Uncertainty In Model Results Research Articles

Sensitivity of Simulating Hydrologic Processes to Gauge and Radar Rainfall Data in Subtropical Coastal Catchments

This research evaluated the impact of three rainfall datasets on hydrologic process simulations in two coastal catchments located in Alabama. In this study, rain gauge time series recorded by the U.S. National Oceanic and Atmospheric Administration (NOAA) and Geological Survey (USGS) along with radar precipitation data derived from NOAA National Weather Service (NWS) were input into the Hydrological Simulation Program—FORTRAN (HSPF). Automatic parameter calibration was performed using daily streamflow data recorded at USGS Fish and Magnolia River gauge stations from 07/01/2002 to 12/31/2008. HSPF parameters were optimized using the Model-Independent Parameter Estimation (PEST) program. Model parameter ranges were refined by incorporating physical characteristic of the study areas and after analyzing observed streamflow time series. This approach, in turn, helped PEST optimization tool to find the most physically-related set of parameters that can be transferred to any watershed with similar characteristics and minimum parameter calibration. On average, annual USGS and radar rainfall values were around 480 mm and 250 mm, respectively lower than NOAA precipitation records. Overall, it is found that the NOAA precipitation input data resulted in better daily flow simulations than results from radar and USGS rainfall time series. Streamflows derived from USGS rainfall time series showed the worst model performance at both catchment outlets because of missing data, low amounts, and temporal delay of peaks. This study found that annual actual evapotranspiration values were closed among rainfall time series and varied from 900 to 958 mm. Deep percolation values for Magnolia and Fish River, regardless of rainfall source, ranged from 66 to 192 mm/year. Major discrepancies were found at storm runoff values. Gauge rainfall time series yielded the closest streamflow values compared to observed flow time series at both watershed outlets. Rainfall derived from radar yielded consistent and acceptable runoff results in Fish and Magnolia River models. In both case studies, the high spatial variability of rainfall storm events was not adequately captured by any of the rainfall datasets and yielded high uncertainty in model results.

Data Assimilation with Soil Water Content Sensors and Pedotransfer Functions in Soil Water Flow Modeling

Soil water flow models are based on simplified assumptions about the mechanisms, processes, and parameters of water retention and flow. That causes errors in soil water flow model predictions. Data assimilation (DA) with the ensemble Kalman filter (EnKF) corrects modeling results based on measured state variables, information on uncertainty in measurement results and uncertainty in modeling results. The objectives of this work were (i) to evaluate pedotransfer functions (PTFs) as a source of data to generate an ensemble of Richards′ equation‐based models for the EnKF application to the assimilation of soil water content data and (ii) to research how effective assimilation of soil moisture sensor data can be in correcting simulated soil water content profiles in field soil. Data from a field experiment were used in which 60 two‐rod time domain reflectometry (TDR) probes were installed in a loamy soil at five depths to monitor the soil water content. The ensemble of models was developed with six PTFs for water retention and four PTFs for the saturated hydraulic conductivity (Ksat). Measurements at all five depths and at one or two depths were assimilated. Accounting for the temporal stability of water contents substantially decreased the estimated noise in data. Applicability of the Richards′ equation was confirmed by the satisfactory calibration results. In absence of calibration and data assimilation, simulations developed a strong bias caused by the overestimation of Ksat from PTFs. Assimilating measurements from a single depth of 15 cm or of 35 cm provided substantial improvements at all other observation depths. An increase in data assimilation frequency improved model performance between the assimilation times. Overall, bringing together developments in pedotransfer functions, temporal stability of soil water patterns, and soil water content sensors can create a new source of data to improve modeling results in soil hydrology and related fields.

