Identification of Synchronicity in Deterministic Chaotic Attractors for the Downscaling Process in the Bogotá River Basin

2021 ◽  
Author(s):  
Santiago Duarte ◽  
Gerald Corzo ◽  
Germán Santos
Keyword(s):  
Time Series ◽  
Time Delay ◽  
River Basin ◽  
Spatial Scales ◽  
Climatic Variables ◽  
Chaotic Attractors ◽  
Multiple Attractors ◽  
Nearest Neighbours ◽  
Basin Scale ◽  
Non Linear

<p>Bogotá’s River Basin, it’s an important basin in Cundinamarca, Colombia’s central region. Due to the complexity of the dynamical climatic system in tropical regions, can be difficult to predict and use the information of GCMs at the basin scale. This region is especially influenced by ENSO and non-linear climatic oscillation phenomena. Furthermore, considering that climatic processes are essentially non-linear and possibly chaotic, it may reduce the effectiveness of downscaling techniques in this region. </p><p>In this study, we try to apply chaotic downscaling to see if we could identify synchronicity that will allow us to better predict. It was possible to identify clearly the best time aggregation that can capture at the best the maximum relations between the variables at different spatial scales. Aside this research proposes a new combination of multiple attractors. Few analyses have been made to evaluate the existence of synchronicity between two or more attractors. And less analysis has considered the chaotic behaviour in attractors derived from climatic time series at different spatial scales. </p><p>Thus, we evaluate general synchronization between multiple attractors of various climate time series. The Mutual False Nearest Neighbours parameter (MFNN) is used to test the “Synchronicity Level” (existence of any type of synchronization) between two different attractors. Two climatic variables were selected for the analysis: Precipitation and Temperature. Likewise, two information sources are used: At the basin scale, local climatic-gauge stations with daily data and at global scale, the output of the MPI-ESM-MR model with a spatial resolution of 1.875°x1.875° for both climatic variables (1850-2005). In the downscaling process, two RCP (Representative Concentration Pathways)  scenarios are used, RCP 4.5 and RCP 8.5.</p><p>For the attractor’s reconstruction, the time-delay is obtained through the  Autocorrelation and the Mutual Information functions. The False Nearest Neighbors method (FNN) allowed finding the embedding dimension to unfold the attractor. This information was used to identify deterministic chaos at different times (e.g. 1, 2, 3 and 5 days) and spatial scales using the Lyapunov exponents. These results were used to test the synchronicity between the various chaotic attractor’s sets using the MFNN method and time-delay relations. An optimization function was used to find the attractor’s distance relation that increases the synchronicity between the attractors.  These results provided the potential of synchronicity in chaotic attractors to improve rainfall and temperature downscaling results at aggregated daily-time steps. Knowledge of loss information related to multiple reconstructed attractors can provide a better construction of downscaling models. This is new information for the downscaling process. Furthermore, synchronicity can improve the selection of neighbours for nearest-neighbours methods looking at the behaviour of synchronized attractors. This analysis can also allow the classification of unique patterns and relationships between climatic variables at different temporal and spatial scales.</p>

TIME-DELAY EMBEDDINGS OF IFS ATTRACTORS

Fractals ◽  
1999 ◽  
Vol 07 (02) ◽  
pp. 133-138
Author(s):  
SONYA BAHAR
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Periodic Orbits ◽  
Topological Structure ◽  
Chaotic Systems ◽  
Iterated Function System ◽  
Function System ◽  
Chaotic Attractors ◽  
Topological Characterization ◽  
Iterated Function

A modified type of iterated function system (IFS) has recently been shown to generate images qualitatively similar to "classical" chaotic attractors. Here, we use time-delay embedding reconstructions of time-series from this system to generate three-dimentional projections of IFS attractors. These reconstructions may be used to access the topological structure of the periodic orbits embedded within the attractor. This topological characterization suggests an approach by which a rigorous comparison of IFS attractors and classical chaotic systems may be attained.

scholarly journals Modeling 25 years of spatio-temporal surface water and inundation dynamics on large river basin scale using time series of earth observation data

2015 ◽  
Vol 12 (11) ◽  
pp. 11847-11903 ◽  
Author(s):  
V. Heimhuber ◽  
M. G. Tulbure ◽  
M. Broich
Keyword(s):  
Time Series ◽  
Surface Water ◽  
River Basin ◽  
Earth Observation ◽  
Water Dynamics ◽  
Observation Data ◽  
Grid Cells ◽  
Modeling Framework ◽  
Basin Scale ◽  
Lag Times

