Climate Change and Water Resources in South Asia - Chapter 2 doc

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2 Hydrologic Modeling Approaches for Climate Impact Assessment in South Asia 2.1 INTRODUCTION The hydrologic and water resources problems in South Asia are discussed in Chapter 1. It is anticipated that the problems will be exacerbated if basin-wide temperature and precipitation would change due to climate change. Quantification of possible changes in river discharge (mean or peak) is achieved with the application of hydrologic models. Four types of hydrologic model - empirical, water-balance, conceptual lumped-parameter and process-based distributed models - are used for hydrologic modeling. A model is usually selected depending on the purpose of the application which includes: runoff-simulation; sediment transport and morphological changes; estimating ground water and changes in ground water volume; forecasting flood volume, depth and duration; assessing changes in land-use; and assessing impacts of changes in climate. Availability of data and resources are also governing factors in a model selection process. This chapter discusses the comparative advantages and limitations of various hydrologic models and their suitability for estimating changes in mean annual and mean peak discharge under selected climate change scenarios for the river basins in South Asia. It examines reduction of input variables for empirical modeling through the sensitivity analysis of runoff to changes in temperature and precipitation. This chapter also discusses application of hydrologic models in Bangladesh as a case study to assess climate change impacts. 2.2 HYDROLOGIC MODELS In planning for water resources and extreme events like floods and droughts, it is essential to know the precipitation-runoff processes in the vegetation, land surface and soil components of the hydrologic cycle. These processes differ in arid, semi-arid and humid climates. Even within a single climate zone, physical processes can vary widely because of the diversity of vegetation, soils and microclimates. Hydrologic models describe these processes by partitioning the water among the various pathways of the hydrologic cycle (Dooge, 1992). Mathematically, hydrologic models incorporate a set of assumptions, equations and procedures intended to describe the performance of a prototype (real-world) system (Linsley et al., 1988). Because of the M. MONIRUL QADER MIRZA Copyright © 2005 Taylor & Francis Group plc, London, UK increase in computing capacity, complex mathematical descriptions of the physical processes of the hydrologic cycle can now be incorporated into hydrologic models. However, because of variations in physical parameters and the limitations of our knowledge and understanding about the complexity of the hydrological processes, no ‘hydrologic model’ is able to reproduce fully the prototype processes. Accuracy of the model is highly dependent on factors such as: adequacy of empirical, statistical and mathematical descriptions of the physical processes; the quantity and quality of input data; the extent of basin coverage; and the magnitude of variability in physical parameters. There are two main aims for using simulation modeling in hydrology. The first is to explore the implications of making certain assumptions about the nature of the real-world system. The second is to predict the behavior of the real-world system under a set of naturally occurring circumstances (Beven, 1989). In order to meet these aims, different types of hydrologic models are required. There are four types of hydrologic models - empirical, water-balance, conceptual lumped-parameter and process-based distributed models. The choice of model type depends partly on the purpose of the application including: simulating runoff, sediment transport and morphological changes; estimating ground water and changes in ground water volume; forecasting flood volume, depth and duration; assessing changes in land-use; and assessing impacts of changes in climate. The choice of model also depends on the availability of data and resources. The various types of hydrologic models and their advantages and limitations are discussed below. 2.2.1 EMPIRICAL MODELS In hydrological modeling, empirical models are generally developed and used for prediction and estimation purposes. These models do not explicitly consider the physical laws governing the processes involving precipitation, temperature, vegetation and soils (Singh, 1988). However, they do implicitly incorporate the fundamental physical fact that, generally, variations in runoff tend to respond proportionally to the variations in climate. Empirical models are developed based on a ‘black box’ modeling approach where empirical equations are used to relate runoff and rainfall, and only the input (rainfall) and output (runoff) have physical meanings. Through statistical techniques, empirical models reflect only the relations between input and output for the