Excess Rainfall Intensity Research Articles

High flow prediction model integrating physically and deep learning based approaches with quasi real-time watershed data assimilation

When operating a flood forecasting system, it is crucial to prioritize both promptness and accuracy, along with reflecting the latest watershed conditions. This study proposes a hybrid model for rainfall-induced high flow prediction that combines an instantaneous physically-based model and a deep learning-based rainfall loss model assimilating with quasi real-time watershed conditions. Its primary objective is to present immediate and reliable high flow predictions, ensuring stability in prediction procedures. The surface runoff component of the model is based on nonlinear instantaneous unit hydrograph (IUH) derived using a dynamic wave model, which considers the nonlinearity between the rainfall excess intensity and the time to peak and peak flow of the IUH. To account for rainfall loss, which can significantly influence rainfall-runoff quantity, Long Short-Term Memory (LSTM) model is employed to establish link between key rainfall loss parameters and the latest watershed conditions obtained from the Global Land Data Assimilation System (GLDAS). The application of the proposed model to 28 high flow events reveals several noteworthy outcomes. Firstly, unlike conventional models that depend on fixed parameter values specific to each event, the proposed model offers immediate, stable, and highly accurate high flow predictions without the need for manual calibration. Secondly, the prioritization of parameters reflecting watershed conditions varies between different watersheds and depends on the rainfall events. These findings indicate the necessity to estimate rainfall loss parameters individually for each rainfall-runoff event in each watershed, as no universal value exists for these parameters. Lastly, despite the limited number of test cases conducted in this study, the LSTM model achieved sufficiently accurate rainfall loss estimation for high flow prediction using only 50 datasets.

Flood prediction using nonlinear instantaneous unit hydrograph and deep learning: A MATLAB program

In this study, we developed a MATLAB program for flood prediction in a watershed. The program consists of three modules. The instantaneous unit hydrograph (IUH) generation module utilizes a power-law based interpolation method to generate IUHs. The generated IUH is a function of the rainfall excess intensity and therefore considers nonlinearity. The long short-term memory (LSTM) module employs “lstmLayer” from the MATLAB deep learning toolbox to predict total rainfall excess; this is then used to estimate the curve number (CN) value for each flood event. The LSTM module uses a land surface modeling dataset and rainfall-runoff data as inputs. The flood hydrograph generation module calculates effective rainfall hyetographs and then predicts flood hydrographs using a convolution integration. A detailed description of the program is provided along with an application example for real watersheds. The application results demonstrated that our program can be effectively used for flood prediction in practice, particularly for large flood events.

Instantaneous physical rainfall–runoff prediction technique using a power–law relationship between time to peak and peak flow of an instantaneous unit hydrograph and the rainfall excess intensity

AbstractThe traditional instantaneous unit hydrograph (IUH) is very useful for theoretical analysis and practical forecasting of floods owing to its linear assumptions. Although various revised methods to overcome the unphysical assumptions have been proposed, it is still difficult to obtain efficiently a nonlinear IUH of diverse rainfall excess intensities in a watershed. In this study, we proposed practical and physical interpolation techniques to derive new IUHs from at least two existing IUHs corresponding to diverse rainfall excess intensities in a watershed. To interpolate the new IUHs, mass conservation law and power–law relationships between rainfall excess intensities and the peak flow and time to peak of IUHs were used. By employing convolution integration, surface rainfall–runoff hydrographs for timely varying rainfall events were derived. For verification, we applied the proposed technique to three real watersheds with different sizes ranging from 0.036 to 1,047 km2. All flood prediction procedures were completed instantly, stably and the prediction results showed the accuracy of Nash–Sutcliffe efficiency (NSE) = 0.55–0.93 and coefficient of determination (R2) = 0.72–0.94.

Timing the time of concentration: shedding light on a paradox

ABSTRACTFrom the origins of hydrology, the time of concentration, tc, has conventionally been tackled as a constant quantity. However, theoretical proof and empirical evidence imply that tc exhibits significant variability against rainfall, making its definition and estimation a hydrological paradox. Adopting the assumptions of the Rational method and the kinematic approach, an effective procedure in a GIS environment for estimating the travel time across a catchment’s longest flow path is provided. By application in 30 Mediterranean basins, it is illustrated that tc is a negative power function of excess rainfall intensity. Regional formulas are established to infer its multiplier (unit time of concentration) and exponent from abstract geomorphological information, which are validated against observed data and theoretical literature outcomes. Besides offering a fast and easy solution to the paradox, we highlight the necessity of implementing the varying tc concept within hydrological modelling, signalling a major shift from current engineering practices.

