Sensitivity Analysis: An operational picture

Modelling is crucial to understand the behavior of environmental systems.Adeeper comprehension of a model can be aided by global sensitivity analysis.Variabilityascribed to model variables could have a stochastic (i.e., lack of knowledge) or an operational (i.e., possible design values) origin. Despite the possible different nature inthe variability,current global sensitivity analysis strategies do not distinguish the latter in their formal derivations/developments. We propose to disentangle the variability inthe operational and stochastic variables while assessing the model output sensitivity with respect to theformer. Two operational sensitivity indices are introduced thatserve to characterize the sensitivity of a model output of interest with respect to an operational variable in terms of (a) its average(with respect to the stochastic variables) intensity and (b)its degree of fluctuation (across the set of possible realizations of the stochastic variables), respectively. We exemplify our developments considering two scenarios. Results highlight the relevance of employing an operational global sensitivity analysis when the focus is on the influence of operational variables on model outpu

Vulnerability of Transboundary River Basins in a Changing Climate: A Case Study of the Saskatchewan River Basin

About half of the Earth’s land surface is covered by transboundary water resources. Approximately 40 percent of the world’s population relies on water resources crossing political borders. Within transboundary river basins, allocating these limited and often depleting resources to states is challenging due to various, and often conflicting interests of stakeholders. Treaties and River Basin Organizations (RBOs) provide the primary means of cooperation between states, building institutional capacity, and lowering the likelihood of hydropolitical tensions. A resilient transboundary river system should be able to tolerate the pressures from different stressors to provide a reliable source of water. However, geopolitical, socio-economic, and biophysical stressors threaten the governance of these basins. Climate change is one of the biophysical stressors which is likely to increasingly challenge transboundary river systems. A thorough understanding of climate-change-induced vulnerabilities of a transboundary system, therefore, can help decision and policy makers to plan for adaptive measures to avoid hydropolitical tensions. The Saskatchewan River Basin, located in western Canada and shared amongst the three Canadian provinces of Alberta, Saskatchewan, and Manitoba and also the American state of Montana, is used as a case study. In particular, this thesis assesses the viability of the 1969 Master Agreement on Apportionment that provides the basis for water allocation of eastward flowing interprovincial streams in face of deep uncertainty around future climate change. To this end, a vulnerability assessment methodology consisting of three main components is proposed. First a large set of plausible weather scenarios is generated by perturbing important features of climate including winter precipitation, summer precipitation, annual temperature, and the annual number of dry days. Second, the weather scenarios are fed into a conceptual hydrological model calibrated to historical record to generate a wide range of plausible future streamflow scenarios. Third, the streamflow scenarios are used as input to a water resources management model that distributes the water throughout the transboundary river system. Results show a moderate risk of failure in the southern part of the basin in meeting the criteria established in the apportionment agreement under certain possible changes in climate regime of the region. The risk of not meeting the minimum flow is accompanied by major deficits to irrigation and non-irrigation demands as well as minimum environmental flows. A lower risk is observed in other parts of the basin, mainly due to lower water usage and abstraction

The Future of Sensitivity Analysis: An essential discipline for systems modeling and policy support

Sensitivity analysis (SA) is en route to becoming an integral part of mathematical modeling. The tremendous potential benefits of SA are, however, yet to be fully realized, both for advancing mechanistic and data-driven modeling of human and natural systems, and in support of decision making. In this perspective paper, a multidisciplinary group of researchers and practitioners revisit the current status of SA, and outline research challenges in regard to both theoretical frameworks and their applications to solve real-world problems. Six areas are discussed that warrant further attention, including (1) structuring and standardizing SA as a discipline, (2) realizing the untapped potential of SA for systems modeling, (3) addressing the computational burden of SA, (4) progressing SA in the context of machine learning, (5) clarifying the relationship and role of SA to uncertainty quantification, and (6) evolving the use of SA in support of decision making. An outlook for the future of SA is provided that underlines how SA must underpin a wide variety of activities to better serve science and society.John Jakeman’s work was supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Scientific Discovery through Advanced Computing (SciDAC) program. Joseph Guillaume received funding from an Australian Research Council Discovery Early Career Award (project no. DE190100317). Arnald Puy worked on this paper on a Marie Sklodowska-Curie Global Fellowship, grant number 792178. Takuya Iwanaga is supported through an Australian Government Research Training Program (AGRTP) Scholarship and the ANU Hilda-John Endowment Fun

