Academia.eduAcademia.edu

Figure 2 – uploaded by Behzad Ahmadi

See full PDFdownloadDownload figure
Table 1. KW Shape Factors for Various Conditions meter per second (cms), but they vary in the rising and falling limbs. This case study verifies that Eqs. (1), (7), and (17) can provide a basis of equivalence to convert a family of watersheds to their different KW planes.

Table 1 KW Shape Factors for Various Conditions meter per second (cms), but they vary in the rising and falling limbs. This case study verifies that Eqs. (1), (7), and (17) can provide a basis of equivalence to convert a family of watersheds to their different KW planes.

Related Figures (16)

Fig. 1. Natural watershed and kinematic wave plane
Fig. 1. Natural watershed and kinematic wave plane
in which X=watershed shape factor, Y=KW shape factor for the KW plane, and K=upper limit of shape factor. For rectangular watersheds, Eq. (5) reduced to the watershed width to its channel length ratio. In practice, it is advisable that a large watershed be divided into smaller subareas and each subarea should have a shape factor not to exceed a limit, K. For instance, the CUHP suggests K=4 (UDFCD 2005); otherwise CUHP would overesti- mate the peak runoff because the subarea is too wide in shape. Aided by Eqs. (5) and (6), Eqs. (3) and (4) can be combined to cancel X,,/L as Eq. (3) implies that the watershed shape must be preserved along the waterways between these two systems. Watershed shape fac- tor is an index that represents how the overland flows are col- lected in a watershed. It was suggested that the watershed length- to-width ratio, circularity ratio, and elongation ratio can be employed to represent the watershed shape (McCuen 1998). Re- ferring to Fig. 1, the shape factors for the real watershed and virtual KW model are defined as
in which X=watershed shape factor, Y=KW shape factor for the KW plane, and K=upper limit of shape factor. For rectangular watersheds, Eq. (5) reduced to the watershed width to its channel length ratio. In practice, it is advisable that a large watershed be divided into smaller subareas and each subarea should have a shape factor not to exceed a limit, K. For instance, the CUHP suggests K=4 (UDFCD 2005); otherwise CUHP would overesti- mate the peak runoff because the subarea is too wide in shape. Aided by Eqs. (5) and (6), Eqs. (3) and (4) can be combined to cancel X,,/L as Eq. (3) implies that the watershed shape must be preserved along the waterways between these two systems. Watershed shape fac- tor is an index that represents how the overland flows are col- lected in a watershed. It was suggested that the watershed length- to-width ratio, circularity ratio, and elongation ratio can be employed to represent the watershed shape (McCuen 1998). Re- ferring to Fig. 1, the shape factors for the real watershed and virtual KW model are defined as
Fig. 3. Watershed shape factor versus KW shape factor Most of the watersheds are asymmetric, depending on the align- ment of the collector channel. The centerline and the boundary of the watershed set the limits of channel alignment. Therefore, Eqs.
Fig. 3. Watershed shape factor versus KW shape factor Most of the watersheds are asymmetric, depending on the align- ment of the collector channel. The centerline and the boundary of the watershed set the limits of channel alignment. Therefore, Eqs.
Fig. 2. Kinematic wave model for square watershed
Fig. 2. Kinematic wave model for square watershed
With K=4, Eq. (17) suggests that the KW factor is determined as
With K=4, Eq. (17) suggests that the KW factor is determined as
Table 2. Widths and Slopes for Equivalent KW Planes Although these five cases shown in Fig. 4 appear similar, none of their KW shape factors is duplicated. As expected, only Case 2 has L,,/L=2.0. The rest have L,,/L<2.0. It is confirmed that the special case of symmetric square cannot be generalized for other shapes. This test reveals that Eq. (17) is adequately sensitive to the difference in watershed shape, X, and can produce the various KW shape factors accordingly. These five hypothetical catch- ments share the same tributary area and vertical fall. The shape factor is the only difference among them. Therefore, they are a system of equivalent KW planes that shall produce similar, but not identical, runoff hydrographs for a given rainfall condition. In this study, EPA SWMMS was employed to produce the hydro- graphs under a 3-h uniform rainfall at 120 mm/h. As shown in Fig. 5, these five hydrographs produce the peak flow at 0.83 cubic
Table 2. Widths and Slopes for Equivalent KW Planes Although these five cases shown in Fig. 4 appear similar, none of their KW shape factors is duplicated. As expected, only Case 2 has L,,/L=2.0. The rest have L,,/L<2.0. It is confirmed that the special case of symmetric square cannot be generalized for other shapes. This test reveals that Eq. (17) is adequately sensitive to the difference in watershed shape, X, and can produce the various KW shape factors accordingly. These five hypothetical catch- ments share the same tributary area and vertical fall. The shape factor is the only difference among them. Therefore, they are a system of equivalent KW planes that shall produce similar, but not identical, runoff hydrographs for a given rainfall condition. In this study, EPA SWMMS was employed to produce the hydro- graphs under a 3-h uniform rainfall at 120 mm/h. As shown in Fig. 5, these five hydrographs produce the peak flow at 0.83 cubic
Note: cms=cubic meter per second. Table 3. Shape Factors Used in CUHP and SWMMS5
Note: cms=cubic meter per second. Table 3. Shape Factors Used in CUHP and SWMMS5
Fig. 6. Comparison of prediced peak flows between CUHP and SWMM5
Fig. 6. Comparison of prediced peak flows between CUHP and SWMM5
Fig. 5. Hydrographs from watersheds with various locations of cen- tral channel
Fig. 5. Hydrographs from watersheds with various locations of cen- tral channel
The next test is the sensitivity of KW shape factor to the level of modeling detail and discretization. Using a | ha illustrated in Fig.
The next test is the sensitivity of KW shape factor to the level of modeling detail and discretization. Using a | ha illustrated in Fig.
Note: Sp=2%. Table 5. Input Parameters for Lumped and Distributed Watershed Models
Note: Sp=2%. Table 5. Input Parameters for Lumped and Distributed Watershed Models
Note: Sy)=2%; and cms=cubic meter per second. Table 4. Conversion of Natural Watershed Geometry into KW Plane
Note: Sy)=2%; and cms=cubic meter per second. Table 4. Conversion of Natural Watershed Geometry into KW Plane
Fig. 8. Lumped and distributed watershed models
Fig. 8. Lumped and distributed watershed models
Fig. 11. Hydrographs predicted by lumped and discrete watershed models
Fig. 11. Hydrographs predicted by lumped and discrete watershed models
Fig. 9. Hydrographs predicted by lumped and distributed watershed models
Fig. 9. Hydrographs predicted by lumped and distributed watershed models
Related topics:
HydrologyStormwater management
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved