Time-varying Sensitivity Analysis Research Articles

Analysis of the Relative Importance of the Main Hydrological Processes at Different Temporal Scales in Watersheds of South-Central Chile

In Chile in recent years, changes in precipitation and temperatures have been reported that could affect water resource management and planning. One way of facing these changes is studying and understanding the behavior of hydrological processes at a regional scale and their different temporal scales. Therefore, the objective of this study is to analyze the importance of the hydrological processes of the HBV model at different temporal scales and for different hydrological regimes. To this end, 88 watersheds located in south-central Chile were analyzed using time-varying sensitivity analysis at five different temporal scales (1 month, 3 months, 6 months, 1 year, and 5 years). The results show that the model detects the temporality of the most important hydrological processes. In watersheds with a pluvial regime, the greater the temporal scale, the greater the importance of soil water accumulation processes and the lower the importance of surface runoff processes. By contrast, in watersheds with a nival regime, at greater temporal scales, groundwater accumulation and release processes take on greater importance, and soil water release processes are less important.

Dynamic analysis and optimal control of a class of SISP respiratory diseases

In this paper, the actual background of the susceptible population being directly patients after inhaling a certain amount of PM is taken into account. The concentration response function of PM is introduced, and the SISP respiratory disease model is proposed. Qualitative theoretical analysis proves that the existence, local stability and global stability of the equilibria are all related to the daily emission of PM and PM pathogenic threshold K. Based on the sensitivity factor analysis and time-varying sensitivity analysis of parameters on the number of patients, it is found that the conversion rate β and the inhalation rate η has the largest positive correlation. The cure rate γ of infected persons has the greatest negative correlation on the number of patients. The control strategy formulated by the analysis results of optimal control theory is as follows: The first step is to improve the clearance rate of PM by reducing the PM emissions and increasing the intensity of dust removal. Moreover, such removal work must be maintained for a long time. The second step is to improve the cure rate of patients by being treated in time. After that, people should be reminded to wear masks and go out less so as to reduce the conversion rate of susceptible people becoming patients.

Time-varying sensitivity analysis of an influenza model with interventions

We formulate an influenza model with treatment and vaccination. Both time invariant and time-dependent uncertainty analyses and sensitivity analysis of the model parameter values are carried out to understand the dependence of the reproduction numbers and model state variables on their components. Results show that the relationship between treatment and epidemic size is nonlinear and that there exists a critical threshold treatment rate under which treatment is beneficial. Sensitivity analysis suggests that the most significant parameters are those related to infection transmission, infectiousness, duration of infectiousness and waning immunity. Further, there are important instances when the relationship between some parameters and model outputs changes behavior from negatively to positively correlated or vice versa because all sensitivity indices, except [Formula: see text] are functions of other parameters and thus will change with the change in parameter values. For example, treatment helps to lower the epidemic size, but may then become a “source” of infection likely due to resistance de novo. This knowledge is critical for proper public health planning and guidance of control strategies.

Diagnosing the Time-Varying Value of Forecasts in Multiobjective Reservoir Control

AbstractThis work forwards time-varying sensitivity analysis of control policies as an approach to identify the value of the alternative timing of forecasts in a complex multipurpose reservoir syst...

Coordination and control – limits in standard representations of multi-reservoir operations in hydrological modeling

Abstract. Major multi-reservoir cascades represent a primary mechanism for dealing with hydrologic variability and extremes within institutionally complex river basins worldwide. These coordinated management processes fundamentally reshape water balance dynamics. Yet, multi-reservoir coordination processes have been largely ignored in the increasingly sophisticated representations of reservoir operations within large-scale hydrological models. The aim of this paper is twofold, namely (i) to provide evidence that the common modeling practice of parameterizing each reservoir in a cascade independently from the others is a significant approximation and (ii) to demonstrate potential unintended consequences of this independence approximation when simulating the dynamics of hydrological extremes in complex reservoir cascades. We explore these questions using the Water Balance Model, which features detailed representations of the human infrastructure coupled to the natural processes that shape water balance dynamics. It is applied to the Upper Snake River basin in the western US and its heavily regulated multi-reservoir cascade. We employ a time-varying sensitivity analysis that utilizes the method of Morris factor screening to explicitly track how the dominant release rule parameters evolve both along the cascade and in time according to seasonal high- and low-flow events. This enables us to address aim (i) by demonstrating how the progressive and cumulative dominance of upstream releases significantly dampens the ability of downstream reservoir rules' parameters to influence flow conditions. We address aim (ii) by comparing simulation results with observed reservoir operations during critical low-flow and high-flow events in the basin. Our time-varying parameter sensitivity analysis with the method of Morris clarifies how independent single-reservoir parameterizations and their tacit assumption of independence leads to reservoir release behaviors that generate artificial water shortages and flooding, whereas the observed coordinated cascade operations avoided these outcomes for the same events. To further explore the role of (non-)coordination in the large deviations from the observed operations, we use an offline multi-reservoir water balance model in which adding basic coordination mechanisms drawn from the observed emergency operations is sufficient to correct the deficiencies of the independently parameterized reservoir rules from the hydrological model. These results demonstrate the importance of understanding the state–space context in which reservoir releases occur and where operational coordination plays a crucial role in avoiding or mitigating water-related extremes. Understanding how major infrastructure is coordinated and controlled in major river basins is essential for properly assessing future flood and drought hazards in a changing world.

