The Research on the Lake Eutrophication with CNOP Method

Using a dynamical model for nutrient cycling in shallow lakes, the approach of conditional nonlinear optimal perturbation (CNOP) was adopted to investigate the instability and the sensitivity of the lake ecosystem to finite-amplitude perturbations both related to the initial condition and the parameter. The results show that the ecosystem can be transformed from an oligotrophic (eutrophic) state to an eutrophic (oligotrophic) state with a CNOP as the perturbation, no matter how large the nutrient loading rate is. Above all, with the same restraints related to the initial perturbation and the parameter perturbation, CNOP has the largest effect on the lake ecosystem, which may be helpful to govern the lake ecosystem.

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The Sensitivity Analysis of a Lake Ecosystem with the Conditional Nonlinear Optimal Perturbation Method

Advances in Meteorology ◽

10.1155/2012/562081 ◽

2012 ◽

Vol 2012 ◽

pp. 1-7 ◽

Cited By ~ 4

Author(s):

Bo Wang ◽

Peijun Zhang ◽

Zhenhua Huo ◽

Qianqian Qi

Keyword(s):

Nutrient Loading ◽

Loading Rate ◽

Initial Perturbation ◽

Finite Amplitude ◽

Lake Ecosystem ◽

Conditional Nonlinear Optimal Perturbation ◽

Optimal Perturbation ◽

Amplitude Parameter ◽

Nutrient Loading Rate ◽

Method Show

The instability and sensitivity of a lake ecosystem to the finite-amplitude perturbations related to the initial condition and the parameter correspondingly are studied. The CNOP-I and CNOP-P methods are adopted to investigate this nonlinear system. The numerical results with CNOP-I method show that the lake ecosystem can be nonlinearly unstable with finite-amplitude initial perturbations when the nutrient loading rate is between the two bifurcation points. A large enough finite amplitude initial perturbation, that is, CNOP-I, can induce a transition from an oligotrophic (eutrophic) state to an eutrophic (oligotrophic) state. With CNOP-P method, it is shown that the lake ecosystem can be transformed from an oligotrophic (eutrophic) state to an eutrophic (oligotrophic) state with a large enough finite amplitude parameter perturbation, that is, CNOP-P, no matter how large the nutrient loading rate is.

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Application of the CNOP Method in the Shallow Lake Ecosystem

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.1010-1012.658 ◽

2014 ◽

Vol 1010-1012 ◽

pp. 658-661 ◽

Cited By ~ 1

Author(s):

Qian Qian Qi ◽

Bo Wang

Keyword(s):

Ecological Restoration ◽

Shallow Lake ◽

Submerged Macrophytes ◽

Finite Amplitude ◽

Water Transparency ◽

Lake Ecosystem ◽

Initial Condition ◽

Turbid Water ◽

Variable Model

It is serious on the degradation of the shallow lake ecosystem at present, while the recovery of the macrophytes vegetations and the increase in water transparency have been the main contents of the ecological restoration. Using a two-variable model, we discuss the instability and sensitivity of the ecosystem to the finite-amplitude perturbations related to the initial condition with CNOP-I method. Results show that the linearly stable clear (turbid) water states can be nonlinearly unstable with the finite-amplitude perturbations. The results also demonstrate that the facilitation interactions between the submerged macrophytes and the water transparency are the main trigger for a shift from the turbid to the clear state.

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Microalgal-based systems for wastewater treatment: Effect of applied organic and nutrient loading rate on biomass composition

Ecological Engineering ◽

10.1016/j.ecoleng.2012.08.021 ◽

2012 ◽

Vol 49 ◽

pp. 112-117 ◽

Cited By ~ 21

Author(s):

B. Riaño ◽

D. Hernández ◽

M.C. García-González

Keyword(s):

Wastewater Treatment ◽

Treatment Effect ◽

Nutrient Loading ◽

Loading Rate ◽

Biomass Composition ◽

Nutrient Loading Rate

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A Parallel Hybrid Intelligence Algorithm for Solving Conditional Nonlinear Optimal Perturbation to Identify Optimal Precursors of North Atlantic Oscillation

10.5194/npg-2019-25 ◽

2019 ◽

Author(s):

Bin Mu ◽

Jing Li ◽

Shijin Yuan ◽

Xiaodan Luo ◽

Guokun Dai

Keyword(s):

