A data assimilation technique applied to a predator-prey model

Lawson, L. M.; Spitz, Yvette H.; Hofmann, Eileen E.; Long, Robert Bryan

doi:10.1007/bf02460785

Cited by 75 publications

(20 citation statements)

References 24 publications

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“…Knowing that a real-life situation follows a particular model. The parameter estimation [41,42] can be done using one of the many well-established algorithms such as trial-and-error processes, numerical optimization techniques such as conjugate gradient method, trust region methods and genetic algorithms (see [43][44][45]). In this particular problem, we use genetic algorithm to estimate the model parameter (m).…”

Section: Introductionmentioning

confidence: 99%

“…Walmag and Delhez [44] used the trust region methods while the conjugate gradient method has been used by Fashman and Evans [51]. Lawson et al [43] have used adjoint method and also given a description of how the adjoint technique is combined with optimization techniques. Recently, Huang et al [52] has discussed the parameter identification of hydrodynamic-phytoplankton model.…”

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confidence: 99%

“…Model formulation When the model data are not present, a twin experiment [43,44] technique is suggested in the literature to study the system behavior. In twin experiment, first the original problem is solved for known value of the system parameter(s), and the system response is sampled at different time instances.…”

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confidence: 99%

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Dynamical analysis of a prey–predator model with Beddington–DeAngelis type function response incorporating a prey refuge

2014

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This paper discusses a prey-predator model with reserved area. The feeding rate of consumers (predators) per consumer (i.e., functional response) is considered to be Beddington-DeAngelis type. The Beddington-DeAngelis functional response is similar to the Holling type II functional response but contains an extra term describing mutual interference by predators. We investigate the role of reserved region and degree of mutual interference among predators in the dynamics of system. We obtain different conditions that affect the persistence of the system. We also discuss local and global asymptotic stability behavior of various equilibrium solutions to understand the dynamics of the model system. The global asymptotic stability of positive interior equilibrium solution is established using suitable Lyapunov functional. It is found that the Hopf bifurcation occurs when the parameter corresponding to reserved region (i.e., m) crosses some critical value. Our result indicates that the predator species exist so long as prey reserve value (m) does not cross a threshold value and after this value the predator species extinct. To mimic the real-world scenario, we also solve the inverse problem of estimation of model parameter (m) using the sampled data of the system. The results can also be interpreted in different contexts such as resource conservation, pest management and

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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Dynamical analysis of a prey–predator model with Beddington–DeAngelis type function response incorporating a prey refuge

2014

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“…DA techniques, such as the Ensemble Kalman Filter [16], the Particle Filter [17,18] or variational methods like 4D-VAR [19], integrate observations into terrestrial models for an enhanced description of real environmental conditions. Numerous applications of single-state assimilation have already been published, e.g., in the context of the hydrological cycle [20–30], the energy balance [31], plant physiology [32–34], the carbon cycle [35,36], nutrient cycles [37] and zoology [38]. However, the additional information contained in data from multiple-state variables compared to single-state variables may significantly improve the description of the full system by assimilation.…”

