Progress in Physical Geography 23,2 (1999) pp. 229–249 From GCMs to river flow: a review of downscaling methods and hydrologic modelling approaches Chong-yu Xu Department of Earth Sciences, Hydrology, Uppsala University, Villavägen 16, S-75236 Uppsala, Sweden Abstract: The scientific literature of the past decade contains a large number of reports detailing the development of downscaling methods and the use of hydrologic models to assess the potential effects of climate change on a variety of water resource issues. This article reviews the current state of methodologies for simulating hydrological responses to global climate change. Emphasis is given to recent advances in climatic downscaling and the problems related to the practical application of appropriate models in impact studies. Following a discussion of the advantages and deficiencies of the various approaches, challenges for the future study of the hydrological impacts of climate change are identified. Key words: climate change, climate scenario, downscaling, general circulation model, hydrological model. I Introduction Global climatic changes caused by increases in the atmospheric concentration of carbon dioxide and other trace gases may begin to appear within the next few decades. It has been estimated by many authors (see, e.g., Loaiciga et al., 1996) that if 1990-level emissions of CO2 to the atmosphere remain unabated, its concentration in the atmosphere could nearly double by the year 2100 or thereabouts. Assessments of the consequences of a possible climate change for ‘double CO2’ (2 × CO2) conditions have become standard practice. Among the most authoritative climate change assessments, the IPCC reports (Houghton et al., 1990; 1992; 1995) give estimates of temperature increases in the Northern Hemisphere between 3 °C and 5°C, together with precipitation change by as much as 15% under the assumption of a doubling of atmospheric CO2. One of the most important impacts on society of future climatic changes will be © Arnold 1999 0309–1333(99)PP212RA 230 Downscaling methods and hydrologic modelling changes in regional water availability. Such hydrologic changes will affect nearly every aspect of human well-being, from agricultural productivity and energy use to flood control, municipal and industrial water supply, and fish and wildlife management. The tremendous importance of water in both society and nature underscores the necessity of understanding how a change in global climate could affect regional water supplies. Global atmospheric general circulation models (GCMs) have been developed to simulate the present climate and have been used to predict future climatic change. While GCMs demonstrate significant skill at the continental and hemispheric spatial scales and incorporate a large proportion of the complexity of the global system, they are inherently unable to represent local subgrid-scale features and dynamics (Wigley et al., 1990; Carter et al., 1994). When considering the impacts of global climate change the focus is primarily on societal responses to the local and regional consequences of largescale changes. The conflict between GCM performance at regional spatial scales and the needs of regional-scale impact assessment is largely related to model resolution in such a way that, while GCM accuracy decreases at increasingly finer spatial scales, the needs of impacts researchers conversely increase with higher resolution (Hostetler, 1994; Schulze, 1997). To circumvent these problems, tools for generating the high-resolution meteorological inputs required for modelling ecohydrological processes are needed (Bass, 1996). ‘Downscaling’ approaches have subsequently emerged as a means of relating largescale atmospheric predictor variables to local- or station-scale meteorological series. Two broad classes of downscaling approaches exist: dynamic methods, involving the explicit solving of the process-based physical dynamics of the system (e.g., Giorgi and Mearns, 1991; Jones et al., 1995); and statistical methods that use identified system relationships derived from observational data (e.g., Wigley et al., 1990; Wilby, 1995; Hewitson and Crane, 1996). Hydrologic models provide a framework in which to conceptualize and investigate the relationship between climate and water resources. The scientific literature of the past two decades contains a large number of reports dealing with the application of hydrologic models to the assessment of the potential effects of climate change on a variety of water resource issues. The use of hydrological models in climate change studies can range from the evaluation of annual and seasonal streamflow variation using simple water-balance models (e.g., Arnell, 1992) to the evaluation of variations in surface and groundwater quantity, quality and timing using complex distributedparameter models that simulate a wide range of water, energy and biogeochemical processes (e.g., Running and Nemani, 1991). This article first reviews the current state of methodologies for generating regional climatic scenarios and assessing hydrological responses to global climate change (section II). Emphasis is given to recent advances in climatic downscaling. The state of the art of hydrological modelling and problems related to the practical application of appropriate models in impact studies are then addressed (section III). Summary and conclusions are presented in section IV. Chong-yu Xu II Methodologies for