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CONTINUOUS FLOOD FORECASTING COMBINED WITH AUTOMATIC FORECAST CORRECTION – APPLICATION ON THE MUR RIVER Christophe Ruch1, Gregers Jø rgensen2, Janez Polajnar3, Mojca Susnik3, Rudolf Hornich4, Robert Schatzl4, Nejc Pogačnik5 1

Institute of Water Resources Managment - Hydrogeology and Geophysics, Joanneum Research Forschungsgesellschaft mbH 8010 Graz, Austria 2 DHI Water - Environment - Health 2970 Hø rsholm, Denmark 3 Environmental Agency of the Republic of Slovenia 1000 Ljubljana, Slovenia 4 Amt der Steiermärkischen Landesregierung - FA19B and FA19A 8010 Graz, Austria 5 University of Ljubljana, Faculty for Civil and Geodetic Engineering, Chair of fluid mechanics 1000 Ljubljana, Slovenia [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]

Abstract In this paper the structure of the trans-boundary flood forecasting for the Mur river is illustrated. This modern system, which is operational since 2006, is built on continous simulations with automatic data assimilation for the hindcast and forecast period. Special attention is given to the hydro-meteorological online network, the meteorological forecasts, the coupled hydrological and hydrodynamic modelling and the automatic data assimilation. Keywords: Trans-boundary flood forecasting, continuous simulation, automatic forecast correction. 1

INTRODUCTION

The development of the Mur Flood Forecasting System is a project with European dimensions. Rivers don’t care about human borders, wishes and needs. The Mur watershed extends over four countries: Austria (about 10000 km²), Slovenia (about 1400 km²), Hungary (about 1900 km²) and Croatia (about 500 km²), whereas the three last mentioned countries are located downstream compared to Austria. Due to these geographical characteristics the probability for a flood genesis is much more significant in Austria than in the other countries but the related flooding risks are distributed over the entire watershed. The project “Hochwasserprognosemodell Mur” (Flood Forecasting Model Mur, Ruch & Jø rgensen 2006a and 2006b) gives a concrete example of international cooperation in the field of Flood management but unfortunately limited to Austria and Slovenia. The good and long cooperation between the four countries concretised in the “Mur Commission” on the one side and the financial support from the European Commission on the other side was the basis for creation of this project. The responsible institutions for water resources management in the Mur watershed have made a decisive step in the direction of an integrated and sustainable watershed

management. The structure developed in this project allows enlarging (1) the study field to topics like water quality, sediment transport and erosion or even low flow and (2) the studied area to Hungary and Croatia or even to the Drau River. The structure that has been established built on an International Flood Forecasting Centre installed in Graz (Austria) and two national centres installed in Ljubljana (Slovenia) and Graz (Austria) illustrates how a trans-boundary flood forecasting system can operate. The main element is the International flood forecasting system. This structure has been presented during the XXIII conference of the Danubian countries (Ruch et al., 2006). Further published information can be found in Schatzl & Ruch (2006). The present paper shall focus more on the online measurement network, the use of meteorological forecasts, the hydrological and hydrodynamic modelling approaches, the implementation of continuous simulation and the automatic data assimilation. It can be estimated that continuous simulation (starting each hour in the Mur flood forecasting system case) combined with automatic data assimilation represents the actual state of the art for flood forecast modelling in meso-scale watersheds. Large flood forecasts uncertainties can be reduced significantly also because meteorological forecasts are renewed each hour. Clearly, this technology can and should be improved in future and there exists great potential to reduce flood impacts to an acceptable level especially if forecast systems are embedded in larger IT structure for warning dissemination. The modules implemented in the Mur flood forecasting system (FFS) are presented in this paper whereas a special focus is given to the added value offered by the use of these modules when implemented simultaneously in one FFS. A short overview regarding the Mur FFS structure is given in the next section. More details about the online meteorological network, the use of meteorological forecasts, the hydrologic and hydrodynamic models, the data assimilation and the automatic simulation are given in section 3 to 8 respectively. 2