Section: Introductionmentioning

confidence: 99%

Multivariate and Multiscale Data Assimilation in Terrestrial Systems: A Review

Montzka

Pauwels

Franssen

et al. 2012

Sensors

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More and more terrestrial observational networks are being established to monitor climatic, hydrological and land-use changes in different regions of the World. In these networks, time series of states and fluxes are recorded in an automated manner, often with a high temporal resolution. These data are important for the understanding of water, energy, and/or matter fluxes, as well as their biological and physical drivers and interactions with and within the terrestrial system. Similarly, the number and accuracy of variables, which can be observed by spaceborne sensors, are increasing. Data assimilation (DA) methods utilize these observations in terrestrial models in order to increase process knowledge as well as to improve forecasts for the system being studied. The widely implemented automation in observing environmental states and fluxes makes an operational computation more and more feasible, and it opens the perspective of short-time forecasts of the state of terrestrial systems. In this paper, we review the state of the art with respect to DA focusing on the joint assimilation of observational data precedents from different spatial scales and different data types. An introduction is given to different DA methods, such as the Ensemble Kalman Filter (EnKF), Particle Filter (PF) and variational methods (3/4D-VAR). In this review, we distinguish between four major DA approaches: (1) univariate single-scale DA (UVSS), which is the approach used in the majority of published DA applications, (2) univariate multiscale DA (UVMS) referring to a methodology which acknowledges that at least some of the assimilated data are measured at a different scale than the computational grid scale, (3) multivariate single-scale DA (MVSS) dealing with the assimilation of at least two different data types, and (4) combined multivariate multiscale DA (MVMS). Finally, we conclude with a discussion on the advantages and disadvantages of the assimilation of multiple data types in a simulation model. Existing approaches can be used to simultaneously update several model states and model parameters if applicable. In other words, the basic principles for multivariate data assimilation are already available. We argue that a better understanding of the measurement errors for different observation types, improved estimates of observation bias and improved multiscale assimilation methods for data which scale nonlinearly is important to properly weight them in multiscale multivariate data assimilation. In this context, improved cross-validation of different data types, and increased ground truth verification of remote sensing products are required.

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“…Data assimilation, which refers to methodologies that systematically combine a mathematical model with observations, is often used in biogeochemical applications Friedrichs, 2001, 2002) to improve estimates of model parameters that are frequently poorly known (Lawson et al, 1995(Lawson et al, , 1996Matear, 1995;Fennel et al, 2001;Friedrichs, 2002;Schartau and Oschlies, 2003;Hemmings et al, 2004;Bagniewski et al, 2011;Doron et al, 2013;Xiao and Friedrichs, 2014a, b;Melbourne-Thomas et al, 2015;Song et al, 2016;Gharamti et al, 2017;Schartau et al, 2017). This entails a smoothing or optimization procedure, in which elements of the model are adjusted to minimize differences between the model output and the observations.…”

Section: Introductionmentioning

confidence: 99%

Assimilating bio-optical glider data during a phytoplankton bloom in the southern Ross Sea

Kaufman¹,

Friedrichs²,

Hemmings³

et al. 2018

Biogeosciences

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Abstract. The Ross Sea is a region characterized by high primary productivity in comparison to other Antarctic coastal regions, and its productivity is marked by considerable variability both spatially (1-50 km) and temporally (days to weeks). This variability presents a challenge for inferring phytoplankton dynamics from observations that are limited in time or space, which is often the case due to logistical limitations of sampling. To better understand the spatiotemporal variability in Ross Sea phytoplankton dynamics and to determine how restricted sampling may skew dynamical interpretations, high-resolution bio-optical glider measurements were assimilated into a one-dimensional biogeochemical model adapted for the Ross Sea. The assimilation of data from the entire glider track using the micro-genetic and local search algorithms in the Marine Model Optimization Testbed improves the model-data fit by ∼ 50 %, generating rates of integrated primary production of 104 g C m −2 yr −1 and export at 200 m of 27 g C m −2 yr −1 . Assimilating glider data from three different latitudinal bands and three different longitudinal bands results in minimal changes to the simulations, improves the model-data fit with respect to unassimilated data by ∼ 35 %, and confirms that analyzing these glider observations as a time series via a one-dimensional model is reasonable on these scales. Whereas assimilating the full glider data set produces well-constrained simulations, assimilating subsampled glider data at a frequency consistent with cruise-based sampling results in a wide range of primary production and export estimates. These estimates depend strongly on the timing of the assimilated observations, due to the presence of high mesoscale variability in this region. Assimilating surface glider data subsampled at a frequency consistent with available satellite-derived data results in 40 % lower carbon export, primarily resulting from optimized rates generating more slowly sinking diatoms. This analysis highlights the need for the strategic consideration of the impacts of data frequency, duration, and coverage when combining observations with biogeochemical modeling in regions with strong mesoscale variability.

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A data assimilation technique applied to a predator-prey model

Cited by 75 publications

References 24 publications

Dynamical analysis of a prey–predator model with Beddington–DeAngelis type function response incorporating a prey refuge

Dynamical analysis of a prey–predator model with Beddington–DeAngelis type function response incorporating a prey refuge

Multivariate and Multiscale Data Assimilation in Terrestrial Systems: A Review

Assimilating bio-optical glider data during a phytoplankton bloom in the southern Ross Sea

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