assessing hydrological responses to global climate change 1 The use of direct GCM-derived hydrological output 231 Global atmospheric GCMs have been used directly to simulate streamflow under present climate and to predict the impact of future climatic change in macroscale watersheds. For the present climate, Manabe (1969) reported what appears to be the first numerical parameterization of the hydrologic cycle within a GCM. This was a simple bucket model assuming that, if precipitation exceeded evaporation, then the soil ‘bucket’ would fill up. If the soil reaches saturation, then runoff occurs. As long as the soil was at or near saturation the actual evaporation rate would be equal to the potential evaporation rate (Manabe’s bucket model did not consider vegetation). Otherwise, the actual evaporation would be proportional to the potential rate. Russell and Miller (1990) used the atmospheric model of Hansen et al. (1983) to calculate the mean annual river runoff from a 5-year GCM simulation and compared the results with observed annual runoff given by Milliman and Meade (1983). They found generally better agreement for river basins with mean annual runoff between 200 and 600 km3/yr–1 and poor agreement for large basins with small total runoff. Miller and Russell (1992) used the same model to calculate the annual river runoff for 33 of the world’s major rivers for the present climate and for a doubled CO2 climate. They showed that there are large errors in GCM-inferred estimates of mean annual runoff. Discrepancies attributed to, among other things, the poor model precipitation fields, the model’s parameterizations of soil moisture and evapotranspiration are also too simplistic. Kuhl and Miller (1992) extended the work of Russell and Miller (1990) to examine the extent to which the atmospheric model simulates the seasonal river runoff of world rivers with an annual discharge greater than 100 km3/yr–1 or drainage areas greater than 5 × 105 km2. The limitations of the model in simulating seasonal river runoffs were discussed in their study. The analysis of GCM-predicted runoff showed that a simplistic representation of the hydrologic cycle within a global model of general atmospheric circulation leads to poor hydrologic predictive skill (e.g., Kuhl and Miller, 1992; Miller and Russell, 1992). The problem, from a hydrologic point of view, is that most GCMs contains no lateral transfer of water within the land phase. Such models carry out a vertical water distribution at each grid point at each time interval using precipitation, evapotranspiration and groundwater storages. However, any ‘water excess’ or overflow is simply discarded and plays no further role in the model computations. This means that, even if the GCMs were able to simulate water excess correctly, they would still be operating with an incomplete hydrological cycle (Kite et al., 1994). 2 Coupling GCMs and macroscale hydrologic models It is clear that the present version of the GCM does not give a good estimation of the hydrologic responses of climatic changes. There is a need to couple hydrological models with GCMs. Few case studies have been carried out on the world’s largest river basins. Liston et al. (1994) used a two-linear reservoir-routing model with daily precipitation and potential evaporation from several GCMs to simulate flows in the Mississippi River basin. The routing model used grid boxes 2 ° latitude by 2.5 ° longitude. Kite et al. (1994) 232 Downscaling methods and hydrologic modelling combined a hydrological model (the SLURP model) with a GCM for a macroscale watershed. A water balance was carried out at 12-hour time intervals for a 10-year period using the Canadian Climate Centre GCM II data set for grid points within and surrounding the 1.6 × 106 km2 Mackenzie River basin in northeastern Canada. The water surpluses from each relevant grid point were accumulated to provide a simulated hydrograph at the outlet of the river. Nash and Gleick (1993) studied the hydrological impact of climate change on the Colorado River basin in the western USA. Several GCMs were used to simulate climate over the Colorado River for double CO2 conditions. Precipitation and temperature predictions from both the GCMs as well as from hypothetical scenarios were then input to the National Weather Service River Forecasting and Simulation (NWSRFS) hydrologic model to simulate the river basin hydrologic cycle, including runoff. By linking atmospheric, hydrologic and river simulation models Nash and Gleick (1993) were able to assess the potential impacts of greenhouse warming in the Colorado River basin. The results of these studies showed that coupling the hydrological model with the GCM produces a better representation of the recorded flow regime than GCM predictions of runoff for very large river basins. However, GCMs cannot ‘see’ smallerscale river basins because of their coarse grid resolution. Subgrid-scale hydrologic models and nesting schemes are needed to resolve the large-scale GCM predictions and to predict smaller-scale hydrologic phenomena (Hostetler and Giorgi, 1993). 