scholarly journals A top-down model to generate ensembles of runoff from a large number of hillslopes

2013 ◽  
Vol 20 (5) ◽  
pp. 683-704 ◽  
Author(s):  
P. R. Furey ◽  
V. K. Gupta ◽  
B. M. Troutman
Keyword(s):  
Water Loss ◽  
Probability Distributions ◽  
Random Variable ◽  
Statistical Hypothesis ◽  
Generation Model ◽  
Loss Ratio ◽  
Rainfall Runoff ◽  
Runoff Generation ◽  
Top Down ◽  
Runoff Event

Abstract. We hypothesize that total hillslope water loss for a rainfall–runoff event is inversely related to a function of a lognormal random variable, based on basin- and point-scale observations taken from the 21 km2 Goodwin Creek Experimental Watershed (GCEW) in Mississippi, USA. A top-down approach is used to develop a new runoff generation model both to test our physical-statistical hypothesis and to provide a method of generating ensembles of runoff from a large number of hillslopes in a basin. The model is based on the assumption that the probability distributions of a runoff/loss ratio have a space–time rescaling property. We test this assumption using streamflow and rainfall data from GCEW. For over 100 rainfall–runoff events, we find that the spatial probability distributions of a runoff/loss ratio can be rescaled to a new distribution that is common to all events. We interpret random within-event differences in runoff/loss ratios in the model to arise from soil moisture spatial variability. Observations of water loss during events in GCEW support this interpretation. Our model preserves water balance in a mean statistical sense and supports our hypothesis. As an example, we use the model to generate ensembles of runoff at a large number of hillslopes for a rainfall–runoff event in GCEW.

scholarly journals Theoretical Estimation of Energy Balance Components in Water Networks for Top-Down Approach

Water ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1011
Author(s):  
Surachai Lipiwattanakarn ◽  
Suparak Kaewsang ◽  
Natchapol Charuwimolkul ◽  
Jiramate Changklom ◽  
Adichai Pornprommin
Keyword(s):  
Energy Balance ◽  
Water Loss ◽  
Distribution Systems ◽  
Minimum Energy ◽  
Head Loss ◽  
Water Networks ◽  
Top Down ◽  
Pressurized Water ◽  
Simple Method ◽  
Energy Balance Approach

The energy balance calculation for pressurized water networks is an important step in assessing the energy efficiency of water distribution systems. However, the calculation generally requires mathematical modelling of the water networks to estimate three important energy components: outgoing energy through water loss (El), friction energy loss (Ef) and energy associated with water loss (EWL). Based on a theoretical energy balance analysis of simplified pipe networks, a simple method is proposed to estimate El, Ef and EWL with minimum data requirements: input energy, water loss (WL) and head loss between the source and the minimum energy point (ΔH). By inclusion of the head loss in water networks into the estimation, the percentages of El and EWL are lower and higher, respectively, than using only the percentage of WL. The percentage of Ef can be a function of the percentage of ΔH. By demonstrating our analysis with the simulation results from the mathematical models of 20 real water networks, the proposed method can be used to effectively estimate El, Ef and EWL as a top-down energy balance approach.

scholarly journals Spatio-Temporal Hydrological Model Structure and Parametrization Analysis

2021 ◽  
Vol 9 (5) ◽  
pp. 467
Author(s):  
Mostafa Farrag ◽  
Gerald Corzo Perez ◽  
Dimitri Solomatine
Keyword(s):  
Hydrological Modeling ◽  
Model Building ◽  
Model Performance ◽  
Model Description ◽  
Generation Model ◽  
Model Structure ◽  
Runoff Generation ◽  
Spatial Sensitivity ◽  
Spatio Temporal ◽  
Set Up

Many grid-based spatial hydrological models suffer from the complexity of setting up a coherent spatial structure to calibrate such a complex, highly parameterized system. There are essential aspects of model-building to be taken into account: spatial resolution, the routing equation limitations, and calibration of spatial parameters, and their influence on modeling results, all are decisions that are often made without adequate analysis. In this research, an experimental analysis of grid discretization level, an analysis of processes integration, and the routing concepts are analyzed. The HBV-96 model is set up for each cell, and later on, cells are integrated into an interlinked modeling system (Hapi). The Jiboa River Basin in El Salvador is used as a case study. The first concept tested is the model structure temporal responses, which are highly linked to the runoff dynamics. By changing the runoff generation model description, we explore the responses to events. Two routing models are considered: Muskingum, which routes the runoff from each cell following the river network, and Maxbas, which routes the runoff directly to the outlet. The second concept is the spatial representation, where the model is built and tested for different spatial resolutions (500 m, 1 km, 2 km, and 4 km). The results show that the spatial sensitivity of the resolution is highly linked to the routing method, and it was found that routing sensitivity influenced the model performance more than the spatial discretization, and allowing for coarser discretization makes the model simpler and computationally faster. Slight performance improvement is gained by using different parameters’ values for each cell. It was found that the 2 km cell size corresponds to the least model error values. The proposed hydrological modeling codes have been published as open-source.

