Journal of Hydrologic Engineering

Dynamic control of the flood limiting water level (FLWL) is a valuable and effective way to maximize the benefits from reservoir operation without exceeding the design risk. In order to analyze the impacts of input uncertainty, a Bayesian forecasting system (BFS) is adopted. Applying quantile water inflow values and their uncertainties obtained from the BFS, the reservoir operation results from different schemes can be analyzed in terms of benefits, dam safety, and downstream impacts during the flood season. When the reservoir FLWL dynamic control operation is implemented, there are two fundamental kinds of dynamic control bounds. One is the flood subseasonal FLWL dynamic control bounds, which are based on the segmentation of the flood season and the ranges of the FLWL in every flood subseason (Scheme I); the other one is the flood seasonal FLWL dynamic control bound, which takes the flood season as a whole, thus producing only one boundary [Scheme II]. The Three Gorges Reservoir (TGR) in China was selected as a case study in this paper. The application results show that the thresholds of maximum outflow, which impact the downstream and maximum reservoir levels, are not exceeded during the flood season under the analyzed FLWL control schemes. The benefits in terms of the floodwater utilization rate, hydropower generation, and water level at the end of the flood season from two dynamic controls of the FLWL scheme are better than the current design, which applies a static FLWL. For comparison, also deterministic water inflow was tested. The proposed model in the paper emphasizes the importance of analyzing the uncertainties of the water inflow forecasting system for real-time dynamic control of the FLWL for reservoir operation. For the case study, the selected quantile inflow from the Bayesian forecasting system and the matching operation are beneficial for the decision makers of the Three Gorges Reservoir.

Reliable estimation of evapotranspiration is important for many hydrological applications, including agriculture, climatology, and assessment of stormwater control measures. An automated chamber system was constructed to measure field evapotranspiration. The system consists of six chambers, sampled consecutively by means of a dynamic closed-chamber design, and is fully automated to allow replicable long-term measurements. However, the use of such a system is subject to measurement errors due to vapor adsorption along the sampling tubes and inappropriate internal ventilation. Because these issues are rarely addressed in the literature on flux chambers, a laboratory calibration was performed to estimate errors in evapotranspiration rates measured by the system. The effects of the sampling tube length and air mixing were investigated. A correction factor for evapotranspiration rates relative to the tube length was established. Appropriate air mixing induced by small fans ensured that the measured rates were representative of the internal conditions of the chambers. With appropriate internal ventilation and correction factors, the relative error of measurements was less than 5% for high evapotranspiration rates.

Drought assessment requires considering not only precipitation but also the other meteorological parameters such as an evapotranspiration. This paper presents the water surplus variability index (WSVI) as an indicator of drought. The calculation procedure incorporates both precipitation and reference evapotranspiration through the estimation of water surplus at different timescales. The WSVI is compared with the standardized precipitation index (SPI) and the reconnaissance drought index (RDI) based on 1-month, 3-month, 6-month, and 12-month timescales using data from four weather stations located in humid and subhumid climate. To approve the proposed procedure, the graphical and statistical tools such as the scatter plots, the linear trend, the coefficient of determination $R^2$, the index of agreement $d$, and the Pearson correlation coefficient $r$ were applied. The WSVI was highly correlated with both the RDI and the SPI whereas $r>0.9$. Moreover, $d$ is greater than 0.93 which indicates near perfect agreement between the WSVI and both the SPI and the RDI. This supports the opinion that the WSVI is capable to quantify drought episodes and duration, identified by the SPI and the RDI.

