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Custom spatial subdivision of N-dimensional lattice region in GPU memory. An extension of the method of a hyper-octree is used to allow for arbitrary subdivision ratios in each dimension. In addition, the decision to refine (or select) a given sub-region is based on a user-provided callback, allowing for arbitrary refinement domains to be expressed either geometrically or programmatically.
We present the first two-dimensional X-ray temperature map of the rich cluster of galaxies Abell 754. We also present an X-ray surface brightness map with improved spatial resolution and sensitivity compared with previous maps. Both the temperature map and the surface brightness map show that A754 is in the throes of a violent merger; it is probably far from hydrostatic equilibrium.
Global maps of rainfall are of great importance in connection with modeling of the earth s climate. Comparison between the maps of rainfall predicted by computer-generated climate models with observation provides a sensitive test for these models. To make such a comparison, one typically needs the total precipitation amount over a large area, which could be hundreds of kilometers in size over extended periods of time of order days or months. This presents a difficult problem since rain varies greatly from place to place as well as in time. Remote sensing methods using ground radar or satellites detect rain over a large area by essentially taking a series of snapshots at infrequent intervals and indirectly deriving the average rain intensity within a collection of pixels , usually several kilometers in size. They measure area average of rain at a particular instant. Rain gauges, on the other hand, record rain accumulation continuously in time but only over a very small area tens of centimeters across, say, the size of a dinner plate. They measure only a time average at a single location. In making use of either method one needs to fill in the gaps in the observation - either the gaps in the area covered or the gaps in time of observation. This involves using statistical models to obtain information about the rain that is missed from what is actually detected. This paper investigates such a statistical model and validates it with rain data collected over the tropical Western Pacific from ship borne radars during TOGA COARE (Tropical Oceans Global Atmosphere Coupled Ocean-Atmosphere Response Experiment). The model incorporates a number of commonly observed features of rain. While rain varies rapidly with location and time, the variability diminishes when averaged over larger areas or longer periods of time. Moreover, rain is patchy in nature - at any instant on the average only a certain fraction of the observed pixels contain rain. The fraction of area covered by rain decreases, as the size of a pixel becomes smaller. This means that within what looks like a patch of rainy area in a coarse resolution view with larger pixel size, one finds clusters of rainy and dry patches when viewed on a finer scale. The model makes definite predictions about how these and other related statistics depend on the pixel size. These predictions were found to agree well with data. In a subsequent second part of the work we plan to test the model with rain gauge data collected during the TRMM (Tropical Rainfall Measuring Mission) ground validation campaign.
The use of a form of remote sensing to aid in the management of large turfgrass fields (e.g. golf courses) has been proposed. A turfgrass field of interest would be surveyed in sunlight by use of an airborne hyperspectral imaging system, then the raw observational data would be preprocessed into hyperspectral reflectance image data. These data would be further processed to identify turfgrass stresses, to determine the spatial distributions of those stresses, and to generate maps showing the spatial distributions. Until now, chemicals and water have often been applied, variously, (1) indiscriminately to an entire turfgrass field without regard to localization of specific stresses or (2) to visible and possibly localized signs of stress for example, browning, damage from traffic, or conspicuous growth of weeds. Indiscriminate application is uneconomical and environmentally unsound; the amounts of water and chemicals consumed could be insufficient in some areas and excessive in most areas, and excess chemicals can leak into the environment. In cases in which developing stresses do not show visible signs at first, it could be more economical and effective to take corrective action before visible signs appear. By enabling early identification of specific stresses and their locations, the proposed method would provide guidance for planning more effective, more economical, and more environmentally sound turfgrass-management practices, including application of chemicals and water, aeration, and mowing. The underlying concept of using hyperspectral imagery to generate stress maps as guides to efficient management of vegetation in large fields is not new; it has been applied in the growth of crops to be harvested. What is new here is the effort to develop an algorithm that processes hyperspectral reflectance data into spectral indices specific to stresses in turfgrass. The development effort has included a study in which small turfgrass plots that were, variously, healthy or subjected to a variety of controlled stresses were observed by use of a hand-held spectroradiometer. The spectroradiometer readings in the wavelength range from 350 to 1,000 nm were processed to extract hyperspectral reflectance data, which, in turn, were analyzed to find correlations with the controlled stresses. Several indices were found to be correlated with drought stress and to be potentially useful for identifying drought stress before visible symptoms appear.
