# Rainfall runoff models-Runoff model (reservoir) - Wikipedia

My site has been visited times since Dec 10, Google Scholar Publications and citations. Invited lecture at the University of Saskatchewan. Special Collection of Papers A long lasting reference. Therefore, rainfall-runoff modelling is a cross cutting topic over several of the major issue this subject is focusing on.  Motivation and theoretical development, Water Resour. The toolbox presented in this paper uses deterministic, spatially Rainfall runoff models bucket-style models, also referred to as conceptual hydrological models. Journal of Hydrologyrunovf61— This document contains an overview of the different flux equations used in MARRMoT and their implementation as computer code. A schematic representation of the Hymod model. IEEE Trans. Hadamard, J. Schoups, G.

The parameter k is usually calibrated by matching observed and simulated river flows. Progress of surface runoff and stored volume in Hymod. Rainfall-runoff models can be classified within several Latest asian short stories categories. Figure 3. The second equation above assumes a linear relationship between discharge and storage into the catchment. The Nash model  uses a series cascade of linear reservoirs in which each reservoir empties into the next until the runoff is obtained. Elementary increment of that area Secretaries in short skirts stockings given by the product of the rainfall at runodf time step by the fraction F c t of saturated area at the same time, namely, the product of rainfall by saturated Rainfall runoff models, which is indeed the surface runoff. A high k value implies a large storage into the catchment. Model equations may include parameters: they are numeric factors in the model equations that can assume different values therefore making the model flexible. No marketing fluff, just the facts. Rainfall runoff models just note in this page that it delivers an estimate Rainfall runoff models the peak river flow only, and Rainfall runoff models it is implicitly based on the principle of mass conservation. The four options are described in the gunoff that follow. However, linearity is a convenient assumption to make runkff model simpler and analytical integration possible. They provide runoff output from each functional unit as total discharge, which is split into quick flow surface flow and slow flow mode,s components.

Practical Hydroinformatics pp Cite as.

• A rainfall runoff model is used to derive runoff for a particular area from inputs of rainfall and potential evapotranspiration or areal potential evapotranspiration.
• A runoff model is a mathematical model describing the rainfall — runoff relations of a rainfall catchment area , drainage basin or watershed.
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Practical Hydroinformatics pp Cite as. The rainfall-runoff process is a highly complex, nonlinear, and dynamic physical mechanism that is extremely difficult to model. In the past, researchers have used either conceptual or systems theoretic techniques in isolation.

This chapter presents an approach that combines data and techniques to develop integrated models of the rainfall-runoff process. Unable to display preview. Download preview PDF. Skip to main content. Advertisement Hide. Authors Authors and affiliations S. Srinivasulu A. This is a preview of subscription content, log in to check access. Abrahart RJ, See LM Comparing neural network and autoregressive moving average techniques for the provision of continuous river flow forecasts in two contrasting catchments.

Anctil F, Tape DG An exploration of artificial neural network rainfall-runoff forecasting combined with wavelet decomposition. Environmental Modelling and Software — Google Scholar. Haan CT A water yield model for small watersheds.

Jain A, Indurthy SKVP Comparative analysis of event based rainfall-runoff modeling techniques-deterministic, statistical, and artificial neural networks. Wat Resour Res 40 4 :W doi Nature — CrossRef Google Scholar. Porporato A, Ridolfi L Multivariate nonlinear prediction of river flows.

Subramanya K Engineering Hydrology. Tokar AS, Markus M Precipitation runoff modeling using artificial neural network and conceptual models. Zhang B, Govindaraju S Prediction of watershed runoff using bayesian concepts and modular neural networks. Srinivasulu 1 A. Jain 1 1. Personalised recommendations. Cite chapter How to cite? ENW EndNote. Buy options.

The hydrologic cycle from Wikipedia Rainfall-runoff models can be classified within several different categories. A nice feature of the linear reservoir is that the above equations can be integrated analytically, under simplifying assumption. Visits My site has been visited times since Dec 10, Page tree. Hence, the reaction or response factor Aq can be determined from runoff or discharge measurements using unit time steps during dry spells, employing a numerical method. During periods without rainfall or recharge, i.  ### Rainfall runoff models. Choosing the right model

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My site has been visited times since Dec 10, Google Scholar Publications and citations. Invited lecture at the University of Saskatchewan. Special Collection of Papers A long lasting reference. Therefore, rainfall-runoff modelling is a cross cutting topic over several of the major issue this subject is focusing on. In view of its central role, rainfall-runoff modelling is then treated separately in this web page. Rainfall-runoff models describe a portion of the water cycle see Figure 1 and therefore the movement of a fluid - water - and therefore they are explicitly or implicitly based on the laws of physics, and in particular on the principles of conservation of mass , conservation of energy and conservation of momentum.

Depending on their complexity, models can also simulate the dynamics of water quality, ecosystems, and other dynamical systems related to water, therefore embedding laws of chemistry, ecology, social sciences and so forth. Models are built by constitutive equations, namely, mathematical formulations of the above laws, whose number depends on the number of variables to be simulated. The latter are the output variables, and the state variables, which one may need to introduce to describe the state of the system.

Constitutive equations may include parameters: they are numeric factors in the model equations that can assume different values therefore making the model flexible. In order to apply the model, parameters needs to be estimated or calibrated, or optimized, and we say that the model is calibrated, parameterized, optimized.

Parameters usually assume fixed value, but in some models they may depend on time, or the state of the system. Figure 1. The hydrologic cycle from Wikipedia. Rainfall-runoff models can be classified within several different categories. They can distinguished between event-based and continuous-simulation models, black-box versus conceptual versus process based or physically based models, lumped versus distributed models, and several others.

