Constraining simulation uncertainties in a hydrological model of the Congo River Basin including a combined modelling approach for channel-wetland exchanges
- Authors: Kabuya, Pierre Mulamba
- Date: 2021-04
- Subjects: Congo River Watershed , Watersheds -- Congo (Democratic Republic) , Hydrologic models , Rain and rainfall -- Mathematical models , Runoff -- Mathematical models , Wetland hydrology
- Language: English
- Type: thesis , text , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/177997 , vital:42897 , 10.21504/10962/177997
- Description: Compared to other large river basins of the world, such as the Amazon, the Congo River Basin appears to be the most ungauged and less studied. This is partly because the basin lacks sufficient observational hydro-climatic monitoring stations and appropriate information on physiographic basin properties at a spatial scale deemed for hydrological applications, making it difficult to estimate water resources at the scale of sub-basins (Chapter 3). In the same time, the basin is facing the challenges related to rapid population growth, uncontrolled urbanisation as well as climate change. Adequate quantification of hydrological processes across different spatial and temporal scales in the basin, and the drivers of change, is essential for prediction and strategic planning to ensure sustainable management of water resources in the Congo River Basin. Hydrological models are particularly important to generate the required information. However, the shortness of the available streamflow records, lack of spatial representativeness of the available streamflow gauging stations and the lack of understanding of the processes in channel-wetland exchanges, are the main challenges that constrain the use of traditional approaches to models development. They also contribute to increased uncertainty in the estimation of water resources across the basin (Chapter 1 and 2). Given this ungauged nature of the Congo River Basin, it is important to resort to hydrological modelling approaches that can reasonably quantify and model the uncertainty associated with water resources estimation (Chapter 4) to make hydrological predictions reliable. This study explores appropriate methods for hydrological predictions and water resources assessment in ungauged catchments of the Congo River Basin. In this context, the core modelling framework combines the quantification of uncertainty in constraint indices, hydrological modelling and hydrodynamic modelling. The latter accounts for channel-wetland exchanges in sub-basins where wetlands exert considerable influence on downstream flow regimes at the monthly time scale. The constraint indices are the characteristics of a sub-basin’s long-term hydrological behaviour and may reflect the dynamics of the different components of the catchment water balance such as climate, water storage and different runoff processes. Currently, six constraint indices namely the mean monthly runoff volume (MMQ in m3 *106), mean monthly groundwater recharge depth (MMR in mm), the 10th, 50th and 90th percentiles of the flow duration curve expressed as a fraction of MMQ (Q10/MMQ, Q50/MMQ, Q90/MMQ) and the percentage of time that zero flows are expected (%Zero), are used in the modelling approach. These were judged to be the minimum number of key indices that can discriminate between different hydrological responses. The constraint indices in the framework help to determine an uncertainty range within which behavioural model parameters of the expected hydrological response can be identified. Predictive equations of the constraint indices across all climate and physiographic regions of the Congo Basin were based only on the aridity index because it was the most influential sub-basin attribute (Chapter 5) for which quantitative information was available. The degree of uncertainty in the constraint Q10/MMQ and Q50/MMQ indices is less than 41%, while it is somewhat higher for the mean monthly runoff (MMQ) and Q90/MMQ constraint indices. The established uncertainty ranges of the constraint indices were tested in some selected sub-basins of the Congo Basin, including the Lualaba (93 sub-basins), Sangha (24 sub-basins), Oubangui (19 sub-basins), Batéké plateaux (4 sub-basins), Kasai (4 sub-basins) and Inkisi (3 sub-basins). The results proved useful through the application of a 2-stage uncertainty approach of the PITMAN model. However, it comes out of this study that the application of the original constraint indices ranges (Chapter 5) generated satisfactory simulation results in some areas, while in others both small and large adjustments were required to fully capture some aspects of the observed hydrological responses (Chapter 6). Part of the reason is attributed to the availability and quality of streamflow data used to develop the constraint indices ranges (Chapter 5). The main issue identified in the modelling process was whether the changes made to the original constraints at headwater-gauged sub-basins can be applied to ungauged upstream sub-basins to match the observed flow at downstream gauging stations. Ideally, only gauged sub-basin’s constraints can be easily revised based on the observed flow. However, the refinement made to gauged sub-basins alone may fail to substantially affect the results if ungauged upstream sub-basins exert a major impact on defining downstream hydrological response. The majority of gauging stations used in this analysis are located downstream of many upstream ungauged sub-basins and therefore adjustments were required in ungauged sub-basins. These adjustments consist of shifting the full range of a constraint index either towards higher or lower values, depending on the degree to which the simulated uncertainty bounds depart from the observed flow. While this modelling approach seems effective in capturing many aspects of the hydrological responses with a reduced level of uncertainty compared to a previous study, it is recommended that the approach be extended to the remaining parts of the Congo Basin and assessed under current and future development conditions including environmental changes. A 2D hydrodynamic river-wetland model (LISFLOOD-FP) has been used to explicitly represent the inundation process exchanges between river channels and wetland systems. The hydrodynamic modelling outputs are used to calibrate the PITMAN wetland sub-model parameters. The five hydrodynamic models constructed for Ankoro, Kamalondo, Kundelungu, Mweru and Tshiangalele wetland systems have been partially validated using independent estimates of inundation extents available from Landsat imagery. Other sources of data such as remote sensing of water level altimetry, SAR images and wetland storage estimates may be used to improve the validation results. However, the important objective in this study was to make sure that flow volume exchanges between river channels and their adjacent floodplains were being simulated realistically. The wetland sub-model parameters are calibrated in a spreadsheet version of the PITMAN wetland routine to achieve visual correspondence between the LISFLOOD-FP and PITMAN wetland sub-model outputs (Storage volumes and channel outputs). The hysteretic patterns of the river-wetland processes were quantified using hysteresis indices and were associated with the spill and return flow parameters of the wetland sub-model and eventually with the wetland morphometric characteristics. One example is the scale parameter of the return flow function (AA), which shows a good relationship with the average surface slope of the wetland when the coefficient parameter (BB) of the same function is kept constant to a value of 1.25. The same parameter (AA) is a good indicator of the wetland emptying mechanism. A small AA indicates a wetland that slowly releases its flow, resulting in a highly delayed and attenuated hydrological response in downstream sub-basins. This understanding has a practical advantage for the estimation of the PITMAN wetland parameters in the many areas where it is not possible, or where the resources are not available, to run complex hydrodynamic