Coastal mangrove forests provide important ecosystem goods and services, including carbon sequestration, biodiversity conservation, and hazard mitigation. However, they are being destroyed at an alarming rate by human activities. To characterize mangrove forest changes, evaluate their impacts, and support relevant protection and restoration decision making, accurate and up-to-date mangrove extent mapping at large spatial scales is essential. Available large-scale mangrove extent data products use a single machine learning method commonly with 30 m Landsat imagery, and significant inconsistencies remain among these data products. With huge amounts of satellite data involved and the heterogeneity of land surface characteristics across large geographic areas, finding the most suitable method for large-scale high-resolution mangrove mapping is a challenge. The objective of this study is to evaluate the performance of a machine learning ensemble for mangrove forest mapping at 20 m spatial resolution across West Africa using Sentinel-2 (optical) and Sentinel-1 (radar) imagery. The machine learning ensemble integrates three commonly used machine learning methods in land cover and land use mapping, including Random Forest (RF), Gradient Boosting Machine (GBM), and Neural Network (NN). The cloud-based big geospatial data processing platform Google Earth Engine (GEE) was used for pre-processing Sentinel-2 and Sentinel-1 data. Extensive validation has demonstrated that the machine learning ensemble can generate mangrove extent maps at high accuracies for all study regions in West Africa (92%–99% Producer’s Accuracy, 98%–100% User’s Accuracy, 95%–99% Overall Accuracy). This is the first-time that mangrove extent has been mapped at a 20 m spatial resolution across West Africa. The machine learning ensemble has the potential to be applied to other regions of the world and is therefore capable of producing high-resolution mangrove extent maps at global scales periodically.
As the world’s water resources come under increasing tension due to dual stressors of climate change and population growth, accurate knowledge of water consumption through evapotranspiration (ET) over a range in spatial scales will be critical in developing adaptation strategies. Remote sensing methods for monitoring consumptive water use (e.g, ET) are becoming increasingly important, especially in areas of significant water and food insecurity. One method to estimate ET from satellite-based methods, the Atmosphere Land Exchange Inverse (ALEXI) model uses the change in mid-morning land surface temperature to estimate the partitioning of sensible and latent heat fluxes which are then used to estimate daily ET. This presentation will outline several recent enhancements to the ALEXI modeling system, with a focus on global ET and drought monitoring. Until recently, ALEXI has been limited to areas with high resolution temporal sampling of geostationary sensors. The use of geostationary sensors makes global mapping a complicated process, especially for real-time applications, as data from as many as five different sensors are required to be ingested and harmonized to create a global mosaic. However, our research team has developed a new and novel method of using twice-daily observations from polar-orbiting sensors such as MODIS and VIIRS to estimate the mid-morning rise in LST that is used to drive the energy balance estimations within ALEXI. This allows the method to be applied globally using a single sensor (in this case, initially MODIS with a planned transition to VIIRS) rather than a global compositing of all available geostationary data. Other advantages of this new method include the higher spatial resolution provided by MODIS and VIIRS and the increased sampling at high latitudes where oblique view angles limit the utility of geostationary sensors. This presentation will focus on global applications for mapping water use and drought using data mining and data fusion across spatial scales extending from 5-km to 30-m “field-scale” estimates.