climate and basin conditions during the time period for which they were developed. These models provide a much more simplified view of reality, particularly when regression techniques are employed (Kirkby et al., 1987). The accuracy of models largely depends on the magnitude of error inherent in the input and output data. As the empirical models are developed with input and output data within a certain range and time period, caution should be exercised regarding the extension of the relationship for climate conditions different from those used for the development of the function (Leavesley, 1994). Models developed for a particular river basin cannot be applied to a different basin. Although empirical models are often criticized for these limitations, they are widely used compared to other models. Despite their limitations, empirical models have some distinct advantages over other types of hydrologic models. For example, they are relatively easy to develop, require less data, can be calibrated simply, require fewer resources, and do not need a huge computing capacity. When other models cannot be developed or used because of the paucity of data, empirical models can be developed for various purposes. In many situations, empirical models can yield accurate results and can, therefore, serve a useful purpose in 24 HYDROLOGIC MODELING APPROACHES Copyright © 2005 Taylor & Francis Group plc, London, UK decision-making (Singh, 1988). In hydrology, empirical models are generally useful in estimating the mean annual flood, monthly and annual mean discharge and bankful discharge (Garde and Kothyari, 1990; Kothyari and Garde, 1991; Mosley, 1979 and 1981; Schumm, 1969; Thomas, 1970; Rodda, 1969; Leopold and Millier, 1956; Natural Environment Research Council (NERC), 1975; Beable and Mckerchar, 1982). There are two important issues which need to be taken into account before developing an empirical model for estimating discharge and floods. First, empirical models require very good spatial distribution of precipitation. Ideally, this can be achieved by acquiring long-term records of precipitation for a large number of stations uniformly distributed over a river basin, covering high and low elevations. Similarly, long-term records of temperature are also necessary if temperature effects are to be considered. Second, a fairly good record of discharge (or runoff) from downstream stations is needed. However, if there is any diversion of flows through the distributary (ies) or by any other means in the upstream areas, this has to be taken into account depending on the magnitude of the diversion. 2.2.2 WATER-BALANCE MODELS Water-balance models were first developed by Thornthwaite (1948) in the 1940s and were subsequently revised by Thornthwaite and Mather (1955) and by others. Palmer (1965) used a water-balance model similar to that of the Thornthwaite model while developing an index of meteorological drought. Thomas (1981) presented an alternative water-balance model with several new features. These water-balance models have very simple structures and are characterized by a limited number of parameters. This kind of model is essentially a ‘book-keeping procedure,’ which uses the following fundamental equation to estimate the balance between the precipitation (as rain and snowmelt), loss of water by evapo-transpiration, stream flow and recharge into the ground water: where P is the precipitation, R is the runoff, G is ground water runoff, ∆S is the changes in storage (snow and soil water) and E is evapo-transpiration. The typical structure of a water-balance model is shown in Figure 2.1. The models can be simple to complex depending on the details of each of the components of the equation (2.1). Most water-balance models calculate direct runoff from precipitation and lagged runoff from the basin storage in the computation of the total runoff (R). The sensitivity and accuracy of water-balance models often depend on the method of calculating potential evapo-transpiration (PET). Various PET-models are available among which Penman (1948), Thornthwaite (1948), Blaney and Criddle (1950), Monteith (1964), Priestley and Taylor (1972), and Hargreaves (1974) are important (see cited references for descriptions of these models). The selection of the PET model is largely dependent on the availability of sufficient climate data, which varies from place to place. Most models compute E as a function of potential ET and water available in soil storage (S). Various methods are in use for calculating E from the PET and soil moisture deficit relationship, including linear, layered and exponential methods. One advantage of water-balance models is that they can potentially be used to determine changes in seasonal snow storage and melt. Within a water-balance model, the storage and melting processes of snow are described by two types of model: energy-balance and temperature-index models. M. M. Q. MIRZA 25 Copyright © 2005 Taylor & Francis Group plc, London, UK Evapo-Transpiration