Excerpt

## Table of Contents

1 Introduction

1.1 General description of Topics

1.2 Participants, locations and dates

1.3 General description of methods and tools

2 Construction of groundwater table map

2.1 Background

2.2 Methodology

2.3 Results

2.4 Discussion

3 Stream discharge measurements

3.1 Background

3.2 Methodology

3.2.1 Float method

3.2.2 Flow meter method

3.2.3 Tracer method

3.3 Results

3.4 Discussion

4 Pumping test

4.1 Background

4.2 Methodology

4.2.1 Methodology for automatic measurements & pumping phase

4.2.2 Methodology for automatic measurements & recovery phase

4.2.3 Methodology for manual measurements & pumping phase

4.2.4 Methodology for manual measurements & recovery phase

4.2.5 Methodology for storativity S

4.3 Results

4.3.1 Results for automatic measurements & pumping phase

4.3.2 Results for automatic measurements & recovery phase

4.3.3 Results for manual measurements & pumping phase

4.3.4 Results for manual measurements & recovery phase

4.4 Discussion

5. Surface- and groundwater sampling

5.1 Background

5.2 Methodology

5.2.1 Multimeter measurements

5.2.2 Titration for alkalinity

5.2.3 Investigations in the lab

5.3 Results

5.3.1 Field results

5.3.2 Lab results

5.4 Discussion

5.4.1 Discussion of field results

5.4.2 Discussion of lab results

6 References

7 Table Of Figures

8 Appendix

8.1 GNU plot program for Topic 1 “Level_b.plt”

8.2 GNU plot Input for Topic 1 'Leveling_d.csv'

8.3 GNU plot program for Topic 1 “Thickness_b.plt”

8.4 Maxima program for Topic 1 “well_a.wxmx”

8.5 GNU plot prog. topic 3 pumping “pump_log.plt”

8.6 GNU plot input topic 3 pumping “PumpLogger0Group1.csv”

8.7 GNU plot input topic 3 pumping “PumpLogger0recov.csv”

8.8 GNU plot progr. topic 3 fitting only “pump_log_fit.plt”

## 1 Introduction

The Hydrogeological Field Course (TuCaN # 3417) is part of Special Modul SM9 “Hydrogeological Methods” of the MSc TropHEE and scheduled for the 2nd semester. This block course complements the Water Analysis Course (TuCaN 3214) scheduled for the 1st semester. Water Analysis (course 3214) containes lectures and a practical part with (surface) water sampling, measuring water temperature, EC, pH, oxygen concentration and alkalinity in the field as well ion concentrations in the lab. This practical part of course 3214 is documented in another report and deals with water sampling in more detail. The water sampling part of field course 3417 repeats this topic in this report.

TropHEE Modul Handbook names as goals of this course: “The students are enabled to apply basic field techniques to characterize groundwater levels, groundwater flow fields, and to characterize aquifers in term of hydraulic properties. Students acquire methodical skills to use standard laboratory equipment to analyse water samples and to evaluate the results. Through the hands-on field and laboratory work they gain soft skills such as organizational skills, team working skills, communication skills, and data presentation skills.”

### 1.1 General description of Topics

The work was divided into 3 topics: Topic 1 Compilation of groundwater table map, Topic 2 Surface water discharge measurements, Topic 3 Pumping test. Another topic (without own number) was the task of water sampling accompanying Topic 2 (for surface water) and 3 (for groundwater). Water sampling was also a part of the Water Analysis (TuCaN 3214) course' exercise part.

### 1.2 Participants, locations and dates

The 25 TropHEE students were assigned to one of 4 groups that worked at different times on Topic 1 to 3. I was one of six members of group 1:

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This group had to do Topic 1 from 8:30 to10:00 and Topic 2 from 10:00 to 12:00 on Friday, June 19 on the campus Lichtwiese and Topic 3 from 8:30 to 10:00 on Friday, June 26 on a field in northern Darmstadt (urban district Arheilgen).

Topic 1 was done on a fenced and locked parcel with many sampling wells of small diameters in the southern part of campus Lichtwiese east of climbing hall. Topic 2 was done in the stream Darmbach at a foot path bridge in the northern part of campus Lichtwiese near Cafe Eulenpick of Vivarium. Topic 3 was done with a diesel generator and electric pump in a bigger well in a field in Arheilgen (in northern Darmstadt).

### 1.3 General description of methods and tools

Measuring the water levels in several wells (3 or more) with an electric sounder and the surface elevations with a theodolite and leveling rods in Topic 1 we can determine the surface table, water table, the groundwater gradient and the groundwater flow direction.