3 Downscaled GCM climate output for use in hydrological models Given the limitations of GCM grid-point predictions for regional climate change impact studies, an alternative option to using direct GCM-derived hydrological output is to downscale the GCM’s climate output for use in hydrological models. Two categories of climatic downscaling, namely, dynamic approaches (in which physical dynamics are solved explicitly) and empirical (the so-called ‘statistical downscaling’) exist, and are discussed in the following sections. a The use of dynamic downscaling approaches: Dynamic downscaling has been attempted with three approaches (Rummukainen, 1997): 1) Running a regional-scale limited-area model with the coarse GCM data as geographical or spectral boundary conditions (also known as ‘one-way nesting’). 2) Performing global-scale experiments with high-resolution AGCMs (atmosphere GCMs), with coarse GCM data as initial (and partially also as boundary) conditions. 3) Using a variable-resolution global model (with the highest resolution over the area of interest). The goal of dynamic downscaling (i.e., to extract the local-scale information from the large-scale GCM data) is achieved by developing and using limited-area models (LAMs) or regional climate models (RCMs). RCMs have recently been developed that can attain horizontal resolution in the order of tens of kilometres or less over selected areas of interest. They have been applied with relative success to numerous regions (e.g., Giorgi and Bates, 1989; Giorgi, 1990; Giorgi and Mearns, 1991; Hostetler and Giorgi, 1992; 1993; Giorgi et al., Chong-yu Xu 233 1990; 1993; 1994; Jones et al., 1995; Jenkins and Barron, 1997). Compared with GCMs the resolution of these RCMs is much closer to that of landscape-scale hydrologic models (LSHMs) and makes coupling of RCMs and LSHMs potentially suitable for evaluating the effects of hydrologic systems. Hostetler and Giorgi (1993) linked an RCM with an LSHM to study the effects of climate on hydrologic systems in Steamboat Creek, Oregon. Their RCM has a 3000 × 3000 km2 domain centred over the Great Basin of the western USA. The streamflow model used is a lumped parameter model that requires monthly average values of solar radiation and precipitation as input. The results of the simulations indicated that it may be feasible to use output data from RCM simulations directly as input to hydrologic models (or other energy balance models) in climate change research aimed at, for example, assessing potential changes in various components of the basin hydrologic budget under increased levels of atmospheric CO2. Another nested model approach was developed by Leavesley et al. (1992) to disaggregate large-scale model output for application in mountainous regions. Output from a coupled GCM–mesoscale atmospheric model is used as input to an orographic–precipitation model. The orographic–precipitation model output, at a resolution of 2.5, 5 or 10 km, is used as input to a distributed-parameter hydrologic model. The nested approach permits the simulation of smaller-scale atmospheric processes and can reflect changes in precipitation frequency, magnitude and duration consistent with the GCM response. While nested modelling is likely to be the most informative approach to driving regional information for 20–50 km horizontal grid spacing and 100–1000 m vertical resolution, there are several acknowledged limitations of the approach. RCMs still require considerable computing resources and are as expensive to run as a global GCM. Dynamical downscaling operates on some (high-resolution) grid-point scales and thus the results will be in the form of spatial averages. These models still cannot meet the needs of spatially explicit models of ecosystems or hydrological systems, and there will remain the need to downscale the results from such models to individual sites or localities for impact studies (DoE, 1996). b The use of statistical downscaling methods: A second, less computationally demanding approach is statistical downscaling. In this approach, regional-scale atmospheric predictor variables (such as area averages of precipitation or temperature) and circulation characteristics (such as mean sea-level pressure or vorticity) are related to station-scale meteorological series (Kim et al., 1984; Karl et al., 1990; Wigley et al., 1990; Hay et al., 1991; 1992; ). The statistics involved can be simple or extensive, but the final relationships are typically arrived at with some form of regression analysis. Statistical downscaling methods can be classified according to the techniques used (Wilby and Wigley, 1997) or according to the chosen predictor variables (Rummukainen, 1997). In Wilby and Wigley’s study, statistical downscaling techniques are described using three categories, namely: regression methods (e.g., Kim et al., 1984; Wigley et al., 1990; von Storch et al., 1993); weather pattern-based approaches (e.g., Lamb, 1972; Hay et al., 1991; Bardossy and Plate, 1992; Wilby, 1995); and stochastic weather generators (e.g., Richardson, 1981; Wilks, 1992; Gregory et al., 1993; Katz, 1996). In Rummukainen’s (1997) study, statistical downscaling methods are classified as follows: 234 Downscaling methods and hydrologic modelling 1) Downscaling with surface variables. This involves the establishment of empirical statistical relationships between large-scale averages of surface variables and localscale surface variables (e.g., Kim et al., 1984; Wilks, 1989). To develop the relationships, large-scale averages constructed from local time series are used. In application, the same local-scale surface variables will be the predictands. 2) The perfect prog(nosis) (PP) method (e.g., Zorita et al., 1992). This involves the development of statistical relationships between large-scale free tropospheric variables and local surface variables. In this method, both the free atmospheric data and the surface data are from observations. 