scholarly journals Modelling monthly runoff generation processes following land use changes: groundwater–surface runoff interactions

2004 ◽  
Vol 8 (5) ◽  
pp. 903-922 ◽  
Author(s):  
M. Bari ◽  
K. R. J. Smettem
Keyword(s):  
Land Use ◽  
Water Balance ◽  
Surface Runoff ◽  
Land Use Changes ◽  
Annual Rainfall ◽  
Rainfall Runoff ◽  
Runoff Generation ◽  
Mean Annual Rainfall ◽  
Monthly Runoff ◽  
Stream Bed

Abstract. A conceptual water balance model is presented to represent changes in monthly water balance following land use changes. Monthly rainfall–runoff, groundwater and soil moisture data from four experimental catchments in Western Australia have been analysed. Two of these catchments, "Ernies" (control, fully forested) and "Lemon" (54% cleared) are in a zone of mean annual rainfall of 725 mm, while "Salmon" (control, fully forested) and "Wights" (100% cleared) are in a zone with mean annual rainfall of 1125 mm. At the Salmon forested control catchment, streamflow comprises surface runoff, base flow and interflow components. In the Wights catchment, cleared of native forest for pasture development, all three components increased, groundwater levels rose significantly and stream zone saturated area increased from 1% to 15% of the catchment area. It took seven years after clearing for the rainfall–runoff generation process to stabilise in 1984. At the Ernies forested control catchment, the permanent groundwater system is 20 m below the stream bed and so does not contribute to streamflow. Following partial clearing of forest in the Lemon catchment, groundwater rose steadily and reached the stream bed by 1987. The streamflow increased in two phases: (i) immediately after clearing due to reduced evapotranspiration, and (ii) through an increase in the groundwater-induced stream zone saturated area after 1987. After analysing all the data available, a conceptual monthly model was created, comprising four inter-connecting stores: (i) an upper zone unsaturated store, (ii) a transient stream zone store, (ii) a lower zone unsaturated store and (iv) a saturated groundwater store. Data such as rooting depth, Leaf Area Index, soil porosity, profile thickness, depth to groundwater, stream length and surface slope were incorporated into the model as a priori defined attributes. The catchment average values for different stores were determined through matching observed and predicted monthly hydrographs. The observed and predicted monthly runoff for all catchments matched well with coefficients of determination (R2) ranging from 0.68 to 0.87. Predictions were relatively poor for: (i) the Ernies catchment (lowest rainfall, forested), and (ii) months with very high flows. Overall, the predicted mean annual streamflow was within ±8% of the observed values. Keywords: monthly streamflow, land use change, conceptual model, data-based approach, groundwater

scholarly journals Probability distributions for explaining hydrological losses in South Australian catchments

2013 ◽  
Vol 10 (4) ◽  
pp. 4597-4626
Author(s):  
S. H. P. W. Gamage ◽  
G. A. Hewa ◽  
S. Beecham
Keyword(s):  
Goodness Of Fit ◽  
Probability Distributions ◽  
Joint Probability ◽  
Accurate Estimation ◽  
Rainfall Runoff ◽  
Design Flood ◽  
Wide Variability ◽  
Multiple Variables ◽  
Two Parameter ◽  
Non Parametric

Abstract. The wide variability of hydrological losses in catchments is due to multiple variables that affect the rainfall-runoff process. Accurate estimation of hydrological losses is required for making vital decisions in design applications that are based on design rainfall models and rainfall-runoff models. Using representative single values of losses, despite their wide variability, is common practice, especially in Australian studies. This practice leads to issues such as over or under estimation of design floods. Probability distributions can be used as a better representation of losses. In particular, using joint probability approaches (JPA), probability distributions can be incorporated into hydrological loss parameters in design models. However, lack of understanding of loss distributions limits the benefit of using JPA. The aim of this paper is to identify a probability distribution function that can successfully describe hydrological losses in South Australian (SA) catchments. This paper describes suitable parametric and non-parametric distributions that can successfully describe observed loss data. The goodness-of-fit of the fitted distributions and quantification of the errors associated with quantile estimation are also discussed a two-parameter Gamma distribution was identified as one that successfully described initial loss (IL) data of the selected catchments. Also, a non-parametric standardised distribution of losses that describes both IL and continuing loss (CL) data were identified. The results obtained for the non-parametric methods were compared with similar studies carried out in other parts of Australia and a remarkable degree of consistency was observed. The results will be helpful in improving design flood applications.