Measuring the cross section of a stream (Darmbach) and the speed of a floating object or the revolutions per minute of propellers (flow meters) at various positions of the cross section or the progress of salt concentration (from measurements of electric conductivity EC) over the time after pouring a known amount of salt into the stream (tracer method) lets us calculate the streams discharge Q in Topic 2.

Pumping a well at constant rate with a generator and electric pump for a longer time for Topic 3 and measuring the related drawdown over time with an electronic data logger/diver (pressure meter with data recorder) lets us calculate the transmissivity T and conductivity Kx of the aquifer the well is tapping as well as the wells specific yield/capacity (drawdown per discharge). Having only one well for the measurements Theis's equation and Jacob-Cooper method was used and storativity S could not be determined.

Water samples were taken during the work on topic 2 (surface water from Darmbach) and on topic 3 (groundwater from the production well in Arheilgen). There were taken two samples (2 plastic bottles) per event: one for anion-analysis and one for cation-analysis (with 1 cubic cm of HCl-acid to stabilize the sample against degrading/precipitation before being taken to the lab). Alkalinity (HCO3+, CO32+ ) was measured by titration with 1.6 normal sulfuric acid (H2SO4) until the related indicator changes color (at pH 4.3). Water temperature, EC, pH and oxygen concentration where measured in the field.

## 2 Construction of groundwater table map

### 2.1 Background

On southern part of Lichtwiese campus with a fenced and locked parcel with 17 groundwater wells the aim was

1. to measure the relative height of the groundwater table in some of the wells

2. to construct the map of groundwater table, and

3. to calculate the direction and the gradient of groundwater flow.

This information is needed e.g. for planing production wells that must not suck contaminants and therefore must be located in a position where contaminants are flowing away. Another application is planing a building ground with pits that must be protected from flooding by groundwater. Questions to be answered are e.g. How deep is the groundwater table? Where should wells be placed to keep groundwater from flowing into the pit? How much water must be pumped to keep the pit dry?

The location for Topic 1 was given as map with Gauss-Krüger (GK) coordinates (easting and northing in meters) and a hyperlink to Google Maps with geographic coordinates (49.861278 °N and 8.67489 °E). The Gauss-Krüger-Map shows the wells as P1, P2, P3, … It is also to be used to draw isolines for the groundwater (piezometric heads) and another time for depicting the thickness of the unsaturated zone (distance between ground surface and water table).

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Fig. 2: GK-map of well leveling parcel

The Gauss-Krüger (GK) coordinates for a Bessel Ellipsoid defined in Potsdam give an easting of 3476xxx (=> center median = 3*3°=9°E, 476 = 476 km relative to middle median “worth 500 km” = 24 km west of middle middle median) and a northing of 5524xxx (= 5524 km north of the equator).

The GK-coordinates are taken to web sites like www.netzwolf.info/kartografie/openlayers/gk or www.deine-berge.de/Rechner/Koordinaten that convert it to other coordinate systems (like UTM that are more likely supported by smart phone applications) and show the location in a geographical map. There we see the location between the large Architecture/FB15 Building (former Lichtwiese Library) in the east and climbing hall (DAV Kletterzentrum) in the west. P7 marks the well we started with and that was the reference for all the other wells we investigated:

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Fig. 3: location of well leveling parcel within campus Lichtwiese

The work on Topic 1 was supervised by Dr. Schiedek on Friday, June 19th. The elevation of the reference point (upper end of well pipe of well P7) was given by Dr. Schiedek as 187 meter above sea level (m.a.s.l.) Later he gave us also data for well number 3 from the previous year, because we were not able to measure this well in the field.

### 2.2 Methodology

We started with reference well P7 in the south eastern corner of the experimental parcel. We measured the distance from the upper rim of the well pipe (= reference point) down to the water table with with an electric sounder (gives optical/acustical signal when 2 electrodes at the lower end get in touch with the water) and the distance between the reference point and ground surface. This was done also for wells 8, 15, 10, 11b and 6a.

With a theodolite (a monocular telescope moveable around a vertical axis controlled by bubble levels) and leveling rod (or a folding yardstick) the levels of the reference points (upper rims of well pipes) of the other wells where measured relative to well P7. With the theodolites telescope we have a perfectly horizontal line of sight: forward to a new well and backward to the well P7 whose level was given (187m a.s.l. for the reference point). The leveling rod / folding yardstick was placed on the upper end of the well pipes and difference of the 2 readings (backsight – foresight) gives how much the new wells reference point is above the one of the referenced well (P7).