models (Chapter 7). The inclusion of these LISFLOOD-FP informed wetland parameters in the basin-scale hydrological modelling results in acceptable simulations for the lower Lualaba drainage system. The small wetlands, like Ankoro and Tshiangalele, have a negligible impact on downstream flow regimes, whereas large wetlands, such as Kamalondo and Mweru, have very large impacts. In general, the testing of the original constraint indices in the region of wetlands and further downstream of the Lualaba drainage system has shown acceptable results. However, there remains an unresolved uncertainty issue related to the under and over-estimation of some aspects of the hydrological response at both Mulongo and Ankoro, two gauging stations in the immediate downstream of the Kamalondo wetland system. It is difficult to attribute this uncertainty to Kamalondo wetland parameters alone because many of the incremental sub-basins contributing to wetland inflows are ungauged. The issue at Mulongo is the under simulation of low flow, while the high flows at the Ankoro gauging station are over-simulated. However, the pattern of the calibrated constraint indices in this region (Chapter 8) shows that the under simulation of low flow at Mulongo cannot be attributed to incremental sub-basins (between Bukama, Kapolowe and Mulongo gauging stations), because their Q90/MMQ constraint indices are even slightly above the original constraint ranges, but maintain a spatial consistency with sub-basins of other regions. Similarly, sub-basins located between Mulongo, Luvua and Ankoro gauging stations have high flow indices slightly below the original constraint ranges and therefore they are unlikely to be responsible for the over simulation of high flow at the Ankoro gauging station. These facts highlight the need for a further understanding of the complex wetland system of Kamalondo. Short-term data collection and monitoring programme are required. Important tributaries that drain to this wetland need to be monitored by installing water level loggers and periodically collecting flow data and river bathymetry. This programme should lead to the development of rating curves of wetland input tributaries. This would partially solve the unresolved uncertainty issues at the Ankoro and Mulongo gauging stations. The integrated modelling approach offers many opportunities in the Congo Basin. The quantified and modelled uncertainty helps to identify regions with high uncertainty and allows for the identification of various data collection and management strategies that can potentially contribute to the uncertainty reduction. The quantified channel-wetland exchanges contribute to the improvement of the overall knowledge of water resources estimation within the regions where the effects of wetlands are evident even at the monthly time scale. In contrast, ignoring uncertainty in the estimates of water resources availability means that water resources planning and management decisions in the Congo Basin will continue to be based on inadequate information and unquantified uncertainty, thus increasing the risk associated with water resources decision making. , Thesis (PhD) -- Faculty of Science, Institute for Water Research, 2021
- Full Text:
- Date Issued: 2021-04
- Authors: Kabuya, Pierre Mulamba
- Date: 2021-04
- Subjects: Congo River Watershed , Watersheds -- Congo (Democratic Republic) , Hydrologic models , Rain and rainfall -- Mathematical models , Runoff -- Mathematical models , Wetland hydrology
- Language: English
- Type: thesis , text , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/177997 , vital:42897 , 10.21504/10962/177997
- Description: Compared to other large river basins of the world, such as the Amazon, the Congo River Basin appears to be the most ungauged and less studied. This is partly because the basin lacks sufficient observational hydro-climatic monitoring stations and appropriate information on physiographic basin properties at a spatial scale deemed for hydrological applications, making it difficult to estimate water resources at the scale of sub-basins (Chapter 3). In the same time, the basin is facing the challenges related to rapid population growth, uncontrolled urbanisation as well as climate change. Adequate quantification of hydrological processes across different spatial and temporal scales in the basin, and the drivers of change, is essential for prediction and strategic planning to ensure sustainable management of water resources in the Congo River Basin. Hydrological models are particularly important to generate the required information. However, the shortness of the available streamflow records, lack of spatial representativeness of the available streamflow gauging stations and the lack of understanding of the processes in channel-wetland exchanges, are the main challenges that constrain the use of traditional approaches to models development. They also contribute to increased uncertainty in the estimation of water resources across the basin (Chapter 1 and 2). Given this ungauged nature of the Congo River Basin, it is important to resort to hydrological modelling approaches that can reasonably quantify and model the uncertainty associated with water resources estimation (Chapter 4) to make hydrological predictions reliable. This study explores appropriate methods for hydrological predictions and water resources assessment in ungauged catchments of the Congo River Basin. In this context, the core modelling framework combines the quantification of uncertainty in constraint indices, hydrological modelling and hydrodynamic modelling. The latter accounts for channel-wetland exchanges in sub-basins where wetlands exert considerable influence on downstream flow regimes at the monthly time scale. The constraint indices are the characteristics of a sub-basin’s long-term hydrological behaviour and may reflect the dynamics of the different components of the catchment water balance such as climate, water storage and different runoff processes. Currently, six constraint indices namely the mean monthly runoff volume (MMQ in m3 *106), mean monthly groundwater recharge depth (MMR in mm), the 10th, 50th and 90th percentiles of the flow duration curve expressed as a fraction of MMQ (Q10/MMQ, Q50/MMQ, Q90/MMQ) and the percentage of time that zero flows are expected (%Zero), are used in the modelling approach. These were judged to be the minimum number of key indices that can discriminate between different hydrological responses. The constraint indices in the framework help to determine an uncertainty range within which behavioural model parameters of the expected hydrological response can be identified. Predictive equations of the constraint indices across all climate and physiographic regions of the Congo Basin were based only on the aridity index because it was the most influential sub-basin attribute (Chapter 5) for which quantitative information was available. The degree of uncertainty in the constraint Q10/MMQ and Q50/MMQ indices is less than 41%, while it is somewhat higher for the mean monthly runoff (MMQ) and Q90/MMQ constraint indices. The established uncertainty ranges of the constraint indices were tested in some selected sub-basins of the Congo Basin, including the Lualaba (93 sub-basins), Sangha (24 sub-basins), Oubangui (19 sub-basins), Batéké plateaux (4 sub-basins), Kasai (4 sub-basins) and Inkisi (3 sub-basins). The results proved useful through the application of a 2-stage uncertainty approach of the PITMAN model. However, it comes out of this study that the application of the original constraint indices ranges (Chapter 5) generated satisfactory simulation results in some areas, while in others both small and large adjustments were required to fully capture some aspects of the observed hydrological responses (Chapter 6). Part of the reason is attributed to the availability and quality of streamflow data used to develop the constraint indices ranges (Chapter 5). The main issue identified in the modelling process was whether the changes made to the original constraints at headwater-gauged sub-basins can be applied