In this study, starting from a time-space nonstationary general random walk formulation, the pure advection and advection-dispersion forms of the fractional ensemble average governing equations of solute transport by time-space nonstationary stochastic flow fields were developed. In the case of the purely advective fractional ensemble average equation of transport, the advection coefficient is a fractional ensemble average advective flow velocity in fractional time and space that is dependent on both space and time. As such, in this case, the time-space nonstationarity of the stochastic advective flow velocity is directly reflected in terms of its mean behavior in the fractional ensemble average transport equation. In fact, the derived purely advective form represents the Lagrangian derivation of the ensemble average mass conservation equation for solute transport in fractional time-space. In the case of the fractional ensemble average advection-dispersion transport equation, the moment and cumulant forms of the equation are derived separately. In the moment form of the fractional ensemble average advection-dispersion equation of transport, the advection coefficient emerges as a combination of the fractional ensemble average advective flow velocity in fractional time and space with an advective term that is due to dispersion. The fractional dispersion coefficient emerges as a $2\beta$-momentof the differential displacement per scaled differential time ${(dt)}^{\alpha }$, where $\beta$ and $\alpha$ denote, respectively, the fractional orders of the space and time derivatives. Since this fractional dispersion coefficient is in moment form, the corresponding ensemble average equation is a moment form of the fractional ensemble average advection-dispersion equation. The cumulant form of the fractional ensemble average advection-dispersion transport equation is derived for two different cases: (1) when the order of the space fractional derivative of the advective term is the same as that of the time derivative, while the order of the space fractional derivative of the dispersion term is twice that of the time derivative, and (2) when the orders of the time and space fractional derivatives are completely different. In case (1), the advection coefficient emerges as a combination of the fractional ensemble average advective flow velocity with an advective term that is due to dispersion, while the cumulant form of the dispersion coefficient emerges as a time-space-dependent variance of the $\alpha$-moment of the differential displacement per scaled time differential ${(dt)}^{\alpha }$, resulting in a fractional advection-dispersion equation. In case (2), when the orders of the time and space derivatives are completely different, the cumulant form of the fractional dispersion coefficient emerges as a combination of the moment form of the fractional dispersion coefficient and the square of a fractional ensemble average advective velocity. The derived fractional ensemble average governing equations of transport are rich in structure and can accommodate both the non-Fickian and the Fickian behavior of transport. The non-Fickian transport behavior can be modeled by the derived fractional ensemble average transport equations either by means of the long memory in the underlying stochastic flow, or by means of the time-space nonstationarity of the underlying stochastic flow, or by means of the time and space fractional derivatives of the transport equations.

In this paper, the second in a series of two, the theory developed in the companion paper is applied to transport by stationary and nonstationary stochastic advective flow fields. A numerical solution method is presented for the resulting fractional ensemble average transport equation (fEATE), which describes the evolution of the ensemble average contaminant concentration (EACC). The derived fEATE is evaluated for three different forms: (1) purely advective form of fEATE, (2) moment form of the fractional ensemble average advection-dispersion equation (fEAADE) form of fEATE, and (3) cumulant form of the fractional ensemble average advection-dispersion equation (fEAADE) form of fEATE. The Monte Carlo analysis of the fractional governing equation is then performed in a stochastic flow field, generated by a fractional Brownian motion for the stationary and nonstationary stochastic advection, in order to provide a benchmark for the results obtained from the fEATEs. When compared to the Monte Carlo simulation-based EACCs, the cumulant form of fEAADE gives a good fit in terms of the shape and mode of the ensemble average concentration of the contaminant. Therefore, it is quite promising that the non-Fickian transport behavior can be modeled by the derived fractional ensemble average transport equations either by means of the long memory in the underlying stochastic flow, by means of the time-space nonstationarity of the underlying stochastic flow, or by means of the time and space fractional derivatives of the transport equations.