An approximate analytical solution for describing surface runoff and sediment transport over hillslope

Soil and water loss from farmland causes land degradation and water pollution, thus continued efforts are needed to establish mathematical model for quantitative analysis of relevant processes and mechanisms. In this study, an approximate analytical solution has been developed for overland flow model and sediment transport model, offering a simple and effective means to predict overland flow and erosion under natural rainfall conditions. In the overland flow model, the flow regime was considered to be transitional with the value of parameter β (in the kinematic wave model) approximately two. The change rate of unit discharge with distance was assumed to be constant and equal to the runoff rate at the outlet of the plane. The excess rainfall was considered to be constant under uniform rainfall conditions. The overland flow model developed can be further applied to natural rainfall conditions by treating excess rainfall intensity as constant over a small time interval. For the sediment model, the recommended values of the runoff erosion calibration constant (cr) and the splash erosion calibration constant (cf) have been given in this study so that it is easier to use the model. These recommended values are 0.15 and 0.12, respectively. Comparisons with observed results were carried out to validate the proposed analytical solution. The results showed that the approximate analytical solution developed in this paper closely matches the observed data, thus providing an alternative method of predicting runoff generation and sediment yield, and offering a more convenient method of analyzing the quantitative relationships between variables. Furthermore, the model developed in this study can be used as a theoretical basis for developing runoff and erosion control methods.

Runoff Prediction for Dam Safety Evaluations Based on Variable Time of Concentration

AbstractThis paper describes a method for estimating runoff hydrographs for dam safety evaluations in which the time of concentration is considered dependent on the magnitude of the excess rainfall intensity. Current practice for hydrologic routing assumes the time of concentration to be invariant and a function of basin characteristics. The proposed method addresses the limitations arising from the assumed linearity in the unit hydrograph by showing that the time of concentration is dependent on the excess rainfall intensity through a power relationship. The proposed method uses a variable flow velocity approach to compute travel time and construct time-area curves for a range of excess rainfall intensities. From the derived relationships between time of concentration, flow, and excess rainfall intensity, an explicit nonlinear convolution is performed to compute runoff hydrographs. In its current implementation, the method assumes a uniform distribution of rainfall over the entire watershed. This method ...

Time of concentration of surface flow in complex hillslopes

Abstract Time of concentration (TC) of surface flow in watersheds depends on the coupled response of hillslopes and stream networks. The important point in this background is to study the effects of the geometry and the shape of complex hillslopes on the time of concentration considering the degree of flow convergence (convergent, parallel or divergent) as well as the profile curvature (concave, straight or convex). In this research, the shape factor of complex hillslopes as introduced by Agnese et al. (2007) is generalized and linked to the TC. A new model for calculating TC of complex hillslopes is presented, which depends on the plan shape, the type and degree of profile curvature, the Manning roughness coefficient, the flow regime, the length, the average slope, and the excess rainfall intensity. The presented model was compared to that proposed by Singh and Agiralioglu (1981a,b) and Agiralioglu (1985). Moreover, the results of laboratory experiments on the travel time of surface flow of complex hillslopes were used to calibrate the model. The results showed that TC for convergent hillslopes is nearly double those of parallel and divergent ones. TC in convex hillslopes was very close to that in straight and concave hillslopes. While the effect of convergence on TC is considerable, the curvature effect confirmed insignificant. Finally, in convergent hillslopes, TC increases with the degree of convergence, but in divergent hillslopes, it decreases as degree of divergence increases.

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

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.

Estimation of sediment yield during storms based on soil and watershed geomorphology characteristics

Concentrated rainfall usually results in serious soil erosion on steep hillslopes. Since the itinerary of the eroded sediment is complicated, estimating watershed erosion during storms is practically difficult. A physically-based approach for sediment yield estimation during storms was proposed in this study. By using soil and watershed geomorphologic information, analytical solutions for sediment travel time in different orders of overland areas and channels were derived to develop a geomorphologic instantaneous unit sedimentgraph (GIUS) which showed the temporal distribution of sediment discharge resulting from an instantaneous rainfall excess input. The resultant GIUS was a function of the rainfall excess intensity and sediment delivery ratio. The linearity restriction of the unit hydrograph theory was relaxed. Sediment yields during storm events were calculated by convoluting rainfall intensities with the proposed GIUS, which had been verified by using data from the Goodwin Creek Experimental Watershed in Mississippi, the United States. The simulated and the measured sediment yields were in good agreement for the test storms. Sensitivity of the sedimentgraph to the model parameters was also investigated. The proposed model was considered a promising application for sediment yield estimation in the field of water resources design.