to ungauged upstream sub-basins to match the observed flow at downstream gauging stations. Ideally, only gauged sub-basin’s constraints can be easily revised based on the observed flow. However, the refinement made to gauged sub-basins alone may fail to substantially affect the results if ungauged upstream sub-basins exert a major impact on defining downstream hydrological response. The majority of gauging stations used in this analysis are located downstream of many upstream ungauged sub-basins and therefore adjustments were required in ungauged sub-basins. These adjustments consist of shifting the full range of a constraint index either towards higher or lower values, depending on the degree to which the simulated uncertainty bounds depart from the observed flow. While this modelling approach seems effective in capturing many aspects of the hydrological responses with a reduced level of uncertainty compared to a previous study, it is recommended that the approach be extended to the remaining parts of the Congo Basin and assessed under current and future development conditions including environmental changes. A 2D hydrodynamic river-wetland model (LISFLOOD-FP) has been used to explicitly represent the inundation process exchanges between river channels and wetland systems. The hydrodynamic modelling outputs are used to calibrate the PITMAN wetland sub-model parameters. The five hydrodynamic models constructed for Ankoro, Kamalondo, Kundelungu, Mweru and Tshiangalele wetland systems have been partially validated using independent estimates of inundation extents available from Landsat imagery. Other sources of data such as remote sensing of water level altimetry, SAR images and wetland storage estimates may be used to improve the validation results. However, the important objective in this study was to make sure that flow volume exchanges between river channels and their adjacent floodplains were being simulated realistically. The wetland sub-model parameters are calibrated in a spreadsheet version of the PITMAN wetland routine to achieve visual correspondence between the LISFLOOD-FP and PITMAN wetland sub-model outputs (Storage volumes and channel outputs). The hysteretic patterns of the river-wetland processes were quantified using hysteresis indices and were associated with the spill and return flow parameters of the wetland sub-model and eventually with the wetland morphometric characteristics. One example is the scale parameter of the return flow function (AA), which shows a good relationship with the average surface slope of the wetland when the coefficient parameter (BB) of the same function is kept constant to a value of 1.25. The same parameter (AA) is a good indicator of the wetland emptying mechanism. A small AA indicates a wetland that slowly releases its flow, resulting in a highly delayed and attenuated hydrological response in downstream sub-basins. This understanding has a practical advantage for the estimation of the PITMAN wetland parameters in the many areas where it is not possible, or where the resources are not available, to run complex hydrodynamic models (Chapter 7). The inclusion of these LISFLOOD-FP informed wetland parameters in the basin-scale hydrological modelling results in acceptable simulations for the lower Lualaba drainage system. The small wetlands, like Ankoro and Tshiangalele, have a negligible impact on downstream flow regimes, whereas large wetlands, such as Kamalondo and Mweru, have very large impacts. In general, the testing of the original constraint indices in the region of wetlands and further downstream of the Lualaba drainage system has shown acceptable results. However, there remains an unresolved uncertainty issue related to the under and over-estimation of some aspects of the hydrological response at both Mulongo and Ankoro, two gauging stations in the immediate downstream of the Kamalondo wetland system. It is difficult to attribute this uncertainty to Kamalondo wetland parameters alone because many of the incremental sub-basins contributing to wetland inflows are ungauged. The issue at Mulongo is the under simulation of low flow, while the high flows at the Ankoro gauging station are over-simulated. However, the pattern of the calibrated constraint indices in this region (Chapter 8) shows that the under simulation of low flow at Mulongo cannot be attributed to incremental sub-basins (between Bukama, Kapolowe and Mulongo gauging stations), because their Q90/MMQ constraint indices are even slightly above the original constraint ranges, but maintain a spatial consistency with sub-basins of other regions. Similarly, sub-basins located between Mulongo, Luvua and Ankoro gauging stations have high flow indices slightly below the original constraint ranges and therefore they are unlikely to be responsible for the over simulation of high flow at the Ankoro gauging station. These facts highlight the need for a further understanding of the complex wetland system of Kamalondo. Short-term data collection and monitoring programme are required. Important tributaries that drain to this wetland need to be monitored by installing water level loggers and periodically collecting flow data and river bathymetry. This programme should lead to the development of rating curves of wetland input tributaries. This would partially solve the unresolved uncertainty issues at the Ankoro and Mulongo gauging stations. The integrated modelling approach offers many opportunities in the Congo Basin. The quantified and modelled uncertainty helps to identify regions with high uncertainty and allows for the identification of various data collection and management strategies that can potentially contribute to the uncertainty reduction. The quantified channel-wetland exchanges contribute to the improvement of the overall knowledge of water resources estimation within the regions where the effects of wetlands are evident even at the monthly time scale. In contrast, ignoring uncertainty in the estimates of water resources availability means that water resources planning and management decisions in the Congo Basin will continue to be based on inadequate information and unquantified uncertainty, thus increasing the risk associated with water resources decision making. , Thesis (PhD) -- Faculty of Science, Institute for Water Research, 2021
- Full Text:
- Date Issued: 2021-04
Assessing MODIS evapotranspiration data for hydrological modelling in South Africa
- Mazibuko, Sbongiseni Christian
- Authors: Mazibuko, Sbongiseni Christian
- Date: 2017
- Subjects: Evapotranspiration , Evapotranspiration -- Measurement , Hydrologic models , Hydrologic models -- South Africa , MODIS (Spectroradiometer)
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/8009 , vital:21334
- Description: Evapotranspiration as a major component of the water balance has been identified as a key factor in hydrological modelling. Water management can be improved by means of increased use of reliable methods for estimating evapotranspiration. The limited availability of measured climate and discharge data sets, particularly in the developing world, restricts the reliability of hydrological models in these regions. Furthermore, rapid changes in hydrological systems with increasing development mean uncertainties in water resource estimation are growing. These changes are related to the modification of catchment hydrological processes with increasing human activity. Dealing with data uncertainty and quantifying the impacts of catchment activities are significant challenges that scientists in the field of hydrology face today. Uncertainties in hydrometeorological data are associated with poor observation networks that provide data at point scales which are not adequately representative of the inherent heterogeneity within catchment processes. Using uncertain data in model applications reduces the predictive power of hydrological models as well as the ability to validate the model outcomes. This study examines the potential of using remote sensing-based evapotranspiration data to reduce uncertainty in the climatic forcing data and constraining