scholarly journals Lattice Paths, Sampling Without Replacement, and Limiting Distributions

10.37236/156 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
M. Kuba ◽  
A. Panholzer ◽  
H. Prodinger
Keyword(s):  
Generating Functions ◽  
Probability Distributions ◽  
Random Variable ◽  
Phase Changes ◽  
Lattice Paths ◽  
Sampling Without Replacement ◽  
Sample Paths ◽  
Quarter Plane ◽  
Explicit Formulae ◽  
Weighted Lattice Paths

In this work we consider weighted lattice paths in the quarter plane ${\Bbb N}_0\times{\Bbb N}_0$. The steps are given by $(m,n)\to(m-1,n)$, $(m,n)\to(m,n-1)$ and are weighted as follows: $(m,n)\to(m-1,n)$ by $m/(m+n)$ and step $(m,n)\to(m,n-1)$ by $n/(m+n)$. The considered lattice paths are absorbed at lines $y=x/t -s/t$ with $t\in{\Bbb N}$ and $s\in{\Bbb N}_0$. We provide explicit formulæ for the sum of the weights of paths, starting at $(m,n)$, which are absorbed at a certain height $k$ at lines $y=x/t -s/t$ with $t\in{\Bbb N}$ and $s\in{\Bbb N}_0$, using a generating functions approach. Furthermore these weighted lattice paths can be interpreted as probability distributions arising in the context of Pólya-Eggenberger urn models, more precisely, the lattice paths are sample paths of the well known sampling without replacement urn. We provide limiting distribution results for the underlying random variable, obtaining a total of five phase changes.

Effects of Geological Structures on Rainfall-Runoff Processes in Headwater Catchments in a Sedimentary Rock Mountain

2021 ◽  
Author(s):  
Jun Inaoka ◽  
Ken'ichirou Kosugi ◽  
Naoya Masaoka ◽  
Tetsushi Itokazu ◽  
Kimihito Nakamura
Keyword(s):  
Sedimentary Rock ◽  
Flow Direction ◽  
Storm Runoff ◽  
Rainfall Runoff ◽  
Runoff Generation ◽  
Geological Structures ◽  
Headwater Catchments ◽  
Average Flow ◽  
Bedding Planes ◽  
Hydraulic Anisotropy

<p>To clarify rainfall-runoff responses in mountainous areas is essential for disaster prediction as well as water resource management. Runoff is considered to be affected by many factors including evapotranspiration, rainfall, topography, geology, vegetation, and land use. Among them, topography is said to be the most affectable factor. However, previous studies focused on geologies revealed that though catchments in crystalline mountains have less differences among runoffs, catchments in sedimentary rock mountains show great variation in their runoffs. To explain this difference, the geological structures were expected to be the key of runoffs in sedimentary rock mountains. In other words, particularly in headwater catchments located in sedimentary rock mountains, dips and strikes may significantly affect rainwater discharge. Moreover, the groundwater system can significantly be affected by the hydraulic anisotropy originated from geological stratigraphy. Additionally, in sedimentary rock mountains, previous studies suggested convergence of groundwater flows in the direction of strikes, but the effects of dips and strikes on rainfall-runoff responses were not investigated. Furthermore, none of these previous studies focused on the effects of geological structures on storm runoff responses. Therefore, based on the simultaneous observation of twelve catchments that lie radially from a single, isolated mountain peak, this study aims to clarify the effects of dips and strikes, which characterize sedimentary rock mountains, on water discharge.</p><p>The results obtained were as follows: (1) Even though the topographic wetness index (TWI) distributions of the twelve catchments were similar, there were significant differences in their runoff characteristics; (2) Catchments with average flow direction oriented toward the strike direction (strike-oriented catchments) are characterized by large baseflows; (3) Catchments with average flow direction oriented toward the opposite dip direction (opposite dip-oriented catchments) are steep, and this results in quick storm runoff generation; (4) Catchments with average flow direction oriented toward the dip direction (dip-oriented catchments) are gentle, and this results in delayed storm runoff generation. It was supposed that in strike-oriented catchments, large quantities of groundwater flowing along the bedding planes owing to hydraulic anisotropy, exfiltrate and sustain the large amount of the observed baseflow, i.e., in strike-oriented catchments, runoff is directly controlled by geological structures. On the other hand, in opposite dip-oriented and dip-oriented catchments, runoff is indirectly controlled by geological structures, i.e., geological structures affect slope gradients, which result in differences in storm runoff generation. Thus, this study clearly explains that geological structures significantly affect rainfall-runoff responses in headwater catchments located in sedimentary rock mountains.</p>