A morpho-climatic instantaneous unit hydrograph model for urban catchments based on the kinematic wave approximation

Summary Stormwater models are valuable tools in urban planning as well as stormwater system design and management. Although the hydraulic simulation of pipes and channels in these models is often quite sophisticated, the hydrologic simulation of the flow contributing to the hydraulic elements is frequently greatly simplified. Hydrologic simulation of urban catchments is made particularly complex due to the presence of features such as streets, small pipes, and channels. In this study, we develop a new model called the U-McIUH (Urban Morpho-climatic Instantaneous Unit Hydrograph), which defines the IUH as the probability density function of the travel time from a random location in the urban terrain to the outlet. Flow paths are extracted from a specially processed digital elevation model that incorporates hillslopes, streets, pipes, and channels, and travel times are computed in each cell using the average wave celerity from kinematic wave theory. These expressions depend on the upstream contribution of flow and the excess rainfall intensity, so they incorporate the so-called climatic dependence of the IUH, which is the dependence of the unit hydrograph on the rainfall intensity. Rainfall pulses of different intensities are convoluted with their respective IUH and superimposed to generate the response to a given storm event. The application of the model to a real catchment provides good reproduction of observed hydrographs, suggesting that the U-McIUH is able to capture some significant hydrologic properties of the catchment. The model is studied by analyzing the effects of (1) the upstream contribution of flow on the travel time formulation, (2) the variation of flow velocities within the urban catchment, (3) the non-linear dependence of the IUH on the rainfall intensity (i.e. the climatic dependence), and (4) the spatial distribution of imperviousness. Overall, these results suggest that the presence of artificial elements in urban watersheds has a significant role in determining the travel times and thus the hydrologic response of the watershed.

Influence of Moving Rainstorms on Watershed Responses

Since rainfall activates watershed responses in hydrologic systems, it is critical information for predicting flow and pollutant transportation, and then impacting watershed management strategies. Therefore, it is important to understand clearly rainfall characteristics in the application of hydrologic and water quality models. The objective of this study was to discuss the influence of storm movement on runoff predictions and pollutant exports in a conceptual catchment. The Virginia stormwater for windows (WinVAST) model was applied to predict watershed responses in this work. The result shows that the storm direction has stronger influence on hydrograph shapes than spatial rainfall excess intensity patterns. However, pollutant exports are significantly influenced by both the direction of storm movement and rainfall patterns. The peak of pollutant concentration could be seriously high, due to the delayed discharge in downstream-moving storms. Key words: hydrology; rainfall movement; runoff; pollutant transportation; watershed response; WinVAST

Nonlinear transformation of unit hydrograph

Unit hydrograph (UH) and its numerous derivatives have been popular for estimation of flood hydrographs. Two major assumptions still overshadow UH applications. One is the linearity and the other is time invariance. In theory, only peak discharge of an equilibrium hydrograph follows linear proportionality to excess rainfall intensity. In trying to relax the linearity constraint, this paper aims to propose a nonlinear way of transforming a given UH to other general hydrographs. The transformation or mapping technique relies on a simple rainfall ratio raised to a power less than unity. The case of nonlinear transformation is illustrated for a number of watershed geometries with either known kinematic wave analytic solutions or observed data. The nonlinear UH approach also relaxes the assumption of constant time base of the UH. The proposed nonlinear UH transformation may thus be viewed as a major step in closing the gap between physically based and traditional UH-based surface runoff simulation approaches.

