Propagation of structural uncertainty in watershed hydrologic models

STRUCTURAL UNCERTAINTY IN HYDROLOGICAL MODELS

<p>A hydrological model incurs three types of uncertainties: measurement, structural and parametric uncertainty. Measurement uncertainty exists due to errors in the measurements of rainfall and streamflow data. Structural uncertainty exists due to errors in the mathematical representation of hydrological processes. Parametric uncertainty is a consequence of limited data available to calibrate the model, and measurement and structural uncertainties.</p><p>Recently, separation of structural and measurement uncertainties was identified as one of the twenty-three unsolved problems in hydrology. The information about measurement and structural uncertainties is typically available in the form of residual time-series, that is, the difference between observed and simulated streamflow time-series. The residual time-series, however, provides only an aggregate measure of measurement and structural uncertainties. Thus, the measurement and structural uncertainties are inseparable without additional information. In this study, we used random forest (RF) algorithm to gather additional information about measurement uncertainties using hydrological data across several watersheds. Subsequently, the uncertainty bounds obtained by RF were compared against the uncertainty bounds obtained by two other methods: rating-curve analysis and recently proposed runoff-coefficient method. Rating curve analysis yields uncertainty in streamflow measurements only and the runoff-coefficient yields uncertainty in both rainfall and streamflow measurements. The results of the study are promising in terms of using data across different watersheds for the construction of measurement uncertainty bounds. The preliminary results of this study will be presented in the meeting.</p>

There are two kinds of uncertainty in science: structural and parametric uncertainty. Parametric uncertainty means that we know the relevant factors and their interrelations for a given phenomenon, but miss the exact (initial) values of these factors. Structural uncertainty means that we are unsure if we know all the relevant factors and their interdependencies. Using this conceptual distinction it is clear that every simulation model for tactical wargaming is necessarily affected by massive structural uncertainty, since the of has not lifted much since the days of Clausewitz. The term fog seeks to capture the uncertainty regarding own capabilities, adversary capabilities and intents, as well as many other factors. However, if war is seen that way, it is necessarily insufficient to base decisions on frameworks that only deal with parametric uncertainty. The classical approach to make decisions, rational analysis, has therefore severe limitations for this application. The major consequence of structural uncertainty for simulation supported decision making is that stochastic parameter variation and subsequent statistical analysis are inadequate as the sole basis for critical decisions. The paper discusses this calamity and, as a solution, suggests tactical wargaming, a method based on assumption based planning, scenario planning, expert intuition and exploratory simulation. This approach significantly differs from standard wargaming, which, in the author's view, is too focused on parametric uncertainty.

The paper explores the impact of the initial-data, parameter and structural model uncertainty on the simulation of a tropical cyclone-like vortex in the National Center for Atmospheric Research’s (NCAR) Community Atmosphere Model (CAM). An analytic technique is used to initialize the model with an idealized weak vortex that develops into a tropical cyclone over ten simulation days. A total of 78 ensemble simulations are performed at horizontal grid spacings of 1.0u, 0.5u and 0.25u using two recently released versions of the model, CAM 4 and CAM 5. The ensemble members represent simulations with random small-amplitude perturbations of the initial conditions, small shifts in the longitudinal position of the initial vortex and runs with slightly altered model parameters. The main distinction between CAM 4 and CAM 5 lies within the physical parameterization suite, and the simulations with both CAM versions at the varying resolutions assess the structural model uncertainty. At all resolutions storms are produced with many tropical cyclone-like characteristics. The CAM 5 simulations exhibit more intense storms than CAM 4 by day 10 at the 0.5u and 0.25u grid spacings, while the CAM 4 storm at 1.0u is stronger. There are also distinct differences in the shapes and vertical profiles of the storms in the two variants of CAM. The ensemble members show no distinction between the initial-data and parameter uncertainty simulations. At day 10 they produce ensemble root-mean-square deviations from an unperturbed control simulation on the order of 1–5 m s 21 for the maximum low-level wind speed and 2–10 hPa for the minimum surface pressure. However, there are large differences between the two CAM versions at identical horizontal resolutions. It suggests that the structural uncertainty is more dominant than the initial-data and parameter uncertainties in this study. The uncertainty among the ensemble members is assessed and quantified.