The future of sensitivity analysis: an essential discipline for systems modeling and policy support

Sensitivity analysis (SA) is en route to becoming an integral part of mathematical modeling. The tremendous potential benefits of SA are, however, yet to be fully realized, both for advancing mechanistic and data-driven modeling of human and natural systems, and in support of decision making. In this perspective paper, a multidisciplinary group of researchers and practitioners revisit the current status of SA, and outline research challenges in regard to both theoretical frameworks and their applications to solve real-world problems. Six areas are discussed that warrant further attention, including (1) structuring and standardizing SA as a discipline, (2) realizing the untapped potential of SA for systems modeling, (3) addressing the computational burden of SA, (4) progressing SA in the context of machine learning, (5) clarifying the relationship and role of SA to uncertainty quantification, and (6) evolving the use of SA in support of decision making. An outlook for the future of SA is provided that underlines how SA must underpin a wide variety of activities to better serve science and society

Developing Efficient Strategies For Global Sensitivity Analysis Of Complex Environmental Systems Models

Complex Environmental Systems Models (CESMs) have been developed and applied as vital tools to tackle the ecological, water, food, and energy crises that humanity faces, and have been used widely to support decision-making about management of the quality and quantity of Earth’s resources. CESMs are often controlled by many interacting and uncertain parameters, and typically integrate data from multiple sources at different spatio-temporal scales, which make them highly complex. Global Sensitivity Analysis (GSA) techniques have proven to be promising for deepening our understanding of the model complexity and interactions between various parameters and providing helpful recommendations for further model development and data acquisition. Aside from the complexity issue, the computationally expensive nature of the CESMs precludes effective application of the existing GSA techniques in quantifying the global influence of each parameter on variability of the CESMs’ outputs. This is because a comprehensive sensitivity analysis often requires performing a very large number of model runs. Therefore, there is a need to break down this barrier by the development of more efficient strategies for sensitivity analysis. The research undertaken in this dissertation is mainly focused on alleviating the computational burden associated with GSA of the computationally expensive CESMs through developing efficiency-increasing strategies for robust sensitivity analysis. This is accomplished by: (1) proposing an efficient sequential sampling strategy for robust sampling-based analysis of CESMs; (2) developing an automated parameter grouping strategy of high-dimensional CESMs, (3) introducing a new robustness measure for convergence assessment of the GSA methods; and (4) investigating time-saving strategies for handling simulation failures/crashes during the sensitivity analysis of computationally expensive CESMs. This dissertation provides a set of innovative numerical techniques that can be used in conjunction with any GSA algorithm and be integrated in model building and systems analysis procedures in any field where models are used. A range of analytical test functions and environmental models with varying complexity and dimensionality are utilized across this research to test the performance of the proposed methods. These methods, which are embedded in the VARS–TOOL software package, can also provide information useful for diagnostic testing, parameter identifiability analysis, model simplification, model calibration, and experimental design. They can be further applied to address a range of decision making-related problems such as characterizing the main causes of risk in the context of probabilistic risk assessment and exploring the CESMs’ sensitivity to a wide range of plausible future changes (e.g., hydrometeorological conditions) in the context of scenario analysis

