scholarly journals A measure of watershed nonlinearity: interpreting a variable instantaneous unit hydrograph model on two vastly different sized watersheds

2011 ◽  
Vol 15 (1) ◽  
pp. 405-423 ◽  
Author(s):  
J. Y. Ding
Keyword(s):  
Shape Factor ◽  
Overland Flow ◽  
Scale Parameter ◽  
Computational Time ◽  
Convolution Integral ◽  
Unit Hydrograph ◽  
Time Step ◽  
N Value ◽  
Instantaneous Unit Hydrograph ◽  
The Impact

Abstract. The linear unit hydrograph used in hydrologic design analysis and flood forecasting is known as the transfer function and the kernel function in time series analysis and systems theory, respectively. This paper reviews the use of an input-dependent or variable kernel in a linear convolution integral as a quasi-nonlinear approach to unify nonlinear overland flow, channel routing and catchment runoff processes. The conceptual model of a variable instantaneous unit hydrograph (IUH) is characterized by a nonlinear storage-discharge relation, q = cNsN, where the storage exponent N is an index or degree of watershed nonlinearity, and the scale parameter c is a discharge coefficient. When the causative rainfall excess intensity of a unit hydrograph is known, parameters N and c can be determined directly from its shape factor, which is the product of the unit peak ordinate and the time to peak, an application of the statistical method of moments in its simplest form. The 2-parameter variable IUH model is calibrated by the shape factor method and verified by convolution integral using both the direct and inverse Bakhmeteff varied-flow functions on two watersheds of vastly different sizes, each having a family of four or five unit hydrographs as reported by the well-known Minshall (1960) paper and the seldom-quoted Childs (1958) one, both located in the US. For an 11-hectare catchment near Edwardsville in southern Illinois, calibration for four moderate storms shows an average N value of 1.79, which is 7% higher than the theoretical value of 1.67 by Manning friction law, while the heaviest storm, which is three to six times larger than the next two events in terms of the peak discharge and runoff volume, follows the Chezy law of 1.5. At the other end of scale, for the Naugatuck River at Thomaston in Connecticut having a drainage area of 186.2 km2, the average calibrated N value of 2.28 varies from 1.92 for a minor flood to 2.68 for a hurricane-induced flood, all of which lie between the theoretical value of 1.67 for turbulent overland flow and that of 3.0 for laminar overland flow. Based on analytical results from the small Edwardsville catchment, the 2-parameter variable IUH model is found to be defined by a quadruplet of parameters N, c, the storm duration or computational time step Δt, and the rainfall excess intensity i(0), and that it may be reduced to an 1-parameter one by defaulting the degree of nonlinearity N to 1.67 by Manning friction. For short, intense storms, the essence of the Childs – Minshall nonlinear unit hydrograph phenomenon is encapsulated in a peak flow equation having a single (scale) parameter c, and in which the impact of the rainfall excess intensity increases from the linear assumption by a power of 0.4. To illustrate key steps in generating the direct runoff hydrograph by convolution integral, short examples are given.

scholarly journals A measure of watershed nonlinearity: interpreting a variable instantaneous unit hydrograph model on two vastly different sized – watersheds

2005 ◽  
Vol 2 (5) ◽  
pp. 2111-2151
Author(s):  
J. Y. Ding
Keyword(s):  
Shape Factor ◽  
Overland Flow ◽  
Convolution Integral ◽  
Unit Hydrograph ◽  
N Value ◽  
Time To Peak ◽  
The Us ◽  
Instantaneous Unit Hydrograph ◽  
Unit Hydrographs ◽  
A Minor

Abstract. This paper reviews the use of an input-dependent kernel in a linear convolution integral as a quasi-nonlinear approach to unify nonlinear overland flow, channel routing and catchment runoff processes. The conceptual model of a variable kernel or instantaneous unit hydrograph (IUH) is characterized by a nonlinear storage-discharge relation, q=cNsN where the storage exponent N is an index or degree of watershed nonlinearity. When the causative rainfall excess intensity of a unit hydrograph is known, parameters N and c can be determined directly from its shape factor, the product of the unit peak ordinate and the time to peak. The model is calibrated by the shape factor and verified by convolution integral on two watersheds of vastly different sizes, each having a family of four or five unit hydrographs, data of which were published by Childs in 1958 for the Naugatuck River and by Minshall in 1960 for the Edwardsville catchment. For an 11-hectare catchment near Edwardsville in southern Illinois, the US, four moderate storms show an average N value of 1.79, which is 7% higher than the theoretical value of 1.67 by Manning friction law, while the heaviest storm, which is three to six times larger than the next two events in terms of the peak discharge and runoff volume, follows the Chezy law of 1.5. At the other end of scale, for the Naugatuck River at Thomaston in Connecticut, the US, having a drainage area of 186.2 km2, the average N value of 2.28 varies from 1.92 for a minor flood to 2.68 for a hurricane-induced flood, all of which lie between the theoretical value of 1.67 for turbulent overland flow and that of 3.0 for laminar overland flow. Short examples and a spreadsheet template are given to illustrate key steps in generating the direct runoff hydrograph by convolution integral with the 2-parameter variable IUH model.