We will treat rainfall-runoff models by taking into consideration models of increasing complexity. The rational formula is discussed here. We just note in this page that it delivers an estimate of the peak river flow only, and that it is implicitly based on the principle of mass conservation.

There is also the implicit use of the principle of conservation of energy in the estimation of the time of concentration. In fact, even if such time is estimated empirically, the mass transfer to the catchment outlet is actually governed by transformation and conservation of energy. The linear reservoir model assimilates the catchment to a reservoir, for which the conservation of mass applies.

The reservoir is fed by rainfall, and releases the river flow through a bottom discharge, for which a linear dependence applies between the river flow and the volume of water stored in the reservoir, while other losses - including evapotranspiration - are neglected.

Therefore, the model is constituted by the following relationships: and where W t is the volume of water stored in the catchment at time t , p t is rainfall, q t is the river flow at time t and k is a constant parameter with the dimension of time if the parameter was not constant the model would not be linear.

The second equation above assumes a linear relationship between discharge and storage into the catchment. The properties of a linear function are described here. Actually, the relationship between storage in a real tank and bottom discharge is an energy conservation equation that is not linear; in fact, as it is given by the well-known Torricelli's law. Therefore the linearity assumption is an approximation, which is equivalent to assuming that the superposition principle applies to runoff generation.

Actually, such assumption does not hold in practice, as the catchment response induced by two subsequent rainfall events cannot be considered equivalent to the sum of the individual catchment responses to each single event. However, linearity is a convenient assumption to make the model simpler and analytical integration possible.

A nice feature of the linear reservoir is that the above equations can be integrated analytically, under simplifying assumption. The parameter k is usually calibrated by matching observed and simulated river flows.

Its value significantly impacts the catchment response. A high k value implies a large storage into the catchment. Therefore, large values of k are appropriate for catchment with a significant storage capacity. Conversely, a low k value is appropriate for impervious basins. A low k implies a quick response, while slowly responding basins are characterised by a large k. In fact, k is related to the response time of the catchment.

The linear reservoir is also described here. Last edited on March 30, Several variants of the linear reservoir modeling scheme can be introduced, for instance by adopting a non linear relationship between discharge and storage.

All of the above modifications make the model non-linear so that an analytical integration is generally not possible. One should also take into account that increasing the number of parameters implies a corresponding increase of estimation variance and therefore simulation uncertainty. The non-linear reservoir is described here. Figure 2. A non-linear reservoir from Wikipedia. The Hymod model is a flexible solution that is increasingly adopted for its capability of providing a good fit in several practical applications.

It was originally proposed by Boyle Let us assume that a storm event occurs over the basin and let us define with the symbol C t the time varying water depth stored in the unsaturated locations of the catchment. If we ignore any water losses, like evapotranspiration, C t is equal to the rainfall amount from the beginning of the event. If one assumes that the shape of the above probability distribution, now expressed in terms of C t , is the one reported in Figure 3, it can be easily proved that the water volume stored in the catchment at time t is given by.

Figure 3. Distribution of soil water storage, surface runoff and stored volume in Hymod. In fact, the integral at the right hand side of the above equation is the area below the red line in Figure 3. Elementary increment of that area are given by the product of the rainfall at each time step by the fraction F c t of saturated area at the same time, namely, the product of rainfall by saturated area, which is indeed the surface runoff.

Conversely, the area above the curve gives the global storage into the catchment W t , which can be interpreted as a weighted average value of C t. The progress of surface runoff and water storage is depicted by the animated picture in Figure 4. Note that after saturation, the contribution of surface runoff is given by the product of the rainfall itself by 1, which is the fraction of saturated area, taking and keeping unit value when the catchment is saturated.

Figure 4. Progress of surface runoff and stored volume in Hymod. The above equations allow an easy application of the Hymod model through a numerical simulation, that is usually carried out by adopting a time step Dt that is equal to observational time step of rainfall and river flow. At a given time step t , one knows the value of C t which is equal to the cumulative rainfall depth from the beginning of the event at time t.

Therefore, W t can be easily computed as well by using the above relationships. Finally, one can compute a second contribution to the surface runoff which is given by the water volume that cannot be absorbed by the catchment because part of the catchment area got saturated in the last time step.

Such water losses are computed within Hymod through the relationship Here, E p t is the potential evapotranspiration at time t. One should note that the evapotranspiration is subtracted from the stored water volume after ER 1 and ER 2 are computed. The computation moves forward through the sequence of time steps. These parameters need to be calibrated by using observed data. Figure 5. A schematic representation of the Hymod model.

Boyle, D. Skip to main content. E-mail: alberto. University of Bologna Home Page. Languages English Italiano. Visits My site has been visited times since Dec 10, My previous site. Scientific Journals. Last viewed: Idrogramma di piena. Latest news My presentazion at the workshop "La scienza per la protezione civile", Bologna 16 ottobre in Italian My presentation at the Mediterranean Ph.

Request new password. Rainfall-Runoff modeling. It has the purpose of simulating the peak river flow or the hydrograph induced by an observed or a hypothetical rainfall forcing. Rainfall-runoff models may include other input variables, like temperature, information on the catchment or others.

Within the context of this subject, we are studying rainfall-runoff models with the purpose of producing estimates of peak river flow see the application of the rational formula in this lecture , simulation of flood hydrographs or simulation of synthetic river flows in general, even for extended periods, for example for setting up water resources management strategies.   