Uncertainty in flood forecast modelling 44 

Since many decisions in water resources are based on model-generated data, it is prudent to acknowledge the importance of uncertainty in the management process (Vrugt et al., 2003b; Jasper et al., 2005; Moore and Doherty, 2005; Brugnach et al., 2008). The sources of these uncertainties are: the input forcing data (such as rainfall and evaporation demand); the parameterisation process of the models and also the structure of the model (Blasone et al., 2006; Kapangaziwiri, 2008; Kapangaziwiri and Hughes, 2008; Brugnach et al., 2008). Therefore it is important to take into consideration all these uncertainties when a flood forecasting model is being selected and applied.

In hydrology, there are many definitions of uncertainty concerning hydrological systems. In the water management context, uncertainties result from a lack of knowledge regarding the hydrologically correct probabilistic structure of a hydrological model, combined with the uncertainty following from this structure. Beven (2001) demonstrated that uncertainty differs to error because an error represents a specific departure from “reality” and uncertainties result from the natural complexity and variability of hydrological systems and a lack of knowledge of the hydrological processes. There have been numerous attempts to distinguish between

different types of uncertainty (Vrugt et al., 2005; Refsgaard et al., 2007; Beven et al., 2008; Smith et al., 2008).

Input data uncertainty: Input data uncertainty arises from errors in measuring the climatic

variables (rainfall, evaporation) and in the observed streamflow (for the gauged catchments). Input data deficiencies arise from limited and infrequent monitoring, sparse and diminishing measuring networks and use of short time series (Vrugt and Bouten, 2002; Wagener and Gupta 2005,). These deficiencies also contribute to uncertainty – this situation is particularly common in developing regions (such as southern Africa) (Hughes and Forsyth, 2006; WMO and USAID, 2012).

Model parameter uncertainty: Parameter uncertainty arises from the manner in which the

parameters are estimated, either through regionalisation or a priori methods (Kuczera and Mroczkowski, 1998; Liu and Gupta, 2007). Reliance on observed data for calibration inevitably introduces input data uncertainty (Hughes and Forsyth, 2006; 2011) and, according to Knutti (2008), parameter uncertainty arises if the values used in the parameterisations are not adequately constrained by the observed evidence. Equifinality (Beven, 1986) also contributes to uncertainty in the regionalisation of parameters; the lack of appropriate physical basin property data suggests that both regionalisation approaches, and any a priori parameter estimation method will be highly uncertain.

Model structure uncertainty: Hydrological models are based on assumptions and simplified

representations of the processes that take place in the real world system and will always be associated with some degree of uncertainty (Hughes et al., 2010; 2011). The complexity of the underlying hydrological processes has resulted in poor or insufficient knowledge of the processes and, consequently, the use of inappropriate assumptions for model conceptualisation and mathematical formulations (Sorooshian and Gupta, 1993; Beven and Freer, 2001; Beven, 2001, Vrugt et al., 2005). Another compounding factor stems from the manner in which the spatial and temporal discretisations are mathematically represented (Refsgaard et al., 2007; Beven et al., 2008). The focus of this study is on flood forecasting and therefore it is necessary to discuss the uncertainties related to the hydrological forecasting caused by the input of quantitative precipitation forecasts, hydrological and operational uncertainties (Lobbrecht and Solomatine, 2002; Danehelka, 2007) and to identify possible solutions using probabilistic approaches (Krzysztofowicz, 2001).

2.7.1. Quantitative precipitation forecasting (QPF) uncertainty in predicting

rainfall

The QPF uncertainty is related to those meteorological models which produce ‘ensemble’ forecasts. Numerical Weather Prediction (NWP) models that generate ensemble forecasts are

mostly global ones that operate at quite coarse grid resolutions. The European Centre for Medium Range Weather Forecast (ECMWF) model provides one main run, one control run (both using a 40 km grid) and 50 ensembles runs (80 km grid) with a lead time of 10 days (Krzysztofowicz, 2001). Since the primary input fluxes for most advanced hydrological models are satellite-derived precipitation and evapotranspiration, the operational data processing system supports the daily processing and distribution of these datasets. The Tropical Rainfall Measuring Mission (TRMM) of the U.S. National Aeronautics and Space Administration (NASA) produces merged three-hourly rainfall rates incorporating space borne radar, microwave data and infrared imagery (Barrett, 2001; Artan et al., 2002).

