Ontological Modeling
Introduction
Groundwater is one of the most important components of the hydrological cycle. It is defined as water that exists underground in saturated zones beneath the land surface (USGS, 2022).
Competency Questions
When developing an ontology is very helpful to first answer some competency questions.
What is the purpose of the Ontology? The purpose of this ontology is to represent the main concepts needed for understanding and modeling a groundwater system that later could be extended to model hydrological processes or groundwater flow. It shall therefore also represent the relationships between the components, so the engineer really gets to understand how a groundwater system works and how the components interact with each other.
What is the scope? The scope are concepts such as soil layers, different soil types, groundwater bodies and the hydrological components in the system.
What is the domain? For the domain a certain section of a groundwater system is chosen represented by a two-dimensional slice having a certain depth and breadth.
Who are the intended users? In the first-place engineers or modelers who want to understand what a groundwater system consists of and need to understand how the components interact with each other. It can also be used by students of the water sciences to study groundwater systems.
What is the intended use? The main use is to understand the conceptual parts of a groundwater system to be able to model it for example in computer code.
The Domain
For the domain an underground area of certain extend is considered, which consists of different soil layers, groundwater bodies and hydrological components. As simplification only a two-dimensional slice of the area is considered. Also, any vegetation or buildings on top of the top soil layer is neglected. Soil layers and groundwater bodies are assumed to have a constant thickness. Furthermore, a groundwater body is considered only as the area where the soil is fully saturated, the capillary fringe is neglected. As stated, before the groundwater system is a component of the hydrological system. An instance of the groundwater system can interact with other parts of the hydrological system such as the atmosphere or water bodies and even with other groundwater systems. It can interact with these systems with its hydrological components such as infiltration, evaporation, inflow and outflow, which represent the flow of water.
Main Components
The system consists of the main components soil layer, soil type, groundwater body and hydrological component. Figure 1 shows a possible domain of the system, of course groundwater system can look different. It consists of 4 soil layers (Aquifer 01, Aquitard, Aquifer 02, Aquiclude), each of them has a soil type (Gravel, Clay, Medium Sand, Impermeable Rock). Both aquifers store a groundwater body inside of them (Unconfined Groundwater Body, Confined Groundwater Body). The hydrological components (Infiltration, Evaporation, Groundwater inflow, Groundwater outflow) here are represented by arrows. Outflow and inflow share the same arrow here as the outflow from one groundwater body is also the inflow to the other one.
Figure 1: Groundwater System Domain
Figure 2 shows a rough sketch of the system with its main components, some subclasses of these and the main relationships that define the interaction in the system.
Figure 2: Rough System Sketch
Development of the Ontology
This ontology was developed using the suggestions by McGuinness and Noy. In a first step the domain was chosen and answers to the competency questions were formulated. Next some research about groundwater was undertaken using resources such as book but also from the web. The main concepts were gathered as well as the relationships. Having all necessary information gathered, the classes were than arranged in a top-down approach. So, first the four main concepts were introduced as classes, and from there the subclasses were developed. While creating the classes, annotations were attached to them, to give users a proper idea of what the classes represent. After defining all classes, the object properties were defined, describing the relationships between the classes, such as has_soil_type. Next the data properties were created to describe attributes of the classes that contain actual values, such as the hydraulic conductivity of a soil. Finally, several instances were created for different classes. They contain boundary values to give modeling engineers an idea of the range of values for the data properties.
Figure 3: Class hierarchy and Data property
Figure 4: OntoGraf
Parametric Model
Introduction
The report at hand provides information on the modeling process of a Dynamo model of an aquifer. Information on the system was already gathered in the previous assignment I. For this assignment the scope was optimized to specify a design challenge which now focusses a single aquifer, rather than a whole complex groundwater system. Parameters and high-performance criteria were identified to find best design solutions.
Design Challenge
Finding a fitting design challenge for this system is rather hard because you usually model groundwater system / aquifers after an actual existing groundwater system / aquifer and want to calculate certain phenomena from this then. The chosen design challenge for this task however is to find an aquifer which provides a certain Darcy velocity of the groundwater. So, you must find parameters which fulfill this and other criteria.
