continuously measured locations at the Williams Lake, Bemidji, Princeton, and Des Moines River sites in Minnesota.

Study results indicate that water-level measurement frequency is important in applying the WTF method. Measurements made less frequently than about once per week resulted in substantially reduced recharge estimates. This result was observed for all WTF recharge estimation approaches and continuous-measurement wells at the Bemidji, Williams Lake, Princeton, Des Moines River, and Glacial Ridge sites. For example, the effects of water-level measurement interval on recharge estimates at Princeton well R2 in 1993 are illustrated in Figure 4. Water levels in this well were measured hourly throughout the year using a datalogger. By successively editing this hourly data set, smaller data sets were generated representing daily, every 3 days, weekly, bi-weekly, and monthly measurements. In using the graphical approach to estimate recharge, there is essentially no change in estimated recharge when reducing the data set from hourly to once daily measurements; there is a 23% underestimation when reducing the data set from hourly to weekly measurements, and a 48% underestimation when reducing the data set from hourly to monthly measurements. Similar results were obtained for the other continuous-measurement wells and for the graphical and MRC approaches to the WTF method.

Figure 4. Effects of measurement frequency on water-table fluctuation (WTF) recharge estimates for Princeton well R2 using three approaches (data from 1993). Figure 4. Effects of measurement frequency on water-table fluctuation (WTF) recharge estimates for Princeton well R2 using three approaches (data from 1993).

We hypothesized that if daily water-level measurements for a well were collected during a single year (and accurate WTF recharge estimates were made) that accurate recharge estimates could also be made in future years where only monthly measurements are available by applying an underestimation factor calculated from the single year’s worth of data. This hypothesis was tested by evaluating water-level data from several wells with multiple years of data. The conclusion was that underestimation of WTF recharge due to reduced measurement frequency is not constant from year to year but is variable, depending on climatic factors.

Recharge during the summer months in this type of climate typically is minimal, although recharge can occur in the summer months if precipitation, soil moisture, and other factors are favorable. Therefore, results of this study indicate that if the hydrologist or water manager wants an accurate recharge estimate, and needs to quantify these types of (unexpected) recharge events, it would be wise to collect water-level data on at least a weekly (and preferably more frequent) basis throughout the year. Unexpected recharge events simply cannot be quantified if the data have not been collected due to use of a measurement interval less frequent than weekly.

Study Conclusions: Of the methods used in this study, the WTF method was the simplest and easiest to apply. Because water-level data are readily available this method could also be considered the least expensive to apply, although results indicate that at least a weekly measurement frequency is required to avoid an unacceptable underestimation of the recharge rate. Of the WTF approaches used, RISE is the most reproducible; any user that applies the program properly should generate exactly the same recharge rate as the next user. With some additional enhancements, the MRC approach could be reproducible in a similar sense as the RISE approach. Recharge estimates on the basis of the MRC approach was consistently greater than recharge estimates made using the graphical and RISE approaches. Of all the WTF approaches, the graphical approach requires the most subjectivity on the part of the user in projecting the groundwater recession curve and thus is the least reproducible.

Table 1. Average recharge rates as a percentage of precipitation estimated using the water-table fluctuation method.

 

Recharge rates

 

Water-table fluctuation method approaches

Fig. 1 ref. no.

Site name or nearest town

MDNR well #

Period of record

Years of record

Sy

 

Graphical (%)

MRC (%)

RISE (%)

39

Akeley

29000

1971-91

17

0.220

 

22

26

20

40

Barnesville

14000

1950-90

33

.109

 

23

41

24

41

Bemidji *

NA

1994-2003

10

.181

 

12

14

11

42

Big Lake

71000

1978

1

.103

 

11

--

--

43

Camp Ripley

49014

1952-93

39

.070

 

20

31

15

44

Clear lake

71006

1978

1

.172

 

31

--

--

45

Cloquet

9002

1952-74

22

.120

 

25

--

--

45

Cloquet

9004

1950-52

3

.141

 

11

11

16

46

Des Moines River *

NA

1991-2001

3

.095

 

20

29

17

47

Eveleth

69003

1944-50

7

.088

 

29

51

25

48

Glacial Ridge*

NA

2003

1

.054

 

14

20

14

49

Grand Rapids

31000

1964-67

3

.326

 

31

28

16

50

Gray’s Bay

27007

1953-62

9

.058

 

22

48

19

51

Hanska

8000

1950-75

25

.042

 

20

16

7

52

Hawley

14004

1960-66

7

.032

 

14

19

--

53

Lake Bronson

35003

1957-58

2

.023

 

10

8

6

54

Little Falls

49017

1967-71

5

.034

 

19

29

15

55

Luce

56017

1970-71

2

.126

 

19

17

10

56

Luxemburg

73002

1978

1

.091

 

12

--

--

57

Marshall

42001

1958-63

4

.060

 

24

32

23

57

Marshall

42002

1958-61

3

.036

 

21

--

--

57

Marshall

42005

1957-62

6

.078

 

19

43

26

58

Merrifield

18000

1974-82

4

.096

 

20

--

--

59

Princeton *

NA

1992-95

4

.127

 

10

14

9

60

Orrock

71007

1977-78

2

.119

 

27

--

--

61

Osage

3005

1980

1

.225

 

11

--

--

62

Perham

56015

1968-73

6

.096

 

11

--

--

63

Redwood Falls

64006

1953-61

9

.030

 

17

25

13

64

Rice

5000

1978-79

2

.255

 

57

--

--

65

Royalton

49001

1974-75

2

.071

 

19

--

--

66

St. James

83000

1966-68

3

.139

 

33

48

32

67

Soderville

2014

1974-76

3

.084

 

22

31

16

68

Togo

31001

1971-78

7

.125

 

11

--

--

69

Verndale

80002

1967-78

8

.132

 

19

21

16

70

Virginia

69010

1955-63

9

.035

 

14

15

12

71

Williams Lake *

NA

1998-2003

6

.228

 

22

28

19

72

Willow River

58000

1969-86

12

.162

 

18

--

--

73

Winnibigoshish

31003

1944-51

8

.094

 

15

11

9

74

Worthington

53000

1962-65

2

.059

 

25

--

--

 

Average

NA

1958-66

7

.112

 

20

26

16

*, USGS site where continuous water-level measurements were made; --, insufficient data to estimate recharge; MDNR, Minnesota Department of Natural Resources; MRC, Master recession curve; RISE, A. Rutledge, U.S. Geological Survey, written commun., 2005; NA, Not applicable; Sy, specific yield; Map ref. no., reference number on Figure 6.

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