NATIONAL INSTITUTE OF HYDROLOGY AND WATER MANAGEMENT (NIHWM), BUCHAREST, ROMANIA
Our expertise forecasting areas: • Short, medium and long range hydrological forecasts • Mathematical modelling of the catchment runoff • Design of flood warning and communication systems • Design and management of the hydrological data base • GIS and remote sensing applications
VIDRA FLOOD SIMULATION AND FORCASTING MODEL V I D R A M O D E L SCOPE VIDRA model is used in flood wave simulation and forecasting both in small and large basins with/without hydraulic structures. DESCRIPTION VIDRA model is a conceptual model with physically based semi-distributed parameters which are related to the basin characteristics: topography, vegetation and soil.
Descriptive diagram of the VIDRA rainfall-runoff deterministic model V I D R A M O D E L
STRUCTURES V I D R A M O D E L • Determination of the snow-melt water - The degree-day method • Calculation of the effective rainfall - PNET deterministic reservoir model • Integration of the effective rainfall on the slopes and in the primary river network - Unit hydrograph method • Composition of the flood waves and their routing along the riverbed - Muskingum transfer function • Flood wave mitigation through reservoirs - Puls method • Forecasting updating - CORA procedure
DETERMINATION OF SNOWMELT WATERComputing equations V I D R A M O D E L In order to determine the daily release of snowmelt water from the snow cover in the intervals without rainfall and during intervals with rainfall respectively the following equations given below are used: where: hz - the daily amount of snowmelt water (mm); Te - the equilibrium temperature ( ºC) whereof any heat exchange between the snow cover and the environment; Tm - the mean daily air temperature (ºC) above the Tetemperature value; M - the melting factor or the degree-day factor (mm/ºC day); hp - the amount of rainfall (mm/day); W - the wind speed (m/s); p - the forest cover coefficient; kv - a parameter having the value 1 for a deforested basin and 0,2 for a completely forested one; ki - a slope coefficient.
The effective rainfall computation model is based on the hypothesis that runoff in a watershed is similar to the runoff in a sequence of four interconnected reservoirs. EFFECTIVE RAINFALLConceptual scheme V I D R A M O D E L
EFFECTIVE RAINFALLComputing equations (1/3) V I D R A M O D E L In view of determining the infiltration, the model uses a variable infiltration curve depending on the initial soil saturation: with: where: FOM - the maximum infiltration capacity, corresponding to the plant withering point and to the rainfall intensity I; FC - the minimum infiltration capacity of the ground, corresponding to soil saturation state and to the rainfall intensity; SF - a factor considering the seasonal variation of infiltration function of the vegetation state of the slopes; USZNN - the field capacity of the reservoir corresponding to the non-saturated zone; USZN - soil moisture; UI - the initial soil moisture content; Is - standard rainfall intensity.
EFFECTIVE RAINFALLComputing equations (2/3) V I D R A M O D E L Function of the amount of precipitation P the mean infiltration INFB over the basin is: The amount of available water for surface flow is: The surface flow SS, sub-surface flow SH, percolation PERC and basic flow SB are computed in terms of the following equations: where: UD - the amount of water available in the depressions; UDM - the maximum capacity of the depression reservoir; CH - the subsurface flow parameter; PSH - the subsurface flow threshold; CB - the base flow parameter; USZN - the amount of water available in the reservoir corresponding to the saturated zone.
EFFECTIVE RAINFALLComputing equations (3/3) V I D R A M O D E L The amount of water available in the depressions will be infiltrated and evaporated. The additional infiltration in depressions is computed as follows: At each time interval the humidity from the depression reservoir and from the reservoirs corresponding to the non-saturated zone and to the saturated one, respectively, are determined as follows: The effective rainfall at each time interval (usually 1 hour) is computed as follows:
TRANSFER FUNCTIONComputing equations V I D R A M O D E L The computation of the discharge hydrographs in small basins (sub-basins) is based on the unit hydrograph method (a discrete transfer function): with: where: uj - the ordinate of the transfer function; kr - the coefficient of the hydrograph falling curve; t - time interval; N - the number of ordinates of the transfer function; T et k - parameters. For a hydrographic basin one considers three transfer functions depending on intensity range of the effective rainfall: small, medium and high.
FLOOD ROUTINGComputing equations V I D R A M O D E L The computation of the flood routing along the river bed is done by use of a Muskingum type equation: with: where: Q1 et Q2 - the ordinates of the outflow hydrograph from the river reach at the moments 1 and 2; I1 et I2 - the ordinates of the inflow hydrograph to the river reach at the moments 1 and 2; et - parameters.