GENERAL STRUCTURE AND THE CONTINUOUS SIMULATION

A short overview over the structure of the Mur Flood Forecasting System (Mur FFS) is given here whereas a more detailed description can be found in the literature mentioned in section 1. The special challenge of the trans-national Mur FFS is to manage measured and forecasted data from Austria (Styria) and Slovenia in a way that allows both countries to access the same information level. This is achieved through the implementation of three FFS (the central international FFS installed in Graz at “Amt der Steiermärkischen Landesregierung - FA19A”, the national Slovenian FFS installed in Ljublana at the Environmental Agency of the Republic of Slovenia, the national (regional) Austrian FFS installed in Graz also at “Amt der Steiermärkischen Landesregierung - FA19A”) that share completely identical model setups, measured hydro-meteorological time series, meteorological forecasts and simulation results data (see figure1). Input data for the models (hydro-meteorological online measurements – section 3 and meteorological forecasts – section 4) are retrieved using the two national FFSs. All data are further imported automatically from the international FFS each hour before a simulation starts. After the simulation (section 5, 6 and 7) that covers two days hindcast and two days forecast is finished, results are published on a password protected homepage. The complete simulation setup is zipped and transferred to a

FTP address to be downloaded automatically from the Slovenian national centre (in Graz this is done via intranet connection). This procedure ensures that responsibilities for issuing flood forecasts over the national part of the Mur river watershed still belong to each country. Furthermore, the only “obligatory” task in Graz is to ensure the correct functioning of the International FFS so that the setup is always available.

Figure 1. The general structure of the Trans-boundary Mur FFS. A second challenge is to build a structure allowing 1) enlarging the system to the entire Mur river watershed, i.e., include both countries Hungary and Croatia in future and 2) extending the modelling structure to other water management topics in the Mur river watershed like low flow forecasting, climate change effects on water resources and/or water temperature modelling. To ensure the realisation of both tasks, the flexible FFS shell Mike Flood Watch combined with the hydrologic and hydrodynamic modelling systems Nam and Mike 11 respectively (DHI – Water and environment , 2005) that are further described in section 5. The Mur FFS structure shown in Figure 1 is conceived so that extensions to Hungary and/or Croatia can be added without affecting the actual data flow. Both countries would be incorporated in the Mike Flood Watch system with a communication framework identical to one implemented for Slovenia. Furthermore, the choice of conceptual rainfall-runoff modelling at the sub-catchment scale (Nam model) coupled with hydrodymamic modelling for the Mur river and its main tributaries (Mike11) permits to simulated many different processes related to water resources management. This is achieved by adding modules in the modelling structure like for example the advection dispersion module for modelling water temperature within the Mike11 modelling system.

3

ONLINE HYDRO-METEOROLOGICAL MEASUREMENT NETWORK

The online measurement network is an important component in modern FFSs because it allows following the evolution of hydro-meteorological conditions in a quasi continuous and real time manner. But online station doesn’t mean necessarily real or quasi real time data transmission. For example field data are retrieved only once a day in Styria during “normal” hydro-meteorological conditions and each hour when rainfall or water level alerts threshold are crossed. Thus, the “best” information is at least one hour old. It is important to note that these limits are due to the costs for data transmission and are not of technical nature. In Styria, it is planned for the near future to reduce the data transmission to one hour for all stations during all conditions. In Slovenia, data are collected each hour independently of the hydrometeorological conditions. There is an important gain in the forecasts quality when online data are available in quasi real time. These allow controlling the model initial conditions, i.e., the conditions at the time of forecast minus one hour, and eventually to correct in an automatic modus the forecasts like it is the case for the Mur FFS (see section 5). Beside the online data availability (in time), it must be recognised that the distribution of the hydro-meteorological stations in space is a second crucial characteristic that influence decisively the forecast quality. This is of paramount importance when hydro-meteorological data vary significantly over short distances like in mountainous environment (Ambroise, 1995). Costs and also limitation of staff members directly determine the data volume or the number of stations that can be surveyed and further the share of online stations compared to the total number of stations. In this respect, it can be seen in Table 1 that the quite dense of hydro-meteorological measurement network in Styria reduces significantly when only online data transmission is considered. Table 1. Number of online hydro-meteorological stations used in the Mur FFS compared to the total number of stations. Precipitation Air temperature Water level Austria Slovenia

Total

149

89

71

Online

50

15

22

Total

10

5

10

Online

2

1

1

Furthermore, considering only the online raingauges and air temperature stations used in the FFS for Austria and Slovenia a network density for each country can be calculated. An important difference appears between Austria (precipitation 0.005 stations/km² or 1 station for 200 km²); Air temperature 0.0015 stations/km² or 1 station for 667 km²) and Slovenia (precipitation 0.0014 stations/km² or 1 station for 700 km²; Air temperature 0.0007 stations/km² or 1 station for 1400 km²). It is to note that in Slovenia some existing hydro-meteorological stations have been modernised since the setup of the Mur FFS. All in all there are now 4 online precipitation and 4 air temperature stations as well as 2 online water level gauging stations. Furthermore, the Environmental Agency of the Republic of Slovenia will modernise its hydrometeorological station network and 129 new online stations will be implemented for

the entire country within the next five years (5 water level gauging stations and 2 raingauges are foreseen in the Slovenian part of the Mur watershed). 4

