Computers Geosciences Uncertainty and Sensitivity in Surface Dynamics Modeling

COMPUTERS & GEOSCIENCES Uncertainty and Sensitivity in Surface Dynamics Modeling

CSDMS annual meeting 2014 Uncertainty and Sensitivity in Surface Dynamics Modeling took place May 20-22, 2014 in Boulder Colorado. One of the outcomes was a special issue of Computers & Geosciences, volume 90 part B, ISSN 0098-3004, published April, 2016. Below is an overview of the papers with their abstracts.
We would like to thank all authors as well as the reviewers for their effort!

Content

Uncertainty and Sensitivity in Surface Dynamics Modeling Albert J. Kettner and James P.M. Syvitski

No abstract is available for this article. Albert J. Kettner and James P.M. Syvitski, 2013. Uncertainty and Sensitivity in Surface Dynamics Modeling, Computers & Geosciences, V.90, Part B, 1-5. DOI: 10.1016/j.cageo.2016.03.003

Uncertainty quantification in modeling earth surface processes: more applicable for some types of models than for others A. Brad Murray, Nicole M. Gasparini, Evan B. Goldstein, and Mick van der Wegen

In Earth-surface science, numerical models are used for a range of purposes, from making quantitatively accurate predictions for practical or scientific purposes (‘simulation’ models) to testing hypotheses about the essential causes of poorly understood phenomena (‘exploratory’ models). We argue in this contribution that whereas established methods for uncertainty quantification (UQ) are appropriate (and crucial) for simulation models, their application to exploratory models are less straightforward, and in some contexts not relevant. Because most models fall between the end members of simulation and exploratory models, examining the model contexts under which UQ is most and least appropriate is needed. Challenges to applying state-of-the-art UQ to Earth-surface science models center on quantifying ‘model-form’ uncertainty—the uncertainty in model predictions related to model imperfections. These challenges include: 1) the difficulty in deterministically comparing model predictions to observations when positive feedbacks and associated autogenic dynamics (a.k.a. ‘free’ morphodynamics) determine system behavior over the timescales of interest (a difficulty which could be mitigated in a UQ approach involving statistical comparisons); 2) the lack of available data sets at sufficiently large space and/or time scales; 3) the inability to disentangle uncertainties arising from model parameter values and model form in some cases; and 4) the inappropriateness of model ‘validation’ in the UQ sense for models toward the exploratory end member of the modeling spectrum. A. Brad Murray, Nicole M. Gasparini, Evan B. Goldstein, and Mick van der Wegen, 2013. Uncertainty quantification in modeling earth surface processes: more applicable for some types of models than for others, Computers & Geosciences, V.90, Part B, 6-16. DOI: 10.1016/j.cageo.2016.02.008

Morphological impact of a storm can be predicted three days ahead F. Baart, M. van Ormondt, J.S.M. van Thiel de Vries, and M. van Koningsveld

People living behind coastal dunes depend on the strength and resilience of dunes for their safety. Forecasts of hydrodynamic conditions and morphological change on a timescale of several days can provide essential information to protect lives and property. In order for forecasts to protect they need be relevant, accurate, provide lead time, and information on confidence. Here we show how confident one can be in morphological predictions of several days ahead. The question is answered by assessing the forecast skill as a function of lead time. The study site in the town of Egmond, the Netherlands, where people depend on the dunes for their safety, is used because it is such a rich data source, with a history of forecasts, tide gauges and bathymetry measurements collected by video cameras. Even though the forecasts are on a local scale, the methods are generally applicable. It is shown that the intertidal beach volume change can be predicted up to three days ahead. F. Baart, M. van Ormondt, J.S.M. van Thiel de Vries, and M. van Koningsveld, 2013. Morphological impact of a storm can be predicted three days ahead, Computers & Geosciences, V.90, Part B, 17-23. DOI: 10.1016/j.cageo.2015.11.011

Shelf sediment transport during hurricanes Katrina and Rita Kehui Xu, Rangley C. Mickey, Qin Chen, Courtney K. Harris, Robert D. Hetland, Kelin Hu, and Jiaze Wang