These data are processed at USGS EROS to convert them to daily accumulations and reformatted to GIS-ready images. The NASA TRMM product (version 3B42) covers the tropics between 50o _{north and 50}o _{south, with grid cells of spatial resolution 8 km by 8 km (Artan et} al., 2002). The NASA TRMM products contain constantly updated (current) and daily

climatology data ever since the collection of this data was initiated in 1998. Operationally, the most current TRMM products are made available approximately 12 hours after the end of the data collection period. While other satellite-derived rainfall products are also available, the NASA TRMM products are used in this application because of their superior performance in regions with limited in situ gauges (Dinku et al., 2007). The operational data processing system also produces and distributes a daily reference evapotranspiration (PET) dataset, with global coverage, as described in Verdin (2000).

The National Oceanic and Atmospheric Administration (NOAA) have developed several satellite-based techniques and an algorithm for rainfall estimation to support weather and flood monitoring activities of USAID. Among them is the system developed at the Climate Prediction Center for Rainfall Estimates known as the CPC-RFE, which was tested and applied in the African region (Funk et al., 2003; Funk and Verdin, 2004; Sawunyama and Hughes, 2010). The CPC-RFE 2.0 is a combined satellite- and surface-based rainfall estimation technique. The CPC-RFE 2.0 product has been available since 2001 on an operational basis and has been applied in South Africa (Sawunyama and Hughes, 2009). It uses a merging technique that increases the accuracy of the rainfall estimates by reducing significant bias and random error when compared with individual precipitation data sources (Xie and Arkin, 1996), thereby adding value to rain gauge interpolations (Shrestha et al., 2008). The disadvantage of this method is the coarse grid cell size of the meteorological output – which is unsuitable for forecasting flows in smaller streams and headwater areas.

Conversely, CPC-RFE 2.0 has a great advantage – the long lead time of the forecast, from daily up to seasonal forecasting (Danehelka, 2007; Shrestha et al., 2008). CPC-RFE 2.0 takes advantage of an Extended Streamflow Prediction (ESP) system of observed historical

precipitation time series instead of a Numerical Weather Prediction (NWP) precipitation forecast. Ensembles are based on current initial conditions of the hydrological model and historical weather analogues for the forecasted periods. The results are clearly statistical and are valuable mainly for the longer period (seasonal) forecasts for water supply reservoir operational decision-making. Unfortunately, this method of probabilistic forecasting is often too coarse to resolve thesmaller catchments and shorter lead times. Another limitation is the lack of historical daily precipitation data because of the few rain gauges employed in most developing countries – including the Zambezi Basin.

2.7.2. Hydrological uncertainty

As with other hydrological models, flood forecasting models are also affected by hydrological uncertainty (Danehelka, 2007). This may be because of model structure uncertainty or model parameter uncertainty. Flood forecasting models are based on assumptions and simplified representations of the processes that take place in the real world system and will always be associated with some degree of uncertainty (Danehelka, 2007). The complexity of the underlying hydrological processes has resulted in poor or insufficient knowledge of the processes and, consequently, the use of inappropriate assumptions for model conceptualisation and mathematical formulations (Sorooshian and Gupta, 1993; Liu and Gupta, 2007). Another difficulty in the choice of a flood forecasting model is related to the modelling structure, since the mathematical representation of each model differs (Ao et al., 2006; Hughes et al., 2006; Refsgaard et al., 2007; Beven et al., 2008; Smith et al., 2008). Uncertainty has been part of all modelling studies because of poor input data, scale and model structure, and the issues related to equifinality, therefore these uncertainties should be taken into consideration when the flood forecasting model is being selected (Vrugt et al., 2003a; 2003b; Danehelka, 2007).

2.7.3.

Operational uncertainty in predicting flood

Operational uncertainty is caused by unpredictable events during the forecasting process – such as dam breaks, reservoir operations, ice jams etc. (Danehelka, 2007). The prior knowledge of the hydrological system and the background of the hydrologists operating the model can both have an important impact on the final hydrological forecast (human impact also belongs to this group of operational uncertainty). Unfortunately, operational uncertainty cannot be quantified in advance and therefore stays unexpressed, not only in deterministic, but also in probabilistic approaches (Danehelka, 2007). The decision-making for flood control is usually effective only for the current period or for the following periods; such decision-making is constrained by the updated results on flood forecasting at each current period on a daily or

hourly basis during flood events (ICOLD, 1992; Beilfuss and Dos Santos, 2001; Meier et al., 2011).Therefore it is very important to generate the feasible flood control alternatives quickly.