Optimal design of unit hydrographs using probability distribution and genetic algorithms

A nonlinear optimization model is developed to transmute a unit hydrograph into a probability distribution function (PDF). The objective function is to minimize the sum of the square of the deviation between predicted and actual direct runoff hydrograph of a watershed. The predicted runoff hydrograph is estimated by using a PDF. In a unit hydrograph, the depth of rainfall excess must be unity and the ordinates must be positive. Incorporation of a PDF ensures that the depth of rainfall excess for the unit hydrograph is unity, and the ordinates are also positive. Unit hydrograph ordinates are in terms of intensity of rainfall excess on a discharge per unit catchment area basis, the unit area thus representing the unit rainfall excess. The proposed method does not have any constraint. The nonlinear optimization formulation is solved using binary-coded genetic algorithms. The number of variables to be estimated by optimization is the same as the number of probability distribution parameters; gamma and log-normal probability distributions are used. The existing nonlinear programming model for obtaining optimal unit hydrograph has also been solved using genetic algorithms, where the constrained nonlinear optimization problem is converted to an unconstrained problem using penalty parameter approach. The results obtained are compared with those obtained by the earlier LP model and are fairly similar.

Runoff hydrograph simulation based on time variable isochrone technique

A new method based on an extension to time–area (TA) concept is proposed for rainfall–runoff transformation in watersheds. The method uses time variable isochrones, such that the runoff hydrograph responds well to temporal changes in excess rainfall intensity. The method employs a kinematic-based travel time scheme, which improves existing isochrone extraction techniques. A raster-based approach deals with spatial domain discretization and supports rainfall–runoff simulations in a modular distributed model. The model uses digital elevation model (DEM) data, ground slope, flow direction, and flow accumulation maps to characterize the watershed terrain. The time series of travel time (or isochrones) maps constitute the basis for incremental and total runoff hydrograph computations. The model was calibrated and validated on a small catchment. The methods and modeling algorithms extend the original TA routing method to a distributed terrain-driven, hydraulic-based, and GIS-compatible technique where isochrones vary as the storm intensity and infiltration rate develop.

DISTRIBUTED ROUTING TECHNIQUES DEVELOPED ON GIS FOR GENERATING SYNTHETIC UNIT HYDROGRAPHS

The increasing interest in small irrigation reservoirs in rural areas of Mediterranean countries requires detailed hydrologic analyses in order to assess water resources and design runoff discharges. Emerging technologies, such as Geographic Information Systems (GIS) and remote sensing, enhance the possibilities of distributed modeling in hydrology. This article presents several distributed approaches, based on precipitation and basin physical properties, which allow generation of synthetic unit hydrographs for routing excess rainfall. The routing models were implemented in compliance with the GRID module of ArcInfo GIS on a 10–m grid cell representation of the watershed. The generated excess rainfall was routed from each cell of the grid to the outlet of the watershed following the steepest slope path. Several approaches considering different runoff rates, distinction between overland and channeled flows, and different excess rainfall intensities were analyzed and used for predicting friction surfaces. A time–area method was finally applied to obtain surface runoff unit hydrographs. The proposed approaches were applied to two small rural watersheds near Madrid, Spain. The estimated unit hydrographs clearly show the need to discriminate between overland and channeled flows. Increase in excess rainfall intensities significantly affects the unit hydrograph by gradually increasing hydrograph peak and decreasing base times. It appears that there is a significant influence of excess rainfall intensity in the resulting hydrographs for small basins, where channel storage is of little importance. The results were compared to those obtained by means of two lumped unit hydrograph techniques for ungaged watersheds (USDA–SCS dimensionless and triangular unit hydrographs). The lumped models give similar results to those based on a variable flow approach with excess rainfall intensity of 3 mm/h, which corresponds to a 2–year return period for the studied watersheds.

Regional analysis using the Geomorphoclimatic Instantaneous Unit Hydrograph

Abstract. The construction of design flood hydrographs for ungauged drainage areas has traditionally been approached by regionalisation, i.e. the transfer of information from the gauged to the ungauged catchments in a region. Such approaches invariably depend upon the use of multiple linear regression analysis to relate unit hydrograph parameters to catchment characteristics and generalised rainfall statistics. The concept of the geomorphological instantaneous unit hydrograph (GIUH), in relating the shape and scale of the catchment transfer function to stream network topology and channel characteristics, offers an alternative methodology. GIUH derivation depends upon a series of assumptions, including that of estimating a "characteristic velocity"; these continue to attract attention and debate. However, if this velocity is expressed in terms of the kinematic wave approximation, the peak and time-to-peak of the IUH may be expressed in terms of a group of catchment and channel characteristics and the intensity of rainfall excess, giving the so-called geomorphoclimatic IUH (GCIUH). Previous studies involving the GCIUH have developed a single IUH relating to the total duration of rainfall excess. In this study, the rainfall excess duration was divided into several (equal) time increments, with separate IUHs being generated for each interval. This quasi-linear approach was applied to 105 storm events from nine catchments in the south-west of England, ranging in size from 6 to 420 (km)2 . The results showed that, providing the time interval chosen is fine enough to capture the shape of the runoff hydrographs, a comparable level of goodness-of-fit can be obtained for catchments covering a range of about 1:75 in area. The modified GCIUH approach as described is therefore recommended for further investigation and intercomparison with regression-based regionalisation methods. Keywords: floods; geomorphology; rainfall-runoff modelling