Hurricanes can greatly modify the sedimentary record, but our coastal scientific community has rather limited capability to predict hurricane-induced sediment deposition. A three-dimensional sediment transport model was developed in the Regional Ocean Modeling System (ROMS) to study seabed erosion and deposition on the Louisiana shelf in response to Hurricanes Katrina and Rita in the year 2005. Sensitivity tests were performed on both erosional and depositional processes for a wide range of erosional rates and settling velocities, and uncertainty analysis was done on critical shear stresses using the polynomial chaos approximation method. A total of 22 model runs were performed in sensitivity and uncertainty tests. Estimated maximum erosional depths were sensitive to the inputs, but horizontal erosional patterns seemed to be controlled mainly by hurricane tracks, wave–current combined shear stresses, seabed grain sizes, and shelf bathymetry. During the passage of two hurricanes, local resuspension and deposition dominated the sediment transport mechanisms. Hurricane Katrina followed a shelf-perpendicular track before making landfall and its energy dissipated rapidly within about 48 h along the eastern Louisiana coast. In contrast, Hurricane Rita followed a more shelf-oblique track and disturbed the seabed extensively during its 84-h passage from the Alabama–Mississippi border to the Louisiana–Texas border. Conditions to either side of Hurricane Rita’s storm track differed substantially, with the region to the east having stronger winds, taller waves and thus deeper erosions. This study indicated that major hurricanes can disturb the shelf at centimeter to meter levels. Each of these two hurricanes suspended seabed sediment mass that far exceeded the annual sediment inputs from the Mississippi and Atchafalaya Rivers, but the net transport from shelves to estuaries is yet to be determined. Future studies should focus on the modeling of sediment exchange between estuaries and shelves and the field measurement of erosional rates and settling velocities. Kehui Xu, Rangley C. Mickey, Qin Chen, Courtney K. Harris, Robert D. Hetland, Kelin Hu, and Jiaze Wang, 2013. Shelf sediment transport during hurricanes Katrina and Rita, Computers & Geosciences, V.90, Part B, 24-39. DOI: 10.1016/j.cageo.2015.10.009

Reprint of: A numerical investigation of fine sediment resuspension in the wave boundary layer—Uncertainties in particle inertia and hindered settling Zhen Cheng, Xiao Yu, Tian-Jian Hsu, and S. Balachandar

The wave bottom boundary layer is a major conduit delivering fine terrestrial sediments to continental margins. Hence, studying fine sediment resuspensions in the wave boundary layer is crucial to the understanding of various components of the earth system, such as carbon cycles. By assuming the settling velocity to be a constant in each simulation, previous turbulence-resolving numerical simulations reveal the existence of three transport modes in the wave boundary layer associated with sediment availabilities. As the sediment availability and hence the sediment-induced stable stratification increases, a sequence of transport modes, namely, (I) well-mixed transport, (II) formulation of lutocline resembling a two-layer system, and (III) completely laminarized transport are observed. In general, the settling velocity is a flow variable due to hindered settling and particle inertia effects. Present numerical simulations including the particle inertia suggest that for a typical wave condition in continental shelves, the effect of particle inertia is negligible. Through additional numerical experiments, we also confirm that the particle inertia tends (up to the Stokes number St = 0.2) to attenuate flow turbulence. On the other hand, for flocs with lower gelling concentrations, the hindered settling can play a key role in sustaining a large amount of suspended sediments and results in the laminarized transport (III). For the simulation with a very significant hindered settling effect due to a low gelling concentration, results also indicate the occurrence of gelling ignition, a state in which the erosion rate is always higher than the deposition rate. A sufficient condition for the occurrence of gelling ignition is hypothesized for a range of wave intensities as a function of sediment/floc properties and erodibility parameters. Zhen Cheng, Xiao Yu, Tian-Jian Hsu, and S. Balachandar, 2013. Reprint of: A numerical investigation of fine sediment resuspension in the wave boundary layer—Uncertainties in particle inertia and hindered settling, Computers & Geosciences, V.90, Part B, 40-56. DOI: 10.1016/j.cageo.2015.11.003

Sensitivity of a third generation wave model to wind and boundary condition sources and model physics: A case study from the South Atlantic Ocean off Brazil coast S. Mostafa Siadatmousavi, Felix Jose, and Graziela Miot da Silva