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Fig. 4 leveling well reference points (upper rims of pipes) with theodolite (from course script)

The data was placed into Libre Office' Calc (OpenSource clone of MS-Excel) and complemented by formulas in calculation columns. Data for well 3 was later given by Dr. Schiedek because we were not able to measure it that morning: we were the 1st group there and found the ground like a jungle we had first to cut forest aisles into but we couldn't make it to this well. The Gauss-Krüger coordinates (Rechts/easting- and Hoch/northing-Value) were taken from map in Fig. 2. The calculations are the following (A,B,C, … = column names):

D = Leveling = backsight – foresight = C-B

E = Elevation of reference point a.s.l. = 187m (P7) + D

F = Elevation of ground/surface at well = E – G

J = Elevation of water table a.s.l. = E-H

M = Delta-x to P7 in meter = K(well) – K(P7)

N = Delta-y to P7 in meter = L(well) – L (P7)

O = Distance in meter from well to P7 = sqrt(M*M + N*N)

P = Thickness of unsaturated zone in meter = F-J

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Fig. 5: Well leveling measurements and calculations in LibreOffice' Calc

Column J contains the elevations in meter a.s.l. of the water table in different wells. The contour lines (equipotential lines as straight lines) of the water table can be constructed graphically by selecting a subset of 3 wells. Let us name the well with maximum head A, the one with minimum head B and the third with head in between C. Then we interpolate the head of C on the line AB (gives point D on AB). We connect D with C. DC is the contour line / equipotential line for the head of well C. The other contour lines are parallel to DC. The gradient has a direction perpendicular to DC. Constructing the plump line from A onto DC delivers the magnitude (and direction) of the gradient. The length of this plump line corresponds to the head difference between point A and C as well to the geometrical distance taken from the GK-map. The quotient of both (head difference / shortest distance on surface between the heads) is the gradients magnitude.

This graphical method delivers straight lines as contour lines. When we measure many wells on the parcel in Fig. 2 and select many sets of 3 wells each out of the 17 wells we will get longer contour lines that are no longer parallel and are no longer equidistant. The modulus and direction of the gradient changes within the area of Fig. 2 as shown by a map from the previous year (not from our measurements):

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Fig. 6: Contour (equipotential) lines (lines of equal head) and gradients of heads from 2014

Being the 1st group on the parcel resembling a jungle we needed a long time for clearing forest aisles and to initially install the equipment. So we had less time for well measurements and got data for only 6 wells in the southern part of the parcel. That means we are anyway not able to produce a contour map like Fig. 6 and should instead produce some straight parallel equidistant contour lines corresponding to only one gradient amount and direction valid only for the south eastern part of the parcel. I'm assuming a flat water table with a constant inclination (for the south eastern part of the parcel).

Since we have data of only 6 wells (7 if we include well 3, but that has to be considered carefully) we have 6 over 3 = 6! / (3! * (6-3)! ) = 6! / (3! * 3!) = 4*5*6 / (1*2*3)= 4*5 = 20 possibilities to select sets of 3 wells out of our 6 wells. I did that with some sets and found graphically similar results as long as I don't consider well P3 because data was from previous year with different climatic situation and different lunar phase (tidal effects) i.e. its data is not fitting with current measurements.

Since graphical solutions were already subject of course HydroGeology (TuCaN 3406) of Basic Module 3 (BM3) with Dr. Marandi, I prefer to document here a more mathematical approach: the least squares method. The water table is described by a plane's equation with heads 'h' as 3rd dimension (z) as a 2-dimensional linear function of x and y, the horizontal distances of a well from P7 (=origin of our rectangular 3-dimensional xyz-coordinate system) on the ground's surface:

h(x,y)= x*a + y*b + c [1]

Equation [1] uses parameter a, b and c, that have to be determined in a way, so that the sum of the squares of distances between the plane and measured heads in the wells is minimized (least sum of squares). We don't have a system of 3 linear equations for 3 unknowns that can be solved exactly, but we have an overestimated system of (in our case) 6 equations (1 per well), that needs other methods than that of Gauss. Expensive mathematical software like Mathematica, Maple, MatLab, … can do that without any effort. But also free (of charge, of ...) Open-Source-software like Maxima, GNU-Octave (MatLab-clone), R (S-clone) and GNUplot can do this task too very easily.