A Simple Time-Varying Sensitivity Analysis (TVSA) for Assessment of Temporal Variability of Hydrological Processes

Time-varying sensitivity analysis (TVSA) allows sensitivity in a moving window to be estimated and the time periods in which the specific components of a model can affect its performance to be identified. However, one of the disadvantages of TVSA is its high computational cost, as it estimates sensitivity in a moving window within an analyzed series, performing a series of repetitive calculations. In this article a function to implement a simple TVSA with a low computational cost using regional sensitivity analysis is presented. As an example of its application, an analysis of hydrological model results in daily, monthly, and annual time windows is carried out. The results show that the model allows the time sensitivity of a model with respect to its parameters to be detected, making it a suitable tool for the assessment of temporal variability of processes in models that include time series analysis. In addition, it is observed that the size of the moving window can influence the estimated sensitivity; therefore, analysis of different time windows is recommended.

Sensitivity analysis of data-driven groundwater forecasts to hydroclimatic controls in irrigated croplands

In the last decades, advancements in computational science have greatly expanded the use of artificial neural networks (ANNs) in hydrogeology, including applications on groundwater forecast, variable selection, extended lead-times, and regime-specific analysis. However, ANN-model performance often omits the sensitivity to observational uncertainties in hydroclimate forcings. The goal of this paper is to implement a data-driven modeling framework for assessing the sensitivity of ANN-based groundwater forecasts to the uncertainties in observational inputs across space, time, and hydrological regimes. The objectives are two-folded. The first objective is to couple an ANN model with the PAWN sensitivity analysis (SA). The second objective is to evaluate the scale- and process-dependent sensitivities of groundwater forecasts to hydroclimate inputs, computing the sensitivity index in groundwater wells (1) across the whole time-series (for the global sensitivity analysis); (2) across the output sub-regions with conditions of water deficit and water surplus (for the ‘regional’ sensitivity analysis); and (3) at each time step (for the time-varying sensitivity analysis). The implementation of the ANN-PAWN occurs in 68 wells across the Northern High Plains aquifer, USA, with pre-time-step rainfall, evapotranspiration, snowmelt, streamflow, and groundwater measurements as inputs. Results show that evapotranspiration and rainfall are the major sources of uncertainty, with the latter being particularly relevant in water surplus conditions and the former in water deficit conditions. The time-varying sensitivity analysis leads to the identification of localized sensitivities to other sources of uncertainty, as snowmelt in spring or river flow during the annual peak period at the groundwater level.

Multidisciplinary robust design optimization based on time-varying sensitivity analysis

The performance of complex mechanical systems often degrades over time primarily due to time-varying uncertainties. Improving the design of such systems entails addressing time-varying uncertainties through Multidisciplinary design optimization (MDO). In this study, a multidisciplinary robust design optimization method that is based on time-varying sensitivity analysis is proposed. First, the indices for the time-varying reliability sensitivity of limit state functions are calculated by combining sensitivity analysis and an empirical correction formula. The propagation effects of these time-varying uncertainties are qualified by combining the simplified implicit uncertainty propagation and sequential quadratic programming methods. Finally, the robust design method is integrated with MDO to reduce the effects of time-varying uncertainties. The feasibility and effectiveness of the proposed method are illustrated with a mathematical problem and an engineering example.