Three different packages describing the white capping dissipation process, and the corresponding energy input from wind to wave were used to study the surface wave dynamics in South Atlantic Ocean, close to the Brazilian coast. A host of statistical parameters were computed to evaluate the performance of wave model in terms of simulated bulk wave parameters. Wave measurements from a buoy deployed off Santa Catarina Island, Southern Brazil and data along the tracks of Synthetic Aperture Radars were compared with simulated bulk wave parameters; especially significant wave height, for skill assessment of different packages. It has been shown that using a single parameter representing the performance of source and sink terms in the wave model, or relying on data from only one period of simulations for model validation and skill assessment would be misleading. The model sensitivity to input parameters such as time step and grid size were addressed using multiple datasets. The wind data used for the simulation were obtained from two different sources, and provided the opportunity to evaluate the importance of input data quality. The wind speed extracted from remote sensing satellites was compared to wind datasets used for wave modeling. The simulation results showed that the wind quality and its spatial resolution is highly correlated to the quality of model output. Two different sources of wave information along the open boundaries of the model domain were used for skill assessment of a high resolution wave model for the study area. It has been shown, based on the sensitivity analysis, that the effect of using different boundary conditions would decrease as the distance from the open boundary increases; however, the difference were still noticeable at the buoy location which was located 200–300 km away from the model boundaries; but restricted to the narrow band of the low frequency wave spectrum. S. Mostafa Siadatmousavi, Felix Jose, and Graziela Miot da Silva, 2013. Sensitivity of a third generation wave model to wind and boundary condition sources and model physics: A case study from the South Atlantic Ocean off Brazil coast, Computers & Geosciences, V.90, Part B, 57-65. DOI: 10.1016/j.cageo.2015.09.025

Understanding hydrological flow paths in conceptual catchment models using uncertainty and sensitivity analysis Eva M. Mockler, Fiachra E. O’Loughlin, and Michael Bruen

Increasing pressures on water quality due to intensification of agriculture have raised demands for environmental modeling to accurately simulate the movement of diffuse (nonpoint) nutrients in catchments. As hydrological flows drive the movement and attenuation of nutrients, individual hydrological processes in models should be adequately represented for water quality simulations to be meaningful. In particular, the relative contribution of groundwater and surface runoff to rivers is of interest, as increasing nitrate concentrations are linked to higher groundwater discharges. These requirements for hydrological modeling of groundwater contribution to rivers initiated this assessment of internal flow path partitioning in conceptual hydrological models. In this study, a variance based sensitivity analysis method was used to investigate parameter sensitivities and flow partitioning of three conceptual hydrological models simulating 31 Irish catchments. We compared two established conceptual hydrological models (NAM and SMARG) and a new model (SMART), produced especially for water quality modeling. In addition to the criteria that assess streamflow simulations, a ratio of average groundwater contribution to total streamflow was calculated for all simulations over the 16 year study period. As observations time-series of groundwater contributions to streamflow are not available at catchment scale, the groundwater ratios were evaluated against average annual indices of base flow and deep groundwater flow for each catchment. The exploration of sensitivities of internal flow path partitioning was a specific focus to assist in evaluating model performances. Results highlight that model structure has a strong impact on simulated groundwater flow paths. Sensitivity to the internal pathways in the models are not reflected in the performance criteria results. This demonstrates that simulated groundwater contribution should be constrained by independent data to ensure results within realistic bounds if such models are to be used in the broader environmental sustainability decision making context. Eva M. Mockler, Fiachra E. O’Loughlin, and Michael Bruen, 2013. Understanding hydrological flow paths in conceptual catchment models using uncertainty and sensitivity analysis, Computers & Geosciences, V.90, Part B, 66-77. DOI: 10.1016/j.cageo.2015.08.015

Reprint of: Active subspaces for sensitivity analysis and dimension reduction of an integrated hydrologic model Jennifer L. Jefferson, James M. Gilbert, Paul G. Constantine, and Reed M. Maxwell

