49225 Catchment Modelling Assignment 2

This report delves into the complexities of catchment modelling, focusing on the kinematic wave and pond model approaches. It discusses the assumptions, analysis, and benefits of each method in understanding urban hydrology and runoff processes. The report highlights the mathematical foundations of these models, their applications in real-world scenarios, and the importance of accurate modelling in resource planning and management.

49225 CATCHMENT MODELLING
ASSIGNMENT 2
STUDENT NAME
STUDENT REGISTRATION NUMBER
COURSE CODE

INTRODUCTION
There has been a large rate of urbanization in the metropolitan areas especially in the vicinity of
the river basins. The rapid rate has caused resource planners and hydrologists to come up with
better models of analysis of the urban hydrology. The kinematic wave model is used for the
channel and the overland flow routing in the precipitation-runoff modelling system in the
Distributed Routing Rainfall Runoff Model. The development of the theory and application of
kinematic wave is complex but it is not readily available in a given text. It is an approximation of
the dynamic wave model as there are developments of the models and the difficulty involved in
applying the solution techniques, the theory is described as a dynamic wave theory applied to
water routing problems.
The open channel flow stand-out as the most experienced kind of flow in the catchment
modelling processes over the recent years. When there is no acceleration experienced in the flow
of the water or runoff, the system is considered to be in steady flow. When there is a change in
the velocity, the flow is not considered steady any more. It is important to consider the impact of
the unsteady flows; therefore, it is added as variable when performing the analysis of a
catchment area. Another type of flow is the uniform flow which follows where the slope of the
water surface does not change with flow. A large water surface slope change is used to
demonstrate the rapidly varied flow. A general description of the runoff is given by the shallow
water equations which are valid for surface flow, gutter flow and the flow in the sewer systems.
The shallow water equations are two partial differential equation that are resultant of the mass
and momentum conservation laws. The shallow water equations are derived as demonstrated in
the illustration below,
The process of the open flow for an unsteady flow is expressed in mathematical terms as is
described by the St. Venant equations as,

The kinematic approach is analyzed as a product of the stage or depth versus the discharge
relationship. It uses the momentum equations to perform the analysis such that the wave occurs
when the process terms are deemed negligible. Such denotation allows a designer or the
hydrologist to assume that the bed slope is very close to the friction slope. Every catchment area
needs to acknowledge the backwater effect and the same is included in the analysis. On the other
hand, the discharge is described as a function of depth of flow only. The run off process occurs
in the surfaces, gutters, and sewers as described by one continuity and momentum equation for
the shallow water equations. (Lyngfelt & Arnell, n.d.).
OBJECTIVE
(i) To advance run-off hydrographs by analyzing the relationship between the kinematic
approach and the pond model approach.
(ii) To deliberate the differences and reasons for the differences between the kinematic
approach and the pond model
ANALYSIS
assumptions
(i) At the outlet of the catchment area, the flow is considered uniform, unidirectional and
one that flows instantaneously from the outlet to the next point in the analysis.
Analytic values or data
Catchment area 2.25ha (150m x 150m)
Slope 2.25%
Roughness 0.150
Rainfall event 90mm/h for 60 mins
Losses Initial losses of 4.5 mm

