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NASA NTRS2004

Cluster II Wideband (WBD) Plasma Wave Investigation Mission Operations and Data Analysis

This Summary of Research is being submitted to NASA Goddard Space Flight Center. A summary of the significant accomplishments of the Cluster Wideband (WBD) Plasma Wave Investigation team achieved during the period of the grant, October 1,2000 through January 14, 2004, and a listing of all of the publications that resulted from work carried out under the grant is presented. Also included is a listing of the numerous public outreach activities that took place during the period of the grant in which the Cluster mission and Cluster WBD science were discussed.

Gurnett, Donald A.↗
DOE OSTI2015

CLASH: The concentration-mass relation of galaxy clusters

We present a new determination of the concentration–mass (c–M) relation for galaxy clusters based on our comprehensive lensing analysis of 19 X-ray selected galaxy clusters from the Cluster Lensing and Supernova Survey with Hubble (CLASH). Our sample spans a redshift range between 0.19 and 0.89. We combine weak-lensing constraints from the Hubble Space Telescope (HST) and from ground-based wide-field data with strong lensing constraints from HST. The results are reconstructions of the surface-mass density for all CLASH clusters on multi-scale grids. Our derivation of Navarro–Frenk–White parameters yields virial masses between 0.53×10{sup 15} M{sub ⊙}/h and 1.76×10{sup 15} M{sub ⊙}/h and the halo concentrations are distributed around c{sub 200c}∼3.7 with a 1σ significant negative slope with cluster mass. We find an excellent 4% agreement in the median ratio of our measured concentrations for each cluster and the respective expectation from numerical simulations after accounting for the CLASH selection function based on X-ray morphology. The simulations are analyzed in two dimensions to account for possible biases in the lensing reconstructions due to projection effects. The theoretical c–M relation from our X-ray selected set of simulated clusters and the c–M relation derived directly from the CLASH data agree at the 90% confidence level.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Clusters of COVID ‐19 in long‐term care hospitals and facilities in Japan from 16 January to 9 May 2020

Aim To clarify the association of cluster number and size of coronavirus disease 2019 (COVID‐19) in long‐term care (LTC) hospitals/facilities, general medical/welfare facilities and non‐medical/welfare facilities with morbidity and mortality in 47 prefectures during 16 January to 9 May 2020 in Japan. Methods Information on COVID‐19 clusters ( n ≥2), and morbidity and mortality of COVID‐19 was collected. Results A total of 381 clusters with 3786 infected cases were collected, accounting for 23.9% of 15 852 cumulated cases on 9 May 2020. Although the cluster number (/10 7 subjects) in LTC hospitals/facilities was significantly smaller compared with those in the other two groups, the cluster size in LTC hospitals/facilities was significantly larger than that in non‐medical/welfare facilities. Cluster numbers in general medical/welfare facilities and in non‐medical/welfare facilities were significantly positively correlated with morbidity (/10 5 ), indicating relatively early identification of clusters in these facilities. Unlike in these facilities, cluster size in LTC hospitals/facilities was significantly positively correlated with morbidity, indicating that clusters in LTC hospitals/facilities were finally identified after already having grown to a large size in areas where infection was prevalent. Multivariate logistic regression analysis showed that both cluster number and cluster size only in LTC hospitals/facilities were independently associated with higher mortality (≥median 0.64/10 5 subjects) after adjustment. Conclusions Preventive efforts against COVID‐19 outbreaks even at the early phase of the epidemic are critically important in LTC hospitals/facilities, as both the larger number and size of clusters only in LTC hospitals/facilities were independently linked to higher mortality in prefectures in Japan. Geriatr Gerontol Int 2020; 20: 715–719 .

Iritani, Osamu↗
NASA NTRS1972

Mapping of terrain by computer clustering techniques using multispectral scanner data and using color aerial film

Two clustering techniques were used for terrain mapping by computer of test sites in Yellowstone National Park. One test was made with multispectral scanner data using a composite technique which consists of (1) a strictly sequential statistical clustering which is a sequential variance analysis, and (2) a generalized K-means clustering. In this composite technique, the output of (1) is a first approximation of the cluster centers. This is the input to (2) which consists of steps to improve the determination of cluster centers by iterative procedures. Another test was made using the three emulsion layers of color-infrared aerial film as a three-band spectrometer. Relative film densities were analyzed using a simple clustering technique in three-color space. Important advantages of the clustering technique over conventional supervised computer programs are (1) human intervention, preparation time, and manipulation of data are reduced, (2) the computer map, gives unbiased indication of where best to select the reference ground control data, (3) use of easy to obtain inexpensive film, and (4) the geometric distortions can be easily rectified by simple standard photogrammetric techniques.