Time-varying sensitivity analysis of hydrologic and sediment parameters at multiple timescales: Implications for conservation practices

Environmental models can be used to better understand the hydrologic and sediment behavior in a watershed system. However, different processes may dominate at different time periods and timescales, which highly complicate the model interpretation. The related parameter uncertainty may be significant and needs to be addressed to avoid bias in the watershed management. In this study, we used the time-varying and multi-timescale (TVMT) method to characterize the temporal dynamics of parameter sensitivity at different timescales in hydrologic and sediment modeling. As a case study, the first order sensitivity indices were estimated with the Fourier amplitude sensitivity test (FAST) method for the Hydrological Simulation Program - Fortran (HSPF) model in the Zhangjiachong catchment in the Three Gorge Reservoir Region (TGRR) in China. The results were compared to those of the traditional aggregate method to demonstrate the merits of the TVMT method. The time-varying nature of the hydrologic and sediment parameters was revealed and explained mainly by the variation of hydro-climatic conditions. The baseflow recession parameter, evapotranspiration (ET) parameter for the soil storage, and sediment washoff parameter showed high sensitivities almost across the whole period. However, parameters related to canopy interception and channel sediment scour varied notably over time due to changes in the climate forcing. The timescale-dependent characteristics was observed and was most evident for the baseflow recession parameter and ET parameter. At last, the parameters affecting the sediment export and transport were discussed together with the inferred conservation practices. Reasonable controls for sediment must be storm-dependent. Compared to management practices on the land surface, practices affecting channel process would be more effective during storm events. Our results present one of the first investigations for sediment modeling in terms of the importance of parameter sensitivity in both time periods and evaluation timescales for the model calibration, diagnostic evaluation, and prioritizing efforts for conservation practices.

Understanding the time‐varying importance of different uncertainty sources in hydrological modelling using global sensitivity analysis

AbstractSimulations from hydrological models are affected by potentially large uncertainties stemming from various sources, including model parameters and observational uncertainty in the input/output data. Understanding the relative importance of such sources of uncertainty is essential to support model calibration, validation and diagnostic evaluation and to prioritize efforts for uncertainty reduction. It can also support the identification of ‘disinformative data’ whose values are the consequence of measurement errors or inadequate observations. Sensitivity analysis (SA) provides the theoretical framework and the numerical tools to quantify the relative contribution of different sources of uncertainty to the variability of the model outputs. In traditional applications of global SA (GSA), model outputs are aggregations of the full set of a simulated variable. For example, many GSA applications use a performance metric (e.g. the root mean squared error) as model output that aggregates the distances of a simulated time series to available observations. This aggregation of propagated uncertainties prior to GSA may lead to a significant loss of information and may cover up local behaviour that could be of great interest. Time‐varying sensitivity analysis (TVSA), where the aggregation and SA are repeated at different time steps, is a viable option to reduce this loss of information. In this work, we use TVSA to address two questions: (1) Can we distinguish between the relative importance of parameter uncertainty versus data uncertainty in time? (2) Do these influences change in catchments with different characteristics? To our knowledge, the results present one of the first quantitative investigations on the relative importance of parameter and data uncertainty across time. We find that the approach is capable of separating influential periods across data and parameter uncertainties, while also highlighting significant differences between the catchments analysed. Copyright © 2016 The Authors. Hydrological Processes. Published by John Wiley & Sons Ltd.

Uncertainty and sensitivity analysis of a Rift Valley fever model

Rift Valley fever (RVF) is a vector-borne viral disease with pronounced health and economic impacts on domestic animals and humans in much of sub-Saharan Africa. Using techniques of uncertainty and sensitivity analysis (both local derivatives and sampling-based methods) of a mathematical model for RVF transmission in livestock by two population of mosquitoes (Aedes and Culex). We systematically investigate the relative importance of each model parameter for both disease epidemic and endemic activities. The relationship between vertical transmission and basic reproduction number reveals that during epidemic activities vertical transmission accelerates the course of the outbreak as it increases the size of infected vectors and reduces the duration of the outbreak. However, during endemic activities, vertical transmission exceeding 20% highly influences the basic reproduction number and disease persistence. Results of both local and global sensitivity analysis agrees that R0 is most sensitive to vertical transmission, probability of transmission from Aedes mosquitoes to host, vector initial density and number of bites an Aedes mosquito would want to bite a host and number of bites that a host can sustain. This suggests that reducing vector population and enhancing control intervention in livestock is a viable preventive strategy. Both time varying and time invariant sensitivity analysis of disease prevalence governed by both asymptomatic and symptomatic state variables indicate that the most significant parameters are: number of bites that an Aedes mosquito would want to bite a host, number of bites a host can sustain, probability of transmission from host to an Aedes mosquito and the host death rate. Furthermore, time varying sensitivity analysis provides a comprehensive overview of the effects of each model input parameter at all important stages of the epidemic.