THE USE OF METEOROLOGICAL FORECASTS

The meteorological forecasts for each national part of the Mur river catchment are provided by each national meteorological survey. These are the Zentralanstalt für Meteorologie und Geodynamik (ZAMG) for Austria and the Environmental Agency of the Republic of Slovenia (ARSO) for Slovenia, i.e., meteorological and hydrological forecasts are issued from the same institution in Slovenia. Both datasets are downloaded from FTP addresses (see Figure 1). Initially, both countries have delivered data from the meteorological modelling system Aladin. Precipitations and air temperature are simulated on a 9.6 km * 9.6 km grid. For each country 48 hours data are saved in one file including both variables whereas the time resolution is 1 hour starting at +1 hour, ending at + 48 hours. It is to note that in Austria Aladin simulations were available twice a day (simulation at 00:00 and 12:00) and in Slovenia only once a day (simulation at 00:00). The Austrian file could be used for the FFS two hours later and the Slovenian one hour later. This difference is due to the fact that Meteorological and Flood forecastings are made in the same Slovenian Institution, namely ARSO. Since the Mur FFS implementation, meteorological data availability has been modified. Now ZAMG delivers INCA forecasts on a 1 km * 1 km grid renewed each hour (Haiden et al., 2006). The INCA data set includes 3 components: 1) the INCA analyse at 00:00, 2) nowcasting results from + 01:00 to + 06:00 and Aladin simulations from + 07:00 to + 48:00. Element 1 is a distribution in space of precipitation measured at the raingauges and radar measurements, element 2 can be considered as an extrapolation of element 1 using complementary information like wind fields whereas element 3 can be seen as a downscaling of Aladin data from 9.6 km *9.6 km to the 1 km *1 km INCA grid scale. Furthermore, In Slovenia tests have been accomplished with Aladin simulations made twice a day but the implementation of these new datasets is not done at the moment. 5

HYDROLOGICAL AND HYDRODYNAMIC MODELLING

As already mentioned above, hydrologic and hydrodynamic simulations are carried out using the MIKE11 modelling system. The MIKE11 setup for the Mur FFS is designed to perform the calculations required to predict the variations in discharge and water levels in the Mur river system as a result of catchment rainfall and tributary inflows. All model calculations required for issuing a forecast are done automatically by utilising a number of individual modules. 1) hydrological module: using the mean areal rainfall, evaporation and temperature as input, the hydrological module based on the so called NAM model, calculates subcatchment inflow to the river system. 2) hydrodynamic module: the hydrodynamic module predicts water levels, river discharges and reservoir inflows, based on NAMcalculated lateral inflow and additional inflow from external boundaries. 3) Data assimilation module: the data assimilation module is used to minimise the deviations between observed and simulated discharges/water levels at the time of forecast and

to correct forecasted discharge values (further details to this module are given in the next section). 5.1 Hydrological module

Figure 2. Structure of the NAM model with the extended altitude distributed snow model The hydrologic calculation is based on the NAM model. The NAM rainfall-runoff model (Nielsen and Hansen 1973) is a deterministic, conceptual, lumped model representing the land phase of the hydrological cycle. The structure of the model is shown in Figure 2. It is based on both physical and semi-empirical formulations to describe the inter relationship between snow storage, surface storage, lower zone storage and groundwater storage. The rainfall-runoff module can either be applied independently or used to represent one or more contributing catchments that generate lateral inflow to the river network in a MIKE11 Hydrodynamic (HD) model. In this manner it is possible to treat a single catchment or a large river basin containing

