Hydrological (rainfall-runoff) models have evolved as our understanding of hydrological processes has increased and as computers have been able to handle more complex model structures (Beven, 2001). Today, computer-based rainfall-runoff models allow relatively quick predictions to be made about a catchment‟s response to a given input of rainfall given specific antecedent conditions. These predictions are based on various sources of information, including field data and
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observations as well as detail about the interactions and processes of the rainfall-runoff relationship (Mulligan and Wainwright, 2004). The output from such models is widely used in decision-making processes, whether for hydro-electricity generation, erosion control, flood management or reservoir design (Moradkhani and Sorooshian, 2008; Todini, 1988; Wagener et al., 2004b).
There are several ways to classify rainfall-runoff models (Becker and Serban, 1990;
Kampf and Burges, 2007; Mulligan and Wainwright, 2004). Becker and Serban (1990) categorise rainfall-runoff models according to their degree of spatial resolution (lumped/semi-distributed/ distributed) and by the degree to which they represent real world processes (empirical/conceptual/physics-based). A lumped model assumes spatial homogeneity, ignoring spatial variation of the rainfall-runoff response by using average or single point data to represent the whole of the catchment (Wagener et al., 2004b). Semi-distributed models allow for some spatial variation, delineating the larger lumped catchment by smaller units such as sub-catchment boundaries. Distributed models aim to more fully represent the heterogeneity of the catchment accounting for the spatial variation of processes and properties over the entire area (Mulligan and Wainwright, 2004).
How well a model represents real world processes will depend on the approach.
Empirical (or metric) models are strongly observation oriented, extracting information from existing data to determine the response of a catchment to rainfall inputs (Kokkonen and Jakeman, 2001). The foundation of empirical models is the unit hydrograph approach developed by Sherman in 1932 (Beven, 2001; Kokkonen and Jakeman, 2001; Todini, 1988). Other examples include the IHACRES model (Jakeman et al., 1990) and artificial neural network models (Dawson and Wilby, 2001; Minns and Hall, 2005).
In contrast to empirical models, physics-based models aim to represent all significant physical processes of the hydrological cycle relevant to the problem of interest using mathematical partial differential equations (Moradkhani and Sorooshian, 2008; Young, 2001). These models are commensurate with a high degree of discretisation. One of the most widely known models of this type is the Système Hydrologique Europèen (SHE) model, developed as a joint project between the Institute of Hydrology (UK), the Danish Hydraulics Institute and SOGREAH in
Rainfall–runoff modelling for reservoir inflow forecasting | 53 France. Others include HILLFLOW (Bronstert and Plate, 1997), IHDM5 (Calver and Wood, 1995) and Topog (Vertessy et al., 1993).
Conceptual models provide a balance between the „top-down‟ empirical and
„bottom-up‟ physics-based models and can be applied at lumped or distributed spatial scales. Conceptual models incorporate knowledge and theory of hydrological processes but generally approximate these processes into a simpler model structure.
The rainfall-runoff relationship is often represented by a number of internal stores connected by a series of component processes controlling their recharge and depletion (Beven, 2001; Kitanidis and Bras, 1980; Kokkonen and Jakeman, 2001;
Young, 2001). The model structure is generally determined a priori based on the perceived importance of the rainfall-runoff mechanisms. Determining the boundaries and interactions between reservoirs is, therefore, a subjective process and calibration is required to ensure the simulations closely match the observed response (Beven, 2001). Numerous conceptual models have been developed that vary in the number of storage elements, exchanges between these elements and model parameters reflecting the modeller‟s perception of the relative importance of the rainfall-runoff mechanisms in the system. The Sacramento Soil Moisture Accounting Model (Burnash, 1995), ARNO model (Todini, 1996) and the HBV6 model (Bergström, 1995) are examples of conceptual type models.
While physically-based conceptual models should, in theory, incorporate the important hydrological components of the rainfall-runoff process, these processes are generally only represented by approximations rather than actual physical representations of the processes themselves (Todini, 1988). The parameters of some conceptual models can, consequently, lack any physical meaning. Hybrid conceptual/physics-based models combine the simplicity of the conceptual approach with the physical interpretation of the „bottom-up‟ physics-based approaches. These models provide a balance between the detail of physical catchment processes and data and computational requirements. TOPMODEL (Beven and Kirkby, 1979) is an example of a hybrid model which identifies units with similar soils and topography that will have a corresponding hydrological response. The model structure is simplified while retaining the physical meaning of parameters within a distributed parameter space. One of the limitations of TOPMODEL is that it has been developed for small watersheds (Bandaragoda et al., 2004). To counter this limitation, the National Institute of Water and Atmospheric
5 Institute of Hydrology distributed model, United Kingdom
6 Hydrologiska Byråns Vattenbalansavdelning model
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Research (NIWA), New Zealand, developed TopNet (Ibbitt and Woods, 2004), a rainfall-runoff model which combines TOPMODEL with a kinematic wave channel routing algorithm which allows larger watersheds to be modelled using smaller sub-catchments as elements (Bandaragoda et al., 2004). NIWA have applied TopNet to a number of New Zealand catchments of various sizes and climate regimes (Clark et al., 2008a; Ibbitt et al., 2005; Poyck et al., 2011). It‟s structure, however, does not allow for catchments where there are multiple runoff-generating stores (McMillan et al., 2010).