TOWARDS IMPROVED HYDROLOGIC LAND SURFACE MODELLING: ENHANCED MODEL IDENTIFICATION AND INTEGRATION OF WATER MANAGEMENT

Large-scale hydrological models are essential tools for addressing emerging water security challenges. They enable us to understand and predict changes in water cycle at river-basin, continental, and global scales. This thesis aimed to improve ‘land surface models’ for large-scale hydrological modelling applications. Specifically, the research contributions were made across four fronts: (1) improving the conventional procedure for parameter identification of hydrological processes by using new sources of remotely-sensed data in addition to streamflow data within a multi-objective optimization and sensitivity analysis framework, (2) developing and integrating an efficient parameterization scheme for the representation of reservoirs into the land surface model for realistic representation of downstream flows, which can further feedback to land surface and atmospheric models, (3) demonstrating how precipitation uncertainty from multiple high-resolution precipitation products influences the performance of a land-surface based hydrological model, and (4) developing an enhanced and comprehensive large-scale hydrologic model for a complex and heavily regulated watershed. The analyses and results of this thesis illuminated important issues and their solutions in large-scale hydrological modelling. First, the multi-objective optimization and sensitivity analysis approach using multiple state and flux variables and performance criteria enables robust model parameterization and lessens issues around parameter equifinality in the highly-parameterized land surface models. Second, the dynamic parameterization of reservoir operation, based on multiple storage zones and reservoir release targets, improves the simulation of reservoir storage dynamics and downstream release, and subsequently, significantly improves the fidelity of land surface models when modeling managed basins. Third, there is a critical need for a rigorous evaluation of precipitation datasets widely used for forcing land surface models. The datasets investigated here showed considerable discrepancies, bringing their utility for land surface modelling into question. Fourth, effective parameterization and calibration of land surface models is critically important, particularly in large, complex, and highly-regulated basins

Sensitivity Analysis

Sensitivity analysis (SA), in particular global sensitivity analysis (GSA), is now regarded as a discipline coming of age, primarily for understanding and quantifying how model results and associated inferences depend on its parameters and assumptions. Indeed, GSA is seen as a key part of good modelling practice. However, inappropriate SA, such as insufficient convergence of sensitivity metrics, can lead to untrustworthy results and associated inferences. Good practice SA should also consider the robustness of results and inferences to choices in methods and assumptions relating to the procedure. Moreover, computationally expensive models are common in various fields including environmental domains, where model runtimes are long due to the nature of the model itself, and/or software platform and legacy issues. To extract using GSA the most accurate information from a computationally expensive model, there may be a need for increased computational efficiency. Primary considerations here are sampling methods that provide efficient but adequate coverage of parameter space and estimation algorithms for sensitivity indices that are computationally efficient. An essential aspect in the procedure is adopting methods that monitor and assess the convergence of sensitivity metrics. The thesis reviews the different categories of GSA methods, and then it lays out the various factors and choices therein that can impact the robustness of a GSA exercise. It argues that the overall level of assurance, or practical trustworthiness, of results obtained is engendered from consideration of robustness with respect to the individual choices made for each impact factor. Such consideration would minimally involve transparent justification of individual choices made in the GSA exercise but, wherever feasible, include assessment of the impacts on results of plausible alternative choices. Satisfactory convergence plays a key role in contributing to the level of assurance, and hence the ultimate effectiveness of the GSA can be enhanced if choices are made to achieve that convergence. The thesis examines several of these impact factors, primary ones being the GSA method/estimator, the sampling method, and the convergence monitoring method, the latter being essential for ensuring robustness. The motivation of the thesis is to gain a further understanding and quantitative appreciation of elements that shape and guide the results and computational efficiency of a GSA exercise. This is undertaken through comparative analysis of estimators of GSA sensitivity measures, sampling methods and error estimation of sensitivity metrics in various settings using well-established test functions. Although quasi-Monte Carlo Sobol' sampling can be a good choice computationally, it has error spike issues which are addressed here through a new Column Shift resampling method. We also explore an Active Subspace based GSA method, which is demonstrated to be more informative and computationally efficient than those based on the variance-based Sobol' method. Given that GSA can be computationally demanding, the thesis aims to explore ways that GSA can be more computationally efficient by: addressing how convergence can be monitored and assessed; analysing and improving sampling methods that provide a high convergence rate with low error in sensitivity measures; and analysing and comparing GSA methods, including their algorithm settings

