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

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>

Uncertainty quantification in watershed hydrology: Which method to use?

Evaluation of hydrological models at gauged and ungauged basins using machine learning-based limits-of-acceptability and hydrological signatures

Evaluation of a watershed scale forest hydrologic model

Propagation of structural uncertainty in watershed hydrologic models

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.

<p>Modelling of soil processes is dependent on the availability of high-quality soil data. Soil properties that are considered difficult to measure are frequently determined through pedotransfer functions (PTFs). Here, readily available data are translated into data that are needed. Aside from these input soil properties, a reference wet chemistry dataset of the soil property of interest is required. However, these calibration and validation data are imperfect due to measurement error caused by various sources. Until now, the uncertainty of calibration and validation data has been ignored when deriving PTFs, and uncertainty quantification remains limited to the propagation of model input, parameter and structural uncertainty. In this contribution, we aimed to take uncertainty analysis one step further by studying how measurement error in wet chemistry calibration and validation soil data affects PTF predictions and associated prediction uncertainty. We focused on PTFs to predict the soil’s cation-exchange capacity (CEC), which is an important indicator of soil fertility and nutrient retention capacity. To predict CEC through PTFs, soil properties such as clay percentage, organic carbon content and pH are commonly included. We aimed to study the effect of measurement error in CEC data on the accuracy of multiple linear regression and random forest prediction models. PTFs were developed for the entire USA, subdivided per soil taxonomic order. Here, wet chemistry data from the National Cooperative Soil Survey’s (NCSS) Soil Characterization Database were used. The PTFs were fitted with and without including measurement error. However, the majority of the samples from the NCSS Soil Characterization Database were not measured in duplicate, which was needed to quantify measurement error. Alternatively, we used data from the Wageningen Evaluating Programmes for Analytical Laboratories (WEPAL) to provide a best estimate for the measurement error. Comparison of PTFs with and without measurement error showed significant differences in model accuracy metrics.</p>

Robust time-optimal control of flexible spacecraft with structured uncertainties

Sampling design optimization for geostatistical modelling and prediction

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.

Learning about Investment Risk: The Effects of Structural Uncertainty on Dynamic Investment and Consumption

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.

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.