Hydro logical forecasting - Prévisions hydrologiques (Proceedings of the Oxford Symposium April 1980; Actes du Colloque d'Oxford, avril 1980): IAHS-AISH Publ. no. 129.

The River flood forecast model

UBALD KOCH University of , GFR

Abstract. A flood forecast model developed for the 6455 km2 Leine basin in southeast Niedersachsen, GFR, is presented. The forecast both provides a more detailed and faster warning for endangered areas, and aids in the control of flood storage basins now under construction or planned. The model is of the deterministic distributed type and is developed from a river basin planning model. It is possible to make on-line forecasts of discrete values of a flood wave at any point within the basin. The time interval is at least 2 h, and forecasts can be made up to 36 h ahead. Results of the off-line precalibration and of the simulated forecasts are presented. Special problems solved during the development phase, and the use of such a model, are discussed in detail.

Le modèle de prévision les crues dans la Rivière Leine Résumé. On présente un modèle de prévision des crues mis au point pour le bassin fluvial de la Leine, le bassin au sud-est de Niedersachsen a une superficie de 6455 km2. La prévision sert d'un part à un avertissement plus détaillé et plus prompt, d'autre part elle sert à la régularisation des bassins de retention déjà aménagés ou projetés. Ce modèle d'un type déterministique-distribué est dérivé d'un modèle de planification. Il doit rendre possible la on-line prévision des valeurs d'une onde de crue dans toutes les parties importantes du bassin fluvial à l'aide d'une précalibration du modèle. Le pas de temps est d'au moins 2 h, le temps de prévision atteint 36 h au maximum. Les résultats de la off-line précalibration et de la prévision simulées sont présentés. Des problèmes spéciaux résolus pendant les phases de mise au point et d'application, sont discutés en detail.

DESCRIPTION OF THE REGION The River Leine rises near in the GDR and after 280 km flows into the River , GFR (Der nieders. Minister fur Ernâhrung, Landwirtschaft und Forsten, 1974). The drainage basin area near Hanover is 5329 km2 and totals 6455 km2 to the Aller confluence (Fig. 1 ). It can be divided into three sections: (1) the upper reaches including the foothills of the 'South-' and 'Soiling'; (2) the middle reaches including '-Leine-Highland'; and (3) the lower reaches, mainly plains. The hydrological character is shown by the boundary between the oceanic and continental climates. The predominant weather direction is from the northwest to the southeast. Most of the precipitation falls on the Harz Mountains, with 1000-1500 mm per year in the Harz foothills and 2000 mm in the 'Oberharz' (Haase et al, 1970). Here a rainfall of 135 mm per day has been observed. The flood discharge ratio in the Harz Mountains can reach 750 1 s-1 km""2, while in the plains values up to a maximum of 100—200 1 s_1 knT2 can be found. To the north of Gôttingen and south of Hanover heavy floods are mostly formed by the coincidence of flood waves on the River and the River with those of the River Leine. These floods are often the result of winter snowmelt and a long period of rain. The existing flood protection by the flood control storage of the five multipurpose reservoirs in the Harz Mountains is insufficient and several retarding basins are planned for the future (Wasserwirtschaftsverwaltung des Landes Niedersachsen, 1975). At the moment the biggest of these is built near the village of Salzderhelden (Fig. 1). This has a storage capacity of 37.4 x 106 m3 and a drainage basin area of 2200 km2.

203 204 . Ubald Koch

FIGURE 1. Drainage basin of the River Leine.