On constructing limits-of-acceptability in watershed hydrology using decision trees

This paper proposes an extended model evaluation method that considers not only the model performance but also the model structure and parameter uncertainties in hydrologic modeling. A simple reservoir model (SFM) and distributed kinematic wave models (KWMSS1 and KWMSS2 using topography from 250-m, 500-m, and 1-km digital elevation models) were developed and assessed by three evaluative criteria for model performance, model structural stability, and parameter identifiability. All the models provided acceptable performance in terms of a global response, but the simpler SFM and KWMSS1 could not accurately represent the local behaviors of hydrographs. Moreover, SFM and KWMSS1 were structurally unstable; their performance was sensitive to the applied objective functions. On the other hand, the most sophisticated model, KWMSS2, performed well, satisfying both global and local behaviors. KMSS2 also showed good structural stability, reproducing hydrographs regardless of the applied objective functions; however, superior parameter identifiability was not guaranteed. A number of parameter sets could result in indistinguishable hydrographs. This result indicates that while making hydrologic models complex increases its performance accuracy and reduces its structural uncertainty, the model is likely to suffer from parameter uncertainty.

Robust time-optimal control of flexible spacecraft with structured uncertainties

Described herein is the parametric and structural uncertainty quantification for the monthly Extended Reconstructed Sea Surface Temperature (ERSST) version 4 (v4). A Monte Carlo ensemble approach was adopted to characterize parametric uncertainty, because initial experiments indicate the existence of significant nonlinear interactions. Globally, the resulting ensemble exhibits a wider uncertainty range before 1900, as well as an uncertainty maximum around World War II. Changes at smaller spatial scales in many regions, or for important features such as Niño-3.4 variability, are found to be dominated by particular parameter choices. Substantial differences in parametric uncertainty estimates are found between ERSST.v4 and the independently derived Hadley Centre SST version 3 (HadSST3) product. The largest uncertainties are over the mid and high latitudes in ERSST.v4 but in the tropics in HadSST3. Overall, in comparison with HadSST3, ERSST.v4 has larger parametric uncertainties at smaller spatial and shorter time scales and smaller parametric uncertainties at longer time scales, which likely reflects the different sources of uncertainty quantified in the respective parametric analyses. ERSST.v4 exhibits a stronger globally averaged warming trend than HadSST3 during the period of 1910–2012, but with a smaller parametric uncertainty. These global-mean trend estimates and their uncertainties marginally overlap. Several additional SST datasets are used to infer the structural uncertainty inherent in SST estimates. For the global mean, the structural uncertainty, estimated as the spread between available SST products, is more often than not larger than the parametric uncertainty in ERSST.v4. Neither parametric nor structural uncertainties call into question that on the global-mean level and centennial time scale, SSTs have warmed notably.

This paper examines the effects of incomplete information on dynamic investment and consumption in a general equilibrium model where shocks to capital are unobservable and there is structural or parameter uncertainty regarding the volatility of these shocks; i.e., the investment risk. In this model higher investment reduces the estimation error on the unobservable state variables, and thereby also reduces the estimation error on the unknown parameter. Investment policy therefore affects the speed of learning and is itself subsequently affected as estimation errors fall over time. We quantify the interaction of learning with investment by numerically computing equilibrium investment and consumption in a version of the model calibrated by aggregate US data. We find that imperfect observability (of productivity shocks) by itself does not significantly affect equilibrium investment and consumption. The introduction of structural or parameter uncertainty has significant effects on equilibrium investment and consumption, however. Moreover, investment and consumption levels in the presence of structural uncertainty are more quantitatively consistent with the data when compared to versions of the model that assume either complete information or incomplete information without structural uncertainty. The presence of structural uncertainty also appears to make consumption growth more volatile compared to the benchmark cases. Finally, and consistent with the theoretical analysis, the marginal propensity to invest is not monotone increasing with time even though the estimation errors are being reduced due to learning.

The concept of an intelligent hybrid aircraft fault-tolerant flight control system operating under complete parametric and structural uncertainty is considered. Fault tolerance in the proposed system is ensured through the efficient integration of model-based and model-free health monitoring and reconfiguring methods.

Understanding natural processes, particularly the water cycle, is inherently challenging due to their unpredictable and complex nature. This complexity is especially pronounced when employing hydrological models, where simplifications introduce various uncertainties. Failing to acknowledge and address these uncertainties can introduce biases into the model outcomes, potentially influencing subsequent decision-making processes. This issue is particularly pertinent in the Indian Himalayan Regions, where significant contributions come from melting of snow and glaciers.  The uncertainties in both model inputs and structures are exacerbated in this region, which is further compounded by the scarcity of reliable data. Consequently, there is a critical need to systematically quantify the diverse sources of uncertainty to ensure accurate and reliable hydrological predictions. This study focuses on the snow-dominant Alaknanda basin within the Indian Himalayan Region (IHR), encompassing three gauging stations. The SWAT+ hydrological model and Modular Assessment of Rainfall-Runoff Models Toolbox (MARRMoT) framework (Trotter et al., 2022) are employed to assess parameter and model structure uncertainties, respectively. The SWAT+ model, calibrated with the Latin Hypercube Sampling (LHS) algorithm, achieved Nash-Sutcliffe Efficiency (NSE) values of 0.56, 0.79, and 0.61. Parameter uncertainty is further examined using diverse parameter sets generated through the LHS algorithm. Furthermore, with the application of 47 lumped conceptual models within MARRMoT framework, assessment of model structure uncertainty underscores the varying importance of processes, particularly snow storage, soil moisture, and routing storage in the study region. The findings reveal that the inclusion of additional storage components in the model leads to a decline in performance, accompanied by an increase in complexity and uncertainties. Notably, the study concludes that, for the investigated region, the contribution of parameter uncertainty surpasses that of model structure uncertainty. These insights emphasize the need for a nuanced understanding of both parameter and structural uncertainties to enhance the reliability of hydrological predictions in data-scarce and complex regions like the IHR.