Precipitation Snow Storage Soil Storage Soil Storage Base Flow/ Delayed Flow Surface Runoff Total Runoff Fig. 2.1 Typical structure of a water-balance model. The energy-balance models simulate the flow of mass and energy in the snow cover. The energy-balance approach for calculating snowmelt applies the law of conservation of energy to a control volume. The control volume has its lower boundary as the snow-ground interface and its upper boundary as the snow-air interface. The use of a volume allows the energy fluxes into the snow to be expressed as internal energy changes (Gray and Prowse, 1993). The energy balance model is physically or meteorologically more explicit than the temperature-index model. It contains parameters that can be extrapolated to a certain degree of confidence from weather maps or from regional climate models (Kuhn, 1993). Various studies have used energy-balance models to estimate runoff from snowmelt (Fitzharris and Grimmond, 1982; Granger and Gray, 1990; Gray and O’Neill, 1974; and Gray and Landine, 1987). Details of an energy-balance model can be found in Gray and Prowse (1993). The second type of model is the temperature-index snowmelt model (Equation (2.2)). Despite its simplicity, the model is widely used in forecasting discharge in snow-covered basins. Using monthly data, for example, Kwadijk (1993) applied a temperature-index snowmelt model in order to assess the impact of climate change on the Rhine River basin and found close fit between the simulated values and observed data. While modeling the effects of climate change on water resources in the Sacramento River basin in the USA, Gleick (1987) found poor performance of a temperature-index snowmelt model using monthly data. The temperature-index models for rain-free and rain conditions are as follows: (i) Rain-Free Condition 26 HYDROLOGIC MODELING APPROACHES Copyright © 2005 Taylor & Francis Group plc, London, UK where M = snowmelt in mm M f = snowmelt factor T i = index temperature T b = base temperature (set as 0 o C) (ii) During Rain For a rain event, the melt factor is modified as follows: M f = (0.74 + 0.007P) (T i – T b ) where P = precipitation (in mm) Snowmelt is calculated by: Overall, water-balance models incorporate soil-moisture characteristics of regions, allow monthly, seasonal, and annual estimates of hydrologic parameters, and use readily available data on meteorological phenomena, soil, and vegetation characteristics. They can often provide efficient estimates of surface runoff when compared to measured runoff, reliable evapo-transpiration estimates under many climate regimes, and estimates of ground water discharge and recharge rates. Typical data requirements are precipitation, temperature, sunshine hour, wind speed, information on characteristics of vegetation (which may include type of vegetation for estimating rooting depths), and soil (such as field capacities and wilting points). While generally the water-balance models require huge amounts of data, they can nevertheless be applied in reasonably large areas with sparse data (Hare and Hay, 1971; Brash and Murray, 1980). For example, Hare and Hay (1971) applied the Lettau’s (1969) empirical model to approximate precipitation in order to analyze the anomalies in the large-scale annual water-balance over Northern North America. Brash and Murray (1980) estimated adjusted equilibrium precipitation from an energy-balance equation. The estimated precipitation was then used to estimate water yield in the Taieri catchment in New Zealand and found to be very closely matched with the measured data. Note, however, that these energy balance techniques require reliable net radiation data, which are not readily available for the major river basins in South Asia. By integrating hydrologic advances with existing water-balance techniques, new insights into hydrologic processes and environmental impacts can be gained for climate impact assessments. Furthermore, water-balance models are well suited to the current generation of microcomputer software and hardware. A number of water-balance models have been developed to assess the impact of climate change on river runoff and soil moisture stress from wet to dry regions (Mather and Feddema, 1986; McCabe and Wolock, 1992; Thompson, 1992; Flaschka et al., 1987; McCabe and Ayers, 1989; Conway, 1993 and Kwadijk, 1993). These studies show various magnitudes of runoff and soil moisture sensitivities on monthly time-scales to possible changes in climate. Overall, such studies demonstrate that the water-balance approach holds good potential for application in the river basins of South Asia (subject to availability of the required data) in order to assess effects of climate change on hydrology and water resources. M. M. Q. MIRZA 27 Copyright © 2005 Taylor & Francis Group plc, London, UK 2.2.3 CONCEPTUAL LUMPED-PARAMETER MODELS Conceptual lumped-parameter models are developed based on approximations or simplifications of physical laws. These models