自然災害研究協議会

中国地区部会

研究論文集

第10号

24 自 27（2023）

A Probe for Measuring 3D Groundwater Velocity
without a Borehole
Joaninha Belo Ornai1), Masataka Aoki2), Koichi Yamamoto1)
1)
Graduate School of Sciences and Technology for Innovation, Yamaguchi University
2)
Faculty of Engineering, Yamaguchi University
1. Introduction
Recently, there has been a growing demand for the investigation of groundwater flow velocity for the purposeof the maintenance of dykes or reservoir for irrigation. In well technique measurement, a Heat Pulse
Flowmeter (HPF) with four channels and electrical conductivity detectors placed inside the well provides
centimeter scale readings for depth profile velocities1). Besides, the point velocity probe (PVP) rapidly
measures direction and magnitude of the water velocity vector to within 9% and 8 degrees at the centimeterscale in porous media without need of calibration2). Similarly, an automated on-line groundwater velocity
probe measures flow velocity within a screened well. It uses a flushed semi-permeable gas chamber with agas tracer, the tracer diffusion period determines groundwater velocity3). Besides, a cost-effective in situ
method for precisely measuring groundwater flow velocity based on groundwater-induced cooling was alsopresented using closed circulation of heated fluid, the experiment established the functional relationshipbetween temperature differences and groundwater velocity4). In response to this need, a power-free,inexpensive, and time-efficient measurement probe has been developed5). This novelty probe is called Paper
Disk Groundwater Velocimeter (PDGVs). In 2016, the PDGVs sensor paper was enhanced, resulting in asingle dot with a 3 mm diameter positioned at the center of the paper. This improved sensor’s paper resulted
in an alignment curve of the relationship between Darcy flow velocity and tailing lengths of giving period 5
and 60 minutes for ranged velocity of 0.3 cm/min -1.5 cm/min6). Furthermore, existing devices can measuregroundwater flow in three dimensions. However, the devices still need boreholes to be measured 7). If noborehole is needed for measurement, the measurement of the groundwater flow in dyke or reservoir will bemuch easier. For this reason, we developed a new small device with absence of boreholes which can measure
3-dimensional groundwater flow velocity and direction.
2. Methods
2.1. Micro-paper disk groundwater velocimeter
The Micro Paper Disk Groundwater Velocimeters (M-PDGVs) were invented based on the principle of thepaper disk groundwater velocimeter6). The M-PDGVs have two types, vertical 2D and horizontal 2D. Thesetypes consist of 1000 mm extension rod along with paper disk of 29 mm x 10 mm size and 2 mm diameterdot for vertical 2D type, and 10 mm x 10 mm size with 1 mm diameter dot for horizontal 2D type. The abilityof these micro types to measure the two directions of the flow both vertical and horizontal directions.
2.2. Experiment methods
The purpose is to verify horizontal and vertical velocity and direction with M-PDGVs. A water tank filledwith quartz sand (d50 = 0.5 mm) was used for calibration of the Micro-PDGVs (Figure 2). Using a peristatic
pump, groundwater flow was generated in the sand tank. The horizontal 2D type setting velocity ranged from
0 cm/min – 0.12 cm/min with changing horizontal flow direction stepwise from 130 deg to 220 degrees overa measurement period of 60 minutes. However, the vertical 2D type measurement condition was undertakenfor 15 minutes period with the measured velocity ranged from 0 cm/min – 0.1 cm/min and vertical inclinationfrom -45 to 45 degrees as omnidirectional and inclinational tests. These experiments were conducted 5 times
for each condition.
2.3. Analysis methods
In the analysis phase, the first step involved the original paper solely with dot ink, which was subsequently
eluted after the probe was submerged into the soil. Thereafter, the dot generated a tailing that aligned withthe water flow directions over a certain period. The dot and tailing length were analyzed with an open-source
image analysis software, Image-J, after scanning the paper. Channel separation for the experiment included
the Red, Green, and Blue (RGB) colors. The brightness, specifically a value of 105 in the red channels, wasused for dot detection and the brightness of blue channels and red channel were used for tailing detection.

