Mathematical models for long-term prediction of mountainous river runoff: methods,information and results

Abstract

Unlike traditional statistical methods, a mathematical model is used to solve the problem of the long-term prediction of mountainous river runoff. The paper describes the structure of a basic model and ways of numerical presentation of macroscale rainfall fields in mountains as well as the computation of their parameters in conditions with complex relief and lack of information. The encouraging results and estimates of forecasts are discussed.     

Multiple model combination methods for annual maximum water level prediction during river ice breakup

The Athabasca River is the largest unregulated river in Alberta, Canada, with ice jams frequently occurring in the vicinity of Fort McMurray. Modelling tools are desired to forecast ice‐related flood events. Multiple model combination methods can often obtain better predictive performances than any member models due to possible variance reduction of forecast errors or correction of biases. However, few applications of this method to river ice forecasting are reported. Thus, a framework of multiple model combination methods for maximum breakup water level (MBWL) Prediction during river ice breakup is proposed. Within the framework, the member models describe the relations between the MBWL (predicted variable) and their corresponding indicators (predictor variables); the combining models link the relations between the predicted MBWL by each member model and the observed MBWL. Especially, adaptive neuro‐fuzzy inference systems, artificial neural networks, and multiple linear regression are not only employed as member models but also as combining models. Simple average methods (SAM) are selected as the basic combining model due to simple calculations. In the SAM, an equal weight (1/n) is assigned to n member models. The historical breakup data of the Athabasca River at Fort McMurray for the past 36 years (1980 to 2015) are collected to facilitate the comparison of models. These models are examined using the leave‐one‐out cross validation and the holdout validation methods. A SAM, which is the average output from three optimal member models, is selected as the best model as it has the optimal validation performance (lowest average squared errors). In terms of lowest average squared errors, the SAM improves upon the optimal artificial neural networks, adaptive neuro‐fuzzy inference systems, and multiple linear regression member models by 21.95%, 30.97%, and 24.03%, respectively. This result sheds light on the effectiveness of combining different forecasting models when a scarce river ice data set is investigated. The indicators included in the SAM may indicate that the MBWL is affected by water flow conditions just after freeze‐up, overall freezing conditions during winter, and snowpack conditions before breakup.     

Revised runoff curve number for runoff prediction in the Loess Plateau of China

The soil conservation service (now Natural Resources Conservation Service) Curve Number (SCS-CN), one of the most commonly used methods for surface runoff prediction. The runoff calculated by this method was very sensitive to CN values. In this study, CN values were calculated by both arithmetic mean (CN_C) and least square fit method (CN_F) using observed rainfall-runoff data from 43 sites in the Loess Plateau region, which are considerably different from the CN₂ values obtained from the USDA-SCS handbook table (CN_T). The results showed that using CN_C instead of CN_T for each watershed produce little improvement, while replacing CN_T with CN_F improves the performance of the original SCS-CN method, but still performs poorly in most study sites. This is mainly due to the SCS-CN method using a constant CN value and discounting of the temporal variation in rainfall-runoff process. Therefore, three factors—soil moisture, rainfall depth and intensity—affecting the surface runoff variability are considered to reflect the variation of CN in each watershed, and a new CN value was developed. The reliability of the proposed method was tested with data from 38 watersheds, and then applied to the remaining five typical watersheds using the optimized parameters. The results indicated that the proposed method, which boosted the model efficiencies to 81.83% and 74.23% during calibration and validation cases, respectively, performed better than the original SCS-CN and the Shi and Wang (2020b) method, a modified SCS-CN method based on tabulated CN value. Thus, the proposed method incorporating the influence of the temporal variability of soil moisture, rainfall depth, and intensity factors suggests an accurate runoff prediction for general applications under different hydrological and climatic conditions on the Loess Plateau region.     

On in-series correlation of minimum river runoff

Field data are used to assess the autocorrelation coefficient between successive terms in the series of minimal 30-day sums of river runoff in the winter and summer-autumn low-flow periods in the Russian territory. Zoning of the autocorrelation coefficient of winter and summer-autumn runoff is carried out within this territory, and the character of its dependence on the module and coefficient of variation of minimal runoff is studied.     

On the importance of training methods and ensemble aggregation for runoff prediction by means of artificial neural networks

ABSTRACT

Artificial neural networks (ANNs) become widely used for runoff forecasting in numerous studies. Usually classical gradient-based methods are applied in ANN training and a single ANN model is used. To improve the modelling performance, in some papers ensemble aggregation approaches are used whilst in others, novel training methods are proposed. In this study, the usefulness of both concepts is analysed. First, the applicability of a large number of population-based metaheuristics to ANN training for runoff forecasting is tested on data collected from four catchments, namely upper Annapolis (Nova Scotia, Canada), Biala Tarnowska (Poland), upper Allier (France) and Axe Creek (Victoria, Australia). Then, the importance of the search for novel training methods is compared with the importance of the use of a very simple ANN ensemble aggregation approach. It is shown that although some metaheuristics may slightly outperform the classical gradient-based Levenberg-Marquardt algorithm for a specific catchment, none performs better for the majority of the tested ones. One may also point out a few metaheuristics that do not suit ANN training at all. On the other hand, application of even the simplest ensemble aggregation approach clearly improves the results when the ensemble members are trained by any suitable algorithms.