embody a series of functions which are considered to describe the relevant catchment processes. The algorithms are usually simplified by the use of empirical relations in order to speed the solution and to adapt the model to cope with the point-to-point variations in the hydrologic processes within the catchment (Crawford and Linsley, 1968; Boughton, 1968; Linsley et al., 1988; Leavesley, 1994). They contain parameters, some of which may have direct physical significance and can, therefore, be estimated by using concurrent observations on input and output. Some widely-used models of this category are: the Sacramento Soil Moisture Accounting model (Burnash et al., 1973), the Institute of Royal Meteorology Belgium (IRMB) model (Bultot and Dupriez, 1976), the HBV model (Bergstorm, 1976), the Hydrologic Simulation Program-FORTRAN (HSPF) model (USEPA, 1984), the Erosion Productivity Impact Calculator (EPIC) model (Williams et al., 1984) and the MODHYDROLOG (Chiew and McMahon, 1993). A schematic diagram of a conceptual lumped-parameter model (MODHYDROLOG) is shown in Figure 2.2. In the conceptual lumped-parameter models, the vertical and lateral movement of water with respect to time is incorporated. Variations in respect of space are ignored. The vertical processes of water movement include interception storage and evaporation, infiltration, soil-moisture storage, evapo-transpiration, percolation to ground water storage, snow-pack accumulation and melt, and capillary rise. The horizontal processes include surface runoff, interflow, ground water flow, and stream flow. Components of the vertical and lateral processes are integrated. The model development starts with the vertical processes. Interception storage is assumed and calibrated usually by trial and error. Empirical algorithms are used for calculating the evaporation from the surface storage. For calculating infiltration calculation, two methods are in practice. First, the maximum infiltration rate is assumed from the field observations and then the infiltration rate is expressed as a function of soil storage (Boughton, 1968). Second, some prominent infiltration models, such as Green-Ampt (1911), Philip (1957 and 1969) and Holtan (1961), can be used directly. For example, the Hydrologic Engineering Center’s HEC-1 model uses the Green-Ampt and Holtan’s infiltration models. One of the important limitations of using these models is the need to estimate a number of parameters, some of which have to be estimated either from laboratory experiments or from field observations. The other vertical and horizontal components that need to be developed are evapo-transpiration, percolation and base flow. Evapo-transpiration is usually calculated as a function of soil moisture storage, soil moisture storage capacity and potential evapo-transpiration (Chiew and McMahon, 1993). A constant is used to calculate the percolation to ground water storage. Another constant is used to estimate the base flow from the ground water storage. The base flow constant is usually determined by calibrating the estimated flows with the observed values. Lumped-parameter models have some distinct advantages. They do not necessarily require direct use of mathematical equations of physical processes and they take into account more physical processes than water-balance models. They also have been shown to be capable of making acceptable estimates of stream flow, evapo-transpiration, soil moisture deficits, and storage changes, including changes in ground water storage, for smaller river basins. 28 HYDROLOGIC MODELING APPROACHES Copyright © 2005 Taylor & Francis Group plc, London, UK Fig. 2.2 Schematic representation of the MODHYDROLOG daily rainfall-runoff model. Source: Courtesy of Chiew and McMahon, 1994. Although lumped-parameter models are widely used, they have a number of limitations. These include: (1) the equations of a lumped-parameter model can only be approximate representations of the real world and must introduce some error arising from the model structure; (2) spatial heterogeneities in system responses may not be well reproduced by catchment-averaged parameters (Sharma and Luxmore, 1979; Freeze, 1980); (3) the accuracy with which a model can be calibrated or validated is very dependent on the observations of both inputs and outputs (Ibbit, 1972; Hornberger et al., 1985). Since input variables, particularly evapo-transpiration estimates, may be subject to considerable uncertainty; (4) there is a great danger of over-parameterization if attempts are made to simulate all hydrological processes thought to be relevant and to fit those parameters by optimization against an observed discharge record (Hornberger et al., 1985), so three to five parameters should be sufficient to reproduce most of the information in a hydrological record; and (5) the calibrated parameters of such models may be expected to show a degree of interdependence, so that equally good results may be obtained with different sets M. M. Q. MIRZA 