Point estimate methods based on Taylor Series Expansion – The perturbance moments method – A more coherent derivation of the second order statistical moment

Point estimate methods (PEMs) have found their niche in application to geotechnical problems and a few other engineering fields, where their relative simplicity matches well with the need for quick and reliable estimates of the uncertainty in model results. In some cases, however, the simplicity of the PEMs has to come to terms with the physical meaning of the stochastic variables and with the non-linearity of the model function. In this study, a general review of PEMs is presented and an improved method is proposed that requires fewer model evaluations, but still provides meaningful results for non-linear problems. Two uncertainty analyses of the hydrologic response to a rainfall event are presented: for a small synthetic basin and for a small mountain basin in Italy. The results of three PEMs are evaluated – Rosenblueth’s method, Li’s method, and the proposed perturbance moments method (PMM), along with the computationally-intensive, Monte Carlo simulation (MCS) approach. It is shown that for the same computational requirements, the derivation of the PMM is more coherent and resolves the problem of the negative variance which can occur when using other PEMs derived from the Taylor Series Expansion. The method is also computationally efficient, both compared to MCS and to other PEMs.

A simple concept for calibrating runoff thresholds in quasi‐distributed variable source area watershed models

AbstractMost semi‐distributed watershed water quality models divide the watershed into hydrologic response units (HRU) with no flow among them. This is problematic when watersheds are delineated to include variable source areas (VSAs) because it is the lateral flows from upslope areas to downslope areas that generate VSAs. Although hydrologic modellers have often successfully calibrated these types of models, there can still be considerable uncertainty in model results. In this paper, a topographic‐index‐based method is described and tested to distribute effective soil water holding capacity among HRUs, which can be subsequently adjusted using the watershed baseflow coefficient. The method is tested using a version of the Soil and Water Assessment Tool (SWAT) model that simulates VSA runoff and is applied to two watersheds: a New York State (NYS) watershed, and one in the head waters of the Blue Nile Basin (BNB) in Ethiopia. Daily streamflow predicted using effective soil water storage capacities based only on the topographic index were reassuringly accurate in both the NYS watershed (daily Nash Sutcliffe (E) = 0·73) and in the BNB (E = 0·70). Using the baseflow coefficient to adjust the effective soil water storage capacity only slightly improved streamflow predictions in NYS (E = 0·75) but substantially improved the BNB predictions (E = 0·80). By comparison, the standard SWAT model, which uses the traditional look‐up tables to determine a runoff curve number, performed considerably less accurately in un‐calibrated form (E = 0·51 for NYS and E = 0·45 for BNB), but improved substantially when explicitly calibrated to streamflow measurements (E = 0·76 for NYS and E = 0·67 for the BNB). The calibration method presented here provides a parsimonious, systematic approach to using established models in VSA watersheds that reduces the ambiguity inherent in model calibration. Copyright © 2011 John Wiley & Sons, Ltd.

Population dynamics of splitnose rockfish ( Sebastes diploproa) in the Northeast Pacific Ocean

We developed an age-structured population model of splitnose rockfish, Sebastes diploproa, in the Northeast Pacific Ocean. Splitnose rockfish is a bycatch species that co-occurs with several commercially important species that are currently declared overfished. Bycatch species are typically not the focus of stock assessment efforts because of their limited economic importance, but they may suffer the same population declines as species with which they co-occur. To examine the dynamics of splitnose rockfish for the first time, we analyzed data from three groundfish fisheries and four research surveys conducted in the Northeast Pacific Ocean. To develop a model, we used Stock Synthesis, a statistical framework for the construction of a population dynamics models utilizing both fishery-dependent and fishery-independent data. In the model, we reconstructed the total catch of the species back to 1900, estimated the dynamics of the stock spawning output and recruitment and evaluated biomass depletion relative to the stock's unfished state, as well as sources of uncertainty in model outputs. The results indicate that the splitnose rockfish is currently not overfished even though it has experienced several periods of abrupt decline in its biomass. Revisiting age data from earlier years, monitoring fishery discard, and investigating the spatial dynamics of splitnose rockfish is important to further improve the understanding of this species’ population dynamics, and decrease uncertainty in model results.