the output of a rainfall-runoff hydrological model. It is common to use fixed seasonally variable potential evapotranspiration (PET) instead of temporally varying PET data as inputs to standard rainfall-runoff models. Part of the reason is that there are relatively few stations available to measure a variety of meteorological input data needed to compute PET, as well as the apparent lack of sensitivity of rainfall-runoff models to different types of PET inputs. As hydrometeorological data become more readily available through the use of earth observation systems, it is important to determine whether rainfall-runoff models are sensitive to time-varying PET derived from these earth observations systems. Further potential includes the use of actual evapotranspiration (ETa) from this type of data to constrain model outputs and improve model realism. It is assumed that a better representation of evapotranspiration demands could improve the efficiency of models, and this study explores some of these issues. The study used evapotranspiration estimates (PET and ETa) from the MOD16 global product with one of the most widely used hydrological models in South Africa. The investigation included applying the Pitman model in a number of case study catchments located in different climatic regions of the country. The main objectives of the study included (i) the establishment of behavioural model parameter sets that generate acceptable hydrological response under both naturalised and present-day conditions, (ii) the use of time-varying PET estimates derived from MOD16 data to force the model, and (iii) the use of MOD16 ETa estimates to constrain model-simulated ETa. Before examining the use of different PET forcing data in the model, a two-step modelling approached was employed both a single-run and an uncertainty version of the Pitman model. During the first step (using a single-run version), available information on catchment physical properties and regionalised groundwater recharge together with model calibration principles were used to develop model functionality understanding and establish initial parameter sets. The outcomes from the first step were used to define uncertain parameter ranges for the use in the uncertainty version of the Pitman model (second step). Further, catchment water uses were quantified to ensure comparability with present-day flow conditions represented by the stream flow records. The effects of forcing the Pitman model with MOD16-based time-varying PET data inputs were evaluated using static and dynamic sensitivity analysis approaches. In the static approach, parameter sets calibrated using fixed seasonal distributions of PET data remain unchanged when forcing the model with other forms of PET, whereas in the dynamic method, the model is recalibrated with changing PET inputs. In both approaches, model sensitivity was assessed by comparing objective function statistics of reference flow simulations with those simulations incorporating changing PET data inputs. The use of the MOD16 ETa data to constrain model- simulated evapotranspiration losses was conducted by calibrating the parameters such that the simulated-ETa matched the evapotranspiration loss estimated from the MOD16 data. Despite issues around model equifinality and significant uncertainty within water use information, the Pitman model simulations were generally satisfactory and compared with observed stream flow data where available. The use of time-varying PET data does not improve the efficiency of the model when both static and dynamic sensitivity approaches are used. This was highly expected with the static approach where fixed model parameter sets do not account for the changes in evapotranspiration demands. However, with the dynamic approach, it was difficult to conclude why the model efficiency did not improve given the flexibility of the model to achieve appropriate parameter sets to different forms of PET. The study noted that the insensitivity of the model to changes in PET demands could be due to uncertainties in the model structure and MOD16 data. Attempts to constrain the model-simulated actual evapotranspiration with MOD16 ETa estimates were hampered by large errors in the MOD16 data and resulted in the non-closure of the catchment annual water balance, even when likely errors in the other components of the water balance were accounted for. There is still a great deal of work that needs to be done to reduce uncertainties associated with the use of earth observation data in hydrological modelling. This study has identified some of the specific gaps within the application of evapotranspiration data from earth observation information. While the MOD16 data applied with the Pitman model did not achieve improved simulations, the study has demonstrated the enormous potential of the data product in the future should the identified uncertainties be resolved. Lastly, the investigation highlighted some of the possible model structural uncertainties specifically associated with the simplified soil-moisture accounting routines within the model. It is possible that amending the model structure through investigating the dynamics of the relationship between soil moisture and evapotranspiration losses would assist in the improved utilisation of earth observation products related to the MOD16 ET data.
- Full Text:
- Date Issued: 2017
- Authors: Mazibuko, Sbongiseni Christian
- Date: 2017
- Subjects: Evapotranspiration , Evapotranspiration -- Measurement , Hydrologic models , Hydrologic models -- South Africa , MODIS (Spectroradiometer)
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/8009 , vital:21334
- Description: Evapotranspiration as a major component of the water balance has been identified as a key factor in hydrological modelling. Water management can be improved by means of increased use of reliable methods for estimating evapotranspiration. The limited availability of measured climate and discharge data sets, particularly in the developing world, restricts the reliability of hydrological models in these regions. Furthermore, rapid changes in hydrological systems with increasing development mean uncertainties in water resource estimation are growing. These changes are related to the modification of catchment hydrological processes with increasing human activity. Dealing with data uncertainty and quantifying the impacts of catchment activities are significant challenges that scientists in the field of hydrology face today. Uncertainties in hydrometeorological data are associated with poor observation networks that provide data at point scales which are not adequately representative of the inherent heterogeneity within catchment processes. Using uncertain data in model applications reduces the predictive power of hydrological models as well as the ability to validate the model outcomes. This study examines the potential of using remote sensing-based evapotranspiration data to reduce uncertainty in the climatic forcing data and constraining the output of a rainfall-runoff hydrological model. It is common to use fixed seasonally variable potential evapotranspiration (PET) instead of temporally varying PET data as inputs to standard rainfall-runoff models. Part of the reason is that there are relatively few stations available to measure a variety of meteorological input data needed to compute PET, as well as the apparent lack of sensitivity of rainfall-runoff models to different types of PET inputs. As hydrometeorological data become more readily available through the use of earth observation systems, it is important to determine whether rainfall-runoff models are sensitive to time-varying PET derived from these earth observations systems. Further potential includes the use of actual evapotranspiration (ETa) from this type of data to constrain model outputs and improve model realism. It is assumed that a better representation of evapotranspiration demands could improve the efficiency of models, and this study explores some of these issues. The study used evapotranspiration estimates (PET and ETa) from the MOD16 global product