3) The model output statistics (MOS) method (e.g., Karl et al., 1990). This is similar to the PP method, except that the free atmospheric variables, which are used to develop the statistical relationships, are taken from GCM output. In reality, many downscaling approaches embrace the attributes of more than one of these methods and therefore tend to be hybrid in nature. The general limitations, theory and practice of downscaling are well described in the literature (e.g., Grotch and MacCracken, 1991; von Storch et al., 1993; Wilby and Wigley, 1997). A summary with respect to their assumptions, uses and limitations is given in Table 1. 4 Using hypothetical scenarios as input to hydrological models Ideally, the climate simulations from the GCMs could be used directly to drive hydrologic models, which in turn could be used to evaluate the hydrologic and water resource effects of climate change. The issue is complicated, as discussed above, by the incompatibility of space (and, to a lesser extent, time) scales between hydrologic processes and GCMs. The former must account for variations at the small-to-medium catchment scale (e.g., tens of kilometres) and must later operate at scales of hundreds to thousands of kilometres and upwards. More importantly, the climate models – including the better parameterized ones (GCMs) – give different values of climate variable changes and so do not provide a single reliable estimate that could be advanced as a deterministic forecast for hydrological planning. Accordingly, methods of simple alteration of the present conditions are widely used by hydrologists. Various hypothetical climate change scenarios have been adopted and climate predictions for ‘double CO2’ conditions have become standard (e.g., Loaiciga et al., 1996). In the simple alteration method, the generation of climate scenarios consists of two steps: 1) Estimate average annual changes in precipitation and temperature using either GCM results or historical measurements of change, or personal estimates (typically, ∆T = +1, +2 and +4 °C and ∆P = 0, ±10%, ±20%). 2) Adjust the historic temperature series by adding ∆T and, for precipitation, by multiplying the values by (1 + ∆P/100). In practice, these annual changes were distributed during the year by various methods. For example, Nemec and Schaake (1982) and Ng and Marsalek (1992) assumed constant distributions of climatic changes, and multiplied historical precipitation records by Chong-yu Xu 235 constant factors and adjusted historical temperatures by constant increments. Sanderson and Smith (1990) used GISS (Goddard Institute of Space Studies) scenarios of predicted monthly changes in temperature and precipitation. The general procedure for estimating the impacts of hypothetical climate change on hydrological behaviour has the following stages: 1) Determine the parameters of a hydrological model in the study catchment using current climatic inputs and observed river flows for model validation. 2) Perturb the historical time series of climatic data according to some climate change scenarios. 3) Simulate the hydrological characteristics of the catchment under the perturbed climate using the calibrated hydrological model. 4) Compare the model simulations of the current and possible future hydrological characteristics. There are a great number of studies that use such altered time series to assess possible effects of climate change. The distinguishing characteristics of some studies are summarized in Table 2. At this juncture it is necessary to make clear that the climate change scenarios used in the above studies should not necessarily be seen as the most likely future climates in the region: they are primarily designed to show the sensitivity to change within a reasonable interval. III 1 Hydrologic modelling methodology The potential applicability of hydrological models to climatic change impact studies Research hydrologists develop simulation models that describe, in mathematical terms, the detail involved in the dynamic and nonlinear transformation of precipitation into streamflow via processes such as interception, infiltration, soil-water redistribution, evaporation, transpiration, snowmelt, surface, subsurface and groundwater flows. Operational hydrologists then use these models to seek solutions to water resource problems, such as flood protection, frequency and duration of extreme hydrological events (floods, droughts), irrigation, spillway design, hydropower evaluation or water supply design, under different climatic conditions at one location or at different locations. Following Schulze (1997), the advantages of such models in climate change impact studies include the following: 1) Models tested for different climatic/physiographic conditions, as well as models structured for use at various spatial scales and dominant process representations, are readily available. 2) GCM-derived climate perturbations (at different levels of downscaling) can be used as model input. 3) A variety of responses to climate changes scenarios can hence be modelled. 