Reconstructing surface temperature changes over the past 600 years using climate model simulations with data assimilation

Ensemble simulations have been performed with a climate model constrained to follow temperature histories obtained from a recent compilation of 56 well‐calibrated surface temperature proxy records, using a new data assimilation technique. First, we demonstrate that the data assimilation technique provides a faithful representation in the Northern Hemisphere of the signal recorded by the climate proxies at both the regional and gridbox scales. Second, by varying the external forcing, the parameters of the data assimilation method, and the parameters controlling the equilibrium climate sensitivity of the climate model, we demonstrate that the uncertainty in model results is much lower in simulations using data assimilation than in those without it. This observation implies that the data assimilation, using a set of 56 proxies, is providing an efficient and robust constraint on the simulated climate variability over the past centuries. At the hemispheric and continental scales, the model reconstructions using data assimilation are in good agreement with both the instrumental record of the past 150 years and reconstructions of climate in past centuries derived from the application of traditional statistical approaches to networks of proxy data. This increases the confidence in both the data assimilation and traditional statistical approaches. Our data assimilation method, however, is unable to provide a reliable reconstruction over the North Atlantic Ocean, which we attribute to the paucity of proxy data in that region.

Groundwater Solution Techniques: Environmental Applications

Groundwater models provide a scientific tool for various groundwater studies which include groundwater flow, solute transport, heat transport and deformation. However, without a good understanding of a model, modeling studies are not well designed or the model does not represent the natural system which being modeled long term effects may results. Thus, this review has focused and reviewed the types of solution techniques in terms of advantages and limitations. The findings are vital to improve the model conceptualization and understanding of the uncertainty in model results. On the same hand, it acts as guide and reference to groundwater modeler, reduces the time spent in understanding the solution technique and complexity of groundwater models, as well as focus ways to address the groundwater problems and deliver modeling output more efficiently.

Modeling the effect of size reduction on the stratification of a large wind‐driven lake using an uncertainty‐based approach

An important source of uncertainty affecting the results of 3‐D hydrodynamic models of wind‐driven lakes, and one which is rarely formally addressed, arises in the development of spatially and temporally varying wind fields used as surface boundary conditions. We analyze one of the sources of uncertainty in this process and propose a simple and straightforward method to assess the uncertainty in model results arising from the construction of wind fields for surface boundary conditions. Taking into account such uncertainty in model results, it is demonstrated that a 3‐D hydrodynamic model is able to represent mathematically the evolution of the stratification in a large wind‐driven lake. Using the Salton Sea as a case study, and taking model uncertainty into consideration, we demonstrate that a reduction of the lake size, as has been proposed for restoration of the Salton Sea, will induce a stronger and more persistent stratification. These changes in stratification are shown to be statistically significant. As the number of weather stations used to reconstruct the wind field over water increases from three to five, agreement between field and simulated data improves, possibly because of reduced uncertainty in the spatial interpolation of wind data. Differences in stratification between the Salton Sea as it currently exists and as it could exist if restoration plans are implemented, with the lake occupying the northern end of the basin and its surface area reduced by 80%, are the result of the spatial variability of the wind and changes in the magnitude of the wind‐driven mechanical energy fluxes into the lake.

Parameter uncertainties in the modelling of vegetation dynamics—Effects on tree community structure and ecosystem functioning in European forest biomes

Dynamic vegetation models are useful tools for analysing terrestrial ecosystem processes and their interactions with climate through variations in carbon and water exchange. Long-term changes in structure and composition (vegetation dynamics) caused by altered competitive strength between plant functional types (PFTs) are attracting increasing attention as controls on ecosystem functioning and potential feedbacks to climate. Imperfect process knowledge and limited observational data restrict the possibility to parameterise these processes adequately and potentially contribute to uncertainty in model results. This study addresses uncertainty among parameters scaling vegetation dynamic processes in a process-based ecosystem model, LPJ-GUESS, designed for regional-scale studies, with the objective to assess the extent to which this uncertainty propagates to additional uncertainty in the tree community structure (in terms of the tree functional types present and their relative abundance) and thus to ecosystem functioning (carbon storage and fluxes). The results clearly indicate that the uncertainties in parameterisation can lead to a shift in competitive balance, most strikingly among deciduous tree PFTs, with dominance of either shade-tolerant or shade-intolerant PFTs being possible, depending on the choice of plausible parameter values. Despite this uncertainty, our results indicate that the resulting effect on ecosystem functioning is low. Since the vegetation dynamics in LPJ-GUESS are representative for the more complex Earth system models now being applied within ecosystem and climate research, we assume that our findings will be of general relevance. We suggest that, in terms of carbon storage and fluxes, the heavier parameterisation requirement of the processes involved does not widen the overall uncertainty in model predictions.