Smedes, H. W.↗
DOE OSTI2019

Optimizing galaxy samples for clustering measurements in photometric surveys

When analysing galaxy clustering in multiband imaging surveys, there is a trade-off between selecting the largest galaxy samples (to minimize the shot noise) and selecting samples with the best photometric redshift (photo-$z$) precision, which generally includes only a small subset of galaxies. In this paper, we systematically explore this trade-off. Our analysis is targeted towards the third-year data of the Dark Energy Survey (DES), but our methods hold generally for other data sets. Using a simple Gaussian model for the redshift uncertainties, we carry out a Fisher matrix forecast for cosmological constraints from angular clustering in the redshift range $z$ = 0.2–0.95. We quantify the cosmological constraints using a figure of merit (FoM) that measures the combined constraints on $Ωm$ and $σ_8$ in the context of Λ cold dark matter ($Λ$CDM) cosmology. We find that the trade-off between sample size and photo-z precision is sensitive to (1) whether cross-correlations between redshift bins are included or not, and (2) the ratio of the redshift bin width $δz$ to the photo-$z$ precision $σ_z$. When cross-correlations are included and the redshift bin width is allowed to vary, the highest FoM is achieved when $δz$ ~ $σ_z$. We find that for the typical case of 5-10 redshift bins, optimal results are reached when we use larger, less precise photo-z samples, provided that we include cross-correlations. For samples with higher $σ_z$, the overlap between redshift bins is larger, leading to higher cross-correlation amplitudes. This leads to the self-calibration of the photo-z parameters and therefore tighter cosmological constraints. These results can be used to help guide galaxy sample selection for clustering analysis in ongoing and future photometric surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Robustness of cluster synchronous patterns in small-world networks with inter-cluster co-competition balance

All edges in the classical Watts and Strogatz's small-world network model are unweighted and cooperative (positive). By introducing competitive (negative) inter-cluster edges and assigning edge weights to mimic more realistic networks, this paper develops a modified model which possesses co-competitive weighted couplings and cluster structures while maintaining the common small-world network properties of small average shortest path lengths and large clustering coefficients. Based on theoretical analysis, it is proved that the new model with inter-cluster co-competition balance has an important dynamical property of robust cluster synchronous pattern formation. More precisely, clusters will neither merge nor split regardless of adding or deleting nodes and edges, under the condition of inter-cluster co-competition balance. Numerical simulations demonstrate the robustness of the model against the increase of the coupling strength and several topological variations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

The 3XMM/SDSS Stripe 82 Galaxy Cluster Survey – II. X-ray and optical properties of the cluster sample

ABSTRACT We present X-ray and optical properties of the optically confirmed galaxy cluster sample from the 3XMM/SDSS Stripe 82 cluster survey. The sample includes 54 galaxy clusters in the redshift range of 0.05–1.2, with a median redshift of 0.36. We first present the X-ray temperature and luminosity measurements that are used to investigate the X-ray luminosity–temperature relation. The slope and intercept of the relation are consistent with those published in the literature. Then, we investigate the optical properties of the cluster galaxies including their morphological analysis and the galaxy luminosity functions (GLFs). The morphological content of cluster galaxies is investigated as a function of cluster mass and distance from the cluster centre. No strong variation of the fraction of early- and late-type galaxies with cluster mass is observed. The fraction of early-type galaxies as a function of cluster radius varies as expected. The individual GLFs of red sequence galaxies were studied in the five ugriz bands for 48 clusters. The GLFs were then stacked in three mass bins and two redshift bins. Twenty clusters of the present sample are studied for the first time in X-rays, and all are studied for the first time in the optical range. Altogether, our sample appears to have X-ray and optical properties typical of ‘average’ cluster properties.