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Joaninha Belo Ornai, Masataka AOKI, Koichi YAMAMOTO：
Probe for Measuring Three-Dimensional Groundwater Velocity without Borehole

The following flowchart illustrates the mechanism. The ideal ink tailings area, shown in Fig. 4 a), was close
to an ellipse. Therefore, in order to assess the quality of the ink tailings, the ratio of thearea of the ellipse to the area of the ink tailings was calculated, with its maximum Feret diameter DFmax as
the major diameter and its minimum Feret diameter DFmin as the minor diameter. For a, the ratio of theapproximate ellipse area to the ink tailings area was 0.9, and for b, in contrast, the ratio was 0.7. The qualityof tailing length Q is calculated using the area of the ink tailing A and ellipsoid area A’ as below (1) and (2).
𝑄=𝐴(1)𝐴′𝜋

A’ = DFmax DFmin(2)4The length of the tailing by the eluted ink from the printed dot was identified from the scanned color imageof the paper disk using blue and red channel based on machine classification. The longitudinal red channel's
brightness distributions of the tailings of ink were used to estimate groundwater flow velocity. The brightness
distributions were acquired using the multiple thresholds of the red channel. When the brightness of the redchannel is correlated to the concentration of the ink on the paper, the relationships between concentration of
the ink on the paper and brightness of the red channel (BR) are written as (3).
𝐶 = 𝛼(255 − 𝐵𝑅 )(3)

(0 ≤ 𝐵𝑅 ≤ 255)

When the relationships between C and velocity v is written as𝑑𝐶𝑑𝐵𝑅
𝛽(𝑡)
= −𝛼
=−𝑑𝑥
𝑑𝑥𝑣
then𝛽(𝑡) 𝑑𝐵𝑅 −1
𝑣=
[]𝛼𝑑𝑥

(4)

Where: C: ink concentration on paper (g cm-2), BR: brightness of red channel (-), 𝑥: distance on paper (cm),  coefficient (g cm-2),  (t): coefficient (g cm-4 s)
Table 1 The details of the M-PDGVs vertical
2D and horizontal 2D types

DeviceTypes

Vertical 2D

Horizontal 2D

Table 2. The velocity and direction measured conditionin the laboratory experiment for both the vertical 2D andhorizontal 2D M-PDGVs.

Materials

Dimensions

Measurement
DevicesPaper

10 mm x 29 mm
2 mm diameter dot

Vertical 2D

Sponge29 mm x 6 mm x 10mm

Paper

10 mm x 10 mm
1 mm diameter dot

SpongeHorizontal 2D10 mm x 6 mm x 29mm (2 units)

Direction
Setting tilt
(0°, 15°, 30°,45°, -15°, 30° & -45°)
Northward
Orientation(-40°, -10°,5°, 20° &50°)

Time(minute)

1560

Mean Tank
Velocity(cm/min)
00.05
0.08
0.1
0.2
0
0.01
0.02
0.04
0.08
0.12

3. Results and Discussion
3.1. Vertical 2D measurement results
Fig. 5 illustrates the relationship between the tailing length of the vertical 2D type M-PDGV and the reciprocal of
the ink brightness differential. This relationship is linear, with a high correlation coefficient (R2 = 0.9267). Fig. 6
depicts the errors in the vertical inclination direction at a velocity of 0.1 cm/min, within a range between -45
degrees and 45 degrees.

－ 25 －自然災害研究協議会

中国地区部会

研究論文集a)

第10号

24 自 27（2023）

b)

c)

d)

Fig 1. Two types of M-PDGVs: a) vertical 2D
type and b) horizontal 2D type. The paper diskof M-PDGVs sensor after measurement isshown in c) vertical 2D type [tilt = 0°] and d)horizontal 2D type [direction = 220°] x axis andy axis are on the horizontal plane. z axis isvertical.

Fig 2. The water tank front and top view were used forvertical 2D and horizontal 2D M-PDGVs experiment.

Fig 3. The channel separation analysis for the scanned
paper dot and tailing, where the range of threshold RT at
175 – 215, the red channel R for dot detection 105 andthe maximum brightness B 255.

Fig 4. The quality of the ink tailing at verticalorientation [tilt = 0̊]. a) tailing quality = 0.9,b) tailing quality = 0.7.

300.004

Error [deg.][dBR/dx]-1 (cm)0.005
0.003
0.002

y = 0.0231x + 0.0006
R² = 0.9267

0.001
000.1

0.2

v (cm/min)

0.3

0-90-60-30

030

60

90-30
Setting direction[deg.]