and continuing losses of
3mm/h
The kinematic data set as well as the pond approach model dataset are as described in the
attached spreadsheet. The above values were used to provide the base ground information of the
site being modelled. The design of a wet pond is modelled using several parameters. the primary
parameter is the area ration which is designed not to be less than 100 for maximum efficiency. It
is given as,
Area Ratio= Drainag e Area
Pon d Area
The two approaches are used in the hydrological analysis of water flow on the ground surfaces.
This refers to the water that flows in stream canals or the overland flow that flows on the land
surface. As indicated in the introduction section, the St. Venant equations are used for the two-
dimensional analysis. It is crucial to note that the kinematic wave approach models use the
highlighted set of equations while considering the impacts of gravity and resistance on flow. The
analysis provides a platform for the analysis of the 1-1 relationship between the depth or the
stage and the discharge. This is done using the equation below,
Q=α hs
n … α ∧n are the constant coefficients
Unfortunately, the kinematic approaches do not manage to denote the flow at the low land
regions or the very high points of the catchment area as a result of intense precipitation on the
hillslope. The kinematic approach model assumes that the friction slope may be approached by
the land surface slope making other effective components of the friction slope negligible. The
pond model seeks to cater for the caveat or shortcomings of the kinematic approaches. The pond
approach seeks to review the surface runoff that enter the drainage system through gulley and
manholes. The sewer flows surcharge from the manhole and the surface overland flow in one or
two dimensions. Once the sinks are full water is passed on to the catchment within which that
sink and its corresponding sink lies in.
Water tends to appear as output in the same water that is identified from the hydrograph. In the
reality substantial portion of the water appearing as the old water. The water that has entered the
watershed from a previous event. The unit hydrograph theory is as demonstrated below,

One is able to determine the inflection point of the flow on the catchment area when a
hydrograph is plotted. The plot uses the semi-logs or log scales as the data being addressed is
very large. The designer notes the time when the recession side follows the trendline. (Li, et al.,
n.d.).
The resulting kinematic hydrographs from the discharge values.

0 5 10 15 20 25 30 35 40 45 50
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
KINEMATIC APPROACH VS POND APROACH MODEL
Kinematic
Pond
Time (mins)
Flow (m3/s)
Benefits of the kinematic wave approach over the pond model.
One may wish to know why they would implement the kinematic approach over any other
approach in the catchment modelling. It provides an alternative routing for the flow of water over
the land surface. Some sections of the land are more pervious than other hence the water flowing
may slip into the land causing a loss. Some of the portions of the catchment area may not allow
the smooth flow as they act as obstacles. It allows non-linear response devoid of complex
solution procedures or very complicated analytics. The parameters in a model are actively
adjusted to account for the complexity of the catchment area. Some of the parameters considered
in this are the channel shape, the boundary roughness, the catchment area length and width, the
channel or area slope as well as the nature of the flow surface. The kinematic wave approach is
acknowledged as the limiting case of an infinite number of non-linear reservoirs.
The slope differs in terms of the flow rate at a given point in time depending on the section of the
catchment area being analyzed. It can be observed that the after the 23rd minute of the
hydrological analysis, the slope has a negative gradient as compared to the previous time. This
demonstrates a catchment area that has an uphill section. The water flows downwards until it
reaches a point where it stalls as it tries to manage the upward movement. The kinematic
approach studies the motion of the fluid flow. The fluid flow tends to move at the same speed at
a given point in time.

CONCLUSION
In a nutshell, the kinematic approach model assumes that the friction slope may be approached
by the land surface slope making other effective components of the friction slope negligible. The
run-off process occurs in the surfaces, gutters, and sewers is described by one continuity and
momentum equation for the shallow water equations. The kinematic wave approximation is
defined by a set of differential equations and boundary conditions. The development of the
theory and application of kinematic wave is complex but it is not readily available in a given
text. It is an approximation of the dynamic wave model as there are developments of the models
and the difficulty involved in applying the solution techniques. It describes a characteristic type
of wave motion that can occur in the many simplistic flow problems.
REFERENCES
Li, R-M, S., Stevens, D. B. & M, A., n.d. Non-linear Kinematic Wave Approximation for Water
Routing. Water Resources Research, 11(2).
Lyngfelt, S. & Arnell, V., n.d. A mathematical runoff model for simulation of storm water runoff
in urban areas. Chalmers university of Technology, Urban Geohydrology Research Group,
Volume 12.
Sjoberg, A., n.d. Calculation of Unsteady Flows in Regulated Rivers and Storm Sewer Systems.
Department of Hydraulics, Chalmers University of Technology, Volume 87.