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Dissertations / Theses on the topic 'Urban hydrology Mathematical models'

Author: Grafiati

Published: 10 December 2022

Last updated: 31 July 2025

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1

Fahy, Benjamin. "Evaluating the Impact and Distribution of Stormwater Green Infrastructure on Watershed Outflow." PDXScholar, 2019. https://pdxscholar.library.pdx.edu/open_access_etds/4732.

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Green Stormwater Infrastructure (GSI) has become a popular method for flood mitigation as it can prevent runoff from entering streams during heavy precipitation. In this study, a recently developed neighborhood in Gresham, Oregon hosts a comparison of various GSI projects on runoff dynamics. The study site includes dispersed GSI (rain gardens, retention chambers, green streets) and centralized GSI (bioswales, detention ponds, detention pipes). For the 2017-2018 water year, hourly rainfall and observed discharge data is used to calibrate the EPA's Stormwater Management Model to simulate rainfal

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2

Psaris, Alexander Michael. "Assessing Hydrologic and Water Quality Sensitivities to Precipitation Changes, Urban Growth and Land Management Using SWAT." PDXScholar, 2014. https://pdxscholar.library.pdx.edu/open_access_etds/1783.

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Precipitation changes and urban growth are two factors altering the state of water quality. Changes in precipitation will alter the amount and timing of flows, and the corresponding sediment and nutrient dynamics. Meanwhile, densification associated with urban growth will create more impervious surfaces which will alter sediment and nutrient loadings. Land and water managers often rely on models to develop possible future scenarios and devise management responses to these projected changes. We use the Soil and Water Assessment Tool (SWAT) to assess the sensitivities of stream flow, sediment, a

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3

Washburne, James Clarke. "A distributed surface temperature and energy balance model of a semi-arid watershed." Diss., The University of Arizona, 1994. http://hdl.handle.net/10150/186800.

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A simple model of surface and sub-surface soil temperature was developed at the watershed scale (-100 km²) in a semi-arid rangeland environment. The model consisted of a linear combination of air temperature and net radiation and assumed: (1) topography controls the spatial distribution of net radiation, (2) near-surface air temperature and incoming solar radiation are relatively homogeneous at the watershed scale and are available from ground stations and (3) soil moisture dominates transient soil thermal property variability. Multiplicative constants were defined to account for clear sky dif

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4

Mahanama, Sarith Prasad Panditha. "Distributed approach of coupling basin scale hydrology with atmospheric processes." Thesis, Hong Kong : University of Hong Kong, 2000. http://sunzi.lib.hku.hk/hkuto/record.jsp?B22088817.

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5

Goodrich, David Charles. "Basin Scale and Runoff Model Complexity." Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1990. http://hdl.handle.net/10150/614028.

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Distributed Rainfall-Runoff models are gaining widespread acceptance; yet, a fundamental issue that must be addressed by all users of these models is definition of an acceptable level of watershed discretization (geometric model complexity). The level of geometric model complexity is a function of basin and climatic scales as well as the availability of input and verification data. Equilibrium discharge storage is employed to develop a quantitative methodology to define a level of geometric model complexity commensurate with a specified level of model performance. Equilibrium storage ra

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6

Bailey, Mark A(Mark Alexander) 1970. "Improved techniques for the treatment of uncertainty in physically-based models of catchment water balance." Monash University, Dept. of Civil Engineering, 2001. http://arrow.monash.edu.au/hdl/1959.1/8271.

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7

Oliver, Marcel 1963. "Mathematical investigation of models of shallow water with a varying bottom." Diss., The University of Arizona, 1996. http://hdl.handle.net/10150/191198.

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This dissertation is a mathematical investigation of the so-called lake and the great lake equations, which are shallow water equations that describe the long-time motion of an inviscid, incompressible fluid contained in a shallow basin with a slowly spatially varying bottom, a free upper surface and vertical side walls, under the influence of gravity and in the limit of small characteristic velocities and very small surface amplitude. It is shown that these equations are globally well-posed, i.e. that they possess unique global weak solutions that depend continuously on the initial data and o

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8

Javaheri, Hamed. "Automatic calibration of urban run-off models using global optimization techniques." Thesis, McGill University, 1998. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=21305.