29 Copyright © 2005 Taylor & Francis Group plc, London, UK of parameter values, even though a model has only a small number of parameters (Ibbitt and O’Donnell, 1971; Pickup, 1977; and Sorooshian and Gupta, 1983). Another potential disadvantage is that the use of lumped-parameter rainfall-runoff models depends essentially on the availability of sufficiently long meteorological and hydrological records for their calibration. Such records are not always available. Their calibration also involves a significant element of curve fitting, thus making any physical interpretation of the fitted parameter values extremely difficult. There are other limitations, too. Because of their inherent structure, these models also make very little use of contour, soil, and vegetation maps, or of the increasing body of information related to soil physics and plant physiology. These models are not suitable for predicting the effects of land-use changes on the hydrological regime of a catchment, particularly when only a part of the catchment is affected. In the case of the lumped models, parameter values are highly dependent on both the model structure and the period of calibration (Beven and O’Connell, 1982). Therefore, as with other hydrologic models, it is not advisable to extrapolate events that are outside the conditions over which the model parameters are estimated. 2.2.4 PHYSICALLY-BASED DISTRIBUTED MODELS Neither the empirical nor the lumped models are capable of addressing the physical processes of the basin which control the basin response, as they do not account for the spatial distribution of basin parameters. This limitation prompted the development of physically-based models aimed at improving the understanding of catchment processes. A schematic diagram of the Système Hydrologique Européen (SHE) distributed model is shown in Figure 2.3. Fig. 2.3 Schematic representation of the SHE model. Source: Adapted from Abbot et al., 1986. 30 H YDROLOGIC MODELING APPROACHES Copyright © 2005 Taylor & Francis Group plc, London, UK Physically-based distributed models require descriptive equations for the hydrological processes involved (Freeze and Harlan, 1969). The equations on which distributed models are developed generally involve one or more space coordinates. They thus have the capability of forecasting the spatial pattern of hydrologic conditions within a catchment as well as the simple outflows and bulk storage volumes. In general, the descriptive equations are non-linear differential equations that cannot be solved analytically for cases of practical interest. Therefore, for simplification, some empirical discretization is made. Indeed, the complexities of hydrological systems are such that all the model components ultimately rely on an empirical relationship. As discussed by Freeze and Harlan (1969), the development of a computational model to simulate physical processes is carried out by: (1) defining a physical system isolating a region of consideration with simplified boundaries and neglecting all physical processes non-essential to the phenomenon being studied; (2) representing the idealized and simplified physical system by a mathematical model, including governing differential equations and boundary/initial conditions; (3) converting the mathematical model into a numerical model using one of the numerical methodologies (finite difference, finite element, boundary element, and characteristics methods) which is most appropriate to the problem; and (4) writing a computer code based on the selected computational algorithm to obtain numerical results in still graphic or animated form. In other words, before the computational model is developed, numerous idealizations, simplifications, approximations and discretizations have to be made. Regarding calibration of the physically-based model, the theoretical idea is that the model has the potential to estimate parameter values by field measurements without having to carry out parameter optimization as required by the simpler models of the lumped, conceptual type (Abbott et al., 1986). But in reality, the situation is different. Such an ideal situation requires comprehensive field data covering all parameters and a model discretization to an appropriate scale (Refsgaard et al., 1992). For example, the SHE model was applied to the Wye catchment in England and in six small catchments in the Narmada basin in India (Bathurst, 1986 and Refsgaard et al., 1992). In these catchments, during the application, optimizations were carried out because of inadequate representation of the hydrological processes, insufficient data, and the possible difference in scale between the measurement and the model grid scale (Bathurst, 1986 and Refsgaard et al., 1992). The distributed nature of physically-based models offers some advantages over other types of models. For example, they are capable of forecasting the effects of land-use changes, the effects of spatially variable inputs and outputs, the movement of pollutants