Socio-hydrology from Local to Large Scales: An Agent-based Modeling Approach

For decades, the interaction between water and people has attracted hydrologists’ attention. However, the coevolution of social and natural processes, which occurs across a range of time scales, has not yet been adequately characterized. This research gap has motivated more research in recent years under the umbrella of “socio-hydrology”. The purpose of socio-hydrology is to posit the endogeneity of humans in a hydrological system and then to investigate feedback mechanisms between hydrological and human systems that might lead to emergent phenomena. The current state-of-the-art in socio-hydrology faces several challenges that include (1) a tenuous connection of socio-hydrology to broader research on social, economic, and policy aspects of water resources, (2) the (in)capability of socio-hydrological models to capture human behavior by generic feedback mechanisms that can be extrapolated to other places, and (3) unsatisfying calibration or validation processes in modeling. To address the first gap, a socio-hydrology study needs to connect proper social theories on water-related human decision making with a water resource model based on a given context and scale. Addressing the second gap calls for socio-hydrology research with case studies in different and contrasting regions and at different scales. In fact, such study can shed light on the similarities and differences in socio-hydrological systems in different contexts and scales as initial steps for future research. The third research gap calls for a socio-hydrology study that improves calibration and validation processes. Thus, to address all these gaps in one thesis, two case studies with completely different environments are chosen to investigate various phenomena at different scales. The research presented here contributes to socio-hydrological understanding at two spatial scales. To account for the heterogeneity of human decision making and its interactions with the hydrologic system, an agent-based modeling (ABM) approach is used in this research. The first objective is to explore human adaptation to drought as well as the subsequent expected or unexpected effects on the agricultural sector and to develop a socio-hydrological model to predict agricultural water demand. To do so, an agent-based agricultural water demand model (ABAD) is developed. This model is applied to the Bow River Basin in Alberta, Canada, as a study region, which has recently experienced drought periods. The second objective is to explore conflict-and-cooperation processes in transboundary rivers as socio-hydrological phenomena at a large scale. The Eastern Nile Basin Socio-hydrological (ENSH) model is developed and applied to the Eastern Nile Basin (ENB) in Africa in which conflict-and-cooperation dynamics can be seen among Egypt, Sudan, and Ethiopia. The ENSH model aims to quantify and simulate these countries’ willingness to cooperate in the ENB. ABAD demonstrates (1) how farmers’ attitudes toward profits, risk aversion, environmental protection, social interaction, and irrigation expansion explain the dynamics of the water demand and (2) how the conservation program may paradoxically lead to the rebound phenomenon whereby the water demand may increase after decreasing through modernized irrigation systems. Through the ABAD model analysis, economic factors are found to dominantly control possible rebounds. Based on the insights gained via the model analysis, it is discussed that several strategies, including community participation and water restrictions, can be adopted to avoid the rebound phenomenon in irrigation systems. Fostering farmers’ awareness about the average water use in their community could be a means to avoid the rebound phenomenon through community participation. Also, another strategy to avoid the rebound phenomenon could be to reassign water allocations to reduce farmers’ water rights. The ENSH model showed that (1) socio-political factors (i.e., relative political stability and foreign direct investment) can explain two historical trends (i.e., (a) fluctuations in Ethiopia’s willingness to cooperate between 1983 and 2009 and (b) a decreasing Ethiopia’s willingness to cooperate between 2009 and 2016); (2) the 2008 food crisis (i.e., Sudan’s food gap) may account for Sudan recovering its willingness to cooperate; and (3) Egypt’s political (in)stability plays a role in its willingness to cooperate. The outcomes of this research can provide valuable insights to support policymakers for the long-term sustainability of water planning. This research investigates two main socio-hydrological phenomena at different spatial scales: the agricultural rebound phenomenon at a small geographical scale and the conflict and cooperation phenomena at a large geographical scale. The emergence of these phenomena can be a complex resultant of interaction and feedback mechanisms between the social system at the individual, institutional, and society levels and the hydrological system. Through developing quantitative socio-hydrological models, this research investigates the feedback mechanisms that may lead to the rebound phenomenon at a small scale and the conflict and cooperation phenomenon at a large scale. Finally, the research shows how these socio-hydrological models can be used for sustainable water management to avoid negative long-term consequences

