Copula-based modeling of hydraulic structures using a nonlinear reservoir model

Multivariate flood frequency analysis has been widely used in the design and risk assessment of hydraulic structures. However, analytical solutions are often obtained based on an idealized linear reservoir model in which a linear routing process is assumed, and consequently, the flood risk is likely to be over- or underestimated. The present study proposes a nonlinear reservoir model in which the relationships of reservoir water level with reservoir volume and discharge are assumed to be nonlinear in order to more accurately describe the routing process as it takes into consideration the interactions between hydrological loading and different discharge structures. The structure return period is calculated based on the copula function and compared with that based on the linear reservoir model and the bivariate return period based on the Kendall distribution function. The results show that the structure return period based on the linear model leads to an underestimation of the flood risk under the conditions of high reservoir water level. For the same reservoir, linear and nonlinear reservoir models give quite different reservoir volume-water level and discharge-water level curves; therefore, they differ substantially in the sensitivity to flood events with different combinations of flood peak and volume. We also analyze the effects of the parameters involved in the reservoir volume-water level and discharge-water level relationships on the maximum water level at different return periods in order to better understand the applicability and effectiveness of the proposed method for different hydraulic projects.

Storage-Discharge Relationships under Forest Cover Change in Ethiopian Highlands

Detecting the impacts of forest cover changes on hydrology is challenging given uncertainties in how changes will manifest in observed streamflow. Considering changes in the rate of change of observed streamflow (e.g., recession characteristics) may offer insights to hydrological shifts driven by forest cover change that are not seen when considering absolute changes of streamflow itself. This study assesses the impacts of forest cover changes on the storage–discharge relationships in three meso-scale watersheds in the highlands of Ethiopia based on a 30-year hydro-climatic and land cover change dataset. We analyze streamflow recessions and fitted parameters of a linear reservoir model to depict fundamental shifts in the storage–discharge relation for these watersheds. Our analysis shows that recession slopes and the total storages increase as natural forest covers decrease in the 273 km2 Woshi-Dimbira and 1980 km2 Upper-Didesa watersheds. The linear reservoir model storage coefficient parameter shows an increasing trend with time for the 41 km2 Sokoru watershed which is afforested, indicating faster drainage and reduction in storage. Our work highlights that considering storage–discharge relationships may be useful for assessing the impacts of forest cover change on water resources in regions where land use change is active and rapid.

Hillslope Contribution to the Clark Instantaneous Unit Hydrograph: Application to the Seolmacheon Basin, Korea

In this study, the time–area curve of an ellipse is analytically derived by considering flow velocities within both channel and hillslope. The Clark IUH is also derived analytically by solving the continuity equation with the input of the derived time–area curve to the linear reservoir. The derived Clark IUH is then evaluated by application to the Seolmacheon basin, a small mountainous basin in Korea. The findings in this study are summarized as follows. (1) The time–area curve of a basin can more realistically be derived by considering both the channel and hillslope velocities. The role of the hillslope velocity can also be easily confirmed by analyzing the derived time–area curve. (2) The analytically derived Clark IUH shows the relative roles of the hillslope velocity and the storage coefficient. Under the condition that the channel velocity remains unchanged, the hillslope velocity controls the runoff peak flow and the concentration time. On the other hand, the effect of the storage coefficient can be found in the runoff peak flow and peak time, as well as in the falling limb of the runoff hydrograph. These findings are also confirmed in the analysis of rainfall–runoff events of the Seolmacheon basin. (3) The effect of the hillslope velocity varies considerably depending on the rainfall events, which is also found to be mostly dependent upon the maximum rainfall intensity.

Integration of multiple observed and model-derived hydrological variables in landslide initiation threshold models in Rwanda