EDITOR D. Koutsoyiannis; ASSOCIATE EDITOR E. Toth     

Discrete dynamic-stochastic model of long-term river runoff variations

A model of long-term river runoff variations is proposed. The model is based on a difference stochastic equation of water balance on a watershed. Precipitation and evaporation on the watershed are simulated by stochastic, dependent, non-Gaussian Markov processes. Long-term river runoff variations are described by a component of three-dimensional non-Gaussian Markov process. It is shown that the autocorrelation and skewness coefficients for river runoff can be negative. The proposed model can be used to assess the effect of climate-induced variations in precipitation and evaporation regimes in a watershed on long-term river runoff variations.     

Interpolation of runoff applying objective methods

The paper treats the problem of interpolating annual runoff from regular streamflow measurements in a regional scale applying objective methods. These methods are adapted to point processes like temperature and precipitation. Modifications are needed to account for the fact that streamflow is an integrated process following the hierarchical structure of river systems. The most straightforward method is therefore to relate the interpolation to the existing river network. For theoretical reasons it is preferable to interpolate the lateral inflow rather than the flow in the river itself. Procedures for the interpolation with the different approaches are developed and discussed. Special attention is put on the question how the equation of continuity can be satisfied. The Laagen drainage basin in southern Norway is used as a test area. The data consist of annual observations of streamflow and digital map information on river networks and drainage basin boundaries.     

Interpolation of runoff applying objective methods

The paper treats the problem of interpolating annual runoff from regular streamflow measurements in a regional scale applying objective methods. These methods are adapted to point processes like temperature and precipitation. Modifications are needed to account for the fact that streamflow is an integrated process following the hierarchical structure of river systems. The most straightforward method is therefore to relate the interpolation to the existing river network. For theoretical reasons it is preferable to interpolate the lateral inflow rather than the flow in the river itself. Procedures for the interpolation with the different approaches are developed and discussed. Special attention is put on the question how the equation of continuity can be satisfied. The Laagen drainage basin in southern Norway is used as a test area. The data consist of annual observations of streamflow and digital map information on river networks and drainage basin boundaries.     

Many-year variations of river runoff in the Selenga basin

Many-year variations of river runoff in the Selenga basin are analyzed along with precipitation, potential evapotranspiration, and basin water storages. Data of ground-based (1932–2015) and satellite observations, as well as the analysis of literature data suggest the presence of within-century cycles in the series of annual and minimum runoff. Compared with 1934–1975, the Selenga Basin shows a general tendency toward a decrease in the maximum (by 5–35%) and mean annual (up to 15%) runoff at an increase in the minimum runoff (by 30%), a decrease in the mean annual precipitation (by 12%), and an increase in potential evapotranspiration by 4% against the background of a decrease in evaporation because of lesser soil moisture content and an increase in moisture losses for infiltration because of permafrost degradation. The observed changes in water balance may have unfavorable environmental effects.     

Year-to-year and many-year river runoff variations in Baikal drainage basin

New approaches, methods, and formulas, proposed by the author, are used to study many-year and year-to-year variations of the annual, maximal, and minimal runoff of rivers in Baikal Lake drainage basin. The stationary character of most changes in the annual and maximal runoff (including major Baikal tributaries at the gages nearest to the lake) is demonstrated and the percentage of transient changes in the minimal runoff is shown to be close to the mean world characteristics. Some effects found in Baikal Basin have been generally recorded only in the data of runoff observations in much larger basins or globally: “the law of the power of minus 0.5” for the dependence of the coefficient of variation and the correlation between neighboring years on the mean runoff depth, a fixed structure of the orders of stochastic (autoregression models), the effect of bifurcation of the models of maximal and minimal runoff at the passage from drier to wetter watersheds.     

Discharge of biogenic substances with river runoff in Selenga basin

Averaged many-year measurement data on the concentrations of mineral forms of biogenic elements are analyzed, and their total concentrations in the rivers of Selenga, Chikoi, Khilok, Uda, Dzhida, and Temnik are evaluated. The monthly variations of the concentrations of major biogenic substances are characterized, and their ratios within a year are determined. Characteristics of river water runoff and biogenic substance concentrations are used to evaluate their within-year discharge by rivers. Characteristic variations in the ratios between the total and mineral forms of biogenic elements discharged by rivers have been revealed. It is established that the share of mineral components in the total input into the Selenga delta N_tot and P_tot are 82 and 22%, respectively.     

The application of the land surface model for calculating river runoff in high latitudes

The potentialities of the land surface model as applied to the calculation of river runoff in high latitudes were examined. Three approaches were used to specify input data based on meteorological data and land surface parameters. A method was developed for automated optimization of some model parameters by using direct search of minimum of root-mean-square deviation between the calculated and measured streamflow values. The global data sets are shown to be applicable in principle for hydrological calculations.     