The hydrologic performance of permeable pavement systems can be affected by clogging at the pavement surface and/or clogging at the interface where the subsurface storage layer meets the underlying soil. The objective of this paper was to evaluate changes in infiltration and exfiltration using three pressure transducers installed in piezometers along the length of two, 2.47-m wide, permeable pavement strips. Each system was retrofitted in the parking lane of a curb-and-gutter system in Louisville, Kentucky. The strips received run-on from a drainage area about $20–25$ times larger than the paver area. Below each permeable pavement strip (16.8-m and 36.6-m long) was a deep (3.0 m) and narrow (0.6 m) infiltration trench. Piezometers were installed at the bottom of the trench about 1 m from the uphill edge, and at roughly one-third and two-thirds along the permeable paver strips, to measure the rise and fall of water for 13 months. Initially, infiltrating run-on was localized near the uphill edge. During periods with intense runoff, the localized inflow accumulated in the trench faster than it could move laterally creating a measureable subsurface gradient between piezometers. Runoff transported solids to the uphill edge where a portion was filtered and accumulated between the paver blocks. With time, surface clogging progressed along the paver strip past the next piezometer. The localized infiltration caused the subsurface water level gradient between piezometers to reverse. After each event, the exfiltration rate per wetted surface area was calculated for fixed 0.15-m intervals. The exfiltration rate decreased drastically after the first few events. The primary cause of the initial exfiltration rate decline was attributed to infiltrating water rinsing the fine solids attached to the washed aggregate and depositing them at the bottom of the trench. Silt and clay-sized particles (particle size smaller than 75 μm) accounted for about 1.7–1.8% of the washed aggregate mass. This large source of fine-grained particles from construction materials can be eliminated if cleaner aggregate is available and used. A continued and significant decrease in exfiltration rate with age was measured during year 1 of use. To optimize the design of these systems, a lifecycle analysis incorporating exfiltration rate decline with age should be included. Another item to consider during the design process is the variability of urban soils. Although these sites are across the street from one another, exfiltration rates were markedly different. Installation should be targeted in soils with larger hydraulic conductivities to improve hydrologic performance, so more preconstruction soil borings and soil tests are necessary to characterize the in situ soils.

This study compares sequential and variational streamflow assimilation techniques for short-term hydrological forecasting based on a lumped conceptual rainfall-runoff model and two dissimilar watersheds (Canada and Germany). The assessment targets the Ensemble Kalman filter (EnKF) and variational data assimilation (VDA). Deterministic streamflow forecasts are computed on a daily time step over a 10-day forecast horizon, using meteorological observations as inputs to the model. Results show that the EnKF leads to the highest performance for all forecast horizons while the optimal set-up for the VDA, which often competes with the EnKF, varies from one watershed to the other. EnKF surpasses forecasts without assimilation for all horizons and for both watersheds where the NSE varies between 0.88 and 0.79 on the au Saumon watershed in Canada and between 0.92 and 0.87 on the Schlehdorf watershed in Germany on a 10-day horizon, which is not always true for the VDA. The naïve output assimilation is also assessed and is only helpful for the first two days of the forecasts.

Past attempts at characterizing the hydrologic response of porous pavement systems have not distinguished between the different behaviors of drained and undrained pavements. Most models used that are appropriate for traditional catchments can be applied successfully to drained porous pavements; however, these models do not match the expected hydrologic behavior of undrained porous pavements. Undrained porous pavements exhibit a fill-and-spill response to rainfall events. While forcing an undrained pavement’s fill-and-spill behavior into a conventional runoff model may simplify design, it does so at the cost of accuracy. This research models the rainfall-runoff relationship for undrained porous pavements and proposes a broken-line model as an appropriate characterization of the behavior. The breakpoint of the model represents the initial abstraction of the pavement, and the slope of the upper line is primarily a function of the infiltration capacity of the underlying soil. Because both the initial abstraction and slope are functions of the pavement storage capacity and 24-h infiltration depth, a broad range of pavements were modeled and the results were compiled into figures, allowing the direct lookup of the model’s parameters. This new characterization of the hydrologic behavior of porous pavement provides a simple but more accurate model of the actual behavior, which will enable designers and regulators to easily calculate and understand an undrained pavement’s hydraulic behavior.