Takey, Ali↗
DOE OSTI2024

LoVoCCS. II. Weak Lensing Mass Distributions, Red-sequence Galaxy Distributions, and Their Alignment with the Brightest Cluster Galaxy in 58 Nearby X-Ray-luminous Galaxy Clusters

The Local Volume Complete Cluster Survey is an ongoing program to observe nearly a hundred low-redshift X-ray-luminous galaxy clusters (redshifts 0.03 < z < 0.12 and X-ray luminosities in the 0.1–2.4 keV band L X500c > 10 44 erg s −1 ) with the Dark Energy Camera, capturing data in the u, g, r, i, z bands with a 5σ point source depth of approximately 25th–26th AB magnitudes. Here, we map the aperture masses in 58 galaxy cluster fields using weak gravitational lensing. These clusters span a variety of dynamical states, from nearly relaxed to merging systems, and approximately half of them have not been subject to detailed weak lensing analysis before. In each cluster field, we analyze the alignment between the 2D mass distribution described by the aperture mass map, the 2D red-sequence (RS) galaxy distribution, and the brightest cluster galaxy (BCG). We find that the orientations of the BCG and the RS distribution are strongly aligned throughout the interiors of the clusters: the median misalignment angle is 19° within 2 Mpc. We also observe the alignment between the orientations of the RS distribution and the overall cluster mass distribution (by a median difference of 32° within 1 Mpc), although this is constrained by galaxy shape noise and the limitations of our cluster sample size. These types of alignment suggest long-term dynamical evolution within the clusters over cosmic timescales.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1995

The reliability of X-ray constraints of intrinsic cluster shapes

Using the simulation of Katz & White (1993) we have tested the viability of X-ray analysis for constraining the intrinsic shapes of clusters of galaxies considering the effects of both substructure and steep temperature gradients. We restrict our analysis to the aggregate shapes of clusters on scales of r approximately 1-2 Mpc in order to reduce our sensitivity to subclustering in the core. For low redshifts (z less than or approximately = 0.25) the X-ray method accurately measures the true ellipticity of the three-dimensional cluster dark matter provided the inclination of the cluster is known to within approximately 30 deg; assuming the gas is isothermal adds only small errors to the derived shapes. At higher redshifts the X-ray method yields unreliable results since the gas does not trace the cluster gravitational potential. We proffer some necessary conditions for the reliability of X-ray methods characterized by both the amount of substructure in the X-ray surface brightness images and the shapes of the isophotes. We conclude that measurements of the aggregate shapes of clusters on scales r approximately 1-2 Mpc are insensitive to core substructure representing scales of a few hundred kpc. Therefore our results suggest that the X-ray measurements of aggregate cluster shapes by Fabricant, Rybicki, & Gorenstein (1984) and Buote & Canizares (1992) are valid provided that they do not suffer from serious projection effects. A substantial number of Abell clusters observed with the ROSAT PSPC will be amenable to X-ray shape analysis.

Buote, David A.↗
DOE OSTI2019

Silver clusters tune up electronic properties of graphene nanoflakes: A comprehensive theoretical study

Graphene-silver composites reflect a synergic effect of both components with enhanced electronic, adsorption and catalytic properties. We introduce here the detailed theoretical study on geometric, thermodynamic and electronic properties of silver clusters Ag n (n=2–10) adsorbed on graphene nanoflakes as a model for silver-graphene composites. First, a benchmark study is performed on Ag n …coronene complexes (n=2, 4) by evaluating various functional against reported high level ab-initio method for the selection of best functional for further calculations. Then, density functional theory study at the best chosen level is performed to inquire how clustering of adsorbate attached with carbon surface can impact geometric, electronic and thermodynamic properties of silver-graphene composites. Furthermore, the interaction energies are corrected for dispersion and basis set superposition error in order to get more realistic estimate of interaction energies. In progression, we investigated the dependence of interaction energy upon cluster size and dimensionality. For Ag n …coronene, the binding energies increase monotonically as the number of atoms in the cluster increases. However, for Ag n …dodecabenzocoronene, the interaction energies show a sudden drop at Ag 7 …dodecabenzocoronene. The difference in behavior between Ag n …dodecabenzocoronene and Ag n …coronene for interaction energy is attributed to edge effect present in coronene. Furthermore, coplanar orientations of the silver clusters on polyaromatic hydrocarbons have higher interaction energies. The 2D-3D transition of the silver cluster is observed for Ag 7 …coronene. CDA analysis reveals that backdonation from dodecabenzocoronene to silver clusters is more dominant in Ag 4 –Ag 7 whereas other clusters have dominant charge transfer to dodecabenzocoronene. Charge transfer analysis via constrained density functional theory (CDFT) reveals significant energy lowering from charge donor-acceptor interactions. Further energy decomposition analysis (EDA) using absolutely-localized molecular orbitals (ALMO) suggests that, while charge-transfer is important in these systems, the sum of electrostatics, Pauli repulsion, and London dispersion are far more significant as silver cluster size increases. NCI results also support the presence of van der Waals and electrostatic interactions. The hollow top is most favorite interaction sites compared to bridge top and head top binding sites over coronene lattice. The ionization potential, electron affinity, frontier molecular orbital analysis, chemical hardness, softness, chemical potential, and Fermi levels are deliberated to verify the stability and reactivity of most stable silver-graphene composites. The remarkable outcome of the current findings makes our silver-graphene composite as a potential applicant for high performance electronic and catalytic devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Rare Earth and Transition Metal Containing Glasses

