Concepts about mathematical models and their uses in water resource management.

1. HYDRAULIC ENGINEERING ANDWATER
RESOURCES MANAGEMENT (UE-418)
OPEN ENDED LAB
Muhammad Muddassir
(UE-16063)
Department of Urban and Infrastructure Engineering, NED University of Engineering andTechnology, Karachi

2. MATHEMATICAL MODELS
A mathematical model is an abstract model that uses mathematical language to describe the
behavior of a system.
Uses InWater Resources Engineering And Management:
Water resources management requires constant monitoring in terms of its qualitative-
quantitative values. Proper assessment of the degree of water pollution is the basis for
conservation and rational utilization of water resources. One of the tools that are used to
solve problems of surface water pollution is modelling of changes which take place in lake
waters and associated water quality changes. Mathematical models can also be used for
assessment of water quality in dam reservoirs.

3. SIMULATION
Simulation is a model of a set of problems or events that can be used to teach someone
how to do something, or the process of making such a model. Across industries and
disciplines, simulation modeling provides valuable solutions by giving clear insights
into complex systems.

4. DIFFERENT MODELS ANDTHEIR DIFFERENCES
Event and Continuous Models:
Event modelling is often used for short-term purposes such as flood forecasting and flow
forecasting in general. Continuous modelling is useful for long-term purposes such as the estimation
of design discharges, impacts of climate and land use change and impacts of water management
strategies.
Lumped and Distributed Models:
In the case of lumped Models, the states are concentrated in single points and are not spatially
distributed.Therefore, lumped systems are described using ordinary differential equations (ODE). In
case of a distributed parameter system, its states depend on both time and location.Therefore a
distributed system can be described by partial differential equations (PDE).

5. Empirical and Conceptual Model:
Models that are represented by concepts or related concepts formed after a conceptualization
process in the mind are Conceptual Models, while a model developed from observations of the
type of system under investigation or one developed from observations of an analog of the
system under investigation is called Empirical Model.
Deterministic and Holistic Model:
A deterministic model is a model where the material properties are well known, i.e.
deterministic, none of them are random. A deterministic model is a model that gives you the
same exact results for a particular set of inputs. Holistic means encompassing the whole of a
thing, and not just the part. It is based on the knowledge of the nature, functions, and properties
of the components, their interactions, and their relationship to the whole along with the room of
randomness.

6. MATHEMATICAL MODELS AND COMPUTER PROGRAMS
Computer models assist us simulate a real life state of affairs or procedure with a few built-in assumptions
(that is, the model is a simplification and works below sure assumptions).A version will help us examine the
effect of changes in some of the variables, without carrying out modifications in the actual bodily
environment. With the assist of computers, it is simple to simulate and model a situation simply by
converting the variables.The processing device of computer can do the modelling for you in no time.

7. LIST OF COMPUTER MODELS USED IN WATER
RESOURCES ENGINEERING AND MANAGEMENT
• EPANET -Water distribution system model
• MODFLOW - Ground water model
• Vflo -Watershed runoff model
• HEC-RAS - Flood control model
• SWAT - River and reservoir water quality model
• HEC-ResPRM - Reservoir/river system operation models