Streamflow simulation: A nonparametric approach

An entropy‐copula method is proposed for single‐site monthly streamflow simulation. In this method, the joint distribution of adjacent monthly streamflows is constructed using the copula method, whereas the marginal distribution of streamflow for each month is derived using the entropy method. Then, the conditional distribution is derived from which monthly streamflow is generated. Moment statistics of monthly streamflow (such as mean, standard deviation and skewness) can be modeled by the entropy‐based marginal distribution while the dependence structure between streamflows of adjacent months can be modeled by the copula‐based joint distribution. The proposed entropy‐copula method can be extended by incorporating an aggregate variable for modeling the interannual dependence. Application to the simulation of monthly streamflow from the Colorado River illustrates the effectiveness of the proposed method.

A conditional beta probability density function is employed to model time-delay measurement errors associated with sensors used in triangulation ranging applications. This type of density function is less restrictive than the beta density used in previous analyses in that end points can be extended out beyond the imposed range constraints and data editing is allowed before range calculations. The resulting conditional range density function is computed along with the mean and variance. Comparisons are made of the pertinent range statistics associated with the beta and conditional beta density functions. Finally, the conditional beta density function range statistics are compared with those obtained from a gated Gaussian density function for equivalent values of time-delay measurement error standard deviation. The Gaussian statistics are determined via Monte-Carlo simulation.

Application of an inappropriate Digital Elevation Model (DEM) might lead to uncertainty in modelling of the hydrological cycle. The novelty of this work is the development of a comprehensive framework to evaluate the effect of DEM resolution (12 to 500 m), source (TanDEM-X, SRTM, AW3D30 and ASTER GDEM2), resampling technique (nearest neighbour, bilinear interpolation, cubic convolution and majority) and area threshold (1000 to 50,000 ha) on Soil and Water Assessment Tool (SWAT) outputs based on five criteria: (1) river network extraction, (2) streamflow simulation, (3) topography, slope and basin characteristics, (4) hydrological and (5) water quality simulations. Kelantan River Basin, a tropical basin in Peninsular Malaysia was selected as study area. The major findings are summarized as follows: (1) TanDEM-X had better river network extraction capability than ASTER GDEM2, (2) better monthly streamflow simulations were obtained between 20 m and 60 m DEM resolutions, with the smallest area threshold (1000 ha), (3) TanDEM-X and SRTM DEMs outperformed ASTER GDEM2 on monthly streamflow simulation, (4) DEM resolution, source and resampling technique were insensitive to most of the hydrological components, except the lateral flow, (5) area threshold was sensitive to SWAT-simulated surface runoff, soil water content and evapotranspiration, (6) DEM scenarios had a larger impact on sediment yield simulations compared to the total nitrogen and total phosphorus simulations. We recommend a preliminary assessment of DEM uncertainties on SWAT outputs to obtain more reliable modelling outputs.

Investigating the dynamic characteristic of hydrological processes is of vital significance for environmental protection. In this study, the stepwise cluster analysis (SCA) method was used for monthly streamflow simulation in a hypothetical case. According to SCA, a cluster tree was formulated through training the data of monthly temperature, precipitation and streamflow from 2004 to 2010. Then, the generated tree was used to reproduce monthly streamflow in calibration period (i.e., 2004-2010) and validation period (i.e., 2011-2013). A comparison of SCA and multiple linear regression (MLR) was conducted to reflect the complex relationship of meteorological parameters (e.g., precipitation) and hydrological parameters. Model performance was assessed using Nash-Sutcliffe efficiencies (NSE), the determination coefficient (R 2), the root-mean-square error (RMSE) and the mean absolute error (MAE). NSE and R2 obtained from SCA are higher than that obtained from MLR. RMSE and MAE obtained from SCA are smaller than that obtained from MLR, indicating a better coincidence between simulated streamflow and the observed values in SCA. Results indicated that SCA has advantage in revealing the nonlinear relationship among precipitation, temperature and streamflow.