Towards Improved Hydrologic Land-Surface Modelling To Represent Permafrost

Permafrost affects hydrological, meteorological, and ecological processes in over one-quarter of the land surface in the Northern Hemisphere. Permafrost degradation has been observed over the last few decades and is projected to accelerate under climatic warming. However, simulating permafrost dynamics is challenging due to process complexity, scarcity of observations, spatial heterogeneity, and permafrost disequilibrium with external climate forcing. Hydrologic-land-surface models (H-LSMs), which act as the lower boundary condition of the current generation of Earth system models (ESMs), are suitable for diagnosing and predicting permafrost evolution, as they couple heat and water interactions across soil-vegetation-atmosphere interfaces and are applicable for large-scale assessments. This thesis aims to improve the ability of H-LSMs to simulate permafrost dynamics and concurrently represent hydrology. Specific research contributions are made on four fronts: (1) assessing the uncertainty introduced to the modelling due to permafrost initialization, (2) investigating the sensitivity of permafrost dynamics to different H-LSM parameters, associated issues of parameter identifiability, and sensitivity to external forcing datasets, (3) evaluating the strength of permafrost-hydrology coupling in H-LSMs in data-scarce regions under parameter uncertainty, and (4) assessing the fate of permafrost thaw and associated changes in streamflow under an ensemble of future climate projections. The analyses and results of this thesis that illuminate these central issues and various solutions for permafrost-based applications of H-LSMs are proposed. First, uncertainty in model initialization determines the length of required spin-up cycles; 200-1000 cycles may be required to ensure proper model initialization under different climatic conditions and initial soil moisture contents. Further, the uncertainty due to initialization can lead to divergent permafrost simulations, such as active layer thickness variations of up to ~2m. Second, the sensitivity of various permafrost characteristics is mainly driven by surface insulation (canopy height and snow-cover fraction) and soil properties (depth and fraction of organic matter content). Additionally, the results underscore the difficulties inherent in H-LSM simulation of all aspects of permafrost dynamics, primarily due to poor identifiability of influential parameters and the limitations of currently-available forcing data sets. Third, different H-LSM parameterizations favor different sources of data (i.e. streamflow, soil temperature profiles, and permafrost maps), and it is challenging to configure a model faithful to all data sources. Overall, the modelling results show that surface insulation (through snow cover) and model initialization are primary regulators of permafrost dynamics and different parameterizations produce different low-flow but similar high-flow regimes. Lastly, severe permafrost degradation is projected to occur under all climate change scenarios, even under the most optimistic ones. The degradation and climate change, collectively, are likely to alter several streamflow signatures, including an increase of winter and summer flows. Permafrost fate has strategic importance for the exchange of water, heat, and carbon fluxes over large areas, and can amplify the rate of climate change through a positive feedback mechanism. However, existing projections of permafrost are subject to significant uncertainty, stemming from several sources. This thesis quantifies and reduces this uncertainty by studying initialization, parameter identification, and evaluation of H-LSMs, which ultimately lead to configuring an H-LSM with higher fidelity to assess the impact of climate change. As a result, this work is a step forward in improving the realism of H-LSM simulations in permafrost regions. Further research is needed to refine simulation capability, and to develop improved observational datasets for permafrost and their associated climate forcing

The influence of climate change and wetland managment on prairie hydrology - insights from Smith Creek, Saskatchewan