scholarly journals Spatial Patterns in Baseflow Mean Response Time across a Watershed in the Loess Plateau: Linkage with Land-Use Types

2020 ◽  
Vol 66 (3) ◽  
pp. 382-391 ◽  
Author(s):  
Xu-dong Huang ◽  
Dong Wang ◽  
Pei-pei Han ◽  
Wen-chuan Wang ◽  
Qing-jie Li ◽  
...  
Keyword(s):  
Land Use ◽  
Response Time ◽  
Overland Flow ◽  
Agricultural Land ◽  
Least Squares Regression ◽  
Unit Hydrograph ◽  
Mean Response Time ◽  
Impervious Area ◽  
Land Use Types ◽  
Instantaneous Unit Hydrograph

Abstract Understanding the relation between land-use types and baseflow mean response time (BMRT) is important to explore the response mechanism of baseflow processes in watersheds. BMRT was determined using an instantaneous unit hydrograph. The instantaneous unit hydrograph parameters were estimated by autocorrelation functions. The relative importance of land-use types in determining BMRT dynamics was assessed by hydrological model and partial least-squares regression. Our study suggests greater effects of urban area on BMRT than the effects of forest and agricultural land. This may be because the urban interception impervious area may impede baseflow generation over a short timescale. The effects of agricultural land are greater than those of forest in areas with steeper hillslopes, but lower than those of the forest in areas with more plains, reflecting the varied ability of forest and agricultural lands with different topography to hinder overland flow. Variations of BMRT are strongly linked to land use in the watershed. Overall, our study provides insight into the BMRT and dominant factors of land-use types in watersheds, planning of sustainable water resource use, and ecological protection in watersheds.

scholarly journals Improvement of anisotropic porosity models with a merging technique

2018 ◽  
Vol 40 ◽  
pp. 06023
Author(s):  
Martin Bruwier ◽  
Pierre Archambeau ◽  
Sébastien Erpicum ◽  
Michel Pirotton ◽  
Benjamin Dewals
Keyword(s):  
Shallow Water ◽  
Flow Characteristics ◽  
Threshold Value ◽  
Computational Grid ◽  
Computational Time ◽  
Time Step ◽  
Shallow Water Models ◽  
The Cost ◽  
The Impact ◽  
Porosity Model

Anisotropic porosity shallow-water models are used to take into account detailed topographic information through porosity parameters multiplying the various terms of the shallow-water equations. A storage porosity is assigned to each cell to reflect the void fraction in the cell and a conveyance porosity is used at each edge to reproduce the impact of subgrid obstacles on the flux terms. To guaranty the numerical stability, the time step depends on the value of the porosity parameters. This may hamper severely the computational efficiency in the presence of cells with low values of storage porosity. Cartesian grids are particularly sensitive to such a case since the meshing stems directly from the choice of the grid size. In this paper, this problem is addressed by using an original merging technique consisting in merging cells with a storage porosity lower than a threshold value with neighbouring cells. The model was tested for modelling a prismatic channel with different orientations between the Cartesian computational grid and the channel direction. The results show that the standard anisotropic porosity model (without merging) improves the reproduction of the flow characteristics; but at the cost of a significantly higher computational time. In contrast, the computational time is drastically reduced and the accuracy preserved when the merging technique is used with the porosity model.

scholarly journals Analysis of Numerical Methods to Include Dynamic Constraints in an Optimal Power Flow Model

Energies ◽  
2019 ◽  
Vol 12 (5) ◽  
pp. 885
Author(s):  
Francisco Arredondo ◽  
Edgardo Castronuovo ◽  
Pablo Ledesma ◽  
Zbigniew Leonowicz
Keyword(s):  
Power Flow ◽  
Optimal Power Flow ◽  
Transient Stability ◽  
Computational Time ◽  
Integration Time ◽  
Time Step ◽  
Dynamic Constraints ◽  
Electromechanical Oscillations ◽  
Optimal Power ◽  
The Impact

The optimization of the operation of power systems including steady state and dynamic constraints is efficiently solved by Transient Stability Constrained Optimal Power Flow (TSCOPF) models. TSCOPF studies extend well-known optimal power flow models by introducing the electromechanical oscillations of synchronous machines. One of the main approaches in TSCOPF studies includes the discretized differential equations that represent the dynamics of the system in the optimization model. This paper analyzes the impact of different implicit and explicit numerical integration methods on the solution of a TSCOPF model and the effect of the integration time step. In particular, it studies the effect on the power dispatch, the total cost of generation, the accuracy of the calculation of electromechanical oscillations between machines, the size of the optimization problem and the computational time.