GIS-based modeling of runoff source areas and pathways

Abstract. The application of runoff models that rely on calibration to future land use and climate conditions is restricted to situations where the reaction of Hydrologic Response Units to environmental change is known. This limitation and the ensuing uncertainty of model results can be avoided when a risk-based approach to landscape and runoff analysis is taken. GIS-based landscape analysis provides the possibility of assessing the risks associated with non-linear responses of Hydrologic Response Units to changing rainfall and land use. In this paper, a runoff module designed for IDRISI-Andes to calculate runoff amount and routing for single or multiple rainfall events on a hillslope at small catchment scale is presented. The module is raster-based and uses layers with topographic and hydrological parameters to calculate a spatially distributed output layer of surface runoff. Conceptually, the module extrapolates point data of infiltration capacity onto a field or hillslope. A spatially distributed runoff map is calculated based on the addition of layers with rainfall data and the routing of runoff through pathways connecting pixels in a digital elevation model. Unlike outlet-based runoff modeling, the need for parameterization of the catchment is kept to a minimum. The application of the RUNOFF module in a test area in the Eifel region of Germany indicated that runoff from grassland is sensitive to small increases in rainfall intensity and soil compaction. The spatial patterns of infiltration capacity also contribute significantly to the non-linearity of the test area reaction to changing rainfall and soil hydrologic properties.

Variability of river plumes off Northwest Iberia in response to wind events

The Western Iberian Buoyant Plume (WIBP) is a low-salinity lens formed by river discharge and continental run-off extending along the shelf off Northwest Iberia. The variability of this structure is evaluated with a numerical model forced by real meteorological data and climatologic river discharge during late 2002, when conditions were those of a typical autumn. The direction and intensity of the wind-induced Ekman transport, but also the previous conditions and the duration of the event are found to determine plume behavior. We have identified three characteristic situations: a) confinement of the plume to the coast during downwelling — southerly-winds, b) expansion of the plume during the declining phase of the downwelling event by relaxation of the wind, and c) expansion of the plume by upwelling — northerly-winds. The short time scale of the response of the plume (1–3 h) adds timing between wind events and the phase of the tide as an additional source of variability. In all cases the Iberian Poleward Current (IPC), a saltier and warmer poleward current flowing over the slope, responds as well to wind changes. Furthermore, our simulations illustrate how topography and differences in the river discharge induce local differences in dynamics. Comparisons to available observations show a reasonable model skill. Differences between wind measurements and wind forcing applied to the model appear to be a major source of uncertainty in model results.

Predicting the morphological and hydraulic consequences of river rehabilitation

AbstractDecisions about reach‐scale river rehabilitation for the purposes of flood protection and ecological enhancement require prediction of the possible consequences of management alternatives. To provide such predictions, an integrative model is necessary that represents the cause–effect relations between rehabilitation options and morphological, hydraulic and ecological consequences. This paper describes the morphological and hydraulic submodel of such an integrative model. This submodel is further subdivided into four modules predicting: (1) channel morphology, (2) flooding (dike overtopping, floodplain flooding and bed moving floods), (3) velocity and depth distribution and (4) riverbed siltation. Model relationships come from results reported in the literature and new data analyses. By using quantities that are all either readily available or easily predictable for changed conditions, the model should be widely applicable, even for data‐limited situations. The overall model is implemented as a probability network to facilitate estimation of uncertainties in model results. An application of the model to a reach of the Thur River in Switzerland demonstrates its utility for predicting morphological and hydraulic consequences of a planned river widening. The full integrative model, including ecological endpoints, will be used together with quantitative assessments of stakeholder preferences to support rehabilitation decisions for a number of Swiss rivers. Copyright © 2007 John Wiley & Sons, Ltd.