In GNUplot with only 3 lines (declaring x,y,h as variables; Equation 1 and a fit-command connecting Equation 1 with the well head measurements in a text file) we get the parameters a,b and c:

set dummy x,y,h

h(x,y)= x*a + y*b + c

fit h(x,y) 'Leveling_d.csv' using 3:4: **2** via a,b,c

With 2 further lines we get the direction/azimut and the modulus (amount) of the gradient from parameters a and b:

azi=90 – 180*atan2(-b, -a)/pi

grad_mod=sqrt(a*a + b*b)

Same program can be changed a little bit to calculate and draw the thickness of the unsaturated zone (column P in the spreadsheet and last = 5th column in the input text file). The fit-command must read column 5 instead 2 of “Leveling_d.csv” and the titles and labels must be adjusted:

fit h(x,y) 'Leveling_d.csv' using 3:4: **5** via a,b,c

For more details see complete GNUplot programs “Level_b.plt” and “Thickness_b.plt” and the input text file “Leveling_d.csv” for both programs in the appendix. All the calculations are also easily done with Maxima an open source replacement for Computer Algebra Systems (CAS) like Mathematica, Maple or CAS(MuPad-) part of Matlab. While GNUplot uses only text files for data, Maxima offers the alternative of vectors and matrices to hold data (see appendix).

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Fig. 7: Well leveling calculation by Maxima (CAS)

2.3 Results

The GNUplot program “Level_b.plt” delivers the parameters a,b and c, the direction/azimuth of the head gradient as angle in degree from north to east and the amount/modulus of the head gradient as:

a = -0.0110027

b = -0.0328005

c = 182.548

print 'direction of strongest dropping of head = azimuth in degree from north clockwise: ', azi

# gives: 18.5436528604653° to NNE

print 'gradient_modulus: ', grad_mod

# gives 0.0345967498276373

The GNUplot program also draws a 3-dimensional graph with the water table as inclined flat plane and the color coded contour lines in the x-y-plane:

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Fig. 8: water table (inclined plane) and contour lines on the ground drawn by GNUplot

The contour lines had also to be drawn into the GK-map from Fig. 2 (Map I in practicum script for Topic 1):

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Fig. 9 well heads in meter a.s.l. & calculated contour lines (of equal head h) in GK-Map I

The GNUplot program “Thickness_b.plt” delivers the parameters a,b and c, the direction / azimuth of the thickness gradient as angle in degree from north to east and the amount/modulus of the thickness gradient as:

a = 0.00694203

b = -0.0219247

c = 3.60797

print 'direction of strongest dropping of thickness = azimuth in degree from north clockwise: ', azi

# gives -17.5693739869805° to NNW

print 'gradient_modulus: ', grad_mod

# gives 0.022997503275160

The GNUplot program also draws a 3-dimensional graph for the thickness of unsaturated zone as inclined flat plane and the color coded contour lines in the x-y-plane (well P7 has coordinates x=0, y=0):

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Fig. 10: Thickness of unsaturated zone as inclined plane and contour lines on the ground

This result was also documented in another piece of the GK-map from Fig. 2 (Map II in the script for Topic 1):

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Fig. 11: Thickness z of unsaturated zone in meter & calculated contour lines in GK-Map II

### 2.4 Discussion

We measured only 6 wells. Data for an additional well (#3) was given but should not be integrated because it was from previous year with different climatic situation and lunar phase and does therefore not fit into current measurements. With this data we are not able to produce complete maps for the whole parcel. By averaging the measurements and calculating parameters for planes (of water table elevation and thickness of unsaturated zone) with methods of least squares only for the southern part of the parcel errors are minimized and calculations should give good results as long as the assumption of flat tables (planes) is acceptable. This hypothesis is only verifiable with measurements in more wells and with more preciseness (better/newer theodolite, better leveling rods, better training in surveying).

The water table declines to NNE (18.5°) with a gradient of 0.035 whereas the thickness of the unsaturated zone declines to NNW (-17.6°) with a gradient of 0.023 i.e. water table and earth's surface are not parallel.

I learned how important are exact measurements because well heads changed only a part of a centimeter in the sight distance. And I learned that groundwater levels are changing with time making it difficult/impossible to combine data from different times.

## 3 Stream discharge measurements

### 3.1 Background

Discharge measurements are necessary for water budgets of watersheds. In a small stream Darmbach 3 different methods of discharge measuring were exercised upstream of a foot path bridge in the northern part of campus Lichtwiese west of Cafe Eulenpick of Vivarium (Schnampelweg 5) to compare them and to explain reasons for uncertainties.

A hyperlink to Google Maps with geographic coordinates (8.6802429 E, 49.8688556 N) was given for the location. Web site www.netzwolf.info/kartografie/openlayers shows maps and coordinates of the mouse point in degrees, UTM, Gauss-Krüger, …

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Fig. 12: Location of Topic 2 stream discharge measurements

**[...]**

- Quote paper
- Dipl.-Ing. Rainer Stickdorn (Author), 2016, Hydrogeological Field Methods. Discharge, Pumping Test and Water Analysis, Munich, GRIN Verlag, https://www.grin.com/document/433463

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