To increase the forecast lead time, to control the retarding basins automatically and to forecast discharges at several points of interest on the rivers Leine, Rhume and Innerste, a mathematical river basin model has been developed, which in the future will be solved by a digital computer. Data from a telemetry network will be used by the model. The River Leine forecast model 205 THE RIVER BASIN MODEL The model (Ludwig, 1979) consists of the application of algorithms by a given system description. The algorithms are presented by subroutines and comprise a program library. ANSI-FORTRAN is used. The model is of the deterministic—distributed type. System description means applying the algorithms in a given order to sections of the drainage basin. There are just two basic elements: river basin sections and river reach sections. Combining these basic elements the whole river basin can be simulated. Confluences, storages, and river sections without contributing area can also be represented. The system description also contains the regional structure and communicates with a data file which contains the following parameters and regional data: (1) area of the river basin sections; (2) surface slope of the sections and the reaches of the river; (3) coordinates of nodes (i.e. confluences, etc.), gauging stations, centres of sections and borders; and (4) several other parameters like storage capacity, area flowing full, etc. For each of these model elements the following items are calculated : (1) areal rainfall depth, (2) effective rainfall, (3) retention in the river basin section, (4) addition of the hydrograph of the section to the hydrograph of the upstream model elements, (5) flood routing of the river section; flood attenuation effect of reservoirs if necessary. These calculations are made for all model elements, beginning at the top of the stream and continuing downstream step by step. At a confluence the data are stored and the calculation is accomplished for the river basin section of the tributary. The tributary results are added to the stored hydrograph and the process continues. To find (1)—(5) mentioned above there are several alternative algorithms, enumerated briefly as follows: (1) Calculation of the depth of areal rainfall: alternatively by the Thiessen or grid-point method. (2) Calculation of the effective rainfall: (a) with constant or variable runoff coefficient; (b) with constant (PHI-INDEX) or variable rainfall infiltration rate (Horton method); (c) with PHI-INDEX method by runoff coefficients or interflow index method. (3) Calculation of the flood hydrographs of the river basin sections: (a) baseflow is assumed to be constant; (b) for calculation of the interflow a single linear reservoir model is used; (c) for direct runoff a modified Clark model or the Nash model is used. (4) Flood routing in the river sections: various methods (time of travel, Kalinin— Miljukov formula, Williams formula, or discharge velocity) are used. (5) Flood attenuation effect of a reservoir: alternatively constant or variable regulated discharge can be chosen.

CALIBRATION OF THE MODEL The calibration is necessary to evaluate the model parameters thus allowing simulation and forecasting of similar flood events. In simulation the parameter values are fixed, while in forecasting, the fixed values are used initially but can be changed during the 206 Ubald Koch forecast process. The data used for the calibration are flood hydrographs and hyetographs which are discretized in 1 -h time intervals and stored in a 'flood event data file' in the computer. There are two basic methods to evaluate the parameters of a river basin model (Ludwig, 1979): (1) sequential calibration, and (2) simultaneous calibration.

Sequential calibration This method considers every river basin section separately and the parameters are determined using conformity between observed and simulated flood hydrographs. The disadvantages are: (1) errors in observed hydrographs and disturbances in the natural runoff process can only be recognized by clearly impossible values of the parameters; and (2) the simulation model could only be used within the range of the parameter which results from various but hydrologically homogeneous observed flood events. Simultaneous calibration This method overcomes the disadvantages of sequential calibration. Suppose that similar drainage basins with approximate geomorphological homogeneity have parameters which more or less vary about a mean value and are related by a multi­ plying factor. Simulating the calibration flood events with these mean values produces discrepancies which may suggest that: (1) the area has a different runoff—precipitation relationship, or (2) there are disturbances in the runoff—precipitation relationship or (3) the data are erroneous. To evaluate the parameter, the trial and error method is used. Beginning with parameters estimated by the precalibration a good conformity with the observed hydrographs will be sought at a point where the river leaves a control section. (A control section may consist of several river basin sections.) Automatic optimization methods intended to replace the trial and error approach are under development. Simultaneous with the determination of parameters, the classification of the area regarding its runoff—precipitation relationship can be corrected. Also, problems with the data can be identified. For example, it may be found that a constant amount of water was carried by a flume from one section into another. It might be expected that such factors would be discovered before model calibration by a hydrologist with a special knowledge of the river basin. But since this is not necessarily the case in the application of river basin models, the application of simultaneous calibration can be a great advantage.