Transition metal (TM) and rare earth (RE) ions have been incorporated into many glass systems such as silicate, phosphate, and borosilicate-based oxide glasses, as well as in halide and chalcogenide glasses, that find applications ranging from optical, photonic, and magnetic devices, solid-state battery, to nuclear waste disposal. Understanding the structural role of RE and TM in these glasses can help to develop glass compositions for targeted applications with either high-optical emission efficiency, electrical conductivity, or chemical durability. In this chapter, we first provide a general introduction of the applications and structural features of RE and TM in glasses, then the critical aspects of molecular dynamics (MD) simulations of these glasses such as interatomic potentials, structural analysis tools to study RE and TM ions in glasses and their clustering behaviors, Quantitative Structure–Property Analysis (QSPR), diffusion and dynamic property calculations, and electronic structure calculations to understand electronic defects such as charge trapping and radiation effects are introduced. Three representative case studies are presented: the first one is on MD simulations of erbium- and europium-doped silica and silicate glasses, as well as cerium doped aluminophosphate glasses, that revealed the effect of glass composition on RE ion local structure and clustering behavior. Electronic structure calculations of cerium-doped glass show how the existence of multioxidation states help to mediate radiation-induced damages caused by excited electron–hole pairs was also discussed. The second one focuses on alkali vanadophosphate glasses where the existence of two vanadium oxidation states help to provide electronic conduction in the glasses while alkali ions provide ionic conduction. MD simulations were used to understand vanadium environments and other structural aspects in the phosphate glasses, as well as the ionic transport behaviors of alkali ions. The third case study is on zirconium-containing borosilicate and aluminosilicate glasses that find wide applications in nuclear waste disposal. MD simulations help to provide structural details of zirconium ions that are validated by diffraction and EXAFS spectra. The structural information was used to interpret changes of mechanical properties and chemical durability by using QSPR and other analyses-based MD-generated structure models.

Du, Jincheng↗
DOE OSTI2019

Structure and Dynamics of Polysulfide Clusters in a Nonaqueous Solvent Mixture of 1,3-Dioxolane and 1,2-Dimethoxyethane

Molecular clustering and associated dynamic processes of lithium polysulfide species were unraveled using classical molecular dynamics and ab initio metadynamics calculations. The spectroscopic signatures of polysulfide clusters were analyzed using a multimodal analysis including experimental and computational nuclear magnetic resonance (NMR) and X-ray absorption spectroscopies. Lithium polysulfide solutes (Li 2 S 4 , Li 2 S 6 , and Li 2 S 8 ) and their mixtures in a 1,3-dioxolane and 1,2-dimethoxyethane (DOL/DME) solvent undergo aggregation driven by intramolecular lithium–sulfur (Li–S) interactions, leading to distributions of cluster sizes, which could critically influence the functioning of lithium–sulfur batteries. Representative polysulfide clusters with systematic increases in molecular size were extracted from the classical molecular dynamics trajectories for subsequent structural and spectroscopic property calculations using density functional theory analysis. Structural analysis of these clusters reveals progressively decreasing solvent involvement in Li+ coordination varying from Li 2 S 4 to Li 2 S 8 , with more pronounced variation and changes in DME compared with those in DOL. These observations are reflected in the analysis of the experimental and theoretical 7 Li and 17 O NMR chemical shifts and pulsed field gradient-NMR diffusion measurements. A comparison of experimental and theoretical S K-edge X-ray absorption near edge spectra shows that relatively large lithium sulfide chain clusters are likely to occur in the DOL/DME-solvated lithium sulfide systems. Ab initio metadynamics simulations and NMR analysis indicate that Li + solvated by only the solvent can occur through Li + dissociation from sulfide chains. However, the occurrence of “sulfide-free” Li + is a minor mechanism compared with the dynamic aggregation and shuttling processes of polysulfide solvates in DOL/DME-based electrolytes of Li–S batteries. Overall, atomistic insights gained about clustering and lithium exchange dynamics will be critical for the predictive understanding of the polysulfide shuttling and nucleation process that dictates the Li–S battery performance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Ionic versus metallic bonding in Al n Na m and Al n Mg m (m ≤ 3, n + m ≤ 15) clusters