Internally drained depressional wetlands are critical landscape features in the Prairie Pothole Region (PPR) of North America. They provide important ecosystems services such as flood attenuation, improved downstream water quality, and diverse species habitat, however they are frequently drained by agriculture producers to manage excess surface water, access more farmland, or improve operational efficiencies. After recent flooding in the Canadian Prairies, there is increased interest in understanding the relative influence of climate change and wetland drainage on prairie hydrology to ensure sustainable economic and social development in the region. Future climate projections show increasing air temperatures and rainfall in the Canadian Prairies, while wetland drainage is expected to persist due to rising land prices. As such, the purpose of this thesis is to determine the influence of wetland drainage and climate change on prairie basin hydrology and develop future wetland management strategies that preserve agricultural land and mitigate downstream impacts during wet periods in the PPR. The objectives are therefore to 1) improve surface water storage capacity estimation methods from high-resolution digital elevation models (DEMs) of agriculturally dominated prairie basins, 2) advance prairie hydrological modelling through improved representation of wetland characteristics, and 3) evaluate the influence of wetland management and projected climate change on prairie basin hydrological responses. A case study of the instrumented and partially drained Smith Creek Research Basin (SCRB) is presented in this thesis. First, surface water storage capacity estimates of depressional wetlands were improved through manual breaching of roads to simulate the function of culverts in surface water drainage and storage modelling, using a 2-m resolution digital elevation model (DEM). Road-breaching at presumed culvert locations was found to decrease estimates of depressional wetland area by 29% and surface water storage capacity by 48% compared to estimates with roads-intact from automated depressional wetland delineation using the 2-m resolution DEM. Importantly, the roads-breached simulation provided wetland area and surface water storage capacity estimates that were 150% higher than estimates from aerial-photos. This result suggests that current prairie hydrological models are subject to uncertainty in estimates of wetland areas and storage capacities depending on wetland delineation methods, which may impact wetland drainage or restoration scenarios modelling results. Next, a new prairie hydrological model was developed for SCRB using the Cold Regions Hydrological Modelling Platform. This model uses primarily physically-based algorithms to simulate cold-regions prairie-specific hydrological processes including precipitation phase, wind redistribution of snow, snow sublimation, snowmelt, infiltration into frozen and unfrozen soils, crop growth, evapotranspiration, soil moisture balance, surface water storage in depressions or wetlands, and runoff routing. The new model, builds upon previous work conducted in the SCRB, but offers improved representation of wetland characteristics using depressional wetlands delineated from the 2-m roads-breached DEM, updated parameters to support multi-year simulations, a new macro to prevent soils from re-freezing after large snowfall events in the late spring, and a novel link to a hydraulic model to simulate culvert-restricted streamflow that occurs in roadside ditches and along stream channels during high runoff events in the SCRB. Finally, the new model was used to evaluate the influence of climate change and wetland drainage on the hydrology of the SCRB. Current and projected future weather variables from the Weather Research and Forecasting model were used to simulate the influence of climate change in the SCRB towards the end of the 21st century. Results suggest that a significantly warmer (5.5 ⁰C) and wetter (44 mm) projected future climate, with less snowfall and more extreme rainfall, will increase mean annual streamflow volume by 26%, with spring peak discharge decreasing by 34% and summer peak discharge increasing by 161%. If wetland drainage continues in the SCRB and wetland area drops below 9% of the basin area, streamflow volume could increase above the climate projected increase. This suggests that continued wetland drainage in prairie basins may have more influence on future streamflow volumes than projected climate change. Wetland restoration to near-historical extents was found to increase storage volumes sufficiently to offset climate projected increases in streamflow volumes, but even complete wetland restoration to historically maximum levels did not offset projected increases in summer peak daily discharge. This means that additional infrastructure upgrades or emergency response plans beyond wetland management strategies will likely be needed to manage future flood risk in the Canadian Prairies. The new methods, analysis, and results presented in this thesis are expected to be relevant to those interested in wetland management in cold-region prairie basins, including policy makers, basin stewardship groups, conservation organisations, water resources engineers, agriculture producers and the public