numerous catchments and a complex network of rivers and channels within the same modelling framework. Based on mean areal rainfall, evaporation and temperature as inputs, NAM simulates sub catchment inflow to the river. In addition, the model also simulates other elements of the land phase of the hydrological cycle, such as the temporal variation of the evapotranspiration, soil moisture content, groundwater recharge, and groundwater levels. The resulting catchment runoff is split conceptually into overland flow, interflow and baseflow components. 5.1.1 Snow melt The NAM model with its extended altitude - distributed snow model was used to calculate the snowmelt from the catchment. Using temperature and precipitation data as input, the snowmelt module maintains individual snow storages and calculates accumulation and melting of snow for each altitude zone (see figure 2). Each subcatchment was subdivided into altitude zones in 100 meters steps. The reference series are adjusted for each altitude zone in order to account for the large variations in precipitation and temperature with altitude. In each altitude zone the following corrections were applied: 1) -0.6 degrees C°/100m during dry conditions and -0.4 degree C°/100m during wet conditions and 2) 0 to 4 % /100m increase in precipitation depending on location and exposure. Precipitation is retained in the snow storage only if air temperature is below the calibrated threshold temperature T0. The snowmelt PS is calculated using the simple degree-day approach: PS = Csnow (T–T0)

for T > T0

PS = 0

for T  T0

(1)

With Csnow in mm/C°/day. Furthermore, the degree-day approach for calculating snow melt has been extended by using a seasonal variation of the degree-day coefficient Csnow (Table 2). This variation reflects the seasonal variation of the incoming short wave radiation and the variation in the albedo of the snow surface during the snow season in a conceptual way.

Month

Table 2. Monthly variation of Csnow [mm/day/C] 06 07 08 09 10 11 01 02 03 04 05

12

Csnow

1

1

1.5

2

3

4

4.5

4.5

4

3

2

1

The generated melt water is retained in the snow storage as liquid water until the total amount of liquid water exceeds the water retention capacity (15% used in the setup) of the snow storage. Finally, to account for the not equally distribution of the snow cover in each altitude zone, the extended snow melt model includes a threshold value for full snow coverage (200 mm used in the setup). The snow melt PS is reduced linearly when the snow cover is below this threshold value.

5.1.2 Surface storage Moisture intercepted on the vegetation as well as water trapped in depressions and in the uppermost, cultivated part of the ground are represented as surface storage. Umax denotes the upper limit of the amount of water in the surface storage. The amount of water U in the surface storage is continuously diminished by evaporative consumption as well as by horizontal leakage (interflow). When there is maximum surface storage, some of the excess water, PN, will enter the streams as overland flow, whereas the remainder is diverted in infiltration into the lower zone and in groundwater storage. 5.1.3 Lower zone (root zone) storage The soil moisture in the root zone, a soil layer below the surface from which the vegetation can draw water for transpiration, is represented as lower zone storage. Lmax denotes the upper limit of the amount of water in this storage. Moisture in the lower zone storage is subject to consumptive loss from transpiration. The moisture content can be considered as the core of the NAM model because it controls the amount of water that enters the groundwater storage as recharge, interflow and overland flow components. 5.1.4 Ground water storage and baseflow The amount of infiltrating water recharging the groundwater storage depends on the soil moisture content in the root zone. Baseflow from the groundwater storage is calculated as the outflow from a linear reservoir using a timing constant. The groundwater level is calculated from a continuity consideration accounting for recharge, capillary flux, net groundwater abstraction and baseflow. The inclusion of capillary flux and groundwater pumping are optional and not used in the model setup. But it is to note that a second lower groundwater storage, i.e., with a larger time constant is implemented in the NAM used for the Mur FFS. This is to account for slowly varying low flow conditions at the sub-catchment scale. Recharge to this second groundwater reservoir is calculated simply as a constant share of the total groundwater recharge. 5.1.5 Routing of Interflow and Overland flow Before the Interflow reaches the streams it is routed through two linear reservoirs. The overland flow routing is also based on the linear reservoir concept but with a variable time constant, depending on the storage in the linear reservoir, where the time constant is decreased at high storages. This ensures in practice that the routing of real surface flow is kinematic, while subsurface flow being interpreted by NAM as overland flow (in catchments with no real surface flow component) is routed as a linear reservoir. 5.2 The Hydrodynamic Module The main purpose of the hydrodynamic modelling in the present work is to provide the basis for the Flood Forecasting modelling and especially the high discharge values at different gauging stations. Whereas in the hydrologic modelling no river

flow is considered, effects of water routing in the river channel are analyzed and simulated in the hydrodynamic modelling part. MIKE11 HD (hydrodynamic module) has been used for the hydrodynamic modelling. It is a one-dimensional model typically used in studies related to flood forecasting and simulation of flood control measures, operation and design of irrigation and surface channel systems and in studies of tides and storm surges in rivers and estuaries. Results from the hydrodynamic simulations build the basis for succeeding in the Flood Forecasting simulations. 5.2.1 Mathematical Background The model is based on the vertically integrated equations of conservation of continuity and momentum, i.e. the Saint Venant equations (DHI – Water and Environment, 2005). The continuity equation is given by: A Q   q0 t x