평창유역의 적설량을 모의하기 위하여 HSPF 모형을 적용하였다. 미래 적설량을 평가하기 위해 CIMIP3에서 제공하는 A1, A1B, B1의 온실가스 배출시나리오에 기반한 GCMs를 이용하였으며, HSPF 모형과 GCMs의 통계학적 오류를 최소화 하기 위해 편의보정(Bias-correction)과 시간적 분해모형(Temporal disaggregation)을 적용하였다. 모형의 검 보정 결과 모의된 유출량과 적설량의 경우 모형 효율이 높게 나타났으며, 특히 모형의 검정 후 상관계수를 분석한 결과 월별 유출량의 상관계수는 0.94로 나타났다. 월별 적설량, 또한, 상관계수가 0.91로 나타나 보정된 HSPF 모형이 평창지역에 대한 유출량과 적설량을 잘 모의하고 있는 것으로 판단된다. GCMs를 이용한 2018년 평창올림픽 경기장의 적설량을 분석한 결과 1월에는 17.62%, 2월에는 9.38%, 3월에는 7.25%의 적설량이 감소되는 것으로 나타났다. Hydrological simulation Program-Fortran (HSPF) model was used to simulate streamflow and snow depth at Pyengchang watershed. The selected Global Climate Models (GCMs) provided by the Coupled Model Intercomparision Project Phase 3 (CMIP3) were utilized to evaluate streamflow and snow depth driven by future climate scenarios, including A1, A1B, and B1. Bias-correlation and temporal downscaling processes have been performed to minimize systematic errors between GCMs and HSPF. Based on simulated monthly streamflow and snow depth after calibration, the results indicate that HSPF performs well. The correlation coefficient between the observed and simulated monthly streamflow is 0.94. Snow depth simulations also show high correlation coefficient, which is 0.91. The results indicate that snow depth in 2018 at Pyongchang winter olympic venues will decrease by 17.62%, 9.38%, and 7.25% in January, February, and March respectively, based on streamflow realizations induced by all GCMs ensembles.

Generalized Laguerre expansions of multivariate probability densities with moments

Reliable long-term streamflow forecasting is invaluable for water resource planning and management which allocates water supply according to the demand of water users. It is necessary to get probabilistic forecasts to establish risk-based reservoir operation policies. Probabilistic forecasts may be useful for the users who assess and manage risks according to decision-making responding forecasting results. Probabilistic forecasting of seasonal inflow to Andong dam is performed and assessed using selected predictors from sea surface temperature and 500 hPa geopotential height data. Categorical probability forecast by Piechota's method and logistic regression analysis, and probability forecast by conditional probability density function are used to forecast seasonal inflow. Kernel density function is used in categorical probability forecast by Piechota's method and probability forecast by conditional probability density function. The results of categorical probability forecasts are assessed by Brier skill score. The assessment reveals that the categorical probability forecasts are better than the reference forecasts. The results of forecasts using conditional probability density function are assessed by qualitative approach and transformed categorical probability forecasts. The assessment of the forecasts which are transformed to categorical probability forecasts shows that the results of the forecasts by conditional probability density function are much better than those of the forecasts by Piechota's method and logistic regression analysis except for winter season data.

In this paper, we present a proportionate-type normalized least mean square algorithm which operates by choosing adaptive gains at each time step in a manner designed to maximize the joint conditional probability that the next-step coefficient estimates reach their optimal values. We compare and show that the performance of the joint maximum conditional probability density function (PDF) one-step algorithm is superior to the proportionate normalized least mean square algorithm when operating on a sparse impulse response. We also show that the new algorithm is superior to a previously introduced algorithm which assumed that the conditional PDF could be represented by the product of the marginal conditional PDFs, i.e., that the weight deviations are mutually conditionally independent.

Bayesian model averaging (BMA) is a popular approach to combine hydrologic forecasts from individual models and characterize the uncertainty induced by model structure. In the original form of BMA, the conditional probability density function (PDF) of each model is assumed to be a particular probability distribution (e.g., Gaussian, gamma, etc.). If the predictions of any hydrologic model do not follow certain distribution, a data transformation procedure is required prior to model averaging. Moreover, it is strongly recommended to apply BMA on unbiased forecasts, whereas it is sometimes difficult to effectively remove bias from the predictions of complex hydrologic models. To overcome these limitations, we develop an approach to integrate a group of multivariate functions, the so‐called copula functions, into BMA. Here we introduce a copula‐embedded BMA (Cop‐BMA) method that relaxes any assumption on the shape of conditional PDFs. Copula functions have a flexible structure and do not restrict the shape of posterior distributions. Furthermore, copulas are effective tools in removing bias from hydrologic forecasts. To compare the performance of BMA with Cop‐BMA, they are applied to hydrologic forecasts from different rainfall‐runoff and land‐surface models. We consider the streamflow observation and simulations for 10 river basins provided by the Model Parameter Estimation Experiment (MOPEX) project. Results demonstrate that the predictive distributions are more accurate and reliable, less biased, and more confident with small uncertainty after Cop‐BMA application. It is also shown that the postprocessed forecasts have better correlation with observation after Cop‐BMA application.