with one of the most widely used hydrological models in South Africa. The investigation included applying the Pitman model in a number of case study catchments located in different climatic regions of the country. The main objectives of the study included (i) the establishment of behavioural model parameter sets that generate acceptable hydrological response under both naturalised and present-day conditions, (ii) the use of time-varying PET estimates derived from MOD16 data to force the model, and (iii) the use of MOD16 ETa estimates to constrain model-simulated ETa. Before examining the use of different PET forcing data in the model, a two-step modelling approached was employed both a single-run and an uncertainty version of the Pitman model. During the first step (using a single-run version), available information on catchment physical properties and regionalised groundwater recharge together with model calibration principles were used to develop model functionality understanding and establish initial parameter sets. The outcomes from the first step were used to define uncertain parameter ranges for the use in the uncertainty version of the Pitman model (second step). Further, catchment water uses were quantified to ensure comparability with present-day flow conditions represented by the stream flow records. The effects of forcing the Pitman model with MOD16-based time-varying PET data inputs were evaluated using static and dynamic sensitivity analysis approaches. In the static approach, parameter sets calibrated using fixed seasonal distributions of PET data remain unchanged when forcing the model with other forms of PET, whereas in the dynamic method, the model is recalibrated with changing PET inputs. In both approaches, model sensitivity was assessed by comparing objective function statistics of reference flow simulations with those simulations incorporating changing PET data inputs. The use of the MOD16 ETa data to constrain model- simulated evapotranspiration losses was conducted by calibrating the parameters such that the simulated-ETa matched the evapotranspiration loss estimated from the MOD16 data. Despite issues around model equifinality and significant uncertainty within water use information, the Pitman model simulations were generally satisfactory and compared with observed stream flow data where available. The use of time-varying PET data does not improve the efficiency of the model when both static and dynamic sensitivity approaches are used. This was highly expected with the static approach where fixed model parameter sets do not account for the changes in evapotranspiration demands. However, with the dynamic approach, it was difficult to conclude why the model efficiency did not improve given the flexibility of the model to achieve appropriate parameter sets to different forms of PET. The study noted that the insensitivity of the model to changes in PET demands could be due to uncertainties in the model structure and MOD16 data. Attempts to constrain the model-simulated actual evapotranspiration with MOD16 ETa estimates were hampered by large errors in the MOD16 data and resulted in the non-closure of the catchment annual water balance, even when likely errors in the other components of the water balance were accounted for. There is still a great deal of work that needs to be done to reduce uncertainties associated with the use of earth observation data in hydrological modelling. This study has identified some of the specific gaps within the application of evapotranspiration data from earth observation information. While the MOD16 data applied with the Pitman model did not achieve improved simulations, the study has demonstrated the enormous potential of the data product in the future should the identified uncertainties be resolved. Lastly, the investigation highlighted some of the possible model structural uncertainties specifically associated with the simplified soil-moisture accounting routines within the model. It is possible that amending the model structure through investigating the dynamics of the relationship between soil moisture and evapotranspiration losses would assist in the improved utilisation of earth observation products related to the MOD16 ET data.
- Full Text:
- Date Issued: 2017
Uncertainties in modelling hydrological responses in gauged and ungauged sub‐basins
- Authors: Tumbo, Madaka Harold
- Date: 2015
- Subjects: Hydrologic models , Watersheds -- Tanzania , Water-supply -- Tanzania -- Great Ruaha River Watershed , Water resources development -- Tanzania -- Great Ruaha River Watershed , Rain and rainfall -- Mathematical models , Rain gauges -- Tanzania -- Great Ruaha River Watershed , Great Ruaha River Watershed (Tanzania)
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:6053 , http://hdl.handle.net/10962/d1018568
- Description: The world is undergoing rapid changes and the future is uncertain. The changes are related to modification of the landscape due to human activities, such as large and small scale irrigation, afforestation and changes to the climate system. Understanding and predicting hydrologic change is one of the challenges facing hydrologists today. Part of this understanding can be developed from observed data, however, there often too few observations and those that are available are frequently affected by uncertainties. Hydrological models have become essential tools for understanding historical variations of catchment hydrology and for predicting future possible trends. However, most developing countries are faced with poor spatial distributions of rainfall and evaporation stations that provide the data used to force models, as well as stream flow gauging stations to provide the data for establishing models and for evaluating their success. Hydrological models are faced with a number of challenges which include poor input data (data quality and poorly quantified human activities on observed stream flow data), uncertainties associated with model complexity and structure, the methods used to quantify model parameters, together with the difficulties of understanding hydrological processes at the catchment or subbasin. Within hydrological modelling, there is currently a trend of dealing with equifinality through the evaluation of parameter identifiability and the quantification of uncertainty bands associated with the predictions of the model. Hydrological models should not only focus on reproducing the past behaviour of a basin, but also on evaluating the representativeness of the surface and subsurface model components and their ability to simulate reality for the correct reasons. Part of this modelling process therefore involves quantifying and including all the possible sources of uncertainty. Uncertainty analysis has become the standard approach to most hydrological modelling studies, but has yet to be effectively used in practical water resources assessment. This study applied a hydrological modelling approach for understanding the hydrology of a large Tanzanian drainage basin, the Great Ruaha River that has many areas that are ungauged and where the available data (climate, stream flow and existing water use) are subject to varying degrees of uncertainty. The Great Ruaha River (GRR) is an upstream tributary of the Rufiji River Basin within Tanzania and covers an area of 86 000 km2. The basin is drained by four main tributaries; the Upper Great Ruaha, the Kisigo, the Little Ruaha and the Lukosi. The majority of the runoff is generated from the Chunya escarpment, the Kipengere ranges and the Poroto Mountains. The runoff generated feeds the alluvial and seasonally flooded Usangu plains (including the Ihefu perennial swamp). The majority of the irrigation water use in the basin is located where headwater sub‐basins drain towards the Usangu plains. The overall objective was to establish uncertain but behavioural hydrological models that could be useful for future water resources assessments that are likely to include issues of land use change, changes in patterns of abstraction and water use, as well the possibility of change in future climates.