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Conceptual urban runoff (CUR) models are commonly used in the Planning and design of urban drainage systems. These models often require a large number of variables and parameters in order to accurately describe, the complex relationships between rainfall, runoff and watershed characteristics. This requirement has often become a barrier to the use of such models, because of the difficulties involved in the estimation of these parameters. Hence, there is a great need to develop a robust and reliable automatic calibration procedure to assist in the identification of the best set of optimal parame

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9

夏激揚 and Jiyang Xia. "Numerical study on wind field and air pollutant dispersion in urban street canopies." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31242509.

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10

Wong, Ching-chi, and 黃精治. "Flow and pollutant dispersion over idealized urban street canyons using large-eddy simulation." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hdl.handle.net/10722/206698.

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Flows and pollutant dispersion over flat rural terrain have been investigated for decades. However, our understanding of their behaviours over urban areas is rather limited. Most cases have either focused on street level or in the roughness sub-layer (RSL) of urban boundary layer (UBL). Whereas, only a handful of studies have looked into the coupling between street-level and UBL-core dynamics, and their effects on pollutant dispersion. In this thesis, computational fluid dynamics (CFD) is employed to examine the flows and pollutant transport in and over urban roughness. Idealised two-dimens

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11

El, Didy Sherif Mohamed Ahmed 1951. "Two-dimensional finite element programs for water flow and water quality in multi-aquifer systems." Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/191110.

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Multiple aquifer systems similar to those that exist at coal gasification sites are complicated groundwater situations. In these types of systems, the aquifers are separated by aquitards through which interaction between aquifers can occur. The movement of the products of combustion into the coal seam and adjacent aquifers is a serious problem of interest. This dissertation presents two-dimensional finite element models for water flow and water quality in multiple aquifer systems. These models can be applied for general problems as well as the problems associated with the burned cavities in co

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12

Ropp, David L. "Numerical study of shallow water models with variable topography." Diss., The University of Arizona, 2000. http://etd.library.arizona.edu/etd/GetFileServlet?file=file:///data1/pdf/etd/azu_e9791_2000_165_sip1_w.pdf&type=application/pdf.

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13

Shi, Wen, and 石雯. "Dynamic simulation and quantitative analysis of urban taxi services." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B45528767.

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14

Henry, Eric James. "Contaminant induced flow effects in variably-saturated porous media." Diss., The University of Arizona, 2001. http://hdl.handle.net/10150/191256.

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Dissolved organic contaminants that decrease the surface tension of water (surfactants) can have an effect on unsaturated flow through porous media due to the dependence of capillary pressure on surface tension. One and two-dimensional (1D, 2D) laboratory experiments and numerical simulations were conducted to study surfactant-induced unsaturated flow. The 1D experiments investigated differences in surfactant-induced flow as a function of contaminant mobility. The flow in a system contaminated with a high solubility, mobile surfactant, butanol, was much different than in a system contaminated

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15

Leung, Ka-kit Pieta, and 梁家杰. "On the study of ventilation and pollutant removal over idealized two-dimensional urban street canyons." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2012. http://hub.hku.hk/bib/B48521863.

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In the last century, there has been a rapid growth and development in economy and modern technology around the world. This phenomenon helped improving wealth and living standard but also brought pollutions to the society and the environment. Among various kinds of pollution, air pollution takes a larger proportion. Therefore, there is increasing concern about the ventilation and pollution removal behavior in the urban environment. Among different academic studies performed, the use of computational fluid dynamics (CFD) had become more popular. Since wind tunnel experiments serve as validat

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16

Namde, Noubassem Nanas 1955. "Simulation of micro catchment water harvesting systems." Diss., The University of Arizona, 1987. http://hdl.handle.net/10150/191121.