<p>This study was conducted using data collected from 3 catchments in North-Western region of Rwanda; Kivu, upper Nyabarongo and Mukungwa. We used two parsimonious  models, a transfer function noise time series model and a linear reservoir conceptual model, to simulate groundwater levels using rainfall and potential evapotranspiration as model inputs. The transfer function noise model was identified as the model with great explanatory predictive power to simulate groundwater levels as compared to the linear reservoir model. Hereafter, the modelled groundwater levels were used together with precipitation to explain the landslide occurrence in the studied catchments. These variables were categorized into landslide predisposing conditions which include the standardized groundwater level on the landslide day h<sub>t</sub> and prior to landslide triggering event h<sub>t-1</sub> and landslide triggering conditions which include the rainfall event, event intensity and duration.  Receiver operating characteristics curve and area under the curve metrics were used to test the discriminatory power of each landslide explanatory variable. The maximum true skill statistics and the minimum radial distance were used to highlight the most informative hydrological and meteorological threshold levels above which landslide are high likely to occur in each catchment. We will discuss our results of incorporation of groundwater information in the landslide predictions and compare these results with landslide prediction capacity which solely use of precipitation thresholds.Here we focus on at the same time on the practicalities of data availability for day-to-day landslide hazard management, both in terms of missed and false alarms</p>

Derivation of instantaneous unit hydrographs using linear reservoir models

In this research, a new conceptual model for producing instantaneous unit hydrographs (IUHs) is introduced by a linear combination of the Nash model, which assumes that the discharge from a reservoir is a linear function of its storage, and a model called inter-connected linear reservoir model (ICLRM), which assumes that the discharge from a reservoir is a linear function of the difference of its storage and its adjacent downstream reservoir. By employing these assumptions, a system of first-order linear differential equations with three degrees of freedom (storage coefficient, number of reservoirs, and weighting coefficient) is obtained as the governing equation for the proposed model. This model may be considered as the general form of the two models and is therefore capable of simulating IUHs laying between these two models. To show the capabilities of the model, linear and curvilinear soil conservation service (SCS) hydrographs are simulated using dimensionless hydrographs obtained by this model. Moreover, several real hydrographs were simulated by the proposed model and compared with hydrographs obtained by Nash, ICLRM, and SCS models. The results show that the model yields more accurate results compared to other studied models and may be considered as a new model for simulating IUHs.

Potensi Debit Aliran Lokal Waduk Saguling Menggunakan Model Hujan Limpasan

Saguling reservoir is one of the three largest reservoirs in the Citarum River Basin. The water source of its reservoir originates from Upper Citarum river basin, with gauging station located in Citarum-Nanjung and local discharge from tributaries around the reservoir. The problem is there is no observation of local discharge from the tributaries, thus its potential is estimated. The purpose of this study is to analyze the potential of local discharge with the Hydrology Engineering Center-Hydrologic Modeling System (HEC-HMS) model. The HEC-HMS Rainfall-runoff method is used for calculating the potential of the local discharge that flows into Saguling resevrvoir. The parameters used in the model are deficit constant (loss parameter), linear reservoir (baseflow parameter), dan lag time (transform parameter). Rainfall-runoff model produced good calibration values for Citarum-Nanjung Gauging Station with R2 of 0.8 and the Nash-Sutcliffe efficiency (NSE) value of 0.788. The verification result carried out in Saguling reservoir gives NSE of 0.8343 and R2 value of 0.83. The simulation shows that the potential discharge from local river contributes about 21.64% of the total discharge that enters into the reservoir with monthly dependable flow for power plants, Q80 and Q85 values at 8,23 m3/s and 5,69 m3/s, respectively. The average discharge of local rivers can generate electricity of 3.89 MW - 162 MW.Keywords: Local discharge, rainfall runoff, potential discharge, Saguling reservoir

Characterizing River Baseflow Recession Using Linear Reservoir Model in Alang Watershed, Central Java, Indonesia

Alang is a sub-watershed emptying into the Gajah Mungkur Reservoir in Wonogiri, Central Java Indonesia, with an area of 51.01 km2 and lithology composed of Baturetno Formation and Wonosari Formation. Baseflow is a major component of river flow during the dry season. Hence, the characterization of its recession becomes necessary, and it can be performed with innovation in baseflow hydrological modeling, that is, the recession curve. This study was designed to describe the distinctive features of baseflow recession using a linear reservoir model, which is depicted in individual and master recession curves. The baseflow recession in AlangSubwatershed was represented by a combination of varying initial recession discharge (Q0), α, and recession constants (Krb). The individual recession curves were typified by Q0=0.19-9.11, α= 0.089-0.243, and Krb=0.7843-0.9148. As for the master recession curve, it had Q0=9.99, α=0.085, and Krb=0.928. These results signify a sloping recession curve, meaning that the water storage and aquifer characteristics that store and transmit water in Alang Subwatershed are in good condition.