North Atlantic Oscillation ◽

North Atlantic ◽

Hybrid Algorithm ◽

Message Passing Interface ◽

Numerical Models ◽

Initial Perturbation ◽

Principal Component ◽

Local Optimum ◽

Conditional Nonlinear Optimal Perturbation ◽

Optimal Perturbation

Abstract. The North Atlantic Oscillation (NAO) is the most prominent atmospheric seesaw phenomenon in North Atlantic Ocean. It has a profound influence on the strength of westerly winds as well as the storm tracks in North Atlantic, thus affecting winter climate in Northern Hemisphere. Therefore, it is necessary to investigate the mechanism related with the NAO events. In this paper, conditional nonlinear optimal perturbation (CNOP), which has been widely used in research on the optimal precursor (OPR) of climatic event, is adopted to investigate which kind of initial perturbation is most likely to trigger the NAO anomaly pattern with the Community Earth System Model (CESM). Since CESM does not have an adjoint model, we propose an adjoint-free parallel principal component analysis (PCA) based genetic algorithm (GA) and particle swarm optimization (PSO) hybrid algorithm (PGAPSO) to solve CNOP in such a high dimensional numerical model. The results demonstrate that the OPRs obtained by CNOP trigger the reference flow into typical NAO mode, which provide the theoretical underpinning in observation and prediction. Furthermore, the hybrid algorithm can accelerate convergence and avoid falling into a local optimum. After parallelization with Message Passing Interface (MPI) and Compute Unified Device Architecture (CUDA), the PGAPSO algorithm achieves a speed-up of 40× compared with its serial version. The results as mentioned above indicate that the proposed algorithm can efficiently and effectively acquire CNOP and can also be generalized to other complex numerical models.

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Effects of Daphnia on the response of mesotrophic lakes to experimental enrichment

Water Science & Technology ◽

10.2166/wst.1995.0178 ◽

1995 ◽

Vol 32 (4) ◽

pp. 157-163 ◽

Cited By ~ 1

Author(s):

K. L. Cottingham ◽

S. E. Knight

Keyword(s):

Simulation Model ◽

Nutrient Loading ◽

Loading Rate ◽

Experimental Results ◽

First Year ◽

Model Simulations ◽

Loading Rates ◽

N:P Ratios ◽

Nutrient Loading Rate ◽

Experimental Enrichment

We are currently involved in a whole-lake experiment designed to assess how Daphnia affect the response of mesotrophic lakes to increased nutrient loading. In the first year of the experiment, we wished to demonstrate that there are P loading rates which eutrophy lakes without Daphnia but not lakes with Daphnia. In order to do this, we needed to choose an appropriate level and schedule for the experimental enrichment. This paper describes how we made that choice, then evaluates whether our choice was successful. Based on the literature, a simulation model, and a mesocosm experiment, we decided that enriching at a rate of 1 μg P L−1 d−1 would create the desired contrast between lakes with and without Daphnia. Model simulations indicated that mean algal response to enrichment would be comparable under monthly, weekly, or continuous additions. We chose to add nutrients continuously at ambient N:P ratios. Experimental results from 1993 suggest that we achieved a nutrient loading rate consistent with our goal: chlorophyll responded less to enrichment in the lake with Daphnia than in the lake without Daphnia. The modeling, mesocosm, and whole-lake studies summarized here support the idea that Daphnia reduce chlorophyll at P loads ≤1 μg P L−1 d−1. However, cyanobacteria may escape control by all grazers at relatively low P loading rates.

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Conditional nonlinear optimal perturbations of the double-gyre ocean circulation

Nonlinear Processes in Geophysics ◽

10.5194/npg-15-727-2008 ◽

2008 ◽

Vol 15 (5) ◽

pp. 727-734 ◽

Cited By ~ 24

Author(s):

A. D. Terwisscha van Scheltinga ◽

H. A. Dijkstra

Keyword(s):

Time Evolution ◽

Ocean Circulation ◽

Initial Perturbation ◽

Normal Modes ◽

Finite Amplitude ◽

Dissipation Function ◽

Stable States ◽

Optimal Perturbation ◽

Rectangular Basin ◽

Double Gyre

Abstract. In this paper, we study the development of finite amplitude perturbations on linearly stable steady barotropic double-gyre flows in a rectangular basin using the concept of Conditional Nonlinear Optimal Perturbation (CNOP). The CNOPs depend on a time scale of evolution te and an initial perturbation threshold δ. Under symmetric wind forcing, a perfect pitchfork perturbation occurs in the model. The CNOPs are determined for all linearly stable states and the time evolution of the CNOPs is studied. It is found that the patterns of the CNOPs are similar to those of the non-normal modes for small te and approach those of the normal modes for larger te. With slightly asymmetric winds, an imperfect pitchfork occurs in the model. Indications are found that the time evolution of the CNOPs is related to the value of the dissipation function of the underlying steady state.

