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The evaluation and verification of landscape evolution models (LEMs) has long been limited by a lack of suitable observational data and statistical measures which can fully capture the complexity of landscape changes. This lack of data limits the use of objective function based evaluation prolific in other modelling fields, and restricts the application of sensitivity analyses in the models and the consequent assessment of model uncertainties. To overcome this deficiency, a novel model function approach has been developed, with each model function representing an aspect of model behaviour, which allows for the application of sensitivity analyses. The model function approach is used to assess the relative sensitivity of the CAESAR-Lisflood LEM to a set of model parameters by applying the Morris method sensitivity analysis for two contrasting catchments. The test revealed that the model was most sensitive to the choice of the sediment transport formula for both catchments, and that each parameter influenced model behaviours differently, with model functions relating to internal geomorphic changes responding in a different way to those relating to the sediment yields from the catchment outlet. The model functions proved useful for providing a way of evaluating the sensitivity of LEMs in the absence of data and methods for an objective function approach.
Each simulation algorithm, including Truncated Gaussian Simulation, Sequential Indicator Simulation and Indicator Kriging is characterized by different operating modes, which variably influence the facies proportion, distribution and association of digital outcrop models, as shown in clastic sediments. A detailed study of carbonate heterogeneity is then crucial to understanding these differences and providing rules for carbonate modelling. Through a continuous exposure of Bajocian carbonate strata, a study window (320 m long, 190 m wide and 30 m thick) was investigated and metre-scale lithofacies heterogeneity was captured and modelled using closely-spaced sections. Ten lithofacies, deposited in a shallow-water carbonate-dominated ramp, were recognized and their dimensions and associations were documented. Field data, including height sections, were georeferenced and input into the model. Four models were built in the present study. Model A used all sections and Truncated Gaussian Simulation during the stochastic simulation. For the three other models, Model B was generated using Truncated Gaussian Simulation as for Model A, Model C was generated using Sequential Indicator Simulation and Model D was generated using Indicator Kriging. These three additional models were built by removing two out of eight sections from data input. The removal of sections allows direct insights on geological uncertainties at inter-well spacings by comparing modelled and described sections. Other quantitative and qualitative comparisons were carried out between models to understand the advantages/disadvantages of each algorithm. Model A is used as the base case. Indicator Kriging (Model D) simplifies the facies distribution by assigning continuous geological bodies of the most abundant lithofacies to each zone. Sequential Indicator Simulation (Model C) is confident to conserve facies proportion when geological heterogeneity is complex. The use of trend with Truncated Gaussian Simulation is a powerful tool for modelling well-defined spatial facies relationships. However, in shallow-water carbonate, facies can coexist and their association can change through time and space. The present study shows that the scale of modelling (depositional environment or lithofacies) involves specific simulation constraints on shallow-water carbonate modelling methods.
Predictability of hydrologic response at the plot and catchment scales: Role of initial conditions
(2004)
This paper examines the effect of uncertain initial soil moisture on hydrologic response at the plot scale (1 m2) and the catchment scale (3.6 km2) in the presence of threshold transitions between matrix and preferential flow. We adopt the concepts of microstates and macrostates from statistical mechanics. The microstates are the detailed patterns of initial soil moisture that are inherently unknown, while the macrostates are specified by the statistical distributions of initial soil moisture that can be derived from the measurements typically available in field experiments. We use a physically based model and ensure that it closely represents the processes in the Weiherbach catchment, Germany. We then use the model to generate hydrologic response to hypothetical irrigation events and rainfall events for multiple realizations of initial soil moisture microstates that are all consistent with the same macrostate. As the measures of uncertainty at the plot scale we use the coefficient of variation and the scaled range of simulated vertical bromide transport distances between realizations. At the catchment scale we use similar statistics derived from simulated flood peak discharges. The simulations indicate that at both scales the predictability depends on the average initial soil moisture state and is at a minimum around the soil moisture value where the transition from matrix to macropore flow occurs. The predictability increases with rainfall intensity. The predictability increases with scale with maximum absolute errors of 90 and 32% at the plot scale and the catchment scale, respectively. It is argued that even if we assume perfect knowledge on the processes, the level of detail with which one can measure the initial conditions along with the nonlinearity of the system will set limits to the repeatability of experiments and limits to the predictability of models at the plot and catchment scales.