Human and natural forces are rapidly modifying the global distribution and structure of terrestrial ecosystems on which all of life depends, altering the global carbon cycle, affecting our climate now and for the foreseeable future, causing steep reductions in species diversity, and endangering Earth s sustainability. To understand changes and trends in terrestrial ecosystems and their functioning as carbon sources and sinks, and to characterize the impact of their changes on climate, habitat and biodiversity, new space assets are urgently needed to produce high spatial resolution global maps of the three-dimensional (3D) structure of vegetation, its biomass above ground, the carbon stored within and the implications for atmospheric green house gas concentrations and climate. These needs were articulated in a 2007 National Research Council (NRC) report (NRC, 2007) recommending a new satellite mission, DESDynI, carrying an L-band Polarized Synthetic Aperture Radar (Pol-SAR) and a multi-beam lidar (Light RAnging And Detection) operating at 1064 nm. The objectives of this paper are to articulate the importance of these new, multi-year, 3D vegetation structure and biomass measurements, to briefly review the feasibility of radar and lidar remote sensing technology to meet these requirements, to define the data products and measurement requirements, and to consider implications of mission durations. The paper addresses these objectives by synthesizing research results and other input from a broad community of terrestrial ecology, carbon cycle, and remote sensing scientists and working groups. We conclude that: (1) current global biomass and 3-D vegetation structure information is unsuitable for both science and management and policy. The only existing global datasets of biomass are approximations based on combining land cover type and representative carbon values, instead of measurements of actual biomass. Current measurement attempts based on radar and multispectral data have low explanatory power outside low biomass areas. There is no current capability for repeatable disturbance and regrowth estimates. (2) The science and policy needs for information on vegetation 3D structure can be successfully addressed by a mission capable of producing (i) a first global inventory of forest biomass with a spatial resolution 1km or finer and unprecedented accuracy (ii) annual global disturbance maps at a spatial resolution of 1 ha with subsequent biomass accumulation rates at resolutions of 1km or finer, and (iii) transects of vertical and horizontal forest structure with 30 m along-transect measurements globally at 25 m spatial resolution, essential for habitat characterization. We also show from the literature that lidar profile samples together with wall-to53 wall L-band quad-pol-SAR imagery and ecosystem dynamics models can work together to satisfy these vegetation 3D structure and biomass measurement requirements. Finally we argue that the technology readiness levels of combined pol-SAR and lidar instruments are adequate for space flight. Remaining to be worked out, are the particulars of a lidar/pol-SAR mission design that is feasible and at a minimum satisfies the information and measurement requirement articulated herein.
The spectral and spatial distribution of radiation from Eta Carinae II and high-resolution infrared maps of the Homunculus are presented. It is found that at the resolution of 1.1 arcsec the source is resolved into two intensity peaks at four wavelengths from 3.6 to 11.2 microns. The separation of the two peaks with wavelength is discussed, concluding that they are produced by an asymmetrical distribution of dust formed by extensive mass loss from the central source. The extension of the wings of the source at various wavelengths provide confirmatory evidence for an enrichment of a grain species such as corundum, relative to silicate material in the outer regions of the source.
High spatial resolution continuum radio maps produced by the Westerbork Synthesis Radio Telescope (WSRT) of The Netherlands at frequencies near the 21 cm HI line have been examined for anomalous sources of emmission coincident with the locations of nearby bright stars. From a total of 542 stellar positions investigated, no candidates for radio stars or ETI signals were discovered to formal limits on the minimum detectable signal ranging from 7.7 x 10(-22) W/m2 to 6.4 x 10(-24) W/m2. This preliminary study has verified that data collected by radio astronomers at large synthesis arrays can profitably be analysed for SETI signals (in a non-interfering manner) provided only that the data are available in the form of a more or less standard two dimensional map format.
Mapping vegetation species is critical to facilitate related quantitative assessment, and mapping invasive plants is important to enhance monitoring and management activities. Integrating high-resolution multispectral remote-sensing (RS) images and lidar (light detection and ranging) point clouds can provide robust features for vegetation mapping. However, using multiple sources of high-resolution RS data for vegetation mapping on a large spatial scale can be both computationally and sampling intensive. Here, we designed a two-step classification workflow to potentially decrease computational cost and sampling effort and to increase classification accuracy by integrating multispectral and lidar data in order to derive spectral, textural, and structural features for mapping target vegetation species. We used this workflow to classify kudzu, an aggressive invasive vine, in the entire Knox County (1362 km2) of Tennessee (U.S.). Object-based image analysis was conducted in the workflow. The first-step classification used 320 kudzu samples and extensive, coarsely labeled samples (based on national land cover) to generate an overprediction map of kudzu using random forest (RF). For the second step, 350 samples were randomly extracted from the overpredicted kudzu and labeled manually for the final prediction using RF and support vector machine (SVM). Computationally intensive features were only used for the second-step classification. SVM had constantly better accuracy than RF, and the producer’s accuracy, user’s accuracy, and Kappa for the SVM model on kudzu were 0.94, 0.96, and 0.90, respectively. SVM predicted 1010 kudzu patches covering 1.29 km2 in Knox County. We found the sample size of kudzu used for algorithm training impacted the accuracy and number of kudzu predicted. The proposed workflow could also improve sampling efficiency and specificity. Our workflow had much higher accuracy than the traditional method conducted in this research, and could be easily implemented to map kudzu in other regions as well as map other vegetation species.