Comparison of the ecohydrological models AnnAGNPS and ZIN-AgriTra for a small agricultural catchment 

2021 ◽  
Author(s):  
Johanna Schwenkel ◽  
Stephanie Zeunert ◽  
Huyen Le ◽  
Hannes Müller-Thomy ◽  
Matthias Schöniger ◽  
...  
Keyword(s):  
Mass Balance ◽  
Plant Protection ◽  
Richards Equation ◽  
Computational Time ◽  
Lower Saxony ◽  
Time Step ◽  
Small Stream ◽  
Physically Based ◽  
The Impact ◽  
Precipitation Events

<p>The ecohydrological models AnnAGNPS and ZIN-AgriTra are compared regarding their performance in a small watershed. Both models are presently applied for the transport simulation of plant protection products (PPP) from an agricultural area to a small stream to quantify the impact of reduction measures as part of a comprehensive study.</p><p>The spatial discretization of AnnAGNPS is based on hydrologic response units with homogeneous characteristics (land use, slope and soil type). For the continuous simulations daily time steps are used, only soil moisture is simulated using hourly time steps. The underlying equations are physically based, mostly simple calculation methods are used.<br>ZIN-AgriTra operates on grid cells, which allows a more accurate representation of the flow paths. The model is physically based, e. g. for the unsaturated soil zone the Richards equation is used. This requires detailed soil properties for its parameterization and leads to small computational time steps (minutes to hours) to fulfil the mass balance requirements. The detailed spatial and temporal scales, as well as the complex equations, result in a long computation time in comparison to AnnAGNPS.   <br>AnnAGNPS and ZIN-AgriTra are compared regarding their accuracy in the water balance and the mass balance simulation. For the mass balance different constituents as e. g. sediment, phosphorus and selected pesticides are simulated.</p><p>The study area is located in southern Lower Saxony, Germany. The catchment area has a size of 5 km<sup>2</sup>. The investigated stream (Lahbach) flows along agriculturally cultivated land. The relatively high slopes and the fine soil texture lead to a high fraction of generated discharge (as surface runoff, erosion and rapid interflow) from precipitation events. In the ongoing study the catchment was intensively monitored regarding meteorological and hydrological data. In addition, an event-based monitoring campaign was performed to quantify the reaction of the Lahbach during precipitation events, particularly the change in constituent concentrations. Due to the close cooperation with a local farmer, management measures are known very precisely.</p><p>The different temporal resolution of the input data and the time step of output parameters lead to differences in the agreement between measured and simulated time series among the two models. Overall, ZIN-AgriTra led to a more accurate reproduction of the rainfall-runoff events.</p>

Assessment of Unsteadiness Modeling for Transient Natural Convection

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
M. Fadl ◽  
L. He ◽  
P. Stein ◽  
G. Marinescu
Keyword(s):  
Natural Convection ◽  
Numerical Stability ◽  
Thermal Design ◽  
Computational Time ◽  
Time Step ◽  
Loosely Coupled ◽  
Accuracy Requirement ◽  
Transient Natural Convection ◽  
Renewable Power ◽  
The Impact

Turbine flexible operations with faster startups/shutdowns are required to accommodate emerging renewable power generations. A major challenge in transient thermal design and analysis is the time scale disparity. For natural cooling, the physical process is typically in hours, but on the other hand, the time-step sizes typically usable tend to be very small (subseconds) due to the numerical stability requirement for natural convection as often observed. An issue of interest is: What time-step sizes can and should be used in terms of stability as well as accuracy? In this work, the impact of flow temporal gradient and its modeling is examined in relation to numerical stability and modeling accuracy for transient natural convection. A source term-based dual-timing formulation is adopted, which is shown to be numerically stable for very large time-steps. Furthermore, a loosely coupled procedure is developed to combine this enhanced flow solver with a solid conduction solver for solving unsteady conjugate heat transfer (CHT) problems for transient natural convection. This allows very large computational time-steps to be used without any stability issues, and thus enables to assess the impact of using different time-step sizes entirely in terms of a temporal accuracy requirement. Computational case studies demonstrate that the present method can be run stably with a markedly shortened computational time compared to the baseline solver. The method is also shown to be more accurate than the commonly adopted quasi-steady flow model when unsteady effects are non-negligible.