and sediments, and the hydrological response of ungauged catchments. Regarding land-use changes in a catchment, deforestation rarely takes place abruptly over a complete basin; it is more common for piecemeal changes to take place over a considerable period of time. In a distributed model the effects of such changes can be examined in their correct spatial context. It is clear from the above discussion that physically-based models require much more information than their empirical, water-balance or lumped-conceptual counterparts. Thus, calibration and validation emerge as major tasks. Extensive field measurements require huge amounts of resources and time, and computing capacities are high. Finally, despite the greater effort required to parameterize, validate and run physically-based models, the simulated results often provide only slightly better (or sometimes worse) correspondence with measured values than lumped-conceptual models (Beven, 1987; Logue, 1990; and Wilcox et al., 1990). Perhaps this results from the equations used to describe the physical variability and the high degree of temporal and spatial variability of critical input M. M. Q. MIRZA 31 Copyright © 2005 Taylor & Francis Group plc, London, UK parameters. Ironically, the description of physical variability is presumed to be a strength for physically-based models (Beven, 1985; Bathurst and O’Connell, 1992). Regarding extrapolation of physically-based distributed models, Beven and O’Connell (1982) mentioned that, because of the physical basis of the model parameters, the measured parameters’ values might be extrapolated to other locations or time periods. However, response of the physical parameters at other locations or other time periods may not be same. Therefore, physically-based distributed models also have limitations regarding extrapolation. Comparisons of various hydrologic models are tabulated in Table 2.1. In this section, the advantages and limitations of various hydrologic models have been discussed. In the next section, the applicability of some hydrologic models for assessing the impact of climate change on water resources is discussed. 2.3 ADVANTAGES AND LIMITATIONS OF HYDROLOGIC MODELS IN CLIMATE CHANGE APPLICATION A number of studies have been carried out to assess the impacts of climate changes using empirical, water-balance and lumped-parameter models (Revelle and Waggoner, 1983; Mather and Feddema, 1986; McCabe et al., 1990; McCabe and Wolock, 1992; Thompson, 1992; Flaschka et al., 1987; MaCabe and Ayers, 1989; Conway, 1993; and Kwadijk, 1993). All these studies used monthly precipitation and temperature time-series data for the assessment. Models were calibrated to the observed data and then validated against the other observed dataset in order to assess the capacity of the model to generate current hydrological output (for example, runoff). Finally, the models were used to predict the possible effect of future climate change on water resources. Most of the models used GCM-based and hypothetical climate scenarios for sensitivity analysis. In the applications noted above, the model parameters were estimated from the current climate as a basis for predicting future conditions. This is one of the major limitations of modeling the effects of climate change. The behavior of physical parameters of a catchment is not necessarily stationary overtime. For example, most pedological processes operate over a very long time-scale, but changes in organic matter content and soil structure may become apparent over a time-scale of less than 10 years (Climate Change Impact Review Group (CCIRG), 1991). Higher temperatures and increased rainfall would lead to a loss of soil organic matter and hence a decrease in ability of the soil to hold moisture; higher temperatures would also encourage clayey soil to shrink and crack, thus assisting the passage of water into and through the soil profile (CCIRG, 1991). Another issue is the response of vegetation to climate changes. For example, Idso and Brazel (1984) estimated that plant evapo-transpiration may be decreased by one-third for a doubling of carbon-dioxide due to partial stomatal closure in plants, increasing their water use efficiency and conserving soil moisture for increased runoff to rivers and streams. Thus, as CO 2 concentrations change over time, so might the relationships between climate and hydrology. Indeed, Dooge (1992) suggested that research should not be used to develop more complex models until the issue of the “antitranspirant effect” of higher atmospheric CO 2 enrichment is effectively resolved. Which type of model should be chosen for assessing changes in runoff from scenarios of climate change? Empirical models can be applied successfully if the processes are ignored and the objective is limited to predicting runoff or discharge on monthly or annual time-scales. Empirical models require less data than the other models. The model performance during the calibration and validation period is highly dependent on good spatial and temporal coverage of the input data. 32 HYDROLOGIC MODELING APPROACHES Copyright © 2005 Taylor & Francis Group plc, London, UK [...]