Abstract. The usage of time series of earth observation (EO) data for analyzing and modeling surface water dynamics (SWD) across broad geographic regions provides important information for sustainable management and restoration of terrestrial surface water resources, which suffered alarming declines and deterioration globally. The main objective of this research was to model SWD from a unique validated Landsat-based time series (1986–2011) continuously through cycles of flooding and drying across a large and heterogeneous river basin, the Murray–Darling Basin (MDB) in Australia. We used dynamic linear regression to model remotely sensed SWD as a function of river flow and spatially explicit time series of soil moisture (SM), evapotranspiration (ET) and rainfall (P). To enable a consistent modeling approach across space, we modeled SWD separately for hydrologically distinct floodplain, floodplain-lake and non-floodplain areas within eco-hydrological zones and 10 km × 10 km grid cells. We applied this spatial modeling framework (SMF) to three sub-regions of the MDB, for which we quantified independently validated lag times between river gauges and each individual grid cell and identified the local combinations of variables that drive SWD. Based on these automatically quantified flow lag times and variable combinations, SWD on 233 (64 %) out of 363 floodplain grid cells were modeled with r2 ≥ 0.6. The contribution of P, ET and SM to the models' predictive performance differed among the three sub-regions, with the highest contributions in the least regulated and most arid sub-region. The SMF presented here is suitable for modeling SWD on finer spatial entities compared to most existing studies and applicable to other large and heterogeneous river basins across the world.

scholarly journals An integration of gauge, satellite and reanalysis precipitation datasets for the largest river basin of the Tibetan Plateau

2020 ◽  
Author(s):  
Yuanwei Wang ◽  
Lei Wang ◽  
Xiuping Li ◽  
Jing Zhou ◽  
Zhidan Hu
Keyword(s):  
Tibetan Plateau ◽  
River Basin ◽  
Spatial Scales ◽  
Water Security ◽  
The Tibetan Plateau ◽  
Brahmaputra River ◽  
Hydrological Simulation ◽  
Precipitation Product ◽  
Basin Scale ◽  
Long Term Trends

Abstract. As the largest river basin of the Tibetan Plateau, the Upper Brahmaputra River Basin (also called “Yarlung Zangbo” in Chinese) has profound impacts on the water security of local and downstream inhabitants. Precipitation in the basin is mainly controlled by the Indian Summer Monsoon and Westerly, and is the key to understand the water resources available in the basin; however, due to sparse observational data constrained by a harsh environment and complex topography, there remains a lack of reliable information on basin-wide precipitation (there are only nine national meteorological stations with continuous observations). To improve the accuracy of basin-wide precipitation data, we integrate various gauge, satellite and reanalysis precipitation datasets, including GLDAS, ITP-Forcing, MERRA2, TRMM and CMA datasets, to develop a new precipitation product for the 1981–2016 period over the Upper Brahmaputra River Basin, at 3-hour and 5-km resolution. The new product has been rigorously validated at different temporal scales (e.g. extreme events, daily to monthly variability, and long-term trends) and spatial scales (point- and basin-scale) with gauge precipitation observations, showing much improved accuracies compared to previous products. An improved hydrological simulation has been achieved (low relative bias: −5.94 %; highest NSE: 0.643) with the new precipitation inputs, showing reliability and potential for multi-disciplinary studies. This new precipitation product is openly accessible at https://doi.org/10.5281/zenodo.3711155 (Wang et al., 2020) and, additionally at the National Tibetan Plateau Data Center (https://data.tpdc.ac.cn, login required).

scholarly journals A multi-approach and multi-scale study on water quantity and quality changes in the Tapajós River basin, Amazon

2018 ◽  
Vol 377 ◽  
pp. 3-7 ◽  
Author(s):  
Rodolfo Luiz Bezerra Nóbrega ◽  
Gabriele Lamparter ◽  
Harold Hughes ◽  
Alphonce Chenjerayi Guzha ◽  
Ricardo Santos Silva Amorim ◽  
...  
Keyword(s):  
Trend Analysis ◽  
River Basin ◽  
Spatial Scales ◽  
Sediment Concentration ◽  
Hydrological Modelling ◽  
Water Quantity ◽  
Small Scale ◽  
Basin Scale ◽  
Forest Catchment ◽  
Water Quantity And Quality