- Full Text:
- Date Issued: 2015
- Authors: Tumbo, Madaka Harold
- Date: 2015
- Subjects: Hydrologic models , Watersheds -- Tanzania , Water-supply -- Tanzania -- Great Ruaha River Watershed , Water resources development -- Tanzania -- Great Ruaha River Watershed , Rain and rainfall -- Mathematical models , Rain gauges -- Tanzania -- Great Ruaha River Watershed , Great Ruaha River Watershed (Tanzania)
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:6053 , http://hdl.handle.net/10962/d1018568
- Description: The world is undergoing rapid changes and the future is uncertain. The changes are related to modification of the landscape due to human activities, such as large and small scale irrigation, afforestation and changes to the climate system. Understanding and predicting hydrologic change is one of the challenges facing hydrologists today. Part of this understanding can be developed from observed data, however, there often too few observations and those that are available are frequently affected by uncertainties. Hydrological models have become essential tools for understanding historical variations of catchment hydrology and for predicting future possible trends. However, most developing countries are faced with poor spatial distributions of rainfall and evaporation stations that provide the data used to force models, as well as stream flow gauging stations to provide the data for establishing models and for evaluating their success. Hydrological models are faced with a number of challenges which include poor input data (data quality and poorly quantified human activities on observed stream flow data), uncertainties associated with model complexity and structure, the methods used to quantify model parameters, together with the difficulties of understanding hydrological processes at the catchment or subbasin. Within hydrological modelling, there is currently a trend of dealing with equifinality through the evaluation of parameter identifiability and the quantification of uncertainty bands associated with the predictions of the model. Hydrological models should not only focus on reproducing the past behaviour of a basin, but also on evaluating the representativeness of the surface and subsurface model components and their ability to simulate reality for the correct reasons. Part of this modelling process therefore involves quantifying and including all the possible sources of uncertainty. Uncertainty analysis has become the standard approach to most hydrological modelling studies, but has yet to be effectively used in practical water resources assessment. This study applied a hydrological modelling approach for understanding the hydrology of a large Tanzanian drainage basin, the Great Ruaha River that has many areas that are ungauged and where the available data (climate, stream flow and existing water use) are subject to varying degrees of uncertainty. The Great Ruaha River (GRR) is an upstream tributary of the Rufiji River Basin within Tanzania and covers an area of 86 000 km2. The basin is drained by four main tributaries; the Upper Great Ruaha, the Kisigo, the Little Ruaha and the Lukosi. The majority of the runoff is generated from the Chunya escarpment, the Kipengere ranges and the Poroto Mountains. The runoff generated feeds the alluvial and seasonally flooded Usangu plains (including the Ihefu perennial swamp). The majority of the irrigation water use in the basin is located where headwater sub‐basins drain towards the Usangu plains. The overall objective was to establish uncertain but behavioural hydrological models that could be useful for future water resources assessments that are likely to include issues of land use change, changes in patterns of abstraction and water use, as well the possibility of change in future climates.
- Full Text:
- Date Issued: 2015
Understanding and modelling of surface and groundwater interactions
- Authors: Tanner, Jane Louise
- Date: 2014
- Subjects: Groundwater -- South Africa , Water-supply -- Management , Integrated water development , Hydrogeology , Water resources development -- South Africa , Water -- Analysis , Groundwater -- Management , Watersheds -- South Africa , Hydrologic models
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:6043 , http://hdl.handle.net/10962/d1012994
- Description: The connections between surface water and groundwater systems remain poorly understood in many catchments throughout the world and yet they are fundamental to effectively managing water resources. Managing water resources in an integrated manner is not straightforward, particularly if both resources are being utilised, and especially in those regions that suffer problems of data scarcity. This study explores some of the principle issues associated with understanding and practically modelling surface and groundwater interactions. In South Africa, there remains much controversy over the most appropriate type of integrated model to be used and the way forward in terms of the development of the discipline; part of the disagreement stems from the fact that we cannot validate models adequately. This is largely due to traditional forms of model testing having limited power as it is difficult to differentiate between the uncertainties within different model structures, different sets of alternative parameter values and in the input data used to run the model. While model structural uncertainties are important to consider, the uncertainty from input data error together with parameter estimation error are often more significant to the overall residual error, and essential to consider if we want to achieve reliable predictions for water resource decisions. While new philosophies and theories on modelling and results validation have been developed (Beven, 2002; Gupta et al., 2008), in many cases models are not only still being validated and compared using sparse and uncertain datasets, but also expected to produce reliable predictions based on the flawed data. The approach in this study is focused on fundamental understanding of hydrological systems rather than calibration based modelling and promotes the use of all the available 'hard' and 'soft' data together with thoughtful conceptual examination of the processes occurring in an environment to ensure as far as possible that a model is generating sensible results by simulating the correct processes. The first part of the thesis focuses on characterising the 'typical' interaction environments found in South Africa. It was found that many traditional perceptual models are not necessarily applicable to South African conditions, largely due to the relative importance of unsaturated zone processes and the complexity of the dominantly fractured rock environments. The interaction environments were categorised into four main 'types' of environment. These include karst, primary, fractured rock (secondary), and alluvial environments. Processes critical to Integrated Water Resource Management (IWRM) were defined within each interaction type as a guideline to setting a model up to realistically represent the dominant processes in the respective settings. The second part of the thesis addressed the application and evaluation of the modified Pitman model (Hughes, 2004), which allows for surface and groundwater interaction behaviour at the catchment scale to be simulated. The issue is whether, given the different sources of uncertainty in the modelling process, we can differentiate one conceptual flow path from another in trying to refine the understanding and consequently have more faith in model predictions. Seven example catchments were selected from around South Africa to assess whether reliable integrated assessments can be carried out given the existing data. Specific catchment perceptual models were used to identify the critical processes occurring in each setting and the Pitman model was assessed on whether it could represent them (structural uncertainty). The available knowledge of specific environments or catchments was then examined in an attempt to resolve the parameter uncertainty present within each catchment and ensure the subsequent model setup was correctly representing the process understanding as far as possible. The confidence in the quantitative results inevitably varied with the amount and quality of the data available. While the model was deemed to be robust based on the behavioural results obtained in the majority of the case studies, in many cases a quantitative validation of the outputs was just not possible based on the available data. In these cases, the model was judged on its ability to represent the conceptualisation of the processes occurring in the catchments. While the lack of appropriate data means there will always be considerable uncertainty surrounding model validation, it can be argued that improved process understanding in an environment can be used to validate model outcomes to a degree, by assessing whether a model is getting the right results for the right reasons. Many water resource decisions are still made without adequate account being taken of the uncertainties inherent in assessing the response of hydrological systems. Certainly, with all the possible sources of uncertainty in a data scarce country such as South Africa, pure calibration based modelling is unlikely to produce reliable information for water resource managers as it can produce the right results for the wrong reasons. Thus it becomes essential to incorporate conceptual thinking into the modelling process, so that at the very least we are able to conclude that a model generates estimates that are consistent with, and reflect, our understanding (however limited) of the catchment processes. It is fairly clear that achieving the optimum model of a hydrological system may be fraught with difficulty, if not impossible. This makes it very difficult from a practitioner's point of view to decide which model and uncertainty estimation method to use. According to Beven (2009), this may be a transitional problem and in the future it may become clearer as we learn more about how to estimate the uncertainties associated with hydrological systems. Until then, a better understanding of the fundamental and most critical hydrogeological processes should be used to critically test and improve model predictions as far as possible. A major focus of the study was to identify whether the modified Pitman model could provide a practical tool for water resource managers by reliably determining the available water resource. The incorporation of surface and groundwater interaction routines seems to have resulted in a more robust and realistic model of basin hydrology. The overall conclusion is that the model, although simplified, is capable of representing the catchment scale processes that occur under most South African conditions.