FLOOD ATTENUATION AND COORDINATED CONTROL OF RESERVOIRS V I D R A M O D E L In watersheds with hydraulic structures there is a close connection between the hydrological forecasting and reservoir control. Therefore, on account of flood wave forecasting the optimum way for reservoir control is established, i.e. the reservoir outflow hydrographs are employ for hydrological forecasting downstream the reservoirs. In view of flood wave attenuation and control through the reservoirs the coordinated operation method is used. It is based on a certain classification of reservoirs into types and defining for each type, the sets of outflow hydrographs that should satisfy certain objectives and meet the operation restrictions.
CORA procedure detects the error type (amplitude, phase or shape) and realises the necessary corrections in two steps: the rough and the fine updating. UPDATING OF THE FORECAST V I D R A M O D E L
UPDATING OF THE FORECASTThe rough updating V I D R A M O D E L The rough updating is applied only in the situations where the forecast error is bigger than 10%. • If the error concerns the amplitude the input variables of the model (average rainfall over the basin and/or the effective rainfall) have to be corrected applying a coefficient. • In the situation where the error concerns the phase one shifts to the left or to right the simulated hydrograph, of such manner that it correspond as better as possible to the measured hydrograph. The phase errors are due to the modifications of the roughness of the bed after the calibration works and the embankment of the various river sectors. • If the errors concern the hydrograph shape, another type of unit hydrograph according to the rainfall intensity range is considered in the model. • In the situations where the forecasted hydrographs have to be updated, it is necessary to adapt the exploitation rules of reservoirs according to the updated hydrographs.
UPDATING OF THE FORECASTThe fine updating V I D R A M O D E L The fine updating is applied for all the situations aiming to achieve a continuity between the measured hydrograph at the moment of the issue of the forecast and the simulated hydrograph after this moment. In the case of the gauged basins, the fine updating is performed by use of the following recurrent relations: with: where: QFj+1 - the forecasted discharge; QMj - the measured discharge at the moment j; kr - the coefficient of the hydrograph falling curve; u1, u2, u3, ... - the ordinates of the transfer function; PNj-1, PNj, PNj+1 - the effective rainfall at the moments j-1, j and j+1. In the situations of river sectors, the fine updating is realized while using the propagation equation in which one replaces the forecasted discharge by the measured discharge to that moment.
CASE STUDIES V I D R A M O D E L The case studies were solved by means of VIDRA model applying aiming to: • flood wave forecasting; • assessment of anthropic influences on the natural hydrological regime; • determination of maximum discharges in basins with hydraulic structures; • computation of probable maximum floods; • assessment of the climate change impact on the hydrological resources of the analyzed basins.
D A N U B I U S M O D E L SCOPE allows the daily elaboration, with a 7 days anticipation, of the levels and discharges forecast on the Romanian sector of the Danube The mathematical model DANUBIUS is operationally applied beginning with 1987 and beginning with 1992 is running the microcomputer version. This model is made up of a simulation model and a updating procedure of the simulated discharges. The bloc scheme of the DANUBIUS model
D A N U B I U S M O D E L SIMULATION MODEL For the simulation of the flood routing on specific river sectors an non-linear model is used, resulted from the application of the system theory at the propagation process study. The nucleus function of a system of Muskingum type has two parameters K and X. The first parameter represents the travel time of the discharges in permanent regime and it is variable depending on the input discharge in the river sector and the second one indicates the degree of attenuation of discharges.
D A N U B I U S M O D E L UPDATING PROCEDURE The used updating procedure, that is applied differently for the increasing limb than for the decreasing one of the simulated discharges hydrograph at the downstream hydrometrical station, takes into account the errors between the simulated hydrograph and the recorded one and also the relation between the slopes of these hydrographs.
D A N U B I U S M O D E L CONCLUSIONS • the used forecast model made up of a simulation model and an updating procedure gives very good results at its real time application. Therefore, the errors between the forecasted levels and the measured ones are lower than 20 cm in 95%, 80%, 68%, 53%, 49%, 44% and 40% of the cases for 1, 2, 3, 4, 5, 6 and 7 days ahead. • the updating procedure leads to substantial improvement of the discharges and simulated levels, especially in the first 14 forecast days. • the errors of the hydrological forecast that occur on the Romanian sector of the Danube are due especially to the unknown with anticipation of output discharges from the Hydropower and Navigation System Iron Gate. These errors are larger for the hydrometric stations immediately situated downstream to Iron Gate and they decrease for the other stations, where the influence of the hydropower plant is lower. • the autocorrelation coefficients of the residuals of the model are lower than 0,5, except the Corabia, Turnu Mãgurele and Giurgiu stations for which the model needs to be recalibrated. • the influence of the Bulgarian tributaries of the Danube is indirectly takes into account through the updating procedure of forecasts, considering, in general, the simultaneity of their hydrological regime with the Romanian tributaries.