scholarly journals Assessment of Unsteadiness Modelling for Transient Natural Convection

2017 ◽  
Author(s):  
M. Fadl ◽  
L. He ◽  
P. Stein ◽  
G. Marinescu
Keyword(s):  
Natural Convection ◽  
Numerical Stability ◽  
Thermal Design ◽  
Computational Time ◽  
Steam Turbines ◽  
Time Step ◽  
Loosely Coupled ◽  
Accuracy Requirement ◽  
Renewable Power ◽  
The Impact

Flexible operations of steam turbines with faster startups and shutdowns are required to accommodate emerging renewable power generations, needing more advanced prediction tools for transient thermal design and analysis. A major challenge is the time scale disparity. For a natural cooling, the physical process is typically in hours or tens of hours, but on the other hand, the time step sizes typically usable tend to be very small (in seconds or sub-seconds) due to the numerical stability requirement for natural convection as often observed. A general issue to be addressed is what time step sizes can be and should be used in terms of stability as well as accuracy. In the present work, the impact of the temporal gradient in unsteady flow and its modelling is examined in relation to numerical stability and modelling accuracy for natural convectio n. A source term based dual timing for mulation is adopted and implemented in a commercial code, which is shown to be numerically stable for very large time steps for natural convection analysis. Furthermore, a loosely coupled partitioned procedure is developed to combine this enhanced flow solver together with a solid conduction solver for solving transient conjugate heat transfer problems for natural convection. This allows very large computational time steps to be used without any stability issues, and thus enables to assess the impact of using different time step sizes entirely in terms of the temporal accuracy requirement. Computational case studies demonstrate that the present method is more stable at a markedly shortened computational time than the baseline solver. The method is also shown to be more accurate than the commonly adopted quasi-steady methods when unsteady effects are non-negligible.

Development of a Simulation System for Estimating the Impact Force of Tsunami Drift Using the Explicit MPS Method

2021 ◽  
Author(s):  
Yasuhiro Aida ◽  
Tomoki Ikoma ◽  
Koichi Masuda
Keyword(s):  
Large Scale ◽  
Impact Force ◽  
Particle Method ◽  
Simulation System ◽  
Computational Time ◽  
Water Tank ◽  
Time Step ◽  
Mps Method ◽  
Fluid Particles ◽  
The Impact

Abstract When a large-scale tsunami occurs, structures in the coastal area will be destroyed by the impact of tsunami drifts. In the design of tsunami evacuation facilities and petroleum complexes, it is necessary to estimate the impact force of tsunami drift, which varies in size, shape and mass. Although some design equations have been proposed to estimate the impact force of tsunami drift, the impact force varies depending on various conditions such as the draft of the tsunami drifts, the attitude of the collision, the condition of the surrounding flow field, and the rigidity of the structure, etc. No reasonable design equation has been developed yet to meet all these conditions. Therefore, it is necessary to estimate the impact force of tsunami drift by water tank experiments and numerical simulations. In order to simulate the impact of a tsunami drift on a structure by numerical simulation, it is necessary to solve the coupling of fluid, floating object and structure. In this study, we have developed a simulation system that can simulate the impact force of a tsunami drift with the MPS method, which is a kind of particle method. This simulation system introduces an explicit method for pressure calculation, which allows for relatively large scale numerical calculations. In addition, the system is able to reproduce the deformation of structures as an elastic body due to the impact of tsunami drift. In particular, we have introduced an analytical method that allows us to set the computational time step that satisfy the CFL conditions for elastic and fluid particles, respectively, for stable simulation even when there is a large difference between the velocity of fluid particles and the velocity of structural particles caused by elastic waves. As a result of the comparison of the impact force on the cantilevered beam of the tsunami drift with the simulation and the water tank test, the deformation of the structure at the time of impact was reproduced with more than 90% accuracy.

Geomorphological Approach to the Skewed Shape of Instantaneous Unit Hydrograph

2015 ◽  
Vol 48 (2) ◽  
pp. 91-103
Author(s):  
Joo-Cheol Kim ◽  
◽  
Kwansue Jung ◽  
Dong Kug Jeong
Keyword(s):  
Unit Hydrograph ◽  
Instantaneous Unit Hydrograph
Sign in / Sign up

Export Citation Format

Share Document