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Nonlinear character analysis for bistability in virus–immune dynamics

Future Virology ◽

10.2217/fvl-2019-0059 ◽

2019 ◽

Vol 14 (10) ◽

pp. 655-662

Author(s):

Xiaofang Liu ◽

Guodong Sun

Keyword(s):

Equilibrium State ◽

Nonlinear Effect ◽

Stable Equilibrium ◽

Initial Perturbation ◽

Equilibrium States ◽

Conditional Nonlinear Optimal Perturbation ◽

Vector Method ◽

Optimal Perturbation ◽

Abrupt Changes ◽

Nonlinear Character

Structured abstract Aim: The nonlinear characters of two linearly stable equilibrium states (virus and immune) for a theoretical virus-immune model are analyzed. Methods: Conditional nonlinear optimal perturbation (CNOP), Lyapunov method and linear singular vector method. Results & conclusion: Two linearly stable equilibrium states (immune-free and immune) with linear methods are nonlinearly unstable using the CNOP method. When the CNOP-type of initial perturbation is used in the model, the immune-free (immune) equilibrium state will be made into the immune (immune-free) equilibrium state. Through computing the variations of nonlinear terms of the model, the nonlinear effect of immune proliferation plays an important role in abrupt changes of the immune-free equilibrium state compared with the linear term. For the immune equilibrium state, the nonlinear effect of viral replication is also an important factor.

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Silage storage runoff characterization: Annual nutrient loading rate and first flush analysis of bunker silos

Agriculture Ecosystems & Environment ◽

10.1016/j.agee.2018.05.015 ◽

2018 ◽

Vol 264 ◽

pp. 85-93 ◽

Cited By ~ 8

Author(s):

Michael A. Holly ◽

Rebecca A. Larson ◽

Eric T. Cooley ◽

Aaron M. Wunderlin

Keyword(s):

Nutrient Loading ◽

Loading Rate ◽

First Flush ◽

Nutrient Loading Rate

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Using Conditional Nonlinear Optimal Perturbation to Generate Initial Perturbations in ENSO Ensemble Forecasts

Weather and Forecasting ◽

10.1175/waf-d-21-0063.1 ◽

2021 ◽

Author(s):

Qian Zhou ◽

Lei Chen ◽

Wansuo Duan ◽

Xu Wang ◽

Ziqing Zu ◽

...

Keyword(s):

Southern Oscillation ◽

Initial Perturbation ◽

Skill Score ◽

Ensemble Forecasting ◽

Conditional Nonlinear Optimal Perturbation ◽

Ensemble Forecasts ◽

Optimal Perturbation ◽

Fully Nonlinear ◽

Enso Events ◽

Forecasting System

AbstractUsing the latest operational version of the ENSO forecast system from the National Marine Environmental Forecasting Center (NMEFC) of China, ensemble forecasting experiments are performed for El Niño-Southern Oscillation (ENSO) events that occurred from 1997 to 2017 by generating initial perturbations of the conditional nonlinear optimal perturbation (CNOP) and Climatically relevant Singular Vector (CSV) structures. It is shown that when the initial perturbation of the leading CSV structure in the ensemble forecast of the CSVs-scheme is replaced by those of the CNOP structure, the resulted ensemble ENSO forecasts of the CNOP+CSVs-scheme tend to possess a larger spread than the forecasts obtained with the CSVs-scheme alone, leading to a better match between the root mean square error and the ensemble spread, a more reasonable Talagrand diagram and an improved Brier skill score (BSS). All these results indicate that the ensemble forecasts generated by the CNOP+CSVs-scheme can improve both the accuracy of ENSO forecasting and the reliability of the ensemble forecasting system. Therefore, ENSO ensemble forecasting should consider the effect of nonlinearity on the ensemble initial perturbations to achieve a much higher skill. It is expected that fully nonlinear ensemble initial perturbations can be sufficiently yielded to produce ensemble forecasts for ENSO, finally improving the ENSO forecast skill to the greatest possible extent. The CNOP will be a useful method to yield fully nonlinear optimal initial perturbations for ensemble forecasting.

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