(2)

and the equation for conservation of momentum:  Q    Q  g QQ Q h A     gA  2 4 / 3  0 t x x M AR

(3)

Where A (m2) is the wetted cross-sectional area, Q (m3s-1) is river discharge, q0 (m3s-1m-1) is lateral inflow as e.g. may be calculated by the rainfall-runoff module, t (s) is the time, x (m) is the distance,  is the non-uniform velocity distribution coefficient, g (=9.81 ms-2) is the gravitational acceleration, M is the Manning number (the Manning number is also seen in the literature as n=M-1) and R (m) is the hydraulic radius. These equations are solved using an implicit finite difference scheme by applying a Double Sweep algorithm. The solution applies to single branched as well as looped and multi branched river systems. The computational grid comprises alternating Q (discharge) and H (water level) points. Cross-sectional data are given at H-points whereas Q-points are automatically placed midway between neighbouring H-points and at hydraulic structures. 5.2.2 Structures MIKE11 includes descriptions for a wide range of structures which act as control points. The formulation of these features permits great flexibility since they range both in their degree of user-intervention and in their level of complexity. The structures are modelled in MIKE 11 as control points at Q-points in the computational grid. Depending on the structure category, a relationship between the discharge and the upstream and downstream water levels is determined based on the flow condition, entrance and exit losses, and a critical flow correction factor. The most important modelled structures are:  Broad crested Weir

     

Special Weir Culverts Control Structures Dam Break structure User Defined Structures PID control structure

Control structures may be used whenever the flow through a structure is to be regulated by the operation of a movable gate which forms as part of the structure. They can also be used to control the flow directly without taking the moveable gate into consideration. The Control structure can be used to define operational rules for a reservoir and hydraulic structures which also can include flow through turbines. With respect to information made available for the setup, 8 hydroelectric power plants on Mur between Bruck and Mureck are included in the Mur application. All structures have been modelled using automatic PID control where 1) the target water level upstream the power plan dam, 2) the turbines discharge capacity, 3) the gauges altitude and their discharge capacity and 4) altitude for the structure crest must be specified in the MIKE11 setup. Because cross sections are available it is possible to simulate water level fluctuations upstream each power plant structure also during flood events with a good accuracy. 6

AUTOMATIC DATA ASSIMILATION

Data assimilation (DA) can be explained in a simple manner as a technique for combining any measurements of the state of a system with the model dynamics in order to improve the knowledge of the system. The MIKE11 data assimilation module can be used in hindcasting mode to provide an improved estimate of the state of the system prior the time of forecast, and hence providing initial conditions for the forecast (at least it can be applied as long as measurements are available). After the time of forecast the model can be corrected using forecasts of model errors. Detailed information can be found in DHI – Water and environment (2005) as well as in Madsen and Skotner (2005). The method used in the Mur FFS for hindcasts and forecasts correction are briefly explained in this section. The MIKE11 DA module is implemented in the Mur FFS using measurements updated with a weighting function approach. This function is used to distribute discharge errors at the measurement location to the neighbouring points in the river network (see figure 3). It is to note that beside the ensemble Kalman filter method also predefined update functions that are assumed constant in time in the MIKE11 DA module exist. On figure 3 the 3 available weighting functions (triangular, constant and mixed) are shown. In the Mur FFS, the weighting function type chosen is “constant” (in space) ensuring that the error correction at the measurement location is distributed evenly over the grid points between lower and upper chainage. Furthermore, the full observed error at the measurement location is applied as error correction (gain on figure 3) at that point meaning implicitly that measurements are estimated to be perfect compared to simulation values. The automatic updating procedure is setup to be applied from the first time step, i.e., 48 hours before time of forecast. Finally, the weighting function update procedure is combined with error forecasting for the forecast period. Up to the time of forecast the observed errors at the

measurement locations are distributed to the neighbouring grid points according to the defined weighting functions. After time of forecast the defined error forecast models (here a first order autoregresive model) are used to forecast the errors at the measurement locations which are then distributed to the neighbouring points. Thus, by applying error correction the model is updated also in the forecast period. Clearly, the DA module can only be applied at locations with frequent measurements update, i.e., at online station locations. In the Mur FFS it is implemented for 18 locations witch correspond to 6 water level gauging stations on the Mur river and 12 on the main tributaries in Austria (during the Mur FFS implementation no online gauging station was available on Slovenian tributaries). Each of these stations can be very easily disabled (and enabled again) in the data assimilation module. This is very important because an online station can transmit erroneous data, e.g. ice, that would makes data assimilation senseless for this station.