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A mathematical model for personal computers was prepared as a planning tool for development of micro catchment water harvesting systems. It computes runoff from natural or treated catchments, using estimated or actual parameters. The model also computes the water balance of the soil zone in the cultivated area and the water balance of the reservoir system which serves it. The model was calibrated with hydrolologic data and site characteristics for a location near Tucson, Arizona. Its prediction of cotton and grain sorghum yields was comparable to that of Morin (1977). An attempt was made to us

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17

Tang, Philip Kwok Fan. "Stochastic Hydrologic Modeling in Real Time Using a Deterministic Model (Streamflow Synthesis and Reservoir Regulation Model), Time Series Model, and Kalman Filter." PDXScholar, 1991. https://pdxscholar.library.pdx.edu/open_access_etds/4580.

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The basic concepts of hydrologic forecasting using the Streamflow Synthesis And Reservoir Regulation Model of the U.S. Army Corps of Engineers, auto-regressive-moving-average time series models (including Greens' functions, inverse functions, auto covariance Functions, and model estimation algorithm), and the Kalman filter (including state space modeling, system uncertainty, and filter algorithm), were explored. A computational experiment was conducted in which the Kalman filter was applied to update Mehama local basin model (Mehama is a 227 sq. miles watershed located on the North Santiam Riv

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18

Lee, Haksu. "Development and performance analysis of a physically based hydrological model incorporating the effects of subgrid heterogeneity." University of Western Australia. School of Environmental Systems Engineering, 2007. http://theses.library.uwa.edu.au/adt-WU2007.0129.

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[Truncated abstract] The balance equations of mass and momentum, defined at the scale of what has been defined as a Representative Elementary Watershed (REW) has been proposed by Reggiani et al. (1998, 1999). While it has been acknowledged that the REW approach and the associated balance equations can be the basis for the development of a new generation of distributed physically based hydrological models, four building blocks have been identified as necessary to transform the REW approach into, at the very least least, a workable modelling framework beyond the theoretical achievements. These a

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19

黃家耀 and Ka-io Wong. "A network equilibrium approach for modeling urban taxi services." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2002. http://hub.hku.hk/bib/B31243769.

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20

Cheng, Wai-chi, and 鄭偉智. "Wind and pollutant removal of urban street canyons under different thermal stratification by RANS and LES models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B46289653.

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21

Tecle, Aregai 1948. "Choice of multicriterion decision making techniques for watershed management." Diss., The University of Arizona, 1988. http://hdl.handle.net/10150/191145.

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The problem of selecting a multicriterion decision making (MCDM) technique for watershed resources management is investigated. Of explicit concern in this research is the matching of a watersned resources management problem with an appropriate MCDM technique. More than seventy techniques are recognized while reviewing the area of MCDM. A new classification scheme is developed to categorize these techniques into four groups on the bases of each algorithm's structural formulation and the possible results obtained by using the algorithm. Other standard classification schemes are also discussed to

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22

Li, Xianxiang, and 李顯祥. "Large-eddy simulation of wind flow and air pollutant transport inside urban street canyons of different aspect ratios." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B40687326.

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23

Luckemeier, Richard Ewald 1948. "A rainfall-runoff model for an urban watershed in Tucson, Arizona." Thesis, The University of Arizona, 1989. http://hdl.handle.net/10150/277165.

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The U.S. Geological Survey and the City of Tucson, Arizona, have been collecting rainfall and runoff data on several watersheds in the Tucson area for several years. Among the purposes of this project is to use the data to test rainfall-runoff models in an effort to find one to successfully simulate flood flows in Tucson. One such model, the Distributed Routing Rainfall-Runoff Model (DR3M), was tested using data collected on Rob Wash in Tucson. It was found DR3M performs about as well as it does in other parts of the United States, although it tends to underestimate flood flows for large storm

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24

Du, Jun 1962. "Short-range ensemble forecasting of an explosive cyclogenesis with a limited area model." Diss., The University of Arizona, 1996. http://hdl.handle.net/10150/191197.

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Since the atmosphere is a chaotic system, small errors in the initial condition of any numerical weather prediction (NWP) model amplify as the forecast evolves. To estimate and possibly reduce the uncertainty of NWP associated with initial-condition uncertainty (ICU), ensemble forecasting has been proposed which is a method of, differently from the traditional deterministic forecasting, running several model forecasts starting from slightly different initial states. In this dissertation, the impact of ICU and short-range ensemble forecasting (SREF) on quantitative precipitation forecasts (QPFs

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25

Hang, Jian, and 杭建. "Wind conditions and urban ventilation in idealized city models." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2009. http://hub.hku.hk/bib/B42841471.