Integrated hydrologic models coupled to land surface models require several input parameters to characterize the land surface and to estimate energy fluxes. Uncertainty of input parameter values is inherent in any model and the sensitivity of output to these uncertain parameters becomes an important consideration. To better understand these connections in the context of hydrologic models, we use the ParFlow-Common Land Model (PF-CLM) to estimate energy fluxes given variations in 19 vegetation and land surface parameters over a 144-hour period of time. Latent, sensible and ground heat fluxes from bare soil and grass vegetation were estimated using single column and tilted-v domains. Energy flux outputs, along with the corresponding input parameters, from each of the four scenario simulations were evaluated using active subspaces. The active subspace method considers parameter sensitivity by quantifying a weight for each parameter. The method also evaluates the potential for dimension reduction by identifying the input–output relationship through the active variable – a linear combination of input parameters. The aerodynamic roughness length was the most important parameter for bare soil energy fluxes. Multiple parameters were important for energy fluxes from vegetated surfaces and depended on the type of energy flux. Relationships between land surface inputs and output fluxes varied between latent, sensible and ground heat, but were consistent between domain setup (i.e., with or without lateral flow) and vegetation type. A quadratic polynomial was used to describe the input–output relationship for these energy fluxes. The reduced-dimension model of land surface dynamics can be compared to observations or used to solve the inverse problem. Considering this work as a proof-of-concept, the active subspace method can be applied and extended to a range of domain setups, land cover types and time periods to obtain a reduced-form representation of any output of interest, provided that an active subspace exists. Jennifer L. Jefferson, James M. Gilbert, Paul G. Constantine, and Reed M. Maxwell, 2013. Reprint of: Active subspaces for sensitivity analysis and dimension reduction of an integrated hydrologic model, Computers & Geosciences, V.90, Part B, 78-89. DOI: 10.1016/j.cageo.2015.11.002

Hydrological model uncertainty due to spatial evapotranspiration estimation methods Xuan Yu, Anna Lamačová, Christopher Duffy, Pavel Krám, and Jakub Hruška

Evapotranspiration (ET) continues to be a difficult process to estimate in seasonal and long-term water balances in catchment models. Approaches to estimate ET typically use vegetation parameters (e.g., leaf area index [LAI], interception capacity) obtained from field observation, remote sensing data, national or global land cover products, and/or simulated by ecosystem models. In this study we attempt to quantify the uncertainty that spatial evapotranspiration estimation introduces into hydrological simulations when the age of the forest is not precisely known. The Penn State Integrated Hydrologic Model (PIHM) was implemented for the Lysina headwater catchment, located 50°03′N, 12°40′E in the western part of the Czech Republic. The spatial forest patterns were digitized from forest age maps made available by the Czech Forest Administration. Two ET methods were implemented in the catchment model: the Biome-BGC forest growth sub-model (1-way coupled to PIHM) and with the fixed-seasonal LAI method. From these two approaches simulation scenarios were developed. We combined the estimated spatial forest age maps and two ET estimation methods to drive PIHM. A set of spatial hydrologic regime and streamflow regime indices were calculated from the modeling results for each method. Intercomparison of the hydrological responses to the spatial vegetation patterns suggested considerable variation in soil moisture and recharge and a small uncertainty in the groundwater table elevation and streamflow. The hydrologic modeling with ET estimated by Biome-BGC generated less uncertainty due to the plant physiology-based method. The implication of this research is that overall hydrologic variability induced by uncertain management practices was reduced by implementing vegetation models in the catchment models. Xuan Yu, Anna Lamačová, Christopher Duffy, Pavel Krám, and Jakub Hruška, 2013. Hydrological model uncertainty due to spatial evapotranspiration estimation methods, Computers & Geosciences, V.90, Part B, 90-101. DOI: 10.1016/j.cageo.2015.05.006

Multi-scale characterization of topographic anisotropy S.G. Roy, P.O. Koons, B. Osti, P. Upton, and G.E. Tucker