Figure 3. The 3 pre-defined weighting functions available in the MIKE11 DA module. 7

CONCLUSION

The trans-boundary Mur FFS provides a good example of an open and modern modelling system. It includes actually only the Austrian and Slovenian part of the watershed whereas the Hungarian and Croatian parts are not integrated. A very important element is that the largest national fraction that is also the upstream fraction of the watershed is located in Austria. Due to these geographical conditions it is clear that flood forecasting in Austria is independent to data and simulations from Slovenia. On the other hand, it is also logic that Slovenia needs to include the upstream part of the watershed, i.e., the Austrian part, to make sense full flood forecasts.

Thus, the challenge of this project was to build a common structure that simultaneously enables Slovenia 1) to optimise flood forecasting performances especially in that case and 2) both countries to keep their own responsibility for flood forecasting on the national territory. Further challenges that had to be addressed were the structure flexibility making possible 1) to include Hungary and Croatia in future and 2) to enlarge the system to other water resources management modelling studies like for low flow or water temperature. Due to the long and good cooperation of both countries in the field of water resources management, it was possible to set a new standard in the frame of trans- boundary flood forecasting systems. A unique structure was set up that fulfil these requirements through the setup of one international and two national Flood Forecasting Centres. All three Centres share a complete identical setup whereas continuous simulations are made at the international centre and automatic transfer to the national centres is completed after each model run. Simulations results are published in German, Slovenian and English language, on a password protected homepage, and are refreshed after each simulation. This structure can easily be extended to Hungary and Croatia according to the setup of a national Flood Forecasting Centre in both countries. Furthermore, the Mur FFS is built up off modern components that are integrated in the system to optimize the Flood Forecasting quality for the Mur River. These elements are:  Incorporation of online data and meteorological forecasts  Hydrological and hydrodynamic modelling including effects of hydropower plants  Continuous simulation starting each hour  Automatic simulation correction during hindcast and forecasts periods  Transfer of each simulation setup and results to the national Flood Forecasting Centres  Internet publication of the most important results Finally, the flexible software solution build up of the rainfall runoff model NAM, the hydrodynamic model MIKE11 and the Flood Forecasting shell MIKE FLOOD WATCH easily allows to extent the entire system to other tasks by adding specific MIKE11 modules. Thus, it can be argued that the Mur FFS establish new standards for international flood forecasting systems especially in the field of data management and communication. Acknowledgments The Mur Forecasting System has been implemented with financial support from the EU INTERREG IIIB Cadses program – Project „Flussraumagenda Alpenraum“. In addition, the Lebensministerium in Austria, Land Steiermark, the Slovenian Government and Environmental Agency of the Republic of Slovenia have supported the project.

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Ruch, C and G Jø rgensen, (2006a): Project Flussraum Agenda Alpenraum, Report (in German) Internationales Hochwasserprognosemodell Mur - Umsetzung In Österreich, March 2006. Ruch, C and G Jø rgensen, (2006b): Project Flussraum Agenda Alpenraum, Report (in English) Internationales Hochwasserprognosemodell Mur - Umsetzung In Slowenien, March 2006. Madsen, H., and Skotner, C., 2005, Adaptive state updating in real-time river flow forecasting A combined filtering and error forecasting procedure, Journal of Hydrology, 308, 302-312. Nielsen, S.A. and E. Hansen, (1973): “Numerical Simulation of the Rainfall-Runoff Process on a daily Basis”. Nordic Hydrology, 4, pp 171-190. Površinski Vodotoki in Vodna Bilanca Slovenije (1998): Surface streams water balance of Slovenia. ISBN 961-6024-04-3, Publ. by Ministrstvo za okolje in prostor. Ruch, C., Jø rgensen, G., Polajnar, Sušnik, M., Hornich, R., Schatzl, R., Pogačnik N. 2006. Trans boundary forecasting system on Mur river, 23. Conference of the Danubian countries on the hydrological forecasting and hydrological basis of water management, 28.-31. August 2006. Belgrade Schatzl, R. and C. Ruch, (2006): Internationales Hochwasserprognosemodell Mur. In: Hochwasservorhersage, D. Gutknecht (ed.); Institut für Wasserbau und Ingenieurhydrologie, TU Wien; Wiener Mitteilungen, Wasser-Abwasser-Gewässer Band 199, Wien, 978-3-85234-090-6, 7-22.