Secondary forest regrowth shapes community succession and biogeochemistry for decades, including in the Upper Great Lakes region. Vegetation models encapsulate our understanding of forest function, and whether models can reproduce multi-decadal succession patterns is an indication of our ability to predict forest responses to future change. We test the ability of a vegetation model to simulate C cycling and community composition during 100years of forest regrowth following stand-replacing disturbance, asking (a) Which processes and parameters are most important to accurately model Upper Midwest forest succession? (b) What is the relative importance of model structure versus parameter values to these predictions? We ran ensembles of the Ecosystem Demography model v2.2 with different representations of processes important to competition for light. We compared the magnitude of structural and parameter uncertainty and assessed which sub-model-parameter combinations best reproduced observed C fluxes and community composition. On average, our simulations underestimated observed net primary productivity (NPP) and leaf area index (LAI) after 100years and predicted complete dominance by a single plant functional type (PFT). Out of 4,000 simulations, only nine fell within the observed range of both NPP and LAI, but these predicted unrealistically complete dominance by either early hardwood or pine PFTs. A different set of seven simulations were ecologically plausible but under-predicted observed NPP and LAI. Parameter uncertainty was large; NPP and LAI ranged from ~0% to >200% of their mean value, and any PFT could become dominant. The two parameters that contributed most to uncertainty in predicted NPP were plant-soil water conductance and growth respiration, both unobservable empirical coefficients. We conclude that (a) parameter uncertainty is more important than structural uncertainty, at least for ED-2.2 in Upper Midwest forests and (b) simulating both productivity and plant community composition accurately without physically unrealistic parameters remains challenging for demographic vegetation models.

Ongoing policy discussions on the reconfiguration of bidding zones in European electricity markets induce structural uncertainty about the future market design. This paper deals with the question of how this structural uncertainty affects market participants and their long-run investment decisions in generation and transmission capacity. We propose a stochastic multilevel model, which incorporates generation capacity investment, network expansion and redispatch, taking into account uncertainty about the future market design. Using a stylized two-node network, we disentangle different effects that uncertainty has on market outcomes. Our results reveal that expectations about future market structures have an important effect on investment decisions. Unlike most parametric uncertainties, structural uncertainty about the future market design can have a positive effect on welfare, even if a market design change does not actually take place, although there are distributional effects. This also implies that the welfare gains of a change to a more efficient market design are lower if market participants already anticipate this change.