There has been no spatial surface wind map even over the conterminous USA due to the difficulty of spatial interpolation of wind field. As a result, the reanalysis data were often used to analyze the statistics of spatial pattern in surface wind speed. Unfortunately, no consistent trend in wind field was found among the available reanalysis data, and that obstructed the further analysis or projection of spatial pattern of wind speed. In this study, we developed the methodology to interpolate the observed wind speed data at weather stations using random forest algorithm. We produced the 1-km daily climate variables over the conterminous USA from 1979 to 2015. The validation using Ameriflux daily data showed that R2 is 0.59. Existing studies have found the negative trend over the Eastern US, and our study also showed same results. However, our new datasets also revealed the significant increasing trend over the southwest US especially from April to June. The trend in the southwestern US represented change or seasonal shift in North American Monsoon. Global analysis of CMIP5 data projected the decrease trend in mid-latitude, while increase trend in tropical region over the land. Most likely because of the low resolution in GCM, CMIP5 data failed to simulate the increase trend in the southwest US, even though it was qualitatively predicted that pole ward shift of anticyclone help the North American Monsoon.
We have used a NanoSIMS ion microprobe to map sub-micron-scale distributions of carbon, nitrogen, sulfur, silicon, and oxygen in organic microfossils and laminae from the approximately 0.85 Ga Bitter Springs Formation of Australia. The data provide clues about the original chemistry of the microfossils, the silicification process, and biosignatures of specific microorganisms and microbial communities. Chemical maps of fossil unicells and filaments reveal distinct wall-and sheath-like structures enriched in C, N and S, consistent with their accepted biological origin. Surprisingly, organic laminae, previously considered to be amorphous, also exhibit filamentous and apparently compressed spheroidal structures defined by strong enrichments in C, N and S. By analogy to data from the well-preserved microfossils, these structures are interpreted as being of biological origin, most likely representing densely packed remnants of microbial mats. Because the preponderance of organic matter in Precambrian sediments is similarly "amorphous," our findings open a large body of generally neglected material to in situ structural, chemical, and isotopic study. Our results also offer new criteria for assessing biogenicity of problematic kerogenous materials and thus can be applied to assessments of poorly preserved or fragmentary organic residues in early Archean sediments and any that might occur in meteorites or other extraterrestrial samples.
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Introduction: The Perseverance rover, which is currently exploring Jezero crater on Mars, is equipped with seven instruments that allow for observation of textures, minerals, color, structure, and chemistry of rocks and sediments in order to search for signs of ancient life, understand the geologic history of the crater, and identify candidates for sample return (Farley et al. 2020). The first of these aims includes the direct detection of potential biosignatures, including textures, organic molecules, minerals, and elemental chemistries that are of biogenic origin (Mustard et al. 2013). The presence of these biosignatures will be constrained by the habitability of the local region, the preservation potential of the host rocks, and the sensitivity of the instrument suite, and their biogenicity will be investigated after return to Earth as part of the Mars Sample Return campaign. Here, we examine key targets on the three planned campaigns, potential biosignatures that may be present, and the capabilities of key rover instruments. High Potential Biosignature Sites in Jezero: To date, measurements have been made on multiple sites that both contain minerals known in terrestrial settings to preserve biosignatures and likely were habitable settings (Williford et al. 2021). Two examples include the fine-grained rocks at the base of the delta fan and the NW inner margin of the crater. Fine-grained Rocks at Base of Delta Fan. Fine-grained, clay-bearing rocks may have been deposited as muddy lake sediments that could have hosted life and preserved biosignatures settling out of the water column. The report of organic molecules by the Curiosity rover in the Sheepbed mudstone and Murray formation has highlighted this site in particular. Potential biosignatures in mudstones, especially those rich in silica (McMahon et al. 2018), microbialites and complex organics. NW Inner Margin of Crater. This unit, located along the inner