A new method for the approximation of multivariate scalar probability density functions (PDFs) in turbulent reacting flow by means of a joint presumed discrete distribution (jPDD) is presented. The jPDDs can be generated with specified mean values and variances as well as covariances. Correlations between variables – e.g. fluctuating mixture fractions and/or reaction progress – can thereby be taken into account. In this way the new approach overcomes an important limitation of ordinary presumed PDF methods, where statistical independence between the variables is often assumed. Different methods are presented to generate discrete distributions, based either on biased random number generators or on mixing models familiar from PDF transport models. The new approach is extensively validated on a turbulent flow configuration with simultaneous mixing and reaction. Large eddy simulation data as well as results from a transported PDF model are used for the validation of the jPDD approach. The comparison shows that in particular distributions generated with mixing models are able to predict mean reaction rates accurately. For the configuration considered, the neglect of correlations results in significant underestimation of reaction rates. Moreover it is found that higher statistical moments (e.g. the skewness) can influence reaction rates. The consequences for the generation of jPDDs are discussed. In summary, the new jPDD model has the potential to be significantly more accurate than established presumed PDF methods, because correlations between fluctuating variables can be taken into account. At the same time, the new approach is nearly as efficient as standard presumed PDF formulations, since mean rates are computed in a pre-processing step and stored in look-up tables as a function of the first and second moments of the relevant variables.

Background modelling is one of the main challenges in particle physics data analysis. Commonly employed strategies include the use of simulated events of the background processes, and the fitting of parametric background models to the observed data. However, reliable simulations are not always available or may be extremely costly to produce. As a result, in many cases uncertainties associated with the accuracy or sample size of the simulation are the limiting factor in the analysis sensitivity. At the same time, parametric models are limited by the a priori unknown functional form and parameter values of the background distribution. These issues become ever more pressing when large datasets become available, as it is already the case at the CERN Large Hadron Collider, and when studying exclusive signatures involving hadronic backgrounds.A widely applicable approach for non-parametric data-driven background modelling is proposed, which addresses these issues for a broad class of searches and measurements. It relies on a relaxed version of the event selection to estimate conditional probability density functions and two different techniques are discussed for its realisation. The first relies on ancestral sampling and uses data from a relaxed event selection to estimate a graph of conditional probability density functions of the variables used in the analysis, while accounting for significant correlations. A background model is then generated from events drawn from this graph, on which the full event selection is applied. In the second, a novel generative adversarial network is trained to estimate the joint probability density function of the variables used in the analysis. The training is performed on a relaxed event selection, which excludes the signal region, and the network is conditioned on a blinding variable. Subsequently, the conditional probability density function is interpolated into the signal region to model the background. The application of each method on a benchmark analysis and on ensemble tests is presented in detail, and the performance is discussed.

