How are water levels calculated?

The data needed to calculate water levels come from a variety of sources. These are the measurement data from our devices, measurement data from a weather station and metadata from the portal. More information of what data is used is visible in the table below.

Source	Name	Unit	Required	Notes
Device	Absolute pressure	Pa	Yes	Default measured every hour.
Weather station	Barometric pressure	Pa	Yes	Third party source like KNMI, nearby weather station.
Portal	Well head offset	m	Yes	How far top well head is from reference like NAP or TAW.
Portal	Sensor offset	m	Yes	Measurement by field worker between top of well head and bottom of device. This value is negative.
Portal	Water density	kg/m3	No	Default 999,7 kg/m3, set by hydrologist based on conductivity measurements.
Portal	Calibration offset	m	No	Default 0 meter, shouldn’t be necessary to use, but can be used for example when a well is tilted.
Portal	Latitude	degrees	No	Used to calculate gravitational acceleration. Defaults to 9,80665 m/s2 if no latitude specified.

Besides this, there is an option to turn on barometric pressure compensation for measurement height. This is default off and only turned on for specific portals/groups on request.

In theory

In this chapter the equations used in our services are explained which are used to calculate the water level. Below that the constants used in our services and the sources can be found. In the next chapter a practical example is shown.

Gravitational acceleration at latitude^[1]

where:

• g_𝜑 is the gravitational acceleration at latitude in m/s²

• g_e is the gravitational acceleration at the equator in m/s²

• β is the first parameter

• β₁ is the second parameter

• 𝜑 is the geographic latitude in degrees

Water column

Where:

• h_column is the water column above logger in meter

• p_logger is the absolute pressure at device in pascals

• p_baro is the barometric pressure in pascals

• ρ is the water density in kg/m³

• g is the gravitational acceleration in m/s²

Water level to reference height

Where:

• h_water is the water level relative to reference height in meter

• h_column is the water column above logger in meter

• h_head is the height difference between the well head and the reference height in meter

• h_sensor is the sensor offset in meter, always negative value

• h_calibration is the calibration offset in meter

Barometric pressure compensation for measurement height^[2]

Where:

• p_compensated is the barometric pressure compensated for the measurement height in pascals

• p₀ is the barometric pressure at reference height in pascals

• g is the gravitational acceleration in m/s²

• h is the difference in height between p₀ and p_compensated in meter

• M is the molar mass of dry air in kg/mol

• R is the universal gas constant in J/mol·K

• T is the temperature in Kelvin

Constants

Constant	Value	Notes
ge	9,780327 m/s2	Gravitational acceleration at the equator as defined in GRS[1]
β	0,0053024	First parameter of series expansion formula as defined in GRS[1]
β1	-0,0000058	Second parameter of series expansion formula as defined in GRS[1]
M	0,02896 kg/mol	Molar mass of dry air[3]
R	8,3144626 J/mol·K	Universal gas constant[4]
T	283,15 K	Temperature is assumed to be 10 °C

Sources

1. Geodetic Reference System 1980 by H. Moritz, found at https://geodesy.geology.ohio-state.edu/course/refpapers/00740128.pdf

2. On the barometric formula by M N Berberan-Santos, E N Bodunov and L Pogliani, found at https://www.researchgate.net/publication/253750340_On_the_barometric_formula

3. Air - Molecular Weight and Composition by The Engineering Toolbox, found at https://www.engineeringtoolbox.com/molecular-mass-air-d_679.html

4. CODATA recommended values of the fundamental physical constants: 2018 by Tiesinga et al, found at https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=931443

In practice

Below is an example of a measurement point in the portal. For this level the barometric pressure was measured as 132986 Pa and barometric pressure as 101952 Pa. The other required values are visible in the diagram. This measurement point is at 52 degrees latitude and has barometric pressure compensation for measurement height enabled.

 

 

Gravitational acceleration at latitude

First the gravitational acceleration at the latitude that the measurement point resides is calculated.

Water column

With that and the pressure measurements the water column is calculated.

Water level to reference

Then it’s put in reference with the portal metadata. This is usually the final answer. Some groups/portals have barometric pressure compensation for measurement height enabled and so also use the next steps.

Barometric pressure compensation for measurement height

The calculated water level is used to calculate what the barometric pressure is at that height.

Water column compensated for measurement height

With the new barometric pressure, a new water column is calculated.

Water level to reference compensated for measurement height

Last it’s put in reference with the portal metadata. This results in an answer that matches with the water level visible in the diagram when rounded to two decimals.