地震资料预测压力方法和展望

综合介绍和评价了地震资料预测压力的各种方法,认为目前提高地震资料预测压力精度的根本方法是提高速度分析的精度和获得有针对目标区块的经验公式;同时详细分析了获取压力预测速度时需要注意的问题和可能的陷阱;提出利用声波时差等测井资料和实测压力资料获得单井压力模型,并应用单井压力模型指导速度拾取的速度分析方法,该方法基本排除各种非压力因素造成的速度异常.     

Statistical estimation of runoff characteristics of watersheds in central Chile

Abstract

Estimation of monthly runoff statistical properties, such as monthly means and variances, is usually needed to design and evaluate water resource systems. If no local recorded data are available, a transfer of information through different alternative procedures can be used. In this paper, the use of linear Transfer Function (TF) models with precipitation series as inputs is proposed to estimate statistical properties of the resulting runoff series. Empirical relationships based on data from watersheds in the mountainous zone of central Chile are suggested to estimate parameters of low-order TF models and some of their properties.     

Statistical analysis of weather-type runoff phenomena in an Alpine environment

In order to get a better insight into the role of hydrologic regime components in an Alpine environment, runoff characteristics were analysed in relation to atmospheric circulation types over a 23-yr. period. For this purpose, atmospheric circulation types were classified into hydrologically relevant classes of weather types using Schüepp's classification which was developed for the European Alpine region. It is found that the magnitude of runoff during each particular class of weather types is largely governed by autocorrelation (related to the characteristic times of the systems active during preceding classes and thus related to the preceding weather types) and by antecedent conditions, rather than by the weather types themselves. The influence of a weather class displays a distinct dependency of the time elapsed since the start of the particular class. This influence does not become manifest until after a 2–3-day period on the average.     

Statistical distributions of phytoplankton concentration in river water

Daily time series of phytoplankton concentration are theoretically analyzed with the use of population dynamics equation with fluctuations in the growth factor and environmental carrying capacity taken into account. The statistical distributions of phytoplankton cell concentration are shown to obey different laws, depending on the season of the year: lognormal in the winter and logarithmic in the vegetation period. The probability of extremely high concentration numbers is described by the normal law. The verification of the obtained relationships against a body of empirical data confirmed the theoretical forecasts. The obtained results make it possible to predict the probabilities of various phytoplankton concentration values within a wide range, including the domain of large values, which are of greatest hazard in terms of water quality, water treatment processes, and aquatic ecosystem well-being.     

Mechanism of wetting and river runoff in the east european plain

The general picture of wetting the East European Plain in 1966–1985 is established by studying the trajectories of more than 5000 cyclones in the Northern Hemisphere. The role of the Arctic High as a regulator of the paths of the Atlantic cyclones is established. It is shown that the majority of rivers of the East European Plain feature higher rate of streamflow in the years with the El Nino effect.Translated from Vodnye Resursy, Vol. 32, No. 1, 2005, pp. 108–114.Original Russian Text Copyright © 2005 by Babkin, Klige.     

Accuracy and precision of methods for estimating river loads

River loads often have to be estimated from continuous discharge data but relatively infrequent sampling of sediment, solute, or pollutant concentrations. Two standard ways of doing this are to multiply mean concentration by mean discharge, and to use a rating curve to predict unmeasured concentrations. Both methods are known from previous empirical studies to underestimate true load. Statistical considerations explain these biases and yield correction factors which can be used to obtain unbiased estimates of load. Simulation experiments with normally-distributed scatter about log-linear trends, and sampling experiments using a natural data set, show that the corrected rating curve method has lower sampling variability than other unbiased methods based on average instantaneous load and is thus the recommended procedure when the rating plot is of the assumed form. The precision of all methods increases with sample size and decreases with increasing rating-curve slope and scatter.     

Estimation of uncertainty sources in the projections of Lithuanian river runoff

Particular attention is given to the reliability of hydrological modelling results. The accuracy of river runoff projection depends on the selected set of hydrological model parameters, emission scenario and global climate model. The aim of this article is to estimate the uncertainty of hydrological model parameters, to perform sensitivity analysis of the runoff projections, as well as the contribution analysis of uncertainty sources (model parameters, emission scenarios and global climate models) in forecasting Lithuanian river runoff. The impact of model parameters on the runoff modelling results was estimated using a sensitivity analysis for the selected hydrological periods (spring flood, winter and autumn flash floods, and low water). During spring flood the results of runoff modelling depended on the calibration parameters that describe snowmelt and soil moisture storage, while during the low water period—the parameter that determines river underground feeding was the most important. The estimation of climate change impact on hydrological processes in the Merkys and Neris river basins was accomplished through the combination of results from A1B, A2 and B1 emission scenarios and global climate models (ECHAM5 and HadCM3). The runoff projections of the thirty-year periods (2011–2040, 2041–2070, 2071–2100) were conducted applying the HBV software. The uncertainties introduced by hydrological model parameters, emission scenarios and global climate models were presented according to the magnitude of the expected changes in Lithuanian rivers runoff. The emission scenarios had much greater influence on the runoff projection than the global climate models. The hydrological model parameters had less impact on the reliability of the modelling results.