Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Earth science
Reexamination Certificate
2001-07-18
2003-02-18
Lefkowitz, Edward (Department: 2862)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Earth science
C405S039000
Reexamination Certificate
active
06522972
ABSTRACT:
1. FIELD OF THE INVENTION
The present invention relates generally to estimating surface water runoff, and, in particular, to deriving an instantaneous unit hydrograph for a watershed.
2. BACKGROUND OF THE INVENTION
Rainfall is partially absorbed into and partially shed by the surface on which it falls. The proportion that is shed will depend on how long and how much it rains at one time, on the type of surfaces on which it falls, the slope of the surface, on the condition of the surface at the particular time it rains (already saturated surfaces absorb more, for example) and on other factors. The water that is shed may have to be managed in some cases rather than allow for it to simply flow into a down-slope stream, river, lake or sea. Management of runoff requires physical structures that control, redirect, or confine the surface water and that protect adjacent areas.
In order to manage surface water runoff, an estimate of the amount of runoff is useful. Structures that manage the runoff will be sized to receive the estimated volume of runoff. The larger the estimated runoff, the larger the structures need to be built in order to cope with it. Also, the size of the structures is typically increased to allow for uncertainty in the estimated runoff.
If surface water could be more accurately estimated, the costs of structures built to manage it can be lowered because they could be built with less margin for uncertainty. Furthermore, the costs associated with the consequences of a structure being under-designed are also reduced. For example, with a more accurate estimate, the structure might be designed to be smaller and therefore require less space and fewer construction materials. On the other hand, a more accurately designed structure may prevent the washing out of roads and the attendant repairs and inconvenience of detours while those repairs are made.
In order to estimate runoff, hydrogeologists attempt to determine how fast rainfall excess occurring uniformly over a particular watershed will reach its outlet. The speed will depend heavily on the nature and number of flow paths, both overland and channel flow paths, that the excess rainfall follows.
This determination can be done by placing gauges at various locations in a watershed to measure rainfall and runoff. However, this type of study is not always practical because of the time and resources involved. In many cases, geohydrologists must rely on estimates made by a mathematical analysis. As a practical matter, this analysis cannot be precise but must employ certain simplifying assumptions.
Estimating surface water runoff involves making a number of assumptions about the weather and combining these assumptions with information about the area on which rain falls. These two components can be viewed separately by using a diagram called a unit hydrograph. A unit hydrograph shows what volume of water as a function of time reaches a drain, or “catchment,” in a watershed following one unit of rainfall. A watershed is a topographically defined region where all surface water tends to flow to a single drain point. For example, a watershed may be a valley where all of the surface water drains to a stream in its lowest point and thence to some other area. This type of graph says nothing about the anticipated weather but is solely directed to what happens to rainfall if it occurs. An “instantaneous” unit hydrograph assumes that the unit of rainfall occurs instantaneously.
To simplify matters conceptually, hydrogeologists assume that a unit of rainfall falls uniformly over the whole watershed. The instantaneous unit hydrograph may then be determined by taking the time derivative of the volume of flow at the outlet that results from the unit of rainfall that has fallen in an instant. Another way of stating the problem is: What is the probability that a drop of rainfall excess has reached the watershed outlet at some time t? The answer is given by the equation:
V
(
t
)
=
∫
0
t
q
(
t
)
ⅆ
t
where q(t) is given by the formula
q
(
t
)
=
IUH
(
t
)
=
ⅆ
V
(
t
)
ⅆ
t
where V(t) is the total volume of rainfall excess at the outlet up to time t and q(t) is the discharge hydrograph at some time t.
Unit hydrographs were first developed in the early 1930's by L. K. Sherman as a way to transform rainfall into runoff. Sherman based his model for hydrographs on observed rainfall in a watershed and the corresponding outflow.
Unit hydrographs are often made in the same way today, that is, by making measurements over a period of time. Records of rainfall can be correlated to surface water outflow at the drain from the basin. However, it is not always possible to make actual measurements of every basin. When measurements are not feasible, unit hydrographs must be derived indirectly or “synthesized” about a watershed using other information. Synthesized unit hydrographs are developed for ungauged watersheds using statistical parameter prediction equations that relate unit hydrographs from gauged watersheds.
In order to perform this analysis, some additional terms are needed. The word “state” refers to the order of the overland flow region or the channel in which the drop is located at time t. The number of the state is determined by the number of linear reservoirs used to define the overland segment of flow. This number can be varied so that the shape of the unit hydrograph can be better approximated. All drops of water eventually pass into the highest numbered, or “trapping,” state N where &OHgr; is the number of states used to represent overland and channel flow for the entire basin and, thus, N=&OHgr;+1. The term “transition” means that the state of the drop has changed.
A major improvement in synthesizing unit hydrographs occurred when Horton in 1945 introduced the use of order numbers and ratios for flow channels. His method was further refined by Strahler in 1957. According to this method, channels that originate at a source are first order streams. When two streams of order i join, a stream of order i+1 is created. Finally, when two streams of different order join, the stream immediately downstream of where they join is assigned the higher of the orders of the two joining streams. This will be referred to herein as the Horton-Strahler method.
Horton proposed that for a given basin with its network of channels, the number of streams of successive orders and the mean lengths of streams of successive orders can be approximated by simple geometric progressions. The mean length Li of a stream of order i is defined by
L
i
=
1
N
∑
j
=
1
N
i
L
ji
where L
ij
, j=1, 2, . . . N
i
, i=1, 2, . . . , &OHgr;, represents the length of the jth stream of order i.
Horton established three ratios, R
B
, R
L
and R
A
The first, R
B
, the bifurcation ratio, is the Horton “law of stream numbers”:
R
B
≅
N
i
-
1
N
i
The first Horton ratio is typically in the range of 3 and 5 for natural areas.
The second ratio, R
L
, is the stream length ratio for the Horton “law of stream lengths”:
R
L
≅
L
i
L
i
-
1
The R
L
ratio for natural areas is typically between 1.5 and 3.5.
A third ratio, R
A
, proposed by Schuum in 1956 and called the Horton “area ratio”, is the drainage area ratio:
R
A
≅
A
i
A
i
-
1
R
A
is found in a manner similar to that of R
B
and R
L
. This third Horton ratio is typically between 3 and 6 for natural areas.
In this equation, the area A
i
is the mean area of the basin region of order i. Specifically,
A
i
=
1
N
i
∑
A
ji
for i=1,2, . . . , &OHgr;. A
ij
refers to the total area that drains eventually into the jth stream of order i and not just the area of the surface region that drains directly into the jth stream of order i. Consequently, A
i
>A
i−1
.
There are several methods known for developing synthetic unit hydrographs, some of which employ the Horton ratios. However, the movement of water through a basin is a very
Gutierrez Anthony
Lefkowitz Edward
Mann Michael A
Nexsen Pruet Jacobs & Pollard LLC
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