We present the every-direction variogram analysis (EVA) method for quantifying orientation and scale dependence of topographic anisotropy to aid in differentiation of the fluvial and tectonic contributions to surface evolution. Using multi-directional variogram statistics to track the spatial persistence of elevation values across a landscape, we calculate anisotropy as a multiscale, direction-sensitive variance in elevation between two points on a surface. Tectonically derived topographic anisotropy is associated with the three-dimensional kinematic field, which contributes (1) differential surface displacement and (2) crustal weakening along fault structures, both of which amplify processes of surface erosion. Based on our analysis, tectonic displacements dominate the topographic field at the orogenic scale, while a combination of the local displacement and strength fields are well represented at the ridge and valley scale. Drainage network patterns tend to reflect the geometry of underlying active or inactive tectonic structures due to the rapid erosion of faults and differential uplift associated with fault motion. Regions that have uniform environmental conditions and have been largely devoid of tectonic strain, such as passive coastal margins, have predominantly isotropic topography with typically dendritic drainage network patterns. Isolated features, such as stratovolcanoes, are nearly isotropic at their peaks but exhibit a concentric pattern of anisotropy along their flanks. The methods we provide can be used to successfully infer the settings of past or present tectonic regimes, and can be particularly useful in predicting the location and orientation of structural features that would otherwise be impossible to elude interpretation in the field. Though we limit the scope of this paper to elevation, EVA can be used to quantify the anisotropy of any spatially variable property. S.G. Roy, P.O. Koons, B. Osti, P. Upton, and G.E. Tucker, 2013. Multi-scale characterization of topographic anisotropy, Computers & Geosciences, V.90, Part B, 102-116. DOI: 10.1016/j.cageo.2015.09.023

Predicting uncertainty in sediment transport and landscape evolution – the influence of initial surface conditions G.R. Hancock, T.J. Coulthard, and J.B.C. Lowry

Numerical landscape evolution models were initially developed to examine natural catchment hydrology and geomorphology and have become a common tool to examine geomorphic behaviour over a range of time and space scales. These models all use a digital elevation model (DEM) as a representation of the landscape surface and a significant issue is the quality and resolution of this surface. Here we focus on how subtle perturbations or roughness on the DEM surface can produce alternative model results. This study is carried out by randomly varying the elevations of the DEM surface and examining the effect on sediment transport rates and geomorphology for a proposed rehabilitation design for a post-mining landscape using multiple landscape realisations with increasing magnitudes of random changes. We show that an increasing magnitude of random surface variability does not appear to have any significant effect on sediment transport over millennial time scales. However, the random surface variability greatly changes the temporal pattern or delivery of sediment output. A significant finding is that all simulations at the end of the 10,000 year modelled period are geomorphologically similar and present a geomorphological equifinality. However, the individual patterns of erosion and deposition were different for repeat simulations with a different sequence of random perturbations. The alternative positions of random perturbations strongly influence local patterns of hillslope erosion and evolution together with the pattern and behaviour of deposition. The findings demonstrate the complex feedbacks that occur even within a simple modelled system. G.R. Hancock, T.J. Coulthard, and J.B.C. Lowry, 2013. Predicting uncertainty in sediment transport and landscape evolution – the influence of initial surface conditions, Computers & Geosciences, V.90, Part B, 117-130. DOI: 10.1016/j.cageo.2011.12.004

LORICA – A new model for linking landscape and soil profile evolution: Development and sensitivity analysis Arnaud J.A.M. Temme, and Tom Vanwalleghem

Soils and landscapes evolve in tandem. Landscape position is a strong determinant of vertical soil development, which has often been formalized in the catena concept. At the same time, soil properties are strong determinants of geomorphic processes such as overland erosion, landsliding and creep. We present a new soilscape evolution model; LORICA, to study these numerous interactions between soil and landscape development. The model is based on the existing landscape evolution model LAPSUS and the soil formation model MILESD. The model includes similar soil formation processes as MILESD, but the main novelties include the consideration of more layers and the dynamic adaption of the number of layers as a function of the soil profile's heterogeneity. New processes in the landscape evolution component include a negative feedback of vegetation and armouring and particle size selectivity of the erosion–deposition process. In order to quantify these different interactions, we present a full sensitivity analysis of the input parameters. First results show that the model successfully simulates various soil–landscape interactions, leading to outputs where the surface changes in the landscape clearly depend on soil development, and soil changes depend on landscape location. Sensitivity analysis of the model confirms that soil and landscape interact: variables controlling amount and position of fine clay have the largest effect on erosion, and erosion variables control among others the amount of chemical weathering. These results show the importance of particle size distribution, and especially processes controlling the presence of finer clay particles that are easily eroded, both for the resulting landscape form as for the resulting soil profiles. Further research will have to show whether this is specific to the boundary conditions of this study or a general phenomenon. Arnaud J.A.M. Temme, and Tom Vanwalleghem, 2013. LORICA – A new model for linking landscape and soil profile evolution: Development and sensitivity analysis, Computers & Geosciences, V.90, Part B, 131-143. DOI: 10.1016/j.cageo.2015.08.004