The soil and water assessment tool (SWAT) is a widely accepted semi-distributed agrohydrological model. In the present study, the SWAT has been calibrated for the agriculture-dominated Kantamal catchment of Mahanadi river basin, Odisha, India, to simulate streamflow at the Kantamal gauging station. The model was run for 19 years from 2000 to 2018 to simulate monthly streamflow. In addition, the model has been calibrated for the period 2004 to 2012, considering the initial 4 years (2000-2003) as a warm-up period and validated for 6 years from 2013 to 2018. Uncertainty analysis was carried out using the SUFI-2 algorithm in SWAT-CUP. The sensitivity of the parameters was determined using the t-stat and p-value. Fifteen distinguished parameters were selected for sensitivity analysis (SA). The performance of the model was evaluated satisfactorily on monthly time scale streamflow simulation using Nash- Sutcliffe Efficiency (NSE), coefficient of determination (R2), and percentage BIAS (PBIAS). The P- and R- factors were used to assess the degree of uncertainty. The values of NSE, R2, and PBIAS were found to be 0.91, 0.94, and -0.07 during the calibration period and 0.82, 0.87, and -0.16 during the validation period, respectively. The P- and R- factors values were 0.77 and 0.98 during calibration and 0.79 and 0.86 during the validation period, respectively. The simulated streamflow is well fitted within the 95% prediction uncertainty (95PPU) band of the SUFI-2 algorithm during the calibration and validation periods, indicating a satisfactory model performance under parameter uncertainty. Overall, it is depicted that the SWAT model can be successfully used for streamflow modeling and water resources assessment in agriculture-dominated catchments.

MRI significantly improves the accuracy and reliability of target delineation in radiation therapy for certain tumors due to its superior soft tissue contrast compared to CT. A treatment planning process with MRI as the sole imaging modality will eliminate systematic CT/MRI co-registration errors, reduce cost and radiation exposure, and simplify clinical workflow. However, MRI lacks the key electron density information necessary for accurate dose calculation and generating reference images for patient setup. The purpose of this work is to develop a unifying method to derive electron density from standard T1-weighted MRI. We propose to combine both intensity and geometry information into a unifying probabilistic Bayesian framework for electron density mapping. For each voxel, we compute two conditional probability density functions (PDFs) of electron density given its: (1) T1-weighted MRI intensity, and (2) geometry in a reference anatomy, obtained by deformable image registration between the MRI of the atlas and test patient. The two conditional PDFs containing intensity and geometry information are combined into a unifying posterior PDF, whose mean value corresponds to the optimal electron density value under the mean-square error criterion. We evaluated the algorithm’s accuracy of electron density mapping and its ability to detect bone in the head for eight patients, using an additional patient as the atlas or template. Mean absolute HU error between the estimated and true CT, as well as receiver operating characteristics for bone detection (HU > 200) were calculated. The performance was compared with a global intensity approach based on T1 and no density correction (set whole head to water). The proposed technique significantly reduced the errors in electron density estimation, with a mean absolute HU error of 126, compared with 139 for deformable registration (p = 2 × 10−4), 283 for the intensity approach (p = 2 × 10−6) and 282 without density correction (p = 5 × 10−6). For 90% sensitivity in bone detection, the proposed method achieved a specificity of 86%, compared with 80, 11 and 10% using deformable registration, intensity and without density correction, respectively. Notably, the Bayesian approach was more robust against anatomical differences between patients, with a specificity of 62% in the worst case (patient), compared to 30% specificity in registration-based approach. In conclusion, the proposed unifying Bayesian method provides accurate electron density estimation and bone detection from MRI of the head with highly heterogeneous anatomy.

Probabilistic distribution coefficients ( Kds) in freshwater for radioisotopes of Ag, Am, Ba, Be, Ce, Co, Cs, I, Mn, Pu, Ra, Ru, Sb, Sr and Th – implications for uncertainty analysis of models simulating the transport of radionuclides in rivers

This paper describes a method for evaluating the effectiveness of the route guidance system, which provides a driver with individual information to accomplish a trip under such objectives as the travel time saving, the fuel saving, the reduced air pollution and the reduced traffic accident etc.. In this paper the travel time saving is chosen as an evaluation criterion of this system. The travel time indicates the time required from a driver's specific origin (O) to his specific destination (D). Multiple routes may be chosen with each specific O-D, owing to his route choice criteria and to his trial and error. The route choice probability is defined, based on a traffic study of a driver's comprehension of road configuration. On the other hand, the travel time along the selected route is affected by the vehicular type, the traffic flow, the traffic regulation, the traffic signal and the weather etc.. In this paper the travel time is defined in terms of a conditional probability density function. The characteristics of the function are examined by a traffic study of travel time using an improved license matching technique.The probability density function of the travel time in the case of the specific O-D is composed of the route choice probability and the conditional probability density functions, mentioned above. Comparing the probability density function of a guided vehicle with that of a non-guided vehicle, a mathematical formula to calculate the amount of travel time saving is derived.