4) The models can convert climate change output to relevant water resource variables related, for example, to reservoir operation, irrigation demand, drinking water supply, etc. 1) Identify a large-scale predictor G, which controls the local parameter L 2) Find a statistical relationship between L and G 3) Validate the relationship with independent data 4) If the relationship is confirmed, G can be derived from GCM experiments to estimate L 1) Simple, less computationally demanding 2) Application is limited to the sites, variables and seasons when the local climate is related well to the conditions in the free troposphere 3) Very long observation series needed Procedures Advantages and shortcomings Regression method 1) Possible to generate daily sequences of precipitation at a point for any number of days based on limited historic data sets 2) Weather classification schemes are somehow parochial and/or subjective. There is a need for more general classification systems (Wilby, 1994) 1) Classify atmospheric circulation pattern into limited number of classes 2) Simulate weather types through the use of stochastic models 3) Link the likelihood of rainfall occurring to weather type, using conditional probabilities 4) Simulate rainfall and/or other hydrometeorological processes using weather types Circulation-based method Table 1 Comparison of statistical downscaling approaches Common assumptions 1) Local-scale parameters are a function of synoptic forcing. 2) The GCM used to derive downscaled relationships is valid at the scale used. 3) The relationship derived remains valid under greenhouse forcing. 1) Able to generate realistic, statistical characteristics of daily rainfall series 2) Relies on GCM predicted changes in mean precipitation, which are known to be unreliable – a problem that is of primary importance to hydrology and that is yet to be resolved (e.g., Mearns et al., 1995) 1) Use observed daily rainfall data to determine the probability of the state of a day 2) Use exponential (or other) distribution to fit and estimate the amount of rainfall on a wet day 3) Condition other weather variables (temperature, radiation, etc.) on the wet/dry status of the day Weather generator method 236 Downscaling methods and hydrologic modelling Examples of applications 1) Large-scale predictors and local-scale 1) Relates regional rainfall to predictands are the same variables synoptic weather patterns: Lamb, 1972; Hay et al., 1991; (Wilks, 1989; Brown et al., 1995; Carbone and Bramante, 1995; Perica Bardossy and Plate, 1992; and Foufoula-Georgiou, 1996) Hughes et al., 1993; Jones et al., 2) Large-scale predictors and local-scale 1993; Bardossy et al., 1994; predictands are different variables 1995; Wilby, 1995; 1997 2) Relates long-term temperature (Wigley et al., 1990; Zorita et al., fluctuations to synoptic weather 1992; von Storch et al., 1993; Kaas, patterns (Sowden and Parker, 1993; 1994; Johannesson et al., 1981; Moses et al., 1987) 1995; Conway et al., 1996; Brandsma and Buishand, 1997) 3) Relates precipitation chemistry 3) Use of artificial neural network to synoptic weather patterns (ANN) approaches (Hewitson and (Davies et al., 1986; Wilby, Crane, 1992; 1996) 1989) 4) Relates river flow to synoptic weather patterns (Duckstein et al., 1993; Wilby, 1993) 1) Use of stochastic weather generators for the present climate (Richardson, 1981; Foufoula-Georgiou and Lettenmaier, 1987; Smith, 1987; Zucchini and Guttorp, 1991) 2) Use of stochastic weather generators for climate change and impacts studies (Wilks, 1992; Gregory et al., 1993; Katz, 1996; Mearns et al., 1996; Semenov and Barrow, 1997) Chong-yu Xu 237 238 Downscaling methods and hydrologic modelling Table 2 Comparison of the characteristics of selected studies that have used hypothetical scenarios as input to hydrological models Reference Study region Climatic scenarios Hydrological models Nemec and Schaake (1982) Two basins in the USA; one basin in Kenya Combination of ∆P = 0, ±10%, ±25%, ∆E = ±4%, +12% uniformly distributed to daily input data Sacramento model Ng and Marsalek (1992) One small basin in Newfoundland, Canada Combination of ∆P = ±5%, ±10%, ±20% ∆T = 1, +2, +3, +4 °C uniformly distributed to hourly input data HSPF model (the Hydrologic Simulation Program – FORTRAN) Bultot et al. (1988) Three catchments in Belgium Range of changes: IRMB model (Royal ∆P = –2.7 mm, ~+10.5 mm Meteorological Institute of Belgium) ∆T = +2.3 ~ +3.4 °C unevenly distributed to daily input data McCabe and Ayers (1989) Delaware, USA Combination of ∆P = ±10%, ±20% ∆T = +2, +4 °C plus three GCMestimated scenarios to 2 × Co2 levels Thornthwaite monthly water-balance model McCabe et al. (1990) USA Different scenarios based on GCMestimated changes of temperature and precipitation to 2 × CO2 levels Thornthwaite moisture index Schaake and Liu (1989) 52 catchments in the southeastern USA ∆P = +10% ∆E = +10% Simple monthly waterbalance model Panagoulia (1991) Acheloos River in central Greece Combination of ∆P = 0, ±10%, ±20% ∆T = +1, +2, +4 °C uniformly distributed to monthly input data US NWS (US National Weather Service snowmelt and soil moisture accounting model) Arnell (1992) 15 catchments in the UK Annual changes in precipitation and evaporation are unevenly distributed during the year Thornthwaite monthly water-balance model Braun et al. (1994) Romanche River, France ∆T = +2, plus changes in radiation HBV Chong-yu Xu 239 Table 2 continued Reference Study region Climatic scenarios Hydrological models Vehviläinen and Lohvansuu (1991) 19 catchments approx. evenly distributed in Finland Within the range: ∆P = +11 m ~ +30 mm/ month ∆T = +2.2 ~ +6 °C ∆E = +1 mm ~ +27 mm/ month depending on the region and season HBV Xu and