Evaluation of aquifer parameters at regional scale by spectral analysis of discharge time series

<p>River stream is the result of several complex processes operating at basin scale. Therefore, the river catchment can be conceptualized as a series of interlinked compartments, which are characterized by their own response time to a rainfall event. Each compartment generates a flow component, such as the direct runoff, the interflow and the baseflow. The latter, typically generating from groundwater, is the slower portion of stream flow and plays a key role in studying the hydrological droughts.</p><p>In many catchment or large-scale hydrologic models, the groundwater dynamics are typically described by a linear reservoir model, which depends on the state of the reservoir and the parameter, known as recession coefficient or characteristic time. The characteristic time can be considered as the time needed until an aquifer reacts to a certain perturbation. So far, the characteristic time has been estimated by analyzing the slope of the recession (discharge) curve. However, as this method assumes that the recharge is zero within the basin, it may lead to inaccurate estimate when such a hypothesis is not fulfilled in reality.</p><p>The present work proposes to infer the characteristic time by using a stochastic approach based on spectral analysis. The catchment aquifer can be viewed as a filter, which modifies an input signal (e.g., rainfall or recharge) into an output signal (e.g., the baseflow or the hydraulic head). Since the transfer function, namely the ratio between the spectrum of baseflow and the spectrum of recharge, is dependent on the aquifer characteristics, it can be used to infer the aquifer parameters. In particular, the characteristic time is evaluated by fitting the spectrum and the variance of the measured baseflow with the analytical stochastic solutions for the linear reservoir. We compare six different methods for hydrograph separation, thereby highlighting a systematic uncertainty in determining the characteristic time due to the choice of filter used. To reduce the uncertainty in fitting, we will use the mesoscale Hydrological Model (mHM) (Samaniego et al., 2010; Kumar et al., 2013) to generate realistic time series for recharge. We apply the spectral analysis method to several river basins in Germany, with the goal to define a regionalization rule for characteristic time.</p><p> </p><p>References:</p><ul><li>Samaniego L., R. Kumar, S. Attinger (2010): Multiscale parameter regionalization of a grid-based hydrologic model at the mesoscale. Water Resour. Res., 46, W05523, doi:10.1029/2008WR007327.</li> <li>Kumar, R., L. Samaniego, and S. Attinger (2013): Implications of distributed hydrologic model parameterization on water fluxes at multiple scales and locations, Water Resour. Res., 49, doi:10.1029/2012WR012195</li> </ul>

Design of rainwater detention basins

<p>Traditionally in Denmark, rainwater detention basins are designed based on an input box rain with a given return period and a constant outflow from the basin. The water authorities specify the outflow rate in order to avoid erosion in the recipient. Intensity-Duration-Frequency (IDF) curves are used as a prerequisite for the method. Given the design return period, and varying the duration of the box rain, the basin volume that prevents spill from the basin can be determined. By analysing for a series of outflow rates, a basin volume curve for the selected return period can be developed. The current practice is revisited, and a new analytical solution for the duration of the design rain is found.</p><p>A constant outflow rate for the basin is, however, not always a realistic assumption, and thus there is a risk for underestimation. An alternative design method has been analysed, assuming that the outflow from the basin takes place corresponding to at linear reservoir with maximum outflow rate equal to the one specified by the water authorities. The method is described in detail, and the results compared with those of the current guidelines.</p>

Analytical River Routing with Alternative Methods to Estimate Seepage

Knowledge of flow exchange between surface and groundwater is of great importance for use of water resources. The determination of seepage between a stream and an underlying aquifer requires an accurate estimation of the river stage and of the head in the aquifer. An approach is presented to estimate analytically river flow and stage while using the SAFE conductance to calculate the seepage. A major contribution of this article lies in the methodology for river routing with its use of a modified Linear Reservoir model. The parameter C is related to discharge based on Manning’s equation. That relation breathes into an empirical model a dynamic character. A second major contribution is to show that it is possible to simultaneously calculate river stage and aquifer head in the aquifer cell that contains the river. As a result iteration is not necessary to estimate that river cell head as river stage changes, as opposed to what is usually done in most numerical groundwater models. Iteration is still needed for the adjacent cells to the river cell. Because the influence of a change in the adjacent cell head on the river cell head is much delayed and attenuated the iteration is not sensitive to that change. A goal of this document is to show how that method can be used within a simple physically based routing procedure [1] to estimate the river stage that has a definite influence on seepage.