Assessment of forest impact on river runoff plays an important role in the rational use of water resources and the choice of optimal land use management. A top priority task of this research is to find out whether the forest increases or decreases the annual river runoff and how significant these changes can be. The influence of forest on river runoff generation is a result of complicated interactions of hydrological, soil and biological processes and, consequently, for reliable estimation of changes of the annual water yield caused by forests, it is necessary to carry out experimental and theoretical studies of the entire hydrological cycle of forest watersheds. Lack of data of systematic observations and experimental studies significantly limited the possibilities of desired research and led to highly variable, often contradictory, qualitative and quantitative estimations of forest impact. It is obvious that these estimations may depend on physiographic conditions and research methods. However, according to experimental studies carried out in most countries, deforestation results in an increase of annual water yield, but in most published Russian studies deforestation decreases annual water yield of large rivers. In addition to geographical differences of the studied watersheds, these findings may be due to methodological errors in investigation or public beliefs. In this paper, we consider the peculiarities of the hydrological cycle of forested watersheds, compare methods and results of experimental investigations of the forest impact on annual water yield carried out in different countries discuss the causes of differences in estimation of the forest effect on annual runoff. We also discuss possibilities of applying mathematical modelling for improving the reliability of assessments of the impact of forest on annual runoff.

A physically based distributed model of mixed snowmelt-rainfall runoff generation in mountainous river basins is proposed. The model is based on the finite-element schematisation of catchment area and river channel network and includes description of spatial change of snow processes, soil moisture dynamics, overland, subsurface and channel flow. A case-study was carried out for the Upper Kuban River basin situated in Northern Caucasus region (the catchment area is 16900 km(2)). In the basin, eleven meteorological stations and five runoff gauges are located. The used data set includes ten years hydrometeorological measurements (1971-1980).The spatial distribution of the input meteorological data was estimated by interpolation of available measurements of these values at the meteorological stations and taking account of their changes with altitude. The mean values of topography, river channel and soil characteristics were assigned for every area or channel finite element using available topography maps, soil data and channel measurements. Six model parameters were calibrated against runoff measurements. The carried out estimations of Nash-Sutcliffe efficiency measures for calibration and verification periods have showed that the developed model gives acceptable accuracy of calculation of the runoff hydrographs. As an additional attempt of verification of the developed model, it was carried out simulation of the catastrophic flood of June 2002 during which the peak discharge was the largest for the entire observation period. The result of this verification can also be referred to satisfactory one.

A physicomathematical model of the hydrological cycle in a forested catchment was constructed. This model describes the interception of liquid and solid precipitation by tree crowns; snow accumulation and melting; vertical transfer of moisture in soil and its evaporation; and surface, subsurface, and channeled runoffs. The model was calibrated and verified using the observation data for the completely forested Taezhnyi catchment within the area of the Valdai Water Balance Station. Then the model was used to assess possible changes in the hydrological cycle after clear cuttings in this catchment. The values of model parameters were compared to the corresponding soil characteristics in the adjacent treeless (field) Usad’evskii catchment. Modeling results demonstrate that the average water reserve in the snow cover before melting can increase by 15% after forest cutting in the Taezhnyi catchment. The losses for snow sublimation are reduced almost two-fold. The snow melting intensity increases by 30% and its duration decreases by 10 days. The annual runoff after cutting increases by 7–10%; however, the seasonal distribution of the runoff and the constituents of the water balance change to a greater degree. During spring flood, the maximal water discharge in the forested catchment is 50% smaller than after forest cutting. The duration of spring flood after cutting is reduced by 5–7 days. The changes in the hydrological cycle depending on the age-related alteration in leaf area index were also studied.

Considered is the possibility of using copula theory for creating joint probability distributions of springflood peak discharges and flow volumes taking account of the relations between discharges and flow volumes. For approximation of marginal distributions, Gumbel distribution was used for peak discharges, and two-parameter gamma distribution, for flow volumes. Joint two-dimensional distribution was built as a marginal distribution function which was set as one of the three one-parameter Archimedean copulas using different ways of determining their parameters. The best results were obtained for Gumbel-Hougaard copula using the method of maximum likelihood to determine its parameters. Major flood risk estimates determined from one- and two-dimensional probability distributions of their characteristics were compared with each other. Demonstrated are the benefits of using two-dimensional probability distributions of flood characteristics as compared with one-dimensional distributions for probabilistic estimation of floods. The data on springflood peak discharges and flow volumes in the Belaya and Vyatka rivers were used for this study.

It is proposed to use the joint distribution of probabilities of minimum water discharges and the river runoff depth to characterize the severity and danger of durable low-flow periods. The copula theory is used to construct this distribution that enables to take account of differences in the types of one-dimensional probability distributions of initial variables and of the correlation between them. The studies were carried out for the vegetation periods using the data of the runoff depth measurements in Georghiu-Dej on the Don River in 1895–1980 and in Kirov on the Vyatka River in 1878–1980. The selection of copulas was based on comparing empirical and theoretical joint distributions of low-flow characteristics. It is demonstrated that the best results for the approximation of the joint probability distribution of low-flow characteristics are obtained from the Frank copula. Plotted are the dependences of low-flow frequency on the specified values of corresponding minimum water discharges and the river runoff depth during vegetation periods. Estimated are the probability and frequency of some most severe lowflow periods observed on the Don and Vyatka rivers.