Abstract. We analyzed changes in water quantity and quality at different spatial scales within the Tapajós River basin (Amazon) based on experimental fieldwork, hydrological modelling, and statistical time-trend analysis. At a small scale, we compared the river discharge (Q) and suspended-sediment concentrations (SSC) of two adjacent micro-catchments (< 1 km2) with similar characteristics but contrasting land uses (forest vs. pasture) using empirical data from field measurements. At an intermediary scale, we simulated the hydrological responses of a sub-basin of the Tapajós (Jamanxim River basin, 37 400 km2), using a hydrological model (SWAT) and land-use change scenario in order to quantify the changes in the water balance components due to deforestation. At the Tapajós' River basin scale, we investigated trends in Q, sediments, hydrochemistry, and geochemistry in the river using available data from the HYBAM Observation Service. The results in the micro-catchments showed a higher runoff coefficient in the pasture (0.67) than in the forest catchment (0.28). At this scale, the SSC were also significantly greater during stormflows in the pasture than in the forest catchment. At the Jamanxim watershed scale, the hydrological modelling results showed a 2 % increase in Q and a 5 % reduction of baseflow contribution to total Q after a conversion of 22 % of forest to pasture. In the Tapajós River, however, trend analysis did not show any significant trend in discharge and sediment concentration. However, we found upward trends in dissolved organic carbon and NO3- over the last 20 years. Although the magnitude of anthropogenic impact has shown be scale-dependent, we were able to find changes in the Tapajós River basin in streamflow, sediment concentration, and water quality across all studied scales.

Reconstruction of Phase Space and Eigenvalue Decomposition from a Biological Time Series: A Malayalam Speech Signal Case Study

2021 ◽  
Author(s):  
K. M. Muraleedharan ◽  
K. T. Bibish Kumar ◽  
Sunil Kumar ◽  
R. K. Sunil John
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Age Groups ◽  
Principal Component ◽  
Eigenvalue Decomposition ◽  
Embedding Dimension ◽  
System Perspective ◽  
Biological Time ◽  
Non Linear ◽  
Pca Method

Our objective is to describe the speech production system from a non-linear physiological system perspective and reconstruct the attractor from the experimental speech data. Mutual information method is utilized to find out the time delay for embedding. The False Nearest Neighbour (FNN) method and Principal Component Analysis (PCA) method are used for optimizing the embedding dimension of time series. The time series obtained from the typical non-linear systems, Lorenz system and Rössler system, is used to standardize the methods and the Malayalam speech vowel time series of both genders of different age groups, sampled at three sampling frequencies (16[Formula: see text]kHz, 32[Formula: see text]kHz, 44.1[Formula: see text]kHz), are taken for analysis. It was observed that time delay varies from sample to sample and, it ought to be better to figure out the time delay with the embedding dimension analysis. The embedding dimension is shown to be independent of gender, age and sampling frequency and can be projected as five. Hence a five-dimensional hyperspace will probably be adequate for reconstructing attractor of speech time series.

scholarly journals Investigating links between rainfall variations in the Ogooué River basin and ENSO in the Pacific Ocean over the period 1940–1999

2021 ◽  
Vol 384 ◽  
pp. 181-186
Author(s):  
Sakaros Bogning ◽  
Frédéric Frappart ◽  
Gil Mahé ◽  
Adrien Paris ◽  
Raphael Onguene ◽  
...  
Keyword(s):  
Time Series ◽  
Pacific Ocean ◽  
River Basin ◽  
Southern Oscillation ◽  
Rainfall Variability ◽  
The Pacific ◽  
Basin Scale ◽  
The Pacific Ocean ◽  
Wavelet Coherence Analysis ◽  
Enso Index

Abstract. This paper investigates links between rainfall variability in the Ogooué River Basin (ORB) and El Niño Southern Oscillation (ENSO) in the Pacific Ocean. Recent hydroclimatology studies of the ORB and surrounding areas resulting in contrasting conclusions about links between rainfall variability and ENSO. Thus, to make the issue clearer, this study investigates the links between ENSO and rainfall in the ORB over the period 1940–1999. The principal component analysis of monthly rainfall in the ORB was done. The temporal mode of the first component corresponds to the interannual variations of rainfall on the ORB. Also, the pattern of the spatial mode of the first component shows that the ORB is a homogeneous hydroclimatic zone. However, no leading mode is significantly correlated to the ENSO index. A cross-wavelet analysis of the time series of basin-scale rainfall and the ENSO index was therefore carried out. The result is a set of periodogram structures corresponding to some ENSO episodes recorded over the study period. And wavelet coherence analysis of both time series confirms that there are significant links between ENSO and rainfall in the ORB.