The potential of ensemble meteorological forecasts in improving ensemble spring peak flow prediction up to 14 days ahead is investigated for the Saguenay-Lac-Saint Jean watershed located in northeastern Canada. Large-scale ensemble meteorological forecasts (precipitation and temperature) generated by the National Center for Environmental Prediction’s (NCEP) Global Forecast System (GFS) are bias corrected for two meteorological stations in the watershed. The bias corrected NCEP ensemble meteorological forecast data are used as input in the hydrological model Hydrologiska Byråns Vattenbalan-avdelning (HBV) to simulate ensemble reservoir inflows and Serpent River flows up to 14 days ahead. The ensemble inflow and flow forecasts are compared with climatology as well as with the case in which only observed historical data are used for spring peak flow forecasting. The study results show that there is a significant improvement for the longer forecast range in the model forecast performance when bias-corrected NCEP forecast data are used. The improvement for forecasts for the spring season as well as for the entire year is revealed by Brier and rank probability skill score (BSS and RPSS, respectively) for reservoir inflow and Serpent River flow forecasts. Visual inspection of scatter plots between observed and simulated flows, and hydrographs of ensemble mean and ensemble members also reveal the potential of NCEP meteorological forecasts for improving spring flow forecasting.

Second order autoregressive [AR(2)] model has been adopted in the likelihood function to calibrate the soil and water assessment tool (SWAT) model for the Canard River watershed, southwestern Ontario, Canada. The Bayesian approach is used for uncertainty analysis of SWAT modeling. The performance of AR(2) model for uncertainty estimation is evaluated by the index called Percentage of observations bracketed by the unit confidence interval (PUCI) for 95% confidence limits. The results are compared with the simple least square (SLS) method of calibration. In the SLS method, the modeling errors are assumed to be uncorrelated. The study reveals that the model parameter uncertainty is high and there exists local optimum values in the parameter space. The reliability of streamflow simulation uncertainty due to parameter uncertainty is increased when AR(2) model is implemented in the calibration process. The comparison of PUCI values between AR(2) method and SLS method shows that the estimation of streamflow simulation uncertainty is more reliable in AR(2) model-based calibration method. But the lower values of PUCI indicate very high uncertainty in 95% confidence limits estimation. The residuals are observed to have nonnormal distribution with nonconstant variance. Therefore, appropriate transformation of data might improve the uncertainty estimation. The model structural uncertainty is high for simulating streamflow in the study area during low-flow and high-flow periods. Therefore, the study suggests applying separate statistical error models in the likelihood function for representing the modeling errors in low-flow and high-flow periods.

Precipitation forecasts play a key role in decision making for the water resource sector. The use of an ensemble numerical weather prediction model known as the ensemble prediction system to account for the uncertainties in weather forecasting has become common practice at various meteorological centers around the world. The current ensemble prediction systems operational at different forecasting centers vary in their parameters, including but not limited to spatial and temporal resolution, ensemble size, model physics, and initial perturbation strategy. This paper presents a comparison of six ensemble systems of varying characteristics, evaluating the quantitative precipitation forecasts issued for the Waikato River catchment in New Zealand. Three derivative products of the ensemble forecasts were used, most likely precipitation event, probability of above average rain, and ensemble mean precipitation, to test the potential application of the ensembles for resource allocation, hazard management, and catchment modeling. The forecasts of three-day cumulative precipitation, issued seven days in advance at different forecasting centers and connected through the Observing System Research and Predictability Experiment (THORPEX) Interactive Grand Global Ensemble (TIGGE) network, were compared with the corresponding areal average precipitation observed in the selected catchment over a one-year period. The research investigated the effect of ensemble size on its performance and provides users an insight into the performance of various operational EPSs of different sizes in different situations of interest. The research presented in this paper also provides a preliminary framework of the evaluation of ensembles based on their intended use by different sectors. The results of the study indicate that an increased ensemble size is not always related to better performance. It was further inferred from the results that a slight gain in accuracy may be achieved by employing larger ensembles for their intended use in hazard management than the other two applications. Additionally, the grand ensemble, constructed by combining forecasts from all other ensembles tested in the study, adds no more value to an ensemble precipitation forecast if used in the context of the three scenarios adopted in this study.