margin of the crater, contains strong carbonate signatures and may have been the littoral zone of a lake (Horgan et al. 2020). The potential biosignatures here include microfossils, microbialites, biominerals, and complex organics. Detectability of Biosignatures by the Mars 2020 Instrument Suite: The Scanning Habitable Environments with Raman and Luminescence for Organics and Chemicals (SHERLOC) instrument comprises a Deep UV spectrometer, context imager, and color camera to generate spatially resolved chemical maps (Bhartia et al. 2020). It is sensitive to trace organics as well as a range of minerals and can detect native fluorescence from aromatic organics; the WATSON and ACI cameras can be used to observe morphologies such as stromatolitic laminations or filaments ranging from the tens of micron to millimeter scale. SHERLOC can detect organics that may be present in either of the high potential biosignature targets, as well as detect carbonates in the latter. However, the presence of high amounts of iron, such as in iron-rich clays, would cause attenuation of spectral response through UV absorption. The Planetary Instrument for X-ray Lithochemistry (PIXL) comprises an X-ray fluorescence spectrometer and camera that can scan rock surfaces to generate elemental maps (Allwood et al. 2020). PIXL can detect chemical biosignatures such as spatial variations of elemental abundances that may have resulted from biological activity. PIXL would be particularly useful in detecting fine textures and elemental chemistries in either high potential biosignature target, but cannot directly detect minerals such as carbonate. The SuperCam instrument performs three types of spectroscopy, color imaging, and acoustic recording to remotely examine elemental composition, minerals, organics, and textures (Maurice et al. 2021). Using laser induced breakdown spectroscopy and time resolved luminescence spectroscopy, SuperCam can detect major elemental building blocks of organics (i.e., C, H, N, O, P, S) and conjugated organic structures, respectively, which may be found in either site. While in other contexts, luminescence is a useful tool for biosignature identification, luminescence generated by the 532 nm laser may obscure the Raman signal. Conclusion: The three instruments discussed can be used collaboratively to establish the presence of potential biosignatures in samples. These high-priority samples may then be returned to Earth for detailed laboratory analysis.
The Scanning Habitable Environments with Raman and Luminescence for Organics and Chemicals (SHERLOC) is a robotic arm-mounted instrument on NASA’s Perseverance rover. SHERLOC has two primary boresights. The Spectroscopy boresight generates spatially resolved chemical maps using fluorescence and Raman spectroscopy coupled to microscopic images (10.1 μm/pixel). The second boresight is a Wide Angle Topographic Sensor for Operations and eNgineering (WATSON); a copy of the Mars Science Laboratory (MSL) Mars Hand Lens Imager (MAHLI) that obtains color images from microscopic scales (~13 μm/pixel) to infinity. SHERLOC Spectroscopy focuses a 40 μs pulsed deep UV neon-copper laser (248.6 nm), to a ~100 μm spot on a target at a working distance of ~48 mm. Fluorescence emissions from organics, and Raman scattered photons from organics and minerals, are spectrally resolved with a single diffractive grating spectrograph with a spectral range of 250 to ~370 nm. Because the fluorescence and Raman regions are naturally separated with deep UV excitation (<250 nm), the Raman region ~ 800 – 4000 cm -1 (250 to 273 nm) and the fluorescence region (274 to ~370 nm) are acquired simultaneously without time gating or additional mechanisms. SHERLOC science begins by using an Autofocus Context Imager (ACI) to obtain target focus and acquire 10.1 μm/pixel greyscale images. Chemical maps of organic and mineral signatures are acquired by the orchestration of an internal scanning mirror that moves the focused laser spot across discrete points on the target surface where spectra are captured on the spectrometer detector. ACI images and chemical maps (< 100 μm/mapping pixel) will enable the first Mars in situ view of the spatial distribution and interaction between organics, minerals, and chemicals important to the assessment of potential biogenicity (containing CHNOPS). Single robotic arm placement chemical maps can cover areas up to 7x7 mm in area and, with the < 10 min acquisition time per map, larger mosaics are possible with arm movements. This microscopic view of the organic geochemistry of a target at the Perseverance field site, when combined with the other instruments, such as Mastcam-Z, PIXL, and SuperCam, will enable unprecedented analysis of geological materials for both scientific research and determination of which samples to collect and cache for Mars sample return.