Analysing the Sub-processes of a Conceptual Rainfall-Runoff Model Using Information About the Parameter Sensitivity and Variance

Sensitivity analyses are often carried out for the main model output and using a predefined evaluation period. It is possible, however, to get much more knowledge about how the system works when estimating the sensitivity for the output of individual modules for each time step (time-varying sensitivity analysis). This is shown here using a variance-based sensitivity analysis for a conceptual rainfall-runoff model applied to a mountainous catchment. The first-order and total sensitivities were computed using Sobol’s method. Since the parameter ranges used in the sensitivity analysis were obtained through a Markov chain Monte Carlo (MCMC) sampling, the sensitivity indices reflect the parameter uncertainty and make a good use of the previous available information. As a first step, the variance of each flow component was calculated. The flow component with the highest variance at each time step can be regarded as the ‘dominant physical control’, which has been defined as the parameter to which the model output reacts in a highly sensitive way when the parameter varies within realistic ranges. This information about the dominant processes can be used for facilitating model calibration by identifying the periods on which to focus when calibrating different parameters. It also can be useful for estimating the amount of data available for calibrating each process. The second part presents the total sensitivity indices and interactions for individual flow components considering a 2-year period. The results show large differences in the time-varying sensitivity patterns of the flow components. It is concluded that such a high-resolution sensitivity analysis for each flow component is a good complement to a sensitivity analysis of the total discharge, increasing our understanding about the internal functioning of individual modules which can be helpful when comparing different model formulations.

From maps to movies: high-resolution time-varying sensitivity analysis for spatially distributed watershed models

Abstract. Distributed watershed models are now widely used in practice to simulate runoff responses at high spatial and temporal resolutions. Counter to this purpose, diagnostic analyses of distributed models currently aggregate performance measures in space and/or time and are thus disconnected from the models' operational and scientific goals. To address this disconnect, this study contributes a novel approach for computing and visualizing time-varying global sensitivity indices for spatially distributed model parameters. The high-resolution model diagnostics employ the method of Morris to identify evolving patterns in dominant model processes at sub-daily timescales over a six-month period. The method is demonstrated on the United States National Weather Service's Hydrology Laboratory Research Distributed Hydrologic Model (HL-RDHM) in the Blue River watershed, Oklahoma, USA. Three hydrologic events are selected from within the six-month period to investigate the patterns in spatiotemporal sensitivities that emerge as a function of forcing patterns as well as wet-to-dry transitions. Events with similar magnitudes and durations exhibit significantly different performance controls in space and time, indicating that the diagnostic inferences drawn from representative events will be heavily biased by the a priori selection of those events. By contrast, this study demonstrates high-resolution time-varying sensitivity analysis, requiring no assumptions regarding representative events and allowing modelers to identify transitions between sets of dominant parameters or processes a posteriori. The proposed approach details the dynamics of parameter sensitivity in nearly continuous time, providing critical diagnostic insights into the underlying model processes driving predictions. Furthermore, the approach offers the potential to identify transition points between dominant parameters and processes in the absence of observations, such as under nonstationarity.

Regression Modeling of Semicompeting Risks Data

Semicompeting risks data are often encountered in clinical trials with intermediate endpoints subject to dependent censoring from informative dropout. Unlike with competing risks data, dropout may not be dependently censored by the intermediate event. There has recently been increased attention to these data, in particular inferences about the marginal distribution of the intermediate event without covariates. In this article, we incorporate covariates and formulate their effects on the survival function of the intermediate event via a functional regression model. To accommodate informative censoring, a time-dependent copula model is proposed in the observable region of the data which is more flexible than standard parametric copula models for the dependence between the events. The model permits estimation of the marginal distribution under weaker assumptions than in previous work on competing risks data. New nonparametric estimators for the marginal and dependence models are derived from nonlinear estimating equations and are shown to be uniformly consistent and to converge weakly to Gaussian processes. Graphical model checking techniques are presented for the assumed models. Nonparametric tests are developed accordingly, as are inferences for parametric submodels for the time-varying covariate effects and copula parameters. A novel time-varying sensitivity analysis is developed using the estimation procedures. Simulations and an AIDS data analysis demonstrate the practical utility of the methodology.