- Full Text:
- Date Issued: 2014
- Authors: Tanner, Jane Louise
- Date: 2014
- Subjects: Groundwater -- South Africa , Water-supply -- Management , Integrated water development , Hydrogeology , Water resources development -- South Africa , Water -- Analysis , Groundwater -- Management , Watersheds -- South Africa , Hydrologic models
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:6043 , http://hdl.handle.net/10962/d1012994
- Description: The connections between surface water and groundwater systems remain poorly understood in many catchments throughout the world and yet they are fundamental to effectively managing water resources. Managing water resources in an integrated manner is not straightforward, particularly if both resources are being utilised, and especially in those regions that suffer problems of data scarcity. This study explores some of the principle issues associated with understanding and practically modelling surface and groundwater interactions. In South Africa, there remains much controversy over the most appropriate type of integrated model to be used and the way forward in terms of the development of the discipline; part of the disagreement stems from the fact that we cannot validate models adequately. This is largely due to traditional forms of model testing having limited power as it is difficult to differentiate between the uncertainties within different model structures, different sets of alternative parameter values and in the input data used to run the model. While model structural uncertainties are important to consider, the uncertainty from input data error together with parameter estimation error are often more significant to the overall residual error, and essential to consider if we want to achieve reliable predictions for water resource decisions. While new philosophies and theories on modelling and results validation have been developed (Beven, 2002; Gupta et al., 2008), in many cases models are not only still being validated and compared using sparse and uncertain datasets, but also expected to produce reliable predictions based on the flawed data. The approach in this study is focused on fundamental understanding of hydrological systems rather than calibration based modelling and promotes the use of all the available 'hard' and 'soft' data together with thoughtful conceptual examination of the processes occurring in an environment to ensure as far as possible that a model is generating sensible results by simulating the correct processes. The first part of the thesis focuses on characterising the 'typical' interaction environments found in South Africa. It was found that many traditional perceptual models are not necessarily applicable to South African conditions, largely due to the relative importance of unsaturated zone processes and the complexity of the dominantly fractured rock environments. The interaction environments were categorised into four main 'types' of environment. These include karst, primary, fractured rock (secondary), and alluvial environments. Processes critical to Integrated Water Resource Management (IWRM) were defined within each interaction type as a guideline to setting a model up to realistically represent the dominant processes in the respective settings. The second part of the thesis addressed the application and evaluation of the modified Pitman model (Hughes, 2004), which allows for surface and groundwater interaction behaviour at the catchment scale to be simulated. The issue is whether, given the different sources of uncertainty in the modelling process, we can differentiate one conceptual flow path from another in trying to refine the understanding and consequently have more faith in model predictions. Seven example catchments were selected from around South Africa to assess whether reliable integrated assessments can be carried out given the existing data. Specific catchment perceptual models were used to identify the critical processes occurring in each setting and the Pitman model was assessed on whether it could represent them (structural uncertainty). The available knowledge of specific environments or catchments was then examined in an attempt to resolve the parameter uncertainty present within each catchment and ensure the subsequent model setup was correctly representing the process understanding as far as possible. The confidence in the quantitative results inevitably varied with the amount and quality of the data available. While the model was deemed to be robust based on the behavioural results obtained in the majority of the case studies, in many cases a quantitative validation of the outputs was just not possible based on the available data. In these cases, the model was judged on its ability to represent the conceptualisation of the processes occurring in the catchments. While the lack of appropriate data means there will always be considerable uncertainty surrounding model validation, it can be argued that improved process understanding in an environment can be used to validate model outcomes to a degree, by assessing whether a model is getting the right results for the right reasons. Many water resource decisions are still made without adequate account being taken of the uncertainties inherent in assessing the response of hydrological systems. Certainly, with all the possible sources of uncertainty in a data scarce country such as South Africa, pure calibration based modelling is unlikely to produce reliable information for water resource managers as it can produce the right results for the wrong reasons. Thus it becomes essential to incorporate conceptual thinking into the modelling process, so that at the very least we are able to conclude that a model generates estimates that are consistent with, and reflect, our understanding (however limited) of the catchment processes. It is fairly clear that achieving the optimum model of a hydrological system may be fraught with difficulty, if not impossible. This makes it very difficult from a practitioner's point of view to decide which model and uncertainty estimation method to use. According to Beven (2009), this may be a transitional problem and in the future it may become clearer as we learn more about how to estimate the uncertainties associated with hydrological systems. Until then, a better understanding of the fundamental and most critical hydrogeological processes should be used to critically test and improve model predictions as far as possible. A major focus of the study was to identify whether the modified Pitman model could provide a practical tool for water resource managers by reliably determining the available water resource. The incorporation of surface and groundwater interaction routines seems to have resulted in a more robust and realistic model of basin hydrology. The overall conclusion is that the model, although simplified, is capable of representing the catchment scale processes that occur under most South African conditions.