First principles electronic structure studies on the ground state geometries, stability, and the electronic structure of Al n Na m and Al n Mg m (m ≤ 3, n + m ≤ 15) clusters have been carried out to examine the nature of bonding between Na or Mg and Al. Identifying whether the bonding is ionic or metallic in bulk materials is typically straightforward; however, in small clusters where quantum confinement is important, the nature of bonding may become unclear. Here, we have performed a critical analysis of the bonding in these bimetallic clusters using charge analysis, electrical dipole moments, hybridization of the atomic orbitals, the Laplacian of the charge density at the bond critical points, and the change in the bonding energy between neutral and anionic forms of the cluster. For Na n Al m clusters, we find that the Na binding is primarily ionic, while the bonding in Al n Mg m is primarily metallic. We find that the Mulliken population of the 3 p orbital of Na and Mg can provide a rapid assessment of the nature of bonding. We also find that the Hirshfeld charge and dipole moments are effective indicators, when placed in context. We found that the Laplacian of the charge density at the bond critical points can be misleading in identifying whether the bonding is ionic or metallic in small clusters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Scalable edge clustering of dynamic graphs via weighted line graphs

Timestamped relational datasets consisting of records (or connections) between pairs of entities are ubiquitous in network science. For applications like peer-to-peer communication, email, various social network interactions, and computer network security, it is useful to organize these records into groups based on how and when they are occurring. Weighted line graphs offer a natural way to model how records are related in such datasets but for large real-world graph topologies, building and utilizing the line graph is prohibitively expensive. Here, we present the framework to cluster the edges of a dynamic graph via the associated line graph that contains two major contributions. The first is a method to work with the line graph implicitly and the second is a distributed scale implementation of an agglomerative hierarchical graph clustering algorithm. We outline a novel hierarchical dynamic graph edge clustering approach that efficiently breaks massive relational datasets into small sets of edges containing events at various timescales. This is in stark contrast to traditional graph clustering algorithms that prioritize highly connected (clique-like) community structures. Our approach relies on constructing a sufficient subgraph of a weighted line graph and applying a hierarchical agglomerative clustering. This approach is related to scalable techniques from spatial clustering, nonlinear-dimension reduction, topological data analysis, and draws particular inspiration from HDBSCAN. As an edge clustering, this method yields an overlapping node clustering. Our algorithm is parallelizable and we demonstrate efficient clustering of a billion-scale, real-world dynamic graph into small edge sets that correlate in topology and time. The entire clustering process for a graph with tens of billions of edges takes just a few minutes of run time on 256 nodes of a distributed compute environment. We argue how the output of the edge clustering is useful for a multitude of data visualization and powerful machine learning tasks, both involving the original massive dynamic graph data and metadata associated with the nodes and edges. Finally, we describe how this approach can be extended to dynamic hypergraphs and dynamic graphs/hypergraphs with unstructured data living on vertices and edges.

Data Analysis↗
DOE OSTI2022

Analysis of spin frustration in an Fe III 7 cluster using a combination of computational, experimental, and magnetostructural correlation methods

The synthesis, structure, and magnetic properties are reported for [Fe 7 O 3 (O 2 C t Bu) 9 (mda) 3 (H 2 O) 3 ] ( 1 ), where mdaH 2 is N -methyldiethanolamine. 1 was prepared from the reaction of [Fe 3 O(O 2 C t Bu) 6 (H 2 O) 3 ](NO 3 ) with mdaH 2 in a 1:~3 ratio in MeCN. The core of 1 consists of a central octahedral Fe III ion held within a non-planar Fe 6 loop by three μ 3 -O 2- and three μ 2 -RO - arms from the three mda 2- chelates. Variable-temperature dc and ac magnetic susceptibility studies revealed dominant antiferromagnetic coupling, leading to a ground state spin of S = 5 / 2 . The ground state was confirmed by a fit of magnetization data collected in the 0.1–7.0 T and 1.8–10.0 K ranges. The four Fe 2 pairwise exchange parameters ( J 1 - J 4 ) were estimated by independent methods: theoretical calculations using either broken symmetry energy differences (-46.3, -16.2, -3.9, and - 28.1 cm -1 , respectively) or Green’s function approximation methods (-41.4, -14.8, -13.2, and - 24.7 cm -1 ), and a magnetostructural correlation (MSC) previously developed for high nuclearity Fe III /O complexes (-39.5, -13.8, -6.7, and - 23.5 cm -1 ). Additionally, the J 1 - J 4 obtained from the MSC and theoretical methods were used with the program PHI to both simulate χ M T vs T as well as to serve as reasonable input values to fit the experimental data (-41.0, -11.4, -5.0, and - 27.3 cm -1 ). Analysis of the J ij led to identification of the spin frustration effects operative and the resultant spin vector alignments at each Fe III ion, thus allowing for the rationalization of the experimental ground state.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Bi-cross validation of spectral clustering hyperparameters