The entropy model allows estimating, in an expeditive way, both water discharge and flow velocity field in open channels. In fact, such a model presents an almost simple analytical structure based on the evaluation of a single parameter calculated through the ratio between the mean and maximum flow velocities in the cross section. Recent studies have demonstrated that for large-scale roughness, the evaluation of the entropy parameter seems to be affected by the local conditions near the bed. In order to investigate such influence, this paper proposes an explicit relationship between the entropy parameter and the relative submergence. This relation was validated using data collected in a rectangular tilting flume of laboratory in which the bed roughness was composed of elements of regular shape such as spheres. Several tests were performed in conditions of large-scale roughness ($1.9<D/d<6.4$) and for different values of slope ($0.05\%<i<1\%$) and water discharge ($7\mathrm{L}/\mathrm{s}<Q<76\mathrm{L}/\mathrm{s}$). The method shows a good agreement between the observed and calculated data for both the velocity profiles and water discharges.

Flood inundation modeling is one of the essential steps in flood hazard mapping. However, the desirable input and calibration data for model building and evaluation are not sufficient or unavailable in many rivers and floodplains of the world. A potential opportunity to fill this gap is offered nowadays by global earth observation data, which can be obtained freely (or at low cost), such as the shuttle radar topography mission (SRTM) and radar altimetry. However, the actual usefulness of these data is still poorly investigated. This study attempts to assess the value of SRTM topography and radar altimetry in supporting flood-level predictions in data-poor areas. To this end, a hydraulic model of a 150-km reach of the Danube River was built by using SRTM topography as input data and radar altimetry of the 2006 flood event as calibration data. The model was then used to simulate the 2007 flood event and evaluated against water levels measured in four stream gauge stations. Model evaluation allows the investigation of the usefulness and limitations of SRTM topography and radar altimetry in supporting hydraulic modeling of floods.

In this work, a one dimensional–two dimensional (1D–2D) coupled hydrodynamic model is developed for prediction of water levels in the lower Tapi River and its coastal urban floodplain (Surat city in Gujarat, India). A one-dimensional (1D) hydrodynamic model, calibrated for the 1998 flood, is coupled with a two-dimensional (2D) hydrodynamic model of an urban floodplain with due consideration of the upstream (releases from Ukai reservoir) and downstream (tidal level of the sea) boundary conditions. The resistance coefficient for the floodplain is estimated using satellite imagery based on the land use and land cover pattern. The coupled hydrodynamic model is validated with independent data for flooding in the year 2006 and is used to develop a stage-discharge curve along the lower Tapi River for computation of the stream power during the flood. The methodology for river flood prediction on a coastal urban floodplain using the 1D–2D coupled hydrodynamic model is generic and can be applied to similar geographical conditions.

The traditional indicator method for water-quality assessment is subjected to uncertainties in assessing water quality and quantity due to different subjective evaluations of the quality and determination of errors in the measured data set. In this study, a water-quality assessment based on the integrated measures of the fuzzy set for water-quality indicators is applied to the Huai River Basin (HRB) in China in order to avoid unnecessary errors. The single-factor method usually overestimates or underestimates the degree of risk of the comprehensive water quality since the class of the water quality is determined based only on the worst indicator. Whereas the fuzzy integrated risk assessment can indicate not only the highest grade of water pollution, but also the possible ranges of water-quality-assessment classification. There is some uncertainty, but this method provides more practical and in-depth indicators than the traditional single-factor method on water pollution risk. The final results, based on the water-quality monitor used in 2006, which collected the most representative and complete data set from 71 sites with 37 indicators in recent years, show that the comprehensive water quality in the HRB falls into Grade V (risky), and almost half of the sampling sites along the HRB have a water-quality grade of V or worse. In addition, the final integrated water-quality risk assessment shown on a geographic information system (GIS) risk map is straightforward and can be easily utilized by management decision makers.