This paper investigates the shock-layer radiative heating uncertainty for hyperbolic Earth entry, with the main focus being a Mars return. In Part I of this work, a baseline simulation approach involving the LAURA Navier-Stokes code with coupled ablation and radiation is presented, with the HARA radiation code being used for the radiation predictions. Flight cases representative of peak-heating Mars or asteroid return are de ned and the strong influence of coupled ablation and radiation on their aerothermodynamic environments are shown. Structural uncertainties inherent in the baseline simulations are identified, with turbulence modeling, precursor absorption, grid convergence, and radiation transport uncertainties combining for a +34% and ..24% structural uncertainty on the radiative heating. A parametric uncertainty analysis, which assumes interval uncertainties, is presented. This analysis accounts for uncertainties in the radiation models as well as heat of formation uncertainties in the flow field model. Discussions and references are provided to support the uncertainty range chosen for each parameter. A parametric uncertainty of +47.3% and -28.3% is computed for the stagnation-point radiative heating for the 15 km/s Mars-return case. A breakdown of the largest individual uncertainty contributors is presented, which includes C3 Swings cross-section, photoionization edge shift, and Opacity Project atomic lines. Combining the structural and parametric uncertainty components results in a total uncertainty of +81.3% and ..52.3% for the Mars-return case. In Part II, the computational technique and uncertainty analysis presented in Part I are applied to 1960s era shock-tube and constricted-arc experimental cases. It is shown that experiments contain shock layer temperatures and radiative ux values relevant to the Mars-return cases of present interest. Comparisons between the predictions and measurements, accounting for the uncertainty in both, are made for a range of experiments. A measure of comparison quality is de ned, which consists of the percent overlap of the predicted uncertainty bar with the corresponding measurement uncertainty bar. For nearly all cases, this percent overlap is greater than zero, and for most of the higher temperature cases (T >13,000 K) it is greater than 50%. These favorable comparisons provide evidence that the baseline computational technique and uncertainty analysis presented in Part I are adequate for Mars-return simulations. In Part III, the computational technique and uncertainty analysis presented in Part I are applied to EAST shock-tube cases. These experimental cases contain wavelength dependent intensity measurements in a wavelength range that covers 60% of the radiative intensity for the 11 km/s, 5 m radius flight case studied in Part I. Comparisons between the predictions and EAST measurements are made for a range of experiments. The uncertainty analysis presented in Part I is applied to each prediction, and comparisons are made using the metrics defined in Part II. The agreement between predictions and measurements is excellent for velocities greater than 10.5 km/s. Both the wavelength dependent and wavelength integrated intensities agree within 30% for nearly all cases considered. This agreement provides confidence in the computational technique and uncertainty analysis presented in Part I, and provides further evidence that this approach is adequate for Mars-return simulations. Part IV of this paper reviews existing experimental data that include the influence of massive ablation on radiative heating. It is concluded that this existing data is not sufficient for the present uncertainty analysis. Experiments to capture the influence of massive ablation on radiation are suggested as future work, along with further studies of the radiative precursor and improvements in the radiation properties of ablation products.

Scientists and decision-makers globally confront systemic challenges posed by the intertwining issues of water scarcity and climate change. These challenges give rise to cascading impacts across ecological and socioeconomic systems, often exacerbated by feedback loops and unforeseeable consequences (UNDRR, 2021). As non-linear changes loom, the reliance on consolidative modeling becomes dangerous, risking the activation of disastrous tipping points with severe implications for both nature and humans (Kreibich et al., 2022). The costs associated with neglecting uncertainties in modeling and policy spans diverse domains, including ecosystems, income, employment, capital value, insurance, etc. (UNDRR, 2022; Parrado et al., 2019; Adamson and Loch, 2021). This aligns with the concept of Knightian or deep uncertainty, where the external context, system dynamics, and conflicting outcomes are not fully known or agreed upon (Knight, 1921; Marchau et al., 2019; Lempert et al., 2006). A growing scientific and policy consensus emphasizes the need to move beyond traditional notions of optimality and deterministic prediction in conditions of deep uncertainty. Resilience and robustness emerge as crucial concepts, requiring the development of socio-ecological system (SES) models that explicitly quantify uncertainties (Adamson and Loch, 2021; Di Baldassarre et al., 2016; IPCC, 2021; UNDRR, 2021).Recent research in SES, including coupled human and natural systems and socio-hydrology science, offers innovative modeling techniques integrating human and natural components. These techniques account for feedbacks and heterogeneity between systems, improving insight and the ability to predict tipping points (Gain et al., 2021). Recent studies demonstrate the potential of linking coupled models of human-water systems with sensitivity analysis and multi-system ensembles for robust water management policies (Basheer et al., 2023; Smith et al., 2021).This review initially identified 2160 papers, filtering them to 198 studies that account quantitatively modelling in, both human and water systems. The geographical focus spans the USA, Europe, Australia, the Middle East, South America, China, and East Africa. The models range from piecewise equations to full-fledged representations. However, structural uncertainties are seldom explored, with only 3.5% of studies conducting multi-model ensemble experiments. This highlights a significant oversight in recognizing biases from simplifications. Conversely, parameter uncertainties are more frequently addressed (20.2%), focusing on hydrology, groundwater, behavioral, infrastructure, climatic, economic, and agronomic variables. Input uncertainties, notably contemporary (discharge data) and future (climate change) inputs, are extensively studied (148 out of 198), employing methods like expert judgment and Monte Carlo simulations. Despite this, the review highlights a limited exploration of structural uncertainties and the potential inadequacy of linear piecewise equations, emphasizing the need for more nuanced and robust approaches to enhance the accuracy and reliability of socio-environmental systems modeling.Based on this study, we make the following recommendations to mainstream uncertainty quantification into SES modeling: (i) Quantify parameter and structural uncertainties within systems, (ii) Quantify structural uncertainties between models, (iii) Input uncertainties must be more thoroughly assessed and model assumptions systematically revised, (iv) Deliver actionable science that mainstreams uncertainty quantification into decision making, (v) Establish balanced stakeholder engagement and clear and transparent science-policy engagement rules, (vi) Balance complexity and usefulness to keep the model relevant.