Introduction to Information Theory

2014 ◽  
Author(s):  
M. Vidyasagar
Keyword(s):  
Information Theory ◽  
Probability Distribution ◽  
Relative Entropy ◽  
Probability Distributions ◽  
Random Variables ◽  
Conditional Entropy ◽  
Random Variable ◽  
Entropy Function ◽  
Concave Functions ◽  
Leibler Divergence

This chapter provides an introduction to some elementary aspects of information theory, including entropy in its various forms. Entropy refers to the level of uncertainty associated with a random variable (or more precisely, the probability distribution of the random variable). When there are two or more random variables, it is worthwhile to study the conditional entropy of one random variable with respect to another. The last concept is relative entropy, also known as the Kullback–Leibler divergence, which measures the “disparity” between two probability distributions. The chapter first considers convex and concave functions before discussing the properties of the entropy function, conditional entropy, uniqueness of the entropy function, and the Kullback–Leibler divergence.

scholarly journals Rapid changes in snow cover at low elevations in the Sierra Nevada, California, U.S.A.

1997 ◽  
Vol 25 ◽  
pp. 367-370 ◽  
Author(s):  
Richard Kattelmann
Keyword(s):  
Snow Cover ◽  
Sierra Nevada ◽  
Mountain Range ◽  
Rainfall Runoff ◽  
Runoff Generation ◽  
Distributed Models ◽  
Rapid Changes ◽  
Spatially Distributed ◽  
Precipitation Type ◽  
River Forecasting

Snow cover in the intermittent snow zone of the Sierra Nevada can occupy more than 10 000 km2 of the mountain range, but it has received relatively little attention in river forecasting. Snow is deposited at lower elevations only during the cold storms of winter, and remains there only for a few days or weeks. When cold storms have created a thin snow cover at low elevations, a subsequent warm storm can melt this snow in just a few hours and increase the runoff response dramatically. Operational hydrological models and river-forecasting procedures have tended to overlook contributions from the intermittent-snow zone, focusing instead on rainfall-runoff or melt from the snowpack zone at higher elevations. Data-collection efforts are minimal in this zone, too. Ideally, spatially distributed models of snowmelt and runoff generation are needed to account for the typically large differences in snow cover on different aspects in the intermittent snow zone. Although aircraft and satellite imagery would be most desirable to monitor the distribution of snow cover in the intermittent-snow zone, even a few climate stations that report precipitation type and snow presence would be a major improvement over the present situation in the Sierra Nevada.

scholarly journals A Statistical Vertically Mixed Runoff Model for Regions Featured by Complex Runoff Generation Process

Water ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 2324
Author(s):  
Peng Lin ◽  
Pengfei Shi ◽  
Tao Yang ◽  
Chong-Yu Xu ◽  
Zhenya Li ◽  
...  
Keyword(s):  
Spatial Heterogeneity ◽  
Mixed Model ◽  
Soil Surface ◽  
Extreme Rainfall ◽  
Distributed Model ◽  
Generation Process ◽  
Efficiency Coefficient ◽  
Rainfall Runoff ◽  
Runoff Generation ◽  
Runoff Model

Hydrological models for regions characterized by complex runoff generation process been suffer from a great weakness. A delicate hydrological balance triggered by prolonged wet or dry underlying condition and variable extreme rainfall makes the rainfall-runoff process difficult to simulate with traditional models. To this end, this study develops a novel vertically mixed model for complex runoff estimation that considers both the runoff generation in excess of infiltration at soil surface and that on excess of storage capacity at subsurface. Different from traditional models, the model is first coupled through a statistical approach proposed in this study, which considers the spatial heterogeneity of water transport and runoff generation. The model has the advantage of distributed model to describe spatial heterogeneity and the merits of lumped conceptual model to conveniently and accurately forecast flood. The model is tested through comparison with other four models in three catchments in China. The Nash–Sutcliffe efficiency coefficient and the ratio of qualified results increase obviously. Results show that the model performs well in simulating various floods, providing a beneficial means to simulate floods in regions with complex runoff generation process.

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