scholarly journals Modeling 25 years of spatio-temporal surface water and inundation dynamics on large river basin scale using time series of Earth observation data

2016 ◽  
Vol 20 (6) ◽  
pp. 2227-2250 ◽  
Author(s):  
Valentin Heimhuber ◽  
Mirela G. Tulbure ◽  
Mark Broich
Keyword(s):  
Time Series ◽  
Surface Water ◽  
River Basin ◽  
Spatial Modeling ◽  
Earth Observation ◽  
Observation Data ◽  
Grid Cells ◽  
Modeling Framework ◽  
Basin Scale ◽  
Lag Times

Abstract. The usage of time series of Earth observation (EO) data for analyzing and modeling surface water extent (SWE) dynamics across broad geographic regions provides important information for sustainable management and restoration of terrestrial surface water resources, which suffered alarming declines and deterioration globally. The main objective of this research was to model SWE dynamics from a unique, statistically validated Landsat-based time series (1986–2011) continuously through cycles of flooding and drying across a large and heterogeneous river basin, the Murray–Darling Basin (MDB) in Australia. We used dynamic linear regression to model remotely sensed SWE as a function of river flow and spatially explicit time series of soil moisture (SM), evapotranspiration (ET), and rainfall (P). To enable a consistent modeling approach across space, we modeled SWE dynamics separately for hydrologically distinct floodplain, floodplain-lake, and non-floodplain areas within eco-hydrological zones and 10km × 10km grid cells. We applied this spatial modeling framework to three sub-regions of the MDB, for which we quantified independently validated lag times between river gauges and each individual grid cell and identified the local combinations of variables that drive SWE dynamics. Based on these automatically quantified flow lag times and variable combinations, SWE dynamics on 233 (64 %) out of 363 floodplain grid cells were modeled with a coefficient of determination (r2) greater than 0.6. The contribution of P, ET, and SM to the predictive performance of models differed among the three sub-regions, with the highest contributions in the least regulated and most arid sub-region. The spatial modeling framework presented here is suitable for modeling SWE dynamics on finer spatial entities compared to most existing studies and applicable to other large and heterogeneous river basins across the world.

scholarly journals An integration of gauge, satellite, and reanalysis precipitation datasets for the largest river basin of the Tibetan Plateau

2020 ◽  
Vol 12 (3) ◽  
pp. 1789-1803 ◽  
Author(s):  
Yuanwei Wang ◽  
Lei Wang ◽  
Xiuping Li ◽  
Jing Zhou ◽  
Zhidan Hu
Keyword(s):  
Tibetan Plateau ◽  
River Basin ◽  
Spatial Scales ◽  
Water Security ◽  
The Tibetan Plateau ◽  
Brahmaputra River ◽  
Hydrological Simulation ◽  
Precipitation Product ◽  
Basin Scale ◽  
Long Term Trends

Abstract. As the largest river basin of the Tibetan Plateau, the upper Brahmaputra River basin (also called “Yarlung Zangbo” in Chinese) has profound impacts on the water security of local and downstream inhabitants. Precipitation in the basin is mainly controlled by the Indian summer monsoon and westerly and is the key to understanding the water resources available in the basin; however, due to sparse observational data constrained by a harsh environment and complex topography, there remains a lack of reliable information on basin-wide precipitation (there are only nine national meteorological stations with continuous observations). To improve the accuracy of basin-wide precipitation data, we integrate various gauge, satellite, and reanalysis precipitation datasets, including GLDAS, ITP-Forcing, MERRA2, TRMM, and CMA datasets, to develop a new precipitation product for the 1981–2016 period over the upper Brahmaputra River basin, at 3 h and 5 km resolution. The new product has been rigorously validated at different temporal scales (e.g., extreme events, daily to monthly variability, and long-term trends) and spatial scales (point and basin scale) with gauge precipitation observations, showing much improved accuracies compared to previous products. An improved hydrological simulation has been achieved (low relative bias: −5.94 %; highest Nash–Sutcliffe coefficient of efficiency (NSE): 0.643) with the new precipitation inputs, showing reliability and potential for multidisciplinary studies. This new precipitation product is openly accessible at https://doi.org/10.5281/zenodo.3711155 (Wang et al., 2020) and additionally at the National Tibetan Plateau Data Center (https://data.tpdc.ac.cn, last access: 10 July 2020, login required).

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