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26

Torchinsky, Raymon Lev. "Individual choice behaviour and urban commuting." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/27552.

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Urban commuting patterns can be viewed as the spatial manifestation of the outcome of labour market processes. Recent theoretical and empirical work investigating urban labour markets has emphasized the role of spatial wage differentials in mediating the interrelationship between labour supply and demand distributions and the dynamics of land-use change. This thesis represents an extension of such research. A simulation approach to commuting modelling, based on the explicit characterization of the interrelationship between urban location and interaction in terms of labour market processes, is

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27

Thyer, Mark Andrew. "Modelling long-term persistence in hydrological time series." Diss., 2000, 2000. http://www.newcastle.edu.au/services/library/adt/public/adt-NNCU20020531.035349/index.html.

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28

Lai, Kwong-kei Murphy, and 賴廣麒. "Two-dimensional computational study on indoor/outdoor air quality relationship in urban buildings." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B38725149.

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29

Zeng, Ning. "Climatic impact of Amazon deforestation: A study of underlying mechanism through simple modeling." Diss., The University of Arizona, 1994. http://hdl.handle.net/10150/186999.

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An intermediate level model for tropical climatology including atmosphere-land-ocean interaction is developed. The model contains basically linearized steady state primitive equations with simplified thermodynamics. A simple hydrological cycle is also included. Special attention has been paid to land surface processes in attempting to study climate change caused by Amazon deforestation. In comparison with previous simple modeling work on tropical climatology or anomaly, the present model is more sophisticated in the sense that it predicts all the important meteorological variables with little

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30

So, Shuk-pan Ellen, and 蘇淑彬. "Large eddy simulations of wind flow and pollution dispersion in an urban street canyon." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2003. http://hub.hku.hk/bib/B29332710.

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31

Ritzi, Robert William. "The use of well response to natural forces in the estimation of hydraulic parameters." Diss., The University of Arizona, 1989. http://etd.library.arizona.edu/etd/GetFileServlet?file=file:///data1/pdf/etd/azu_e9791_1989_119_sip1_w.pdf&type=application/pdf.

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32

Hyun, Yunjung. "Multiscale anaylses of permeability in porous and fractured media." Diss., The University of Arizona, 2002. http://etd.library.arizona.edu/etd/GetFileServlet?file=file:///data1/pdf/etd/azu_e9791_2002_321_sip1_w.pdf&type=application/pdf.

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33

Schmid, Wolfgang. "A farm package for MODFLOW-2000 simulation of irrigation demand and conjunctively managed surface-water and ground-water supply /." Diss., The University of Arizona, 2004. http://etd.library.arizona.edu/etd/GetFileServlet?file=file:///data1/pdf/etd/azu_e9791_2004_287_sip1_w.pdf&type=application/pdf.

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34

Vionnet, Leticia Beatriz, and Leticia Beatriz Vionnet. "Investigation of stream-aquifer interactions using a coupled surface water and groundwater flow model." Diss., The University of Arizona, 1995. http://hdl.handle.net/10150/187414.

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A finite element numerical model is developed for the modeling of coupled surface-water flow and ground-water flow. The mathematical treatment of subsurface flows follows the confined aquifer theory or the classical Dupuit approximation for unconfined aquifers whereas surface-water flows are treated with the kinematic wave approximation for open channel flow. A detailed discussion of the standard approaches to represent the coupling term is provided. In this work, a mathematical expression similar to Ohm's law is used to simulate the interacting term between the two major hydrological componen

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35

Samper, Calvete F. Javier(Francisco Javier) 1958. "Statistical methods of analyzing hydrochemical, isotopic, and hydrological data from regional aquifers." Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/191115.