One challenge impeding the analysis of terabyte scale X-ray scattering data from the Linac Coherent Light Source (LCLS) is determining the number of clusters required for the execution of traditional clustering algorithms. Here, we demonstrate that the previous work using bi-cross validation to determine the number of singular vectors directly maps to the spectral clustering problem of estimating both the number of clusters and hyperparameter values. Here by applying this method to LCLS X-ray scattering data enables the identification of dropped shots without manually setting boundaries on detector fluence and provides a path toward identifying rare and anomalous events.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Nontargeted virus sequence discovery pipeline and virus clustering for metagenomic data

The analysis of large microbiome data sets holds great promise for the delineation of the biological and metabolic functioning of living organisms and their role in the environment. In the midst of this genomic puzzle, viruses, especially those that infect microbial communities, represent a major reservoir of genetic diversity with great impact on biogeochemical cycles and organismal health. Overcoming the limitations associated with virus detection directly from microbiomes can provide key insights into how ecosystem dynamics are modulated. Here, we present a computational protocol for accurate detection and grouping of viral sequences from microbiome samples. Our approach relies on an expanded and curated set of viral protein families used as bait to identify viral sequences directly from metagenomic assemblies. This protocol describes how to use the viral protein families catalog (~7 h) and recommended filters for the detection of viral contigs in metagenomic samples (~6 h), and it describes the specific parameters for a nucleotide-sequence-identity-based method of organizing the viral sequences into quasi-species taxonomic-level groups (~10 min).

Paez-Espino, David↗
DOE OSTI2018

Exploring the effects of climatic variables on monthly precipitation variation using a continuous wavelet-based multiscale entropy approach

Highlights: • Developed a wavelet transform entropy approach to study precipitation. • Multiscale entropy values were the basis for precipitation regionalization. • Various entropy-based bands were introduced to segregate the CWME values for each cluster. • The relationship between changes of CWME and mean monthly precipitation were investigated. • Central rain gauges of each cluster were used for further analysis. Understanding precipitation on a regional basis is an important component of water resources planning and management. The present study outlines a methodology based on continuous wavelet transform (CWT) and multiscale entropy (CWME), combined with self-organizing map (SOM) and k-means clustering techniques, to measure and analyze the complexity of precipitation. Historical monthly precipitation data from 1960 to 2010 at 31 rain gauges across Iran were preprocessed by CWT. The multi-resolution CWT approach segregated the major features of the original precipitation series by unfolding the structure of the time series which was often ambiguous. The entropy concept was then applied to components obtained from CWT to measure dispersion, uncertainty, disorder, and diversification of subcomponents. Based on different validity indices, k-means clustering captured homogenous areas more accurately, and additional analysis was performed based on the outcome of this approach. The 31 rain gauges in this study were clustered into 6 groups, each one having a unique CWME pattern across different time scales. The results of clustering showed that hydrologic similarity (multiscale variation of precipitation) was not based on geographic contiguity. According to the pattern of entropy across the scales, each cluster was assigned an entropy signature that provided an estimation of the entropy pattern of precipitation data in each cluster. Based on the pattern of mean CWME for each cluster, a characteristic signature was assigned, which provided an estimation of the CWME of a cluster across scales of 1–2, 3–8, and 9–13 months relative to other stations. The validity of the homogeneous clusters demonstrated the usefulness of the proposed approach to regionalize precipitation. Further analysis based on wavelet coherence (WTC) was performed by selecting central rain gauges in each cluster and analyzing against temperature, wind, Multivariate ENSO index (MEI), and East Atlantic (EA) and North Atlantic Oscillation (NAO), indeces. The results revealed that all climatic features except NAO influenced precipitation in Iran during the 1960–2010 period.

54 ENVIRONMENTAL SCIENCES↗