... rainfall totals in Step 2, the mean annual rainfall and standard deviation for each station were determined Step 4: Using the 196 7-1 9 92 mean rainfall and standard deviation, the 20 -year rainfall for each station was calculated by: 20 -year rainfall = (1.645 * sd (196 7-1 9 92) + mean (196 7-1 9 92) ) Step 5: The ratio between the 20 -year rainfall (from Step 4) and the mean (196 7-1 9 92) rainfall was determined... Meghna Rivers in Bangladesh Climatic Change 57 (20 03), pp .28 7-3 18 Morrison, J., Quick, M and Foreman, M.: Climate Change in the Fraser River Watershed: Flow and Temperature Projections Journal of Hydrology 26 3 (20 02) , pp .23 0 -2 44 Monteith, J L.: Evaporation and Environment The State and Movement of Water in Living Organisms, New York, Academic Press, 1964, pp .20 5 -2 34 Mosley, M P.: Semi-Determinate Hydraulic... h-point Q-point Figure 2. 6 A MIKE 11 network is an interconnected system of branches representing rivers and floodplains Along the branches h-points and Q-points are located Flood levels are calculated at h-points and discharge at Q-points Source: FAP 25 , 1994 In order to generate flood maps, GIS techniques (available with ARC/INFO GIS) are applied in combination with the MIKE 11 model In a MIKE 11-GIS... capacities and with no new reservoir added to the system Box 2. 2 The Indus basin The Indus River basin stretches from the Himalayan Mountains in the North, to the dry alluvial plains of the Sindh Province of Pakistan in the South The basin is shared by India and Pakistan The alluvial plains of the Indus basin cover an area 2 of 20 7, 20 0 km , which is approximately 25 % of the land area of Pakistan (WCD, 20 00)... of Changes in Stratospheric Ozone and Global Climate Vol.3, 1986 Copyright © 20 05 Taylor & Francis Group plc, London, UK M M Q MIRZA 53 McCabe Jr., G J and Ayers, M A.: Hydrologic Effects of Climate Change in the Delware River Basin Water Resources Bulletin 25 (1989), pp. 123 1-1 24 2 McCabe Jr., G J and Wolock, D M.: Effects of Climate Change and Climate Variability on the Thornthwaite Moisture Index in. .. C.: Flood Estimation in Indian Catchments Journal of Hydrology 113 (1990), pp.13 5-1 46 Gleick, P.: The Development and Testing of a Water- Balance Model for Climate Impact Assessment: Modeling the Sacramento Basin Water Resources Research 23 (6) (1987), pp.104 9-1 061 Gosain, A K and Rao, S.: Impacts of Climate Change on Water Sector In: Climate Change and India: Vulnerability Assessment and Adaptation (P... application in the GBM basins in order to determine the effects of climate change on annual discharge and flooding in Bangladesh But the use of the water- balance approach was hindered by the lack of adequate hydro-meteorological (radiation, wind speed and humidity) and land-use data Although the water- balance approach has been employed successfully in smaller basins with sparse data, as discussed in Section 2. 2,... relationships in (a) and (b) can be linear or non-linear while in (c) the stage-discharge relationship is non-linear These can be checked by plotting the y variable against the x variable(s) Linearity or non-linearity can be bi-variate or multi-variate depending on the number of independent variables For the regression model building, non-linearity can be transformed to linearity by applying standard transformation... Delware Basin Climate Change 20 (19 92) , pp.14 3-1 53 McCabe Jr., G J., Wolock, D M., Hay, H E and Ayers, M A.: Effects of Climate Change on the Thornthwaite Moisture Index Water Resources Bulletin 26 (1990), pp.63 3-6 43 McCuen, R H and Snyder, W M.: Hydrologic Modeling: Statistical Methods and Applications, New Jersey, Prentice-Hall, 1987 Micovic, Z and Quick, M C.: A Rainfall and Snowmelt Runoff Modeling Approach... Civil Engineering, Technical Report 39, 1968 Dooge, J C I.: Hydrologic Models and Climate Change Journal of Geophysical Research 97(D3) (19 92) , pp .26 7 7 -2 686 Fitzharris, B B and Grimmond, C S B.: Assessing Snow Storage and Melt in a New Zealand Mountain Environment, IAHS Publication 138 (19 82) , pp.16 1-1 68 Flaschka, I C., Stockton, C.W and Boggess, W R.: Climate Variation to Surface Water Resources in the . sediment transport and morphological changes; estimating ground water and changes in ground water volume; forecasting flood volume, depth and duration; assessing changes in land-use; and assessing impacts of changes. 2 Hydrologic Modeling Approaches for Climate Impact Assessment in South Asia 2. 1 INTRODUCTION The hydrologic and water resources problems in South Asia are discussed in Chapter 1. It. and duration; assessing changes in land-use; and assessing impacts of changes in climate. Availability of data and resources are also governing factors in a model selection process. This chapter discusses
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