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This dissertation is concerned with the development of mathematical aquifer models that combine hydrological, hydrochemical and isotopic data. One prerequisite for the construction of such models is that prior information about the variables and parameters be quantified in space and time by appropriate statistical methods. Various techniques using multivariate statistical data analyses and geostatistical methods are examined in this context. The available geostatistical methods are extended to deal with the problem at hand. In particular, a three-dimensional interactive geostatistical package

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36

Chavez, Rodriguez Adolfo 1951. "Modeling mountain-front recharge to regional aquifers." Diss., The University of Arizona, 1987. http://hdl.handle.net/10150/191124.

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The estimation of mountain-front recharge to regional aquifers is approached from a hydroclimatic standpoint. Analytical models of the seasonal water yield and streamflow are developed in this dissertation. These models are specialized for hard-rock mountainous watersheds where deep percolation occurs through fractures exclusively. Input variables are considered to be stochastic, and a relationship between precipitation and surface runoff is derived by using a deterministic physical process. Streamflow models for the summer and winter rainy seasons are developed separately in terms of known pa

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37

Ernst, Wolfgang F. "The economic rationale for stochastic urban transport models and travel behaviour : a mathematical programming approach to quantitative analysis with Perth data." UWA Business School, 2003. http://theses.library.uwa.edu.au/adt-WU2005.0004.

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[Formulae and special characters can only be approximated here. Please see the pdf version of the abstract for an accurate reproduction.] This thesis reviews, extends and applies to urban traffic analysis the entropy concept of Shannon and Luce's mathematical psychology in a fairly complex and mathematically demanding model of human decision making, if it is solved as a deeply nested structure of logit calculus. Recognising consumers' different preferences and the universal propensity to seek the best choice when going to some desired goal (k), a transparent mathematical program (MP) is deve

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38

黃潤棠 and Yun-tong Anton Wong. "Computational study of wind flow and pollution dispersion in an urban street canyon of various geometries." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2002. http://hub.hku.hk/bib/B31226905.

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39

Mwelwa, Elenestina Mutekenya. "The application of the monthly time step Pitman rainfall-runoff model to the Kafue River basin of Zambia." Thesis, Rhodes University, 2005. http://hdl.handle.net/10962/d1006171.

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This thesis presents a discussion on the study undertaken in the application of the monthly time step Pitman rainfall-runoff model to the Kafue River basin. The study constituted one of the initial steps in the capacity building and expansion of the application of hydrologic models in the southern African region for water resources assessment, one of the core areas of the Southern African FRIEND project (Flow Regimes from International Experimental Network Data). The research process was undertaken in four major stages, each stage working towards achieving the research objectives. The first st

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40

Keefer, Timothy Orrin, and Timothy Orrin Keefer. "Likelihood development for a probabilistic flash flood forecasting model." Thesis, The University of Arizona, 1993. http://hdl.handle.net/10150/192077.

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An empirical method is developed for constructing likelihood functions required in a Bayesian probabilistic flash flood forecasting model using data on objective quantitative precipitation forecasts and their verification. Likelihoods based on categorical and probabilistic forecast information for several forecast periods, seasons, and locations are shown and compared. Data record length, forecast information type and magnitude, grid area, and discretized interval size are shown to affect probabilistic differentiation of amounts of potential rainfall. Use of these likelihoods in Bayes' Theorem

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41

Bosch, David Dean 1958. "Derivation and application of effective parameters for modeling moisture flow in heterogeneous unsaturated porous media." Diss., The University of Arizona, 1990. http://hdl.handle.net/10150/191158.

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Spatial variability of porous media often prevents precise physical characterization of the system. In order to model moisture and solute transport through this media, certain sacrifices in precision must be made. Physical characteristics of the system must be averaged over large scales, lumping the small scale variability into the large scale characterization. Although this precludes a precise definition of the small scale flow characteristics, parameterization is much more attainable. This study addresses methods for determining effective hydraulic conductivity of unsaturated porous media. E

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42

Sawunyama, Tendai. "Evaluating uncertainty in water resources estimation in Southern Africa : a case study of South Africa." Thesis, Rhodes University, 2009. http://hdl.handle.net/10962/d1006176.