FORECAST WITH OBSERVED DISCHARGE AND PRECIPITATION The two differences between the forecast and simulation model are: (1) simplification with regard to the system description and the algorithms; and (2) extension by fore­ cast error correcting algorithms. Simplifications are possible because forecasts are only necessary for some points on the main rivers and because the methods are fixed by calibration so that there is no need for alternative methods. The forecast error correction is necessary because the first forecasts are calculated from insufficient information at the gauging stations and using mean values of the model parameters estimated from simultaneous calibration. There are two possibilities (Rademacher, 1979): (1) adaptive on-line optimization, and (2) error correction methods. The first method uses the optimization method by Gauss-Marquardt. Before a forecast for the (« + l)th step is made, the forecasted and the observed hydrographs of the n previous steps are compared and the parameter corrected. This could be called post calibration. The corrected parameters are used to make a forecast for the The River Leine forecast model 207 (n + l)th step. The second method does not correct the parameters but it rejects the forecast using the ARIMA model. This model is built up from the time series of the error of the n past forecast steps. The model provides an estimate of the forecast error for the (n + l)th step. This error will be added to the forecast of the river basin model. The forecast model is therefore given a memory. Good results have been achieved with error terms based on only two past forecast steps. Furthermore, it was found that the autocorrelation coefficients of the ARIMA model are very stable and transferable from other river basins. For each forecast at a time step the whole flood event is simulated for each control point (gauging station) using all known values of the hydrograph. Then follows the correction of the forecast. For a flood event which is eight days long, the forecast model must be used 96 times if a forecast is to be made every 2 h. The whole calculation takes 170 s using a CDC CYBER 76/12 computer. The calculations are obtained for 206 river basin sections and 140 river reach sections. There are 17 gauging stations and for each of these up to 10 optimization steps are necessary. Also seven rainrecording and 32 raingauging stations are used. Error correction is accomplished by an (2, 2, 0) ARIMA model.

EXTENSION OF THE TIME OF FORECASTS The possibility of increasing the lead time of forecasts depends on information about the precipitation in the next time interval. As yet, accurate quantitative precipitation forecasts are not available. Tests have shown that the assumption of the same rainfall depth as in the last time interval provides useful results. However, this project uses a different procedure. Only certain precipitations are important for flood warning and controlling critical discharges. They are known for the retarding basin and the most endangered areas and they are caused by the critical mean areal depth of precipitation. The conditional probability that such a critical value follows an observed value can be estimated. The problem is then reduced to estimating the conditional probability and it is therefore not necessary to estimate a certain rainfall depth for a single time interval. Another project is planned to find out if the estimation of the probability can be supported using synoptical weather data (from the atmosphere and the soil surface) from an area of about 100—200 km around the investigated river basin.

Acknowledgements. This paper is a report of a research project financed by the Volkswagen- werk Foundation.

REFERENCES Der niedeis. Minister fur Ernàhrung, Landwirtschaft und Forsten (editor) (1974) Bewirtschaftungs- plan Leine (The Leine water management plan): Eigenverlag. Haase, H., Schmidt, M. and Lenz, J. (1970) Der Wasserhaushalt des Westharzes (Regimen of the west Harz Mountains). Schr. wasserwirtschaftlichen Ges. zum Studium Niedersachsens e. V. Reihe A, 95. Ludwig, K. (1979) Das Programmsystem FGMOD zur Berechnung von Hochwasser-Abflussvor- gângen in Flussgebieten (FGMOD, a program for calculation of flood runoff processes in river basins). Wasserwirtschaft 7/8, Verlag Kosmos, Stuttgart. Rademacher, O. (1979) Adaptive optimization for discharge forecast and discharge control. Preprint, Symposium on Specific Aspects of Hydrological Computations for Water Projects, Leningrad, USSR, September 1979. Wasserwirtschaftsverwaltung des Landes Niedersachsen (1975) Hochwasser-Rùckhaltebecken Sahderhelden (The retarding basin at Salzderhelden) l.Auflage: Eigenverlag.