Lucy Marshall

Object-oriented crop classification using multitemporal ETM+ SLC-off imagery and random forest

The utility of Enhanced Thematic Mapper Plus (ETM+) has been diminished since the 2003 scan-line corrector (SLC) failure. Uncorrected images have data gaps of approximately 22% and gap-filling schemes have been developed to improve their usability. We present a method to classify a northeast Montana agricultural landscape using ETM+ SLC-off imagery without gap-filling. We use multitemporal data analysis and employ an object-oriented approach to define objects, agricultural fields, with cadastral data. This approach was assessed by comparison to a pixel-based approach. Results indicate that an ETM+ SLC-off image can be classified with better than 85% overall accuracy without gap-filling.

Exploring uncertainty and model predictive performance concepts via a modular snowmelt-runoff modeling framework

Model selection is an extremely important aspect of many hydrologic modeling studies because of the complexity, variability, and uncertainty that surrounds the current understanding of watershed-scale systems. However, development and implementation of a complete precipitation-runoff modeling framework, from model selection to calibration and uncertainty analysis, are rarely confronted. This paper introduces a modular precipitation-runoff modeling framework that has been developed and applied to a research site in Central Montana, USA. The case study focuses on an approach to hydrologic modeling that considers model development, selection, calibration, uncertainty analysis, and overall assessment. The results of this case study suggest that a modular framework is useful in identifying the interactions between and among different process representations and their resultant predictions of stream discharge. Such an approach can strengthen model building and address an oft ignored aspect of predictive uncertainty; namely, model structural uncertainty.

Hydrologic Modeling in Dynamic Catchments: A Data Assimilation Approach

The transferability of conceptual hydrologic models in time is often limited by both their structural deficiencies and adopted parameterizations. Adopting a stationary set of model parameters ignores biases introduced by the data used to derive them, as well as any future changes to catchment conditions. Although time invariance of model parameters is one of the hallmarks of a high quality hydrologic model, very few (if any) models can achieve this due to their inherent limitations. It is therefore proposed to consider parameters as potentially time varying quantities, which can evolve according to signals in hydrologic observations. In this paper, we investigate the potential for Data Assimilation (DA) to detect known temporal patterns in model parameters from streamflow observations. It is shown that the success of the DA algorithm is strongly dependent on the method used to generate background (or prior) parameter ensembles (also referred to as the parameter evolution model). A range of traditional parameter evolution techniques are considered and found to be problematic when multiple parameters with complex time variations are estimated simultaneously. Two alternative methods are proposed, the first is a Multilayer approach that uses the EnKF to estimate hyperparameters of the temporal structure, based on apriori knowledge of the form of nonstationarity. The second is a Locally Linear approach that uses local linear estimation and requires no assumptions of the form of parameter nonstationarity. Both are shown to provide superior results in a range of synthetic case studies, when compared to traditional parameter evolution techniques.

Approximate Bayesian Computation and Bayes’ Linear Analysis: Toward High-Dimensional ABC

Bayes’ linear analysis and approximate Bayesian computation (ABC) are techniques commonly used in the Bayesian analysis of complex models. In this article, we connect these ideas by demonstrating that regression-adjustment ABC algorithms produce samples for which first- and second-order moment summaries approximate adjusted expectation and variance for a Bayes’ linear analysis. This gives regression-adjustment methods a useful interpretation and role in exploratory analysis in high-dimensional problems. As a result, we propose a new method for combining high-dimensional, regression-adjustment ABC with lower-dimensional approaches (such as using Markov chain Monte Carlo for ABC). This method first obtains a rough estimate of the joint posterior via regression-adjustment ABC, and then estimates each univariate marginal posterior distribution separately in a lower-dimensional analysis. The marginal distributions of the initial estimate are then modified to equal the separately estimated marginals, thereby providing an improved estimate of the joint posterior. We illustrate this method with several examples. Supplementary materials for this article are available online.

Efficient hydrological model parameter optimization with Sequential Monte Carlo sampling

Bayesian inference provides an ideal platform for assessing parameter uncertainty for complex physical models, such as conceptual hydrological models. Sequential Monte Carlo (SMC) samplers are well suited for its implementation as they are effective in sampling from posterior distributions with the non-linear dependency structures and multiple modes often present in hydrological models. A challenge in implementing SMC samplers is in the construction of a suitable sequence of intermediary distributions leading to the posterior distribution, in such a way that the sampler performs both efficiently in that minimal computation is needed, and robustly in that the samplers particle population is effectively maintained. In this article we demonstrate that naive implementation of an SMC sampler in a hydrological model can cause the sampler to collapse. To address this, we propose a new method of dynamically constructing the transition path between the intermediary distributions that effectively increases the amount of computation at the point where it is needed to avoid this collapse. We analyse the performance of our approach through the analysis of real and simulated hydrological data, and discuss related SMC sampler implementation issues. In addition we consider the question of the appropriate number of particles in the sampler as the dimensionality of the model increases.