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Hydrological models are widely used tools in water resources estimation, but they are simple representations of reality and are frequently based on inadequate input data and uncertainties in parameter values. Data observation networks are expensive to establish and maintain and often beyond the resources of most developing countries. Consequently, measurements are difficult to obtain and observation networks in many countries are shrinking, hence obtaining representative observations in space and time remains a challenge. This study presents some guidelines on the identification, quantificatio

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Kapangaziwiri, Evison. "Revised parameter estimation methods for the Pitman monthly rainfall-runoff model." Thesis, Rhodes University, 2008. http://hdl.handle.net/10962/d1006172.

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In recent years, increased demands have been placed on hydrologists to find the most effective methods of making predictions of hydrologic variables in ungauged basins. A huge part of the southern African region is ungauged and, in gauged basins, the extent to which observed flows represent natural flows is unknown, given unquantified upstream activities. The need to exploit water resources for social and economic development, considered in the light of water scarcity forecasts for the region, makes the reliable quantification of water resources a priority. Contemporary approaches to the probl

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44

Kim, Kihong. "Recent Advances in Activity-Based Travel Demand Models for Greater Flexibility." PDXScholar, 2018. https://pdxscholar.library.pdx.edu/open_access_etds/4225.

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Most existing activity-based travel demand models are implemented in a tour-based microsimulation framework. Due to the significant computational and data storage benefits, the demand microsimulation allows a greater amount of flexibility in terms of demographic market segmentation, temporal scale, and spatial resolution, and thus the models can represent a wider range of travel behavior aspects associated with various policies and scenarios. This dissertation proposes three innovative methodologies, one for each of the three key dimensions, to fulfill the greater level of details toward a mor

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45

Leung, Shuk-yee Betty, and 梁淑儀. "Urban taxi service in Hong Kong." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1999. http://hub.hku.hk/bib/B31952148.

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46

Zhao, Yunzhong. "Analysis and comparison of blood lead risk area models for selected urban areas in Indiana." Muncie, Ind. : Ball State University, 2009. http://cardinalscholar.bsu.edu/679.

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47

Edelstein, Christopher. "Climatic conditions and storm hydrology of a small agricultural watershed." Virtual Press, 2005. http://liblink.bsu.edu/uhtbin/catkey/1314224.

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Climatic conditions (precipitation, evapotranspiration, available soil moisture, and temperature) are important variables when considering cumulative storm streamflow for a watershed. The objective of this study was to determine what climatic conditions, if any, could be used to mathematically model cumulative storm streamflow for an extensively-drained small agricultural watershed in northwest Delaware County, Indiana. A water-level recorder was installed in Killbuck Creek during autumn 2002, spring, summer, and autumn 2003 and 2004. To determine discharge, velocity measurements were collecte

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48

Latham, Michael John. "An assessment of models and methodologies used in the design of detention facilities for small urban watersheds." Thesis, This resource online, 1996. http://scholar.lib.vt.edu/theses/available/etd-09182008-063108/.

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Abeykoon, Mahinda. "Stepwise application of unconstrained linear mixture model for classification of urban land cover." Virtual Press, 2004. http://liblink.bsu.edu/uhtbin/catkey/1306381.

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This study involves stepwise application of Unconstrained Linear Mixer Model (ULMM) for sub-pixel classification of residential areas using Land sat 7 TM image. The image was geometrically and radiometrically corrected and spectral enhancement and classifications were done to determine the possible number of target classes. In the first step, five end-members were used as inputs and the pixels which were considered as well fit to ULMM were identified as outputs. The unidentified pixels were separated and taken to the second step with new end members. This method identified 52% of the mixed pix

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50

Lopes, Vicente Lucio 1952. "A numerical model of watershed erosion and sediment yield." Diss., The University of Arizona, 1987. http://hdl.handle.net/10150/191125.

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A physically based, distributed parameter, event oriented, nonlinear, numerical model of watershed response is developed to accommodate the spatial changes in topography, surface roughness, soil properties, concentrated flow patterns and geometry, and land use conditions. The Green and Ampt equation with the ponding time calculation for an unsteady rain is used to compute rainfall excess rates. The kinematic wave equations are used to describe the unsteady one-dimensional overland and channel flow. The unsteady and spatially varying erosion/deposition process on hillslopes and channel systems

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