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# Developing Block Kinematic Wave Model for Direct Runoff Hydrograph Estimate

Date Issued

2011

Date

2011

Author(s)

Hu, Shiou-Hua

Abstract

Open channel hydraulics show that the main factor determining discharge of a long channel is the water depth (or storage) near the channel exit, not the rainfall intensity on the river, not the upstream inflow. The later two factors affect discharge by increasing or decreasing storage. However, unit hydrograph (UH) and other traditional black-box rainfall-runoff models assume direct runoff respond linearly to excess rainfall intensity. The effect of storage within the watershed is not considered in UH, and the linear assumption does not really valid in a watershed. Estimation error maybe large if rainfall intensity varies significantly within a catchment’s time of concentration (which is a function of rainfall intensity too), or when the average rainfall intensity used to create UH is very different from that using UH to estimate runoff hydrograph.

In recent years, Digital Elevation Model and GIS make possible to construct a watershed’s runoff flow path network. Apply Kinematic Wave (KW) model to compute the flow speed on the flow paths, runoff hydrograph can be calculated without using linear assumption. The KW model computation is time-consuming. When KW is applied to flood forecast, the state variables of each link must be saved at the end of one forecast and retrieved at the beginning of next. Numerical problems may occur applying the essentially steady-state KW model to rapidly varying hyetograph. The numerical problem is more serious at the upstream flow paths where the channel storages are less.

We propose a rainfall-runoff model called Block Kinematic Wave (BKW). It does not apply the linear assumption, and it does not have the numerical problem of KW. It’s algorithm follows. First, apply the ArcInfo geographic information system and HEC GeoHMS tool module to construct the 40-meter resolution flow paths and river network. Then, compute the Topographic Index (TI) of each flow path. Thirdly, utilize TI to parameterize the cross-section and Manning’s n of each flow path. Fourth, assume different excess rainfall intensity and compute the travel time (TT) of all pixels to watershed exit for all intensities. Fifth, divide the catchment into several equal area blocks, handle the pixels go across block boundaries at different rainfall intensities. Sixth, calculate the storage on each flow path and total the flow path storage, S, of a block given an effective rainfall intensity. Also, compute the total discharge at all block boundaries, Q. Construct the storage – discharge relationship for each block using all different steady-state excess rainfall intensity results. Seventh, compute the direct runoff from each block using reservoir routing. That is using continuity equation and S-Q relationship. By doing so, the discharge from a block is mainly determined by its storage. Here, excess rainfall intensity is only one of the inputs to the block storage.

The BKW model uses steady state rainfall intensities to construct the S-Q relationship for each block. No linear assumption is involved. The BKW model does not suffer the numerical problem of KW given non-constant hyetograph because it uses KW for steady-state computation only. The BKW model for direct runoff is computationally very efficient, because most of the calculations are pr-processed and carried out offline. There are only a few reservoir routing computations to be executed online. With these three nice properties, BKW model is especially suitable to calculate direct runoff hydrograph within Taiwan''s flash flood forecast system.

Observing Systerm Experiments are designed to compare the performances of BKW. A Muskingum-Cunge based flow-path computation model is assumed to produce the “true direct runoff hydrograph” from a watershed. BKW model is then validated with some other “the true direct runoff hydrographs”. Computation time of BKW and the “True” model are also compared.

In recent years, Digital Elevation Model and GIS make possible to construct a watershed’s runoff flow path network. Apply Kinematic Wave (KW) model to compute the flow speed on the flow paths, runoff hydrograph can be calculated without using linear assumption. The KW model computation is time-consuming. When KW is applied to flood forecast, the state variables of each link must be saved at the end of one forecast and retrieved at the beginning of next. Numerical problems may occur applying the essentially steady-state KW model to rapidly varying hyetograph. The numerical problem is more serious at the upstream flow paths where the channel storages are less.

We propose a rainfall-runoff model called Block Kinematic Wave (BKW). It does not apply the linear assumption, and it does not have the numerical problem of KW. It’s algorithm follows. First, apply the ArcInfo geographic information system and HEC GeoHMS tool module to construct the 40-meter resolution flow paths and river network. Then, compute the Topographic Index (TI) of each flow path. Thirdly, utilize TI to parameterize the cross-section and Manning’s n of each flow path. Fourth, assume different excess rainfall intensity and compute the travel time (TT) of all pixels to watershed exit for all intensities. Fifth, divide the catchment into several equal area blocks, handle the pixels go across block boundaries at different rainfall intensities. Sixth, calculate the storage on each flow path and total the flow path storage, S, of a block given an effective rainfall intensity. Also, compute the total discharge at all block boundaries, Q. Construct the storage – discharge relationship for each block using all different steady-state excess rainfall intensity results. Seventh, compute the direct runoff from each block using reservoir routing. That is using continuity equation and S-Q relationship. By doing so, the discharge from a block is mainly determined by its storage. Here, excess rainfall intensity is only one of the inputs to the block storage.

The BKW model uses steady state rainfall intensities to construct the S-Q relationship for each block. No linear assumption is involved. The BKW model does not suffer the numerical problem of KW given non-constant hyetograph because it uses KW for steady-state computation only. The BKW model for direct runoff is computationally very efficient, because most of the calculations are pr-processed and carried out offline. There are only a few reservoir routing computations to be executed online. With these three nice properties, BKW model is especially suitable to calculate direct runoff hydrograph within Taiwan''s flash flood forecast system.

Observing Systerm Experiments are designed to compare the performances of BKW. A Muskingum-Cunge based flow-path computation model is assumed to produce the “true direct runoff hydrograph” from a watershed. BKW model is then validated with some other “the true direct runoff hydrographs”. Computation time of BKW and the “True” model are also compared.

Subjects

Block-Kinematic-Wave

kinematic wave

Geo-morphology

unit hydrograph

direct runoff

topographic index

Type

thesis

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