Fire and flood expand the floodplain shifting habitat mosaic concept

The floodplain shifting habitat mosaic concept suggests that habitat patch dynamics are influenced by hydrologic disturbances driven by flood pulses of sufficient power to initiate incipient motion of the substratum and maintain cut-and-fill alluviation of the channel and banks. However, floodplain habitat mosaics are subject to other important landscape-scale disturbance regimes. In the Rocky Mountains of the USA and Canada, fire also affects floodplain habitat patch composition. The floodplain exists at the intersection of disturbance regimes that shape the riverscape and those that shape the landscape. We extended the shifting habitat mosaic concept by examining the effects of multiple disturbance elements on habitat patch composition across the aquatic–terrestrial ecotone of the North Fork of the Flathead River, a free-flowing river in southeastern British Columbia, Canada, and northwestern Montana, USA. We used remotely sensed imagery, meteorological records, empirical and modeled rainfall-runoff data, extent and frequency of past wildfires, and anthropogenic landuse data for 1991–2013 to examine the relationships among hydrology, fire, landuse, geomorphic position, and floodplain habitat patch dynamics. Exploratory path analysis revealed that fire had the strongest total effect and stream power and geomorphic position had moderate total effects on the variability of floodplain habitat patch composition along the North Fork. These 3 factors explained 13 to 26% of the variance in floodplain habitat patch composition between study reaches across all years. We used graphical analysis to examine the locations and intensity of disturbance and recovery pathways across floodplain transition zones throughout the study period. Our results support the hypothesis that hydrologic and fire disturbances and recovery pathways maintain the shifting habitat mosaic across the floodplains of this river system.

Predicting hydrologic response through a hierarchical catchment knowledgebase: A Bayes empirical Bayes approach

Making useful Predictions in Ungauged Basins is an incredibly difficult task given the limitations of hydrologic models to represent physical processes appropriately across the heterogeneity within and among different catchments. Here, we introduce a new method for this challenge, Bayes empirical Bayes, that allows for the statistical pooling of information from multiple donor catchments and provides the ability to transfer parametric distributions rather than single parameter sets to the ungauged catchment. Further, the methodology provides an efficient framework with which to formally assess predictive uncertainty at the ungauged catchment. We investigated the utility of the methodology under both synthetic and real data conditions, and with respect to its sensitivity to the number and quality of the donor catchments used. This study highlighted the ability of the hierarchical Bayes empirical Bayes approach to produce expected outcomes in both the synthetic and real data applications. The method was found to be sensitive to the quality (hydrologic similarity) of the donor catchments used. Results were less sensitive to the number of donor catchments, but indicated that predictive uncertainty was best constrained with larger numbers of donor catchments (but still adequate with fewer donors).

A Bayesian method for multi-pollution source water quality model and seasonal water quality management in river segments

Abstract Excessive pollutant discharge from multi-pollution resources can lead to a rise in downriver contaminant concentration in river segments. A multi-pollution source water quality model (MPSWQM) was integrated with Bayesian statistics to develop a robust method for supporting load ( I ) reduction and effective water quality management in the Harbin City Reach of the Songhua River system in northeastern China. The monthly water quality data observed during the period 2005–2010 was analyzed and compared, using ammonia as the study variable. The decay rate ( k ) was considered a key factor in the MPSWQM, and the distribution curve of k was estimated for the whole year. The distribution curves indicated small differences between the marginal distribution of k of each period and that water quality management strategies can be designed seasonally. From the curves, decision makers could pick up key posterior values of k in each month to attain the water quality goal at any specified time. Such flexibility is an effective way to improve the robustness of water quality management. For understanding the potential collinearity of k and I , a sensitivity test of k for I 2i (loadings in segment 2 of the study river) was done under certain water quality goals. It indicated that the posterior distributions of I 2i show seasonal variation and are sensitive to the marginal posteriors of k . Thus, the seasonal posteriors of k were selected according to the marginal distributions and used to estimate I 2i in next water quality management. All kinds of pollutant sources, including polluted branches, point and non-point source, can be identified for multiple scenarios. The analysis enables decision makers to assess the influence of each loading and how best to manage water quality targets in each period. Decision makers can also visualize potential load reductions under different water quality goals. The results show that the proposed method is robust for management of multi-pollutant loadings under different water quality goals to help ensure that the water quality of river segments meets targeted goals.

The ensemble Kalman filter is an ABC algorithm

The ensemble Kalman filter is the method of choice for many difficult high-dimensional filtering problems in meteorology, oceanography, hydrology and other fields. In this note we show that a common variant of the ensemble Kalman filter is an approximate Bayesian computation (ABC) algorithm. This is of interest for a number of reasons. First, the ensemble Kalman filter is an example of an ABC algorithm that predates the development of ABC algorithms. Second, the ensemble Kalman filter is used for very high-dimensional problems, whereas ABC methods are normally applied only in very low-dimensional problems. Third, recent state of the art extensions of the ensemble Kalman filter can also be understood within the ABC framework.

A comparison of methods for discretizing continuous variables in Bayesian Networks

Abstract Bayesian Networks (BNs) are an increasingly popular method for modelling environmental systems. The discretization of continuous variables is often required to use BNs. There are three main methods of discretization; manual, unsupervised, and supervised. Here, we compare and demonstrate each approach with a BN that predicts coastal erosion. Results reveal that supervised discretization methods produced BNs of the highest average predictive skill (73.8%), followed by manual discretization (69.0%) and unsupervised discretization (64.8%). However, each method has specific advantages that may make them more suitable for particular applications. Manual methods can produce physical meaningful BNs, which is favorable in environmental modelling. Supervised methods can autonomously and optimally discretize variables and may be preferred when predictive skill is a modelling priority. Unsupervised methods are computationally simple and versatile. The optimal discretization scheme should consider both the performance and practicality of the scheme.