Geomorphology and Kinematic-Wave–Based Hydrograph Derivation

Geomorphology-based instantaneous unit hydrographs have been proposed by several engineers as a tool to produce runoff hydrographs from rainfall for ungauged watersheds. A difficulty in applying the geomorphology-based instantaneous unit hydrographs is the determination of travel time that is actually a hydraulic problem. In this paper, kinematic-wave theory is used to analytically determine the travel times for overland and channel flows in a stream-ordering subbasin system. The resultant instantaneous unit hydrograph is a function of the intensity of rainfall excess; hence the linearity restriction of the unit hydrograph theory is relaxed. In applying the instantaneous unit hydrographs for hydrograph simulation, the model deals with temporally nonuniform rainfall through convolution integration of the instantaneous unit hydrographs applied to the rainfall excess of varying intensities with time. The proposed model is tested by comparing the simulated and observed hydrographs of an example watershed for several rainstorms with good results. Sensitivity of surface runoff unit hydrographs to the model parameters is also investigated.

Time to equilibrium for spatially variable watersheds

An algorithm for calculating the time to equilibrium of complex watersheds is developed for spatially varied watershed characteristics and excess rainfall intensity. The wave travel time through the flow path originating from the hydraulically most remote point in the basin essentially determines the equilibrium time of the system. The wave travel time is computed for two distinct phases: overland flow and channel flow. The hydraulically most remote point is stationary for all spatially uniform rainstorms but may vary for spatially distributed storms. The time to equilibrium varies inversely with rainfall intensity raised to the power 0.4. Using a raster-based approach, algorithms were developed to determine the distance-drainage area relationship and to perform the numerical integration of the time to equilibrium. Although approximate, the algorithm provides maps showing the isochromes of surface runoff and travel time to the outlet, along with time-area histograms for uniform or spatially distributed rainstorms. Isochrones determine the response time required for water, dilute suspensions and pollutants to reach the watershed outlet under complete equilibrium. The effects of infiltration in delaying the time to equilibrium are significant only when δ/ K is large.

The influence of storm temporal patterns on catchment response—Reply

Abstract Previous investigations have shown that an estimate of the catchment response to a storm event can be obtained from a consideration of kinematic waves flowing over planar surfaces. For a singular plane, analytical solutions have been presented previously for storm events with a constant intensity of rainfall excess. However, these solutions have limited applicability owing to the non-uniform distribution of precipitation and, hence, rainfall excess in most real storm events. Analytical and numerical solutions for a number of non-uniform patterns of rainfall excess are presented. Solutions obtained show that the pattern of rainfall excess has a considerable influence on the catchment response. This influence is evident in the different time-to-peak of the resultant runoff hydrographs and in the hydrograph shape itself. Therefore, the time of concentration is not a constant characteristic of the catchment which can be determined without consideration of the temporal pattern of rainfall excess. Finally, the predicted hydrographs obtained for variable rates of rainfall excess have higher peak flowrates than that obtained for a constant intensity of rainfall excess.

The influence of storm temporal patterns on catchment response

Previous investigations have shown that an estimate of the catchment response to a storm event can be obtained from a consideration of kinematic waves flowing over planar surfaces. For a singular plane, analytical solutions have been presented previously for storm events with a constant intensity of rainfall excess. However, these solutions have limited applicability owing to the non-uniform distribution of precipitation and, hence, rainfall excess in most real storm events. Analytical and numerical solutions for a number of non-uniform patterns of rainfall excess are presented. Solutions obtained show that the pattern of rainfall excess has a considerable influence on the catchment response. This influence is evident in the different time-to-peak of the resultant runoff hydrographs and in the hydrograph shape itself. Therefore, the time of concentration is not a constant characteristic of the catchment which can be determined without consideration of the temporal pattern of rainfall excess. Finally, the predicted hydrographs obtained for variable rates of rainfall excess have higher peak flowrates than that obtained for a constant intensity of rainfall excess.