- Full Text:
- Date Issued: 2014
Evaluating uncertainty in water resources estimation in Southern Africa : a case study of South Africa
- Authors: Sawunyama, Tendai
- Date: 2009
- Subjects: Water supply -- South Africa , Water supply -- Africa, Southern , Hydrology -- South Africa , Hydrology -- Africa, Southern , Hydrologic models , Hydrology research -- South Africa , Hydrology research -- Africa, Southern , Rain and rainfall -- Mathematical models , Runoff -- Mathematical models
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:6035 , http://hdl.handle.net/10962/d1006176
- Description: Hydrological models are widely used tools in water resources estimation, but they are simple representations of reality and are frequently based on inadequate input data and uncertainties in parameter values. Data observation networks are expensive to establish and maintain and often beyond the resources of most developing countries. Consequently, measurements are difficult to obtain and observation networks in many countries are shrinking, hence obtaining representative observations in space and time remains a challenge. This study presents some guidelines on the identification, quantification and reduction of sources of uncertainty in water resources estimation in southern Africa, a data scarce region. The analyses are based on example sub-basins drawn from South Africa and the application of the Pitman hydrological model. While it has always been recognised that estimates of water resources availability for the region are subject to possible errors, the quantification of these uncertainties has never been explicitly incorporated into the methods used in the region. The motivation for this study was therefore to contribute to the future development of a revised framework for water resources estimation that does include uncertainty. The focus was on uncertainties associated with climate input data, parameter estimation (and recognizing the uncertainty due model structure deficiencies) methods and water use data. In addition to variance based measures of uncertainty, this study also used a reservoir yield based statistic to evaluate model output uncertainty, which represents an integrated measure of flow regime variations and one that can be more easily understood by water resources managers. Through a sensitivity analysis approach, the results of the individual contribution of each source of uncertainty suggest regional differences and that clear statements about which source of uncertainty is likely to dominate are not generally possible. Parameter sensitivity analysis was used in identifying parameters which are important withinspecific sub-basins and therefore those to focus on in uncertainty analysis. The study used a simple framework for evaluating the combined contribution of uncertainty sources to model outputs that is consistent with the model limitations and data available, and that allows direct quantitative comparison between model outputs obtained by using different sources of information and methods within Spatial and Time Series Information Modelling (SPATSIM) software. The results from combining the sources of uncertainties showed that parameter uncertainty dominates the contribution to model output uncertainty. However, in some parts of the country especially those with complex topography, which tend to experience high rainfall spatial variability, rainfall uncertainty is equally dominant, while the contributions of evaporation and water use data uncertainty are relatively small. While the results of this study are encouraging, the weaknesses of the methods used to quantify uncertainty (especially subjectivity involved in evaluating parameter uncertainty) should not be neglected and require further evaluations. An effort to reduce data and parameter uncertainty shows that this can only be achieved if data access at appropriate scale and quality improves. Perhaps the focus should be on maintaining existing networks and concentrating research efforts on making the most out of the emerging data products derived from remote sensing platforms. While this study presents some initial guidelines for evaluating uncertainty in South Africa, there is need to overcome several constraints which are related to data availability and accuracy, the models used and the capacity or willingness to adopt new methods that incorporate uncertainty. The study has provided a starting point for the development of new approaches to modelling water resources in the region that include uncertain estimates.
- Full Text:
- Date Issued: 2009
- Authors: Sawunyama, Tendai
- Date: 2009
- Subjects: Water supply -- South Africa , Water supply -- Africa, Southern , Hydrology -- South Africa , Hydrology -- Africa, Southern , Hydrologic models , Hydrology research -- South Africa , Hydrology research -- Africa, Southern , Rain and rainfall -- Mathematical models , Runoff -- Mathematical models
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: vital:6035 , http://hdl.handle.net/10962/d1006176
- Description: Hydrological models are widely used tools in water resources estimation, but they are simple representations of reality and are frequently based on inadequate input data and uncertainties in parameter values. Data observation networks are expensive to establish and maintain and often beyond the resources of most developing countries. Consequently, measurements are difficult to obtain and observation networks in many countries are shrinking, hence obtaining representative observations in space and time remains a challenge. This study presents some guidelines on the identification, quantification and reduction of sources of uncertainty in water resources estimation in southern Africa, a data scarce region. The analyses are based on example sub-basins drawn from South Africa and the application of the Pitman hydrological model. While it has always been recognised that estimates of water resources availability for the region are subject to possible errors, the quantification of these uncertainties has never been explicitly incorporated into the methods used in the region. The motivation for this study was therefore to contribute to the future development of a revised framework for water resources estimation that does include uncertainty. The focus was on uncertainties associated with climate input data, parameter estimation (and recognizing the uncertainty due model structure deficiencies) methods and water use data. In addition to variance based measures of uncertainty, this study also used a reservoir yield based statistic to evaluate model output uncertainty, which represents an integrated measure of flow regime variations and one that can be more easily understood by water resources managers. Through a sensitivity analysis approach, the results of the individual contribution of each source of uncertainty suggest regional differences and that clear statements about which source of uncertainty is likely to dominate are not generally possible. Parameter sensitivity analysis was used in identifying parameters which are important withinspecific sub-basins and therefore those to focus on in uncertainty analysis. The study used a simple framework for evaluating the combined contribution of uncertainty sources to model outputs that is consistent with the model limitations and data available, and that allows direct quantitative comparison between model outputs obtained by using different sources of information and methods within Spatial and Time Series Information Modelling (SPATSIM) software. The results from combining the sources of uncertainties showed that parameter uncertainty dominates the contribution to model output uncertainty. However, in some parts of the country especially those with complex topography, which tend to experience high rainfall spatial variability, rainfall uncertainty is equally dominant, while the contributions of evaporation and water use data uncertainty are relatively small. While the results of this study are encouraging, the weaknesses of the methods used to quantify uncertainty (especially subjectivity involved in evaluating parameter uncertainty) should not be neglected and require further evaluations. An effort to reduce data and parameter uncertainty shows that this can only be achieved if data access at appropriate scale and quality improves. Perhaps the focus should be on maintaining existing networks and concentrating research efforts on making the most out of the emerging data products derived from remote sensing platforms. While this study presents some initial guidelines for evaluating uncertainty in South Africa, there is need to overcome several constraints which are related to data availability and accuracy, the models used and the capacity or willingness to adopt new methods that incorporate uncertainty. The study has provided a starting point for the development of new approaches to modelling water resources in the region that include uncertain estimates.
- Full Text:
- Date Issued: 2009
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