Physically based model of the hydrological cycle of a forest basin was developed.The model includes description of processes of liquid water and snow interception by forest canopy, snow accumulation and melt, vertical soil moisture transfer and evapotranspiration, overland, subsurface and channel flow.The case-study has been carried out on the basis of experimental observations on the Valday water balance station, situated in the north-western part of Russia.The model has been calibrated and validated using 5-year hydrometeorological observations at the completely forested Tayozhny Creek experimental basin.Then the 17-years hydrometeorological observations were used to estimate the possible change of hydrological cycle of this basin after forest cutting.The numerical experiments have shown that the averaged snow water equivalent before snowmelt for the Tayozhny Creek basin can increase in case of forest cutting by 15%.The snow sublimation losses can decrease almost twice .The snowmelt rates after forest cutting turned out to be about 30% larger and the duration of snowmelt, on average, on 10 days longer.The simulated annual runoff from the Tayozhny Creek basin (mainly of snowmelt origin) averaged for 17 years appeared to be only about 10% higher than in case of forest cutting.However, its seasonal distribution and water balance components changed essentially.The spring flood peak discharge from the forested basin appeared to be, on average, 50% lower, the spring floods started 5-7 days later and the flood recession turned out to be much longer.About 80% of the total runoff from the Tayozhny Creek basin is now subsurface flow, while in case of deforestation overland flow may become dominant.The numerical experiments were carried out to estimate the sensitivity of the hydrological cycle to changes of leaf area index as a forest age characteristic.The estimates obtained by simulation are quite consistent with the estimates obtained on the basis of experimental research.

A technique is proposed of precomputing the snowmelt runoff hydrograph on the basis of physical and mathematical models of river runoff formation, available standard data of surface hydrometeorological measurements, and satellite measurements of Earth’s surface conditions. The computations were carried out for two regions including the basins of the Vyatka and Don rivers. It is demonstrated that, in spite of the possible errors and gaps depending on meteorological conditions, the satellite snow cover measurements can be an important addition to the surface measurements for simulating a spatial picture of the runoff formation. The use of physical and mathematical models of the runoff formation enables to reduce the errors of satellite snow cover data and to ensure the spatiotemporal continuity of its monitoring.

A dynamic‐stochastic model of flood generation consisting of a distributed physically based model of snowmelt runoff genesis and a stochastic weather generator has been used for the assessment of extreme flood risk. Coupling this model with Monte‐Carlo simulations of meteorological series allows one to calculate long series of runoff hydrographs and the exceedance probabilities of flood peak discharges and volumes. The implementation of such a dynamic‐stochastic methodology may provide an improvement in extreme flood risk assessment in comparison with the traditional flood frequency analysis of the hydrological series. However, for very rare events, the uncertainty in estimating flood risk may increase significantly. To decrease this uncertainty, it has been suggested to combine the peak discharge series obtained by dynamic‐stochastic simulations with the probable maximum discharge (PMD) calculated through the physically based model of snowmelt runoff generation. This combination is achieved by fitting the estimated exceedance probabilities of simulated peak discharges by the Johnson distribution with the PMD as the parameter. The sensitivity of the fitted Johnson distribution to the errors of the PMD estimations is analysed. A case study in Russia is carried out for the Vyatka River basin (the catchment area is 124 000 km2).

A technique of using satellite-derived data for constructing continuous snow characteristics fields for distributed snowmelt runoff simulation is presented. The satellite-derived data and the available ground-based meteorological measurements are incorporated in a physically based snowpack model. The snowpack model describes temporal changes of the snow depth, density and water equivalent (SWE), accounting for snow melt, sublimation, refreezing melt water and snow metamorphism processes with a special focus on forest cover effects. The remote sensing data used in the model consist of products include the daily maps of snow covered area (SCA) and SWE derived from observations of MODIS and AMSR-E instruments onboard Terra and Aqua satellites as well as available maps of land surface temperature, surface albedo, land cover classes and tree cover fraction. The model was first calibrated against available ground-based snow measurements and then applied to calculate the spatial distribution of snow characteristics using satellite data and interpolated ground-based meteorological data. The satellite-derived SWE data were used for assigning initial conditions and the SCA data were used for control of snow cover simulation. The simulated spatial distributions of snow characteristics were incorporated in a distributed physically based model of runoff generation to calculate snowmelt runoff hydrographs. The presented technique was applied to a study area of approximately 200 000 km2 including the Vyatka River basin with catchment area of 124 000 km2. The correspondence of simulated and observed hydrographs in the Vyatka River are considered as an indicator of the accuracy of constructed fields of snow characteristics and as a measure of effectiveness of utilizing satellite-derived SWE data for runoff simulation.