The role of measurement uncertainties for the simulation of grassland net ecosystem exchange (NEE) in Europe

Ecosystem models are used to explore scientific questions and as a means of decision support. It is therefore essential to assess the quality of the outputs from these. One important measure of quality of model outputs is their uncertainty that arise from uncertainties in measurements. In this study, uncertainty associated with simulation of NEE (net ecosystem exchange) by the PaSim (pasture simulation model) model was tested at four grassland sites. The effect of measurement uncertainties in the main input factors for climate (temperature, precipitation, global radiation), atmospheric CO 2 concentration, soil characteristics (bulk density, clay fraction, pH, carbon content of different pools), and management (N input) on output uncertainty of NEE prediction was explored. Monte Carlo runs were performed for 2 years, 2002 and 2003, using Latin Hypercube sampling from probability density functions (PDF) for each input factor. Global uncertainty, represented by the standard deviation of the NEE estimates, was generally higher in 2003 than in 2002 per site with full data records for both years. There was considerable variation in global uncertainty from site to site and between years. These results indicate that output uncertainty does not depend solely on absolute input uncertainties. The mean NEE of the global uncertainty distribution was also different from the NEE result of the single model run using the default set of input factors. The results clearly indicate the dependency of factor importance and uncertainty in model simulations on the environmental conditions of the system under study. One indication is that more environmentally constrained systems produce higher uncertainties in model results. We conclude that any application of the model within decision support should be accompanied by a case specific uncertainty analysis presenting the mean of the output distribution as model results. The consequences of these findings for the application of PaSim at the continental scale are discussed.

EVALUATION OF MODELING TOOLS FOR TMDL DEVELOPMENT AND IMPLEMENTATION

The Total Maximum Daily Load (TMDL) program, established by U.S. federal law, drives U.S. water quality policy and management today. Mathematical models, in combination with field monitoring data, are widely used when developing TMDLs since they can potentially save time, reduce cost, and minimize the need for experimentally evaluating management alternatives. This article introduces the collective effort of a multidisciplinary panel of experts to evaluate the current status of TMDL modeling technology available for the most common waterbody impairment factors, along with issues of proper model use, uncertainty of modeling results, and economic tools to optimize the selection and application of these tools for TMDL development. Each of these topics is developed in individual articles within this collection. The review indicates that the status of TMDL modeling tools for the most common stream impairments is inconsistent. Research must continue to advance our understanding of many of the processes leading to stream impairment, and to address many of the existing model limitations. Reviews of case studies within this collection of articles show that users must be better trained to improve the application of TMDL models. In some cases, lack of adequate data sets limits model development and application. Existing computer models are considered capable of simulating sediment and nutrients, lacking for dissolved oxygen, and grossly insufficient for biological indicators. Quantification of modeling uncertainty, communication to end users, and economic optimization of the results are suggested as indispensable components to improve the success of the TMDL program.

Using Mathematical Models to Assess Sediment Stability

The application of mathematical models to a sediment stability study is presented, with an emphasis on using models as a component of an effort to develop, refine, and potentially validate a conceptual site model (CSM) for sediment transport at a study site. The utility of mathematical models is discussed, in which the modeling framework consists of linked hydrodynamic, sediment transport, and contaminant fate and transport models. Benefits and drawbacks of empirically based mechanistic models are presented. An approach for integrating modeling analyses into the development, refinement and validation of a CSM is provided. This approach focuses on a phased study that combines modeling and data-based analyses to test hypotheses related to the CSM and sediment stability. Uncertainty in modeling results is a primary concern in sediment stability studies, and issues related to model uncertainty are discussed. Finally, communication of modeling results to stakeholders is addressed.

A guidance for assessing and communicating uncertainties

In the daily practice of science for policy, as experienced by governmental agencies which inform the policy and the public on the state and outlook of the environment, there is a pressing need for guidance in assessing and communicating uncertainties. This need extends beyond the quantitative assessment of uncertainties in model results, and focuses on the entire process of environmental assessment, running from problem framing towards reporting the results of the study. Using the Netherlands Environmental Assessment Agency (RIVM/MNP) as a case, the development, structure and content of such a guidance system is highlighted. Conditions for a successful implementation of the guidance system are discussed, and some prospects for future work are outlined.