The models outlined above can be classified further into deterministic or stochastic.
Deterministic models take a given a set of inputs and parameter values and generate a single possible response or outcome for a corresponding point in time and space from a simulation (Beven, 2001). Stochastic models, on the other hand, require the uncertainty to be quantified in some manner as part of the modelling process (Young, 2001). Stochastic models are particularly useful where inadequate data prevents actual (deterministic) estimates of flow from being obtained. For example, where only streamflow data exists (or is available) probabilistic approaches can be used to consider all possible flow values and to assign a probability to each of them being the right one (Maidment, 1993).
The distinction between deterministic and stochastic models is not always clear cut.
Some deterministic models, such as the probability distributed model (PDM) of Moore (2007), will characterise a particular aspect of the hydrological system using a stochastic approach. The PDM groups the catchment into a series of stores with different storage capacities. Each store represents a dynamic contributing area for runoff generation, and the response of each store to rainfall is represented by a probability distribution function (Moore, 2007). As is common with empirical models, the distribution of responses has been determined with little consideration to the physical processes and characteristics of the store‟s response.
3.2 Rainfall-runoff modelling for reservoir inflow forecasting
The type of model suitable for any given application will depend on the desired outcome of the project, model assumptions and resource constraints (Beven, 2001).
In reservoir inflow forecasting applications, where short-term predictions are the main aim, computational efficiency is imperative as well as the accuracy and reliability of model output.
Rainfall–runoff modelling for reservoir inflow forecasting | 55 Although physics-based models are of value to the understanding of catchment hydrological processes, their application to forecasting problems has been limited due to their heavy data and computational requirements (Daniel et al., 2011;
Graham and Butts, 2005). To run such models at the appropriate resolution requires considerable computational resources, and in some cases even modern computers (and supercomputers) are unable to meet these requirements. Large amounts of data are required which can also be prohibitively costly (Pechlivanidis et al., 2011).
There are numerous data driven techniques which have been applied to reservoir inflow forecasting including empirical regression, fuzzy-rule based systems and artificial neural network models (Coulibaly et al., 2000; Harte and Thomson, 2007;
Lohani et al., 2012; Taghi Sattari et al., 2012; Xu and Li, 2002). Empirical models can be parametrically efficient, but in their development they give little consideration to the physical processes that generate the system‟s runoff response (Kokkonen and Jakeman, 2001; Xu and Li, 2002). This can restrict their utility when seeking further understanding of catchment hydrological processes and extrapolating beyond the observation set or to other catchments.
Conceptual models provide the necessary computational efficiency while maintaining an underlying physical basis. For this reason, they have been extensively applied for reservoir inflow forecasting to derive reservoir operation policies, improve existing operational procedures, simulate climate change, assess the impact on flow regimes, and predict short-term inflows (Amenu and Killingtveit, 2001; Collischonn et al., 2007; Druce, 2001; Hotchkiss et al., 2000; Welsh et al., 2012, in review; Yang et al., 2005). They can also be applied at a range of spatial (lumped/semi-distributed/distributed) and temporal scales and are suitable for estimating inflows from ungauged basins. Wagener et al. (2004b) state that conceptual models are likely to perform just as well as physics-based models without the intensive data and computational requirements.
The HBV hydrological model (Bergström, 1995; Lindström et al., 1997), was originally developed to forecast streamflow in hydro-power generation regions of Scandinavia and has since been applied in numerous countries world-wide (Amenu and Killingtveit, 2001; Yang et al., 2005). In another example, the conceptual UBC watershed model has been used to forecast seasonal inflows to Kinbasket Lake (storage capacity: 14.8 km3) and Mica Dam (drainage basin area: 21500 km2) on the Columbia River for more than 20 years (Druce, 2001). Outflow from the Mica Dam
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is regulated based on these forecasts. Collischonn et al. (2005) also used a conceptual model to forecast hourly inflows to the Machadinho dam and reservoir located on the Uruguay River, southern Brazil. This same model was also used to model daily inflows between Itumbiara and Sāo Simāo power plants (drainage basin between the two power plants: 76,746 km2) on the Paranaíba River basin in Brazil (Collischonn et al., 2007).
In the majority of examples found in the literature, it is principally the unregulated inflows to regulated systems that are simulated. The problem of reservoir inflow forecasting is more complicated when regulated inflows need to be modelled. This requires the incorporation of specific reservoir operational information into the traditional model structure.
Although there are numerous examples where regulated catchments have been modelled, (Bulygina et al., 2012; Hotchkiss et al., 2000; Sayama et al., 2006; Zhang et al., 2011, amongst others) the success of these applications relies on obtaining extensive data and information pertinent to the schemes operation. In the Lake Taupo catchment, three competing power companies control approximately 60% of the inflows through three hydro power schemes, while Mighty River Power Ltd manages lake level and outflow. Although some streamflow data is available, there is little information relating to the control of water storage and release for the respective power schemes. The challenge is, therefore, to find alternative ways in which this regulation can be quantified. This thesis, therefore, sets out to provide some guidance on how some of this regulation (using various physical and legislative constraints) can be incorporated into a conceptual model structure in the absence of direct operational information.