First-order uncertainty analysis using Algorithmic Differentiation of morphodynamic models Catherine Villaret, Rebekka Kopmann, David Wyncoll, Jan Riehme, Uwe Merkel, and Uwe Naumann

We present here an efficient first-order second moment method using Algorithmic Differentiation (FOSM/AD) which can be applied to quantify uncertainty/sensitivities in morphodynamic models. Changes with respect to variable flow and sediment input parameters are estimated with machine accuracy using the technique of Algorithmic Differentiation (AD). This method is particularly attractive for process-based morphodynamic models like the Telemac-2D/Sisyphe model considering the large number of input parameters and CPU time associated to each simulation. The FOSM/AD method is applied to identify the relevant processes in a trench migration experiment (van Rijn, 1987). A Tangent Linear Model (TLM) of the Telemac-2D/Sisyphe morphodynamic model (release 6.2) was generated using the AD-enabled NAG Fortran compiler. One single run of the TLM is required per variable input parameter and results are then combined to calculate the total uncertainty. The limits of the FOSM/AD method have been assessed by comparison with Monte Carlo (MC) simulations. Similar results were obtained assuming small standard deviation of the variable input parameters. Both settling velocity and grain size have been identified as the most sensitive input parameters and the uncertainty as measured by the standard deviation of the calculated bed evolution increases with time. Catherine Villaret, Rebekka Kopmann, David Wyncoll, Jan Riehme, Uwe Merkel, and Uwe Naumann, 2013. First-order uncertainty analysis using Algorithmic Differentiation of morphodynamic models, Computers & Geosciences, V.90, Part B, 144-151. DOI: 10.1016/j.cageo.2015.10.012

Towards uncertainty quantification and parameter estimation for Earth system models in a component-based modeling framework Scott D. Peckham, Anna Kelbert, Mary C. Hill, and Eric W.H. Hutton

Component-based modeling frameworks make it easier for users to access, configure, couple, run and test numerical models. However, they do not typically provide tools for uncertainty quantification or data-based model verification and calibration. To better address these important issues, modeling frameworks should be integrated with existing, general-purpose toolkits for optimization, parameter estimation and uncertainty quantification. This paper identifies and then examines the key issues that must be addressed in order to make a component-based modeling framework interoperable with general-purpose packages for model analysis. As a motivating example, one of these packages, DAKOTA, is applied to a representative but nontrivial surface process problem of comparing two models for the longitudinal elevation profile of a river to observational data. Results from a new mathematical analysis of the resulting nonlinear least squares problem are given and then compared to results from several different optimization algorithms in DAKOTA. Scott D. Peckham, Anna Kelbert, Mary C. Hill, and Eric W.H. Hutton, 2013. Towards uncertainty quantification and parameter estimation for Earth system models in a component-based modeling framework, Computers & Geosciences, V.90, Part B, 152-161. DOI: 10.1016/j.cageo.2016.03.005

Exploring temporal and functional synchronization in integrating models: A sensitivity analysis Getachew F. Belete, and Alexey Voinov

When integrating independently built models, we may encounter components that describe the same processes or groups of processes using different assumptions and formalizations. The time stepping in component models can also be very different depending upon the temporal resolution chosen. Even if this time stepping is handled outside of the components (as assumed by good practice of component building) the use of inappropriate temporal synchronization can produce either major run-time redundancy or loss of model accuracy. While components may need to be run asynchronously, finding the right times for them to communicate and exchange information becomes a challenge. We are illustrating this by experimenting with a couple of simple component models connected by means of Web services to explore how the timing of their input–output data exchange affects the performance of the overall integrated model. We have also considered how to best communicate information between components that use a different formalism for the same processes. Currently there are no generic recommendations for component synchronization but including sensitivity analysis for temporal and functional synchronization should be recommended as an essential part of integrated modeling. Getachew F. Belete, and Alexey Voinov, 2013. Exploring temporal and functional synchronization in integrating models: A sensitivity analysis, Computers & Geosciences, V.90, Part B, 162-171. DOI: 10.1016/j.cageo.2015.09.006