Application of the physically based model of runoff generation developed at Water Problems Institute of RAS is presented. The model is based on the finite-element schematization of the river basin. To describe the subgrid effects, we proposed that some parameters inside of finite elements are gamma-distributed. To assign the coefficient of spatial variation of these parameters, we used empirical relationships or apply scaling of gamma-distribution parameters based on the statistical self-similarity theory. The hypothesis of statistical self-similarity was applied for snow water equivalent spatial fields and for log of saturated hydraulic conductivity of soils. To test the hypothesis of statistical self-similarity for snow cover, the snowpack measurements at the river basin areas from 16000 to 100000 sq. km in five different physiographic regions of Russia were analysed. It was shown that the semi-variograms of snow water equivalent for all these regions have a power structure and the fractal dimensions varies from 2.67 to 2.92. The numerical experiments were carried out to estimate the sensitivity of runoff hydrographs to fractal dimension of the snow water equivalent fields.

The method of the plotting of probabilistic distributions of maximum runoff characteristics on the base of the dynamic-stochastic model of the river runoff formation, enabling to take account of the changes in runoff formation conditions caused by the anthropogenic activity at the river catchment, is described. To approximate the plotted distributions, it is proposed to use Johnson distribution where one of parameters is assumed to be equal to the deterministic estimate of the limiting value of the runoff characteristic. It is assumed that such an approach will increase the accuracy of the determination of the runoff values of small exceedance probabilities. The potential of the proposed method is shown by the example of determination of probabilistic characteristics of the River Vyatka maximum runoff.

A spatial model is proposed of snowmelt-rainfall runoff formation of the mountain river enabling to take account of spatial inhomogeneity of the river catchment and vertical zoning of physiographic and meteorological conditions. The model describes the processes of snow cover formation at various altitudes and snow melting, infiltration into the soils, evaporation, and overland, subsurface and riverbed flows. The verification of the model was carried out from the observational data in the Kuban River basin up to the town of Armavir.

A physically based model of runoff generation is presented which is founded on the finite-element schematization of a catchment area and describes processes of interception of liquid and solid precipitation by vegetation, snow accumulation and melt, soil freezing and thawing, infiltration of rainfall and melt water into the frozen and unfrozen soil, overland, subsurface and channel flow. The structure of the models is identified by the analysis of specific peculiarities of runoff generation mechanisms in a particular catchment. The model parameters have physical meaning and can be, in principle, measured or estimated directly from the empirical dependencies relating the model parameters to the measured catchment characteristics (topography, soil and vegetation properties, etc.). However, because of a number of reasons (e.g. inadequacy of the model, poorly defined boundary and initial conditions, heterogeneity of catchment characteristics) some key parameters need to be back-calculated from runoff data. Lack of local runoff data that could be used for calibrating the model parameters is the main challenge with application of the presented model to runoff prediction in ungauged or poorly gauged catchments. As the alternatives to calibration on runoff data two approaches are considered: (1) transferring parameters from hydrologically similar catchment, and (2) adjusting parameters through calibration against available observations (other than runoff observations) in the catchment of interest. Applicability of these approaches and their effectiveness for runoff prediction in ungauged catchments are studied by the developed model for river basins located in different physiographic zones of Russia.

In this paper, possible ways to increase effectiveness of the long-term ensemble spring floods forecasting and to assess their uncertainty based on the physical-mathematical model of the runoff formation (for the Vyatka River case study) are studied. It is shown that deterministic forecasts issued by using this approach are more accurate than those obtained from the traditional forecasting methods based on regression relationships. Probabilistic methods of forecasting of the spring flood volume and maximum discharge, which are issued by using various ways of the weather ensembles setting, are compared. Reliability of probabilistic forecasts of the volume and maximum discharge is estimated.

The flow of almost all large Russian rivers is regulated by means of reservoir cascades. Long-range forecasts of snowmelt flood characteristics have a special significance for regulation of flood runoff and mitigation of flood damages. The use of these forecasts in Russia commonly results in increases of the hydropower output by 3-5%. At the same time, the application of current methods and techniques has on many occasions led to serious failures and damage (e.g. the enormous errors in forecasting of the Volga River spring flood runoff in 1973, the prediction of variations of the Caspian Sea water level). Analysis of these failures has shown that the damage could, to a significant extent, be avoided if the decision makers had an opportunity to take into account the uncertainty in prediction and could use more cautious strategies in water resources planning and operations. At present, most hydrological forecasts and predictions that are issued in Russia are based on methods and techniques developed in the period 1950-1970. Development of distributed physically-based and dynamic―stochastic models, which properly describe the main spatiotemporal processes of runoff generation, has created, in principle, a new basis for hydrological forecasting and prediction, providing the means to improve the accuracy and reliability of hydrological predictions as well as enabling their presentation in a probabilistic form. This approach is illustrated for forecasting of the spring-summer flood volume and peak discharge of the Vyatka River.

The possibility of using a priori information to reduce the amount of hydrological observation series data needed for the calibration of physically-based models of runoff generation has been studied. It is shown that by using measurements and runoff generation models in proxy-basins, the number of parameters requiring calibration can be limited to two toor three. Investigations were carried out using a physically- based model of runoff generation in the Kolyma and Seim river basins, Russia. The possibility of using observations from water-balance stations and experimental catchments as a priori data for assigning parameters of the models is demonstrated.