Fig 5. The calibration line of calculated tank (Darcy)
velocity v and inverse of the derivative of brightness of
red channel with respect to distance on the paper x; t =15min.

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Fig 6. Relationship between setting directionand error direction of vertical 2D type atvelocity = 0.1 cm/min

0.006
0.005
0.004
0.003
0.002
0.001
0.000y = -0.4827x2 + 0.0911x + 0.0007
R² = 0.9903
00.050.1v (cm/min)

0.15

Fig 7. The calibration line of calculated tank (Darcy)
velocity v and inverse of the derivative of brightness of
red channel with respect to distance on the paper x; t=60 min

Error direction[deg.][dBR/dx]-1 (cm)

Joaninha Belo Ornai, Masataka AOKI, Koichi YAMAMOTO：
Probe for Measuring Three-Dimensional Groundwater Velocity without Borehole

180.0
120.0
60.00.0-60.0 100-120.0-180.0150200

Setting direction [deg.]

Fig 8. Relationship between setting directionand error direction of horizontal 2D type
[direction = 130̊ – 220̊].

Table 3 The omnidirectional and inclinational test results of horizontal 2D and vertical 2D groundwater flow
directions measurements by M-PDGVs.
TypeVelocity [cm/min]
Time [mins]
SD [deg.]
RMSE [deg.]
Horizontal 2D
0.01 – 0.135
60
12.89
12.52
Vertical 2D
0.05 - 0.2
15
10.25
11.12
3.2. Horizontal 2D measurement results
Fig. 7 illustrates the regression curve of the horizontal groundwater flow and the measurement results. Since
there is convex curve on the top, the upper limit of measurement is around 0.06 cm/min. Horizontal directions
are shown in Fig. 8. Table 3 shows standard deviation (SD) and root mean square error (RSME) values forhorizontal 2D and vertical 2D measurements. For horizontal 2D, the standard deviation measured was 12.89
degrees, showing a range of variability within -40 to 50 degrees based on horizontal orientation. The
corresponding RSME is 12.52 degrees. As for vertical 2D device, the standard deviation of the verticaldirection was 10.25 degrees and RSME was 11.12 degrees.
4. Conclusions
The set of groundwater velocity probes, M-PDGVs, which can measure three-dimensional groundwater flow
velocity without a borehole was invented and evaluated. The velocity probes consistently showed linear
responses to velocities ranging from 0 to 0.2 cm/min. In addition, both horizontal and vertical directional
incline tests revealed that tailing tilt fitted alignment of the sensor inclination. This measurement emphasized
the capability of M-PDGVs in detecting small-scale subsurface water movements. While the experiments
were conducted in laboratory testing, the adaptability and precision of this probe suggest potential
applications in such relevant field environments. This novelty is applicable in measuring groundwater flowin diverse environments were found to be challenging, including river embankment, ponds, tidal flat, wetland
and micro-scale contamination areas.
References
1) Devlin J.F. (2020): Groundwater Velocity. ISBN: 978-1-77470-000-6, 2020.
2) Labaky W. et. al (2007): Prove for measuring Groundwater at the Centimeter Scale. Journal of Environ.
Sci. Technol. 2007, 41, 8453–8458.
3) Patterson B. M. et al. (2010): On-line Groundwater Velocity Probe: Laboratory Testing and Field
Evaluation. Journal of Contaminant Hydrology 117 (2010) 109-118.
4) Sun Z. et. al (2023): Measuring Groundwater Velocity: Method Based on Groundwater Flow-InducedCooling. Journal of Hydrologic Engineering, 2023, Vol. 29, 1.
5) Ono et.al (2014): Observation of the Behavior of Groundwater on a Coastal Sandbar using a Paper DiskGroundwater Velocimeter. Journal of JSCE Transaction G (Environment), 2014, Vol.70, No.70, III_355III_363.
6) Yamamoto et.al (2016): Development of the Single Dot Type Paper Disk Groundwater Velocimeter.
Journal of JSCE, Ser. B1 (Hydraulic Engineering), 2016, Vol.72, 4, Pages I_907-I_912.
7) Yamamoto K. and Murai D. (2022): Groundwater Flow in Sandy Beach Adjacent to Tidal Flat. Journal ofJapan Society of Civil Engineers, Ser. B3 (Ocean Engineering), 2022, Vol.78, 2, Pages I_787-I_792.

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