Halldin (1997) 11 catchments in central Sweden Combination of ∆P = 0, ±10%, ±20% ∆T = +1, +2, +4 °C uniformly distributed to monthly input NOPEX monthly water-balance model Lettenmaier and Gan (1990) Four catchments in the USA Scenarios to 2 × CO2 levels simulated by three GCMs are used Sacramento model 2 The practical application of hydrological models to climatic change impact studies The scientific literature over the past two decades contains a large number of reports dealing with the application of hydrologic models to the assessment of the potential effects of climate change on a variety of water resource issues. These investigations can range from the evaluation of annual and seasonal streamflow variation using simple water-balance models to the evaluation of variations in surface and groundwater quantity, quality and timing using complex distributed-parameter models that simulate a wide range of water, energy and biogeochemical processes. Based on the level of complexity, these models can be grouped into four categories (Leavesley, 1994): 1) 2) 3) 4) Empirical models (annual base). Water-balance models (monthly base). Conceptual lumped-parameter models (daily base). Process-based distributed-parameter models (hourly or finer base). The choice of a model for a particular case study depends on many factors (Gleick, 1986), with the purpose of the study and model availability being the dominant ones (Ng and Marsalek, 1992). Examples of such applications follow. For assessing water resource management on a regional scale, monthly water-balance models were found useful for identifying the hydrologic consequences of changes in temperature, precipitation and other climatic variables (Alley, 1984; Gleick, 1986; Xu and Singh, 1998). Arnell (1992) used a three-parameter water-balance model developed by Thornthwaite and Mather (1955) in 15 basins in the UK to estimate changes in the monthly river flow regimes and to investigate the factors controlling the effects of climate change on river flow regimes in a humid temperate climate. Gleick (1987a) 240 Downscaling methods and hydrologic modelling developed and applied a monthly water-balance model to simulate and evaluate changes in runoff and soil moisture under 18 assumed climate scenarios. A monthly water-balance model that also accounts for snow process was developed and applied by Mimikou et al. (1991) for evaluating regional hydrologic effects of climate change in the central mountainous region of Greece. Schaake and Liu (1989) developed and applied a nonlinear monthly water-balance model for the evaluation of regional changes in annual runoff associated with assumed changes in climate. Recently, Xu and Halldin (1997) and Xu (1998a) used a monthly water-balance model developed by Xu et al. (1996) to study the effects of climate change on river flow and snow cover in 11 and 25 catchments in central Sweden, respectively. For detailed assessments of surface flow, conceptual lumped-parameter models are used. One of the more frequently used models in this group is the Sacramento Soil Moisture Accounting Model (Burnash et al., 1973). This model has been used by many researchers in the USA when studying the impact of climate change (e.g., Nemec and Schaake, 1982; Gleick, 1987b; Cooley, 1990; Lettenmaier and Gan, 1990; Schaake, 1990; Nash and Gleick, 1991). Panagoulia (1992) used the same model to assess the effects of climate change on a basin in central Greece. The HBV (Hydrologiska Bryång Vattenbalansavdelning) model (Bergström, 1976) is widely used in Nordic countries as a tool to assess the climate change effects. Vehviläinen and Lohvansuu (1991) applied the model to evaluate the effects of climate changes on river flow and snowpack in Finland. Climate change impacts on runoff and hydropower in the Nordic countries have been studied by using the HBV model (e.g., Saelthun et al., 1994; Erichsen and Saelthun, 1995; Saelthun, 1995). Other examples of using the HBV model in climate change studies are available from the literature. (e.g., Bergström et al., 1997; Bergström, 1998) Several other models that have a similar structure to the above-mentioned two models but that have different process conceptualizations, have been used to assess the effect of climate change on many regions of the globe (see Leavesley, 1994). Among others, the Institute of Royal Meteorology, Belgium, model (Bultot and Dupriez, 1976) has been applied to basins in Belgium (Bultot et al., 1988) and Switzerland (Bultot et al., 1992). The HYDROLOG model (Porter and McMahon, 1971) was applied to two basins in South Australia (Nathan et al., 1988). The Hydrologic Simulation Program – FORTRAN (HSPF) model (USEPA, 1984) has been applied to a basin in Newfoundland, Canada (Ng and Marsalek, 1992). For the simulation of spatial patterns of hydrologic response within a basin, processbased distributed-parameter models are needed (Beven, 1989; Bathurst and O’Connell, 1992). Thomsen (1990) proposed the use of the European Hydrological System (SHE) model in the assessment of climate variability and change impacts on groundwater in the Arhus region of Denmark. Running and Nemani (1991) used a process-level ecosystem model to examine climate change-induced forest response for a 1540 km2 region in northwestern Montana using a grid resolution of 1 × 1 km2. For estimating changes in the average annual runoff for different climate change scenarios, simple empirical and regression models