High Performance Criteria
The first high performance criterium already mentioned above is the Darcy velocity. It refers to the average flow velocity of the groundwater considering the whole cross section of the aquifer. To determine Darcy velocity Vf in a simplified system you can use the following equation:
𝑣𝑓 = −𝑘𝑓 ∗ 𝑑ℎ/𝑑𝑥 = −𝑘𝑓 ∗ 𝑖 [ 𝑚/𝑠 ]
The term kf refers to the hydraulic conductivity [m/s], which was already introduced in assignment I. The term i denotes the hydraulic gradient [-], which consists of the fraction of dh, the difference in hydraulic heads at start and end, and the dx being the length of the flow path, that is the length of the aquifer in this model. The second criterium is the just mentioned hydraulic gradient.
Related Parameters
The most basic parameters are the one defining the dimensions of the aquifer, being the length, width and thickness (height) of the aquifer. You can only choose positive values for these parameters, and they have a certain ceiling value to keep the model simple. The most important parameter of these is the length, as it affects the hydraulic gradient.
Next up are the hydraulic heads [m] which can be given values from 0 to 30 (?), so they can also have a higher value than the aquifer thickness, which means the water is then under pressure. Both values are important to determine the hydraulic gradient and also influence the direction of the groundwater flow.
The last related parameter is the hydraulic conductivity [m/s], which refers to the ability of the soil to conduct groundwater. A coarse sand has larger values for this parameter than for example clay. In this model the soil types are not considered, but only the order of magnitude of the hydraulic conductivity ranging from 10-9 to 10-1 , from which a soil type could be guessed.
Parametric Model in Dynamo
The representation of the physical embodiment of the aquifer is kept very simple in this model. The shape is just a cuboid, which gets its dimension from the length, width, and thickness of the aquifer. For these values 3 different number sliders are implemented. To create the shape of a cuboid, first a point is created. From this point a line of the aquifer line is drawn in x direction. This line is then translated in y-direction by the aquifer width, and those created lines are again translated by the aquifer thickness in the z-direction. The necessary start and end points are then connected by lines to complete the shape of a cuboid.
The hydraulic heads are then represented by lines over the whole width of the aquifer at the start and end of the aquifer, respectively. The height (z-coordinates) of these lines is then determined by the values of the hydraulic heads, which are drawn from a number slider. The main element of this model is then created by creating a surface spanning from one hydraulic head to the other. This visualizes the course of the hydraulic head and gives you a good idea of the hydraulic gradient, taking the aquifer length into account.
Coming now to the calculation of the high-performance criteria, first a number slider for the order of magnitude of the hydraulic conductivity is implemented, where you choose between -9 and -1, which function as the power in the calculation. In a next step using a code-block the hydraulic gradient is determined from the hydraulic heads and the length of the aquifer. Having now these parameters, the Darcy velocity is calculated and shown by a watch-block.
Chosen Alternatives
The goal for the chosen alternatives was to find design solutions, where the Darcy velocity would be vf = 0,0002 m/s and the modulus of the hydraulic gradient should be small, so there is not a great difference between the two hydraulic heads at start and end of the aquifer. The chosen parameters are listed for each alternative and then discussed. All alternatives fulfill the criteria very good, so they are considered good alternatives.
Alternative 1
As Table 1 shows, the length of the aquifer is the highest possible value of 50 m. The difference of the hydraulic heads is only 1 m. This results in a very small hydraulic gradient (0,02). With a hydraulic conductivity of 0,01 m/s, this leads to a Darcy velocity of 0,0002 m/s. So the main goal is achieved.
Figure 5: Alternative 1
Alternative 2
A major change for the alternative 2 is to put the order of magnitude of the hydraulic conductivity to -4, which results in kf = 0,0001 m/s. Therefore, the Hydraulic heads had to be chosen to have the extreme values of 30 m and 0 m. The change also affected the length of the aquifer, now set to 15 m. All these parameters again lead to a Darcy velocity of 0,0002 m/s, but the hydraulic gradient is now much steeper with a modulus of 2. Alternative.
Figure 6: Alternative 2
Figure 7: Alternative 3
Alternative 3
Alternative 3 has a much smaller embodiment of both other alternatives. But with the given parameters, it still fulfills the criteria. The different alternatives show, how you can achieve a similar result regarding the velocity, with very different sets of parameters. The parameters with the greatest impact would be the hydraulic conductivity, as you then need a much larger gradient to fulfil the criteria, which also affects the embodiment.
References
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