On the sensitivity of total electron content (TEC) to upper atmospheric/ionospheric parameters

The total electron content (TEC) is a key ionospheric parameter for various space weather applications. Over the last decade an extensive database of TEC measurements has become available from both space- and ground-based observations, and these measurements have established the general morphology of the global TEC distributions. In particular, the TOPEX TEC measurements have shown strong longitudinal variations of TEC in addition to the observed day-to-day variabilities. To better understand the observed TEC variations and to better guide its modeling, we have studied the sensitivity of quiet-time TEC to the following key atmospheric and ionospheric parameters: neutral density, neutral wind, plasma temperatures, plasmaspheric flux, and the O +–O collision frequency. These parameters are often only roughly known and can cause large uncertainties in model results. For this study, we have developed a numerical mid-latitude ionospheric model, which solves the momentum and continuity equations for the O + density and a simplified set of equations for the H + density. To obtain TEC, the calculated ion densities have been integrated from the bottom altitude (100 km) to the altitude of the TOPEX satellite (1336 km). Our study shows that during the day the neutral wind and the neutral composition have the most important effect on TEC. In particular, the zonal component of the neutral wind can have a large effect on TEC in the southern hemisphere where the magnetic declination angle is large. During the night, most of the above-mentioned parameters can play a significant role in the TEC morphology, except for the plasma temperature, which has only a small effect on TEC. Finally, the TEC varies roughly linearly with respect to all of the parameters except for the neutral wind.

Simulating nonequilibrium transport of atrazine through saturated soil.

Atrazine, an herbicide widely used for selective control of grassy weeds in the fields where maize is grown, is a potential ground water contaminant in China and, consequently, there is interest in predicting its mobility in agricultural soils. In this study, we determined the nonequilibrium transport characteristics of atrazine in Shahe soil (Beijing sandy loam) using the advection-dispersion equation, and using a sensitivity analysis, we evaluated the contribution of the uncertainty in a given input parameter to the overall uncertainty in model results. The asymmetrical shape and tailing of the atrazine breakthrough curve (BTC) showed that atrazine was subject to nonequilibrium transport. The observed atrazine BTC was best fitted by the chemical nonequilibrium model with a nonlinear least-squares optimization approach. Results from the sensitivity analysis indicated that the retardation factor was the most sensitive parameter. Considering the reliability of the estimated parameters, the best fit to the atrazine BTC was obtained by fixing the retardation factor based on the linear distribution coefficient, and by calculating the dispersion coefficient from the bromide BTC and the average pore water velocity from the measured data; nonequilibrium parameters were the only unknown parameters that were optimized. Model verification procedures were based on best-fit parameters optimized from one soil column experiment and applied to simulate the transport of atrazine in the duplicate experiment. The results showed there was good agreement between measured and simulated concentrations for atrazine leaching in the soil column.

Simulation of transport and chemical transformations in the atmospheric boundary layer review on the past 20 years developments in science and practice

The scientific progress in simulating transport and chemical transformations of tracers in the atmospheric boundary layer is summarised, starting from the 1980s. An overview on the current status of boundary layer resolving transport models and their use in practice is given. Selected model results are presented in comparison to measured data. Some examples for the uncertainty of model results are discussed. Perspectives on future developments of transport models for the atmospheric boundary layer are given.

The Importance of Classification Differences and Spatial Resolution of Land Cover Data in the Uncertainty in Model Results over Boreal Ecosystems

Abstract One of the governing scientific objectives of the Boreal Ecosystem–Atmosphere Study (BOREAS) is the development of methods for applying process models over large spatial scales using remote sensing and other integrative modeling techniques. This paper presents the first step in a modeling strategy that focuses on scaling a point model up to the BOREAS regional scale. The objective of this paper is to compare the effect of differences in spatial resolution of land cover data to land–atmosphere model results relative to the effect of differences in land cover sensors and classification schemes. The analysis suggests that the uncertainty in model results arises mainly from the uncertainty in the land cover classification and that the lack of spatial resolution has a lower effect. Overall, an uncertainty of approximately 15% in modeled energy and water balance fluxes and states has to be assigned because of the uncertainty in land cover classification.