have been used. Examples include Stockton and Boggess (1979) and Revelle and Waggoner (1983) in the USA, and Arnell and Reynard (1989) in the UK. Chong-yu Xu 3 241 Modelling approaches: discussion Gleick (1986) reviewed various modelling approaches for evaluating the regional hydrologic impacts of global climatic changes and concluded that monthly waterbalance models appear to offer significant advantages over other methods in terms of accuracy, flexibility and ease of use. One of the limitations of monthly water-balance models is their inability to account adequately for possible changes in individual storm runoff characteristics at the time steps to which they are applied. Compared with monthly water-balance models, conceptual lumped-parameter models enable a more detailed assessment of the magnitude and timing of process response to climate change. However, these capabilities are accompanied by an increase in the number of process parameters, and in the amount and types of data, needed as input to run the simulations. The applicability of process-based distributed-parameter models to the simulation of spatial patterns of hydrologic response within a basin has been recognized (Beven, 1989; Bathurst and O’Connell, 1992), but few applications have been presented to date. The major limitations to the application of these models are the availability and quality of basin and climate data at the spatial and temporal resolution needed to estimate model parameters and to validate model results at this level of detail. Since empirical models reflect only the relations between input and output for the climate and basin conditions during the time period in which they were developed, the extension of these relations to climate or basin conditions different from those used for the development of the function is questionable (Leavesley, 1994). 4 Validation of hydrologic models in climate change studies Hydrologic models (either for forecasting or simulation) were designed for stationary conditions. However, in climate change studies, the hydrologic models employed will be applied to changing conditions. Special validation (testing) methods, therefore, have to be performed. Klemes (1986) discussed most of the types of validation tests in current use. He considered the general problem of validating catchment hydrological models and proposed a testing framework. The proposed scheme is termed hierarchical because the modelling tasks are ordered according to their increasing complexity; the demands of the test also increase in the same direction. The general hierarchical scheme proposed by Klemes (1986) is summarized in Table 3. Simple split-sample testing involves dividing the available measured time-series data for the test catchment into two sets, each of which should be used in turn for calibration and validation and the results from both arrangements compared. The model is considered acceptable only if the model validation results, in both cases, are acceptable. The proxy-basin test for geographic transferability is required for any model that is assumed to be geographically transferable within a region hydrologically and climatically homogeneous. If the goal is to simulate streamflow for an ungauged basin C, then the model to be used should be tested on two gauged basins, A and B. The model should be calibrated on basin A and validated on basin B and vice versa. Only if both proxy-basin tests are acceptable should one consider the model as geographically transferable. The differential split-sample test (for climatic transferability) applies when testing hydrologic models under conditions different from those used to calibrate them. 242 Downscaling methods and hydrologic modelling Table 3 Hierarchical scheme for the operational testing of hydrologic simulation models Stationary conditions Transient conditions Basin A Basin B Basin A Basin B Basin A Split-sample test Proxy-basin test Differential split-sample test Proxy-basin differential splitsample test Basin B Proxy-basin test Split-sample test Proxy-basin differential split-sample test Differential split-sample test The basic idea behind this test is to split the record into different climatic regimes and to demonstrate that the model has general validity in predicting the values of the output variables for different climatic conditions. For example, if it is intended that the model should simulate streamflow for a wet climate scenario, then it should be calibrated on a dry set of the historic record and validated on a wet set. The most involved model test is the proxy-basin differential split-sample test for geographic, land-use and climatic transferability. Such a broad transferability is probably the ultimate objective of most hydrologic models. The test aims, for example, to assess whether a model calibrated to a dry climate on basin A can simulate streamflow for a wet climate on basin B, and vice versa. The differential split-sample test and the proxy-basin differential split-sample test are clearly needed when testing hydrologic models embedded in GCMs. Changes in climate justify using these complex model-testing methodologies. In a recent study, Xu (1998b) discusses the importance of the differential split-sample test in some detail. A procedure for the calibration and uncertainty estimation of physically based distributed-parameter models was developed by Beven and Binley (1992). This provides a methodology for evaluating the uncertainty limits of the model for future events for which observed data are not available. Ewen and Parkin (1996) proposed a new method (a ‘blind’ approach) for testing the ability of SHETRAN (a physically based, distributed flow and transport modelling system based on the SHE model) to predict the effects of changes in land use and climate. The results of the first application of the method are reported in Parkin et al. (1996). The central feature of the method is that it involves making predictions for a test catchment as if it were a hypothetical catchment. The modeller is, therefore, not allowed sight of the output data for the test catchment (i.e., the method involves ‘blind’ testing) and, as a result, cannot calibrate the model for the test catchment. IV Summary and conclusions GCMs (the only available tool for the detailed modelling of future climate evolution) are not well suited for answering questions of primary interest to hydrologists concerning regional hydrologic variability. GCMs were not designed for climate change impact studies in hydrology. There were originally developed to predict the average, Chong-yu Xu 243 synoptic-scale, general-circulation patterns of the atmosphere. Their direct representations of hydrological quantities are thus still generally highly simplified large-scale averages with little spatial reliability or relevance to specific regions. In this regard it has been noted that GCM skill decreases with increasing resolution, and that alternative methodologies need to be adopted to circumvent this difficulty. The hydrologic literature now abounds with regional-scale hydrologic simulations under greenhouse scenarios. Such scenarios are either GCM-simulated or hypothetical. One of the most widely used methods of scenario generation has been to estimate average annual changes in precipitation and temperature for a region using one or more GCM and then applying these estimates to adjust the historic time series of precipitation and temperature. In the simplest procedure, the adjustment is made by multiplying the historic precipitation by a percentage change and adding an absolute change to the historic temperature. Hypothetical scenarios using personal estimates or historic measurements of change instead of GCM results were also generated using this procedure. This procedure does not provide for a change in the variance. To address the variability problem, a number of methods have been developed to disaggregate (downscale) the GCM output for direct application to hydrologic models. Current downscaling research, in spite of some shortcomings as discussed above, is starting to provide hydrologically useful regional algorithms. Recent higher-resolution regional climate models provide better agreement with observations on synoptic and regional scales and on monthly, seasonal and interannual timescales. Statistical downscaling approaches linking GCMs to meteorologic and hydrologic models resolved at finer scales have been developed and implemented. This is the state-of-theart approach to bridge the gap between the coarse-resolution GCMs and hydroclimatic modelling at the river-basin scale. The challenges for future studies of the hydrological impacts of climate change include, among others, the following: 1) Improved methodologies to develop climate change scenarios. Scenarios must provide the spatial and temporal resolution required by assessment models and they must incorporate the simulated changes in both the mean and variability of the climate variables. 2) There remain considerable opportunities for the development and comparison of existing downscaling methods. Given the range of downscaling techniques and the fact that each approach has its own advantages and shortcomings, there exists no universal method which works for all situations. In fact, all downscaling methods are still at the stage of development and testing. It is recommended, in particular, that rigorous testing and comparison of statistical downscaling approaches should be undertaken with LAMs. 3) Rigorous model validation procedures must be applied to the selected and developed models before they are used to simulate future climate change impacts. In particular, the model’s climatic transferability must be checked to demonstrate that the model has general validity for predicting the values of the output variables for different climatic conditions. 4) A major limitation in performing downscaling and in using hydrological model approaches is the lack of sufficient data at spatial and temporal scales. Detailed data sets in a variety of climatic and physiographic regions collected at a range of spatial 244 Downscaling methods and hydrologic modelling and temporal scales are critical to improving our understanding of hydrologic processes and in testing and validating the downscaling techniques and hydrological models that are being developed. Acknowledgements This article is abstracted from the author’s annual report to SWECLIM (Swedish Regional Climate Modelling Programme). The author has also received research funding from NFR (Swedish Natural Science Research Council). The valuable support and advice offered by Dr Wilby (National Center for Atmospheric Research, USA) and Professor Bardossy (Stuttgart University) are acknowledged gratefully. I am also grateful to the referees who provided helpful suggestions that led to an improved manuscript. 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