The Scanning Habitable Environments with Raman and Luminescence for Organics and Chemicals (SHERLOC) is a robotic arm-mounted instrument on NASA’s Perseverance rover. SHERLOC has two primary boresights. The Spectroscopy boresight generates spatially resolved chemical maps using fluorescence and Raman spectroscopy coupled to microscopic images (10.1 μm/pixel). The second boresight is a Wide Angle Topographic Sensor for Operations and eNgineering (WATSON); a copy of the Mars Science Laboratory (MSL) Mars Hand Lens Imager (MAHLI) that obtains color images from microscopic scales (∼13 μm/pixel) to infinity. SHERLOC Spectroscopy focuses a 40 μs pulsed deep UV neon-copper laser (248.6 nm), to a ∼100 μm spot on a target at a working distance of ∼48 mm. Fluorescence emissions from organics, and Raman scattered photons from organics and minerals, are spectrally resolved with a single diffractive grating spectrograph with a spectral range of 250 to ∼370 nm. Because the fluorescence and Raman regions are naturally separated with deep UV excitation (<250 nm), the Raman region ∼ 800 – 4000 cm−1 (250 to 273 nm) and the fluorescence region (274 to ∼370 nm) are acquired simultaneously without time gating or additional mechanisms. SHERLOC science begins by using an Autofocus Context Imager (ACI) to obtain target focus and acquire 10.1 μm/pixel greyscale images. Chemical maps of organic and mineral signatures are acquired by the orchestration of an internal scanning mirror that moves the focused laser spot across discrete points on the target surface where spectra are captured on the spectrometer detector. ACI images and chemical maps (< 100 μm/mapping pixel) will enable the first Mars in situ view of the spatial distribution and interaction between organics, minerals, and chemicals important to the assessment of potential biogenicity (containing CHNOPS). Single robotic arm placement chemical maps can cover areas up to 7x7 mm in area and, with the < 10 min acquisition time per map, larger mosaics are possible with arm movements. This microscopic view of the organic geochemistry of a target at the Perseverance field site, when combined with the other instruments, such as Mastcam-Z, PIXL, and SuperCam, will enable unprecedented analysis of geological materials for both scientific research and determination of which samples to collect and cache for Mars sample return.
Development of a fast spatial scanning pyrometer for temperature measurements above 1500 K is described. The salient features of the pyrometer are: (1) it measures spectral radiance temperature (at 0.65 micron) at 1024 points along a straight line (25 mm long) on the target; (2) it has no moving parts and uses a self-scanning linear array of silicon photodiodes as the detector; (3) its output is recorded digitally every 1 microsec with a full-scale resolution of about 1 part in 4000, permitting performance of a complete cycle of measurements (1024 points) in about 1 ms. Operational characteristics of the pyrometer are given. Examples of measurements of the temperature along rapidly heated (resistive self-heating) specimens (rod, tube, strip) are presented. Potential use of the pyrometer in the experiments, both ground-based and in microgravity, requiring temperature mapping and property distribution of the specimen at high temperatures is discussed.
Patterned nanomagnet arrays (PNAs) have been shown to exhibit a strong geometrically frustrated dipole interaction. Some PNAs have also shown emergent domain wall dynamics. Previous works have demonstrated methods to physically probe these magnetization dynamics of PNAs to realize neuromorphic reservoir systems that exhibit chaotic dynamical behavior and high-dimensional nonlinearity. These PNA reservoir systems from prior works leverage echo state properties and linear/nonlinear short-term memory of component reservoir nodes to map and preserve the dynamical information of the input time-series data into nondelay spatial embeddings. Such mappings enable these PNA reservoir systems to imitate and predict/forecast the input time series data. However, these prior PNA reservoir systems are based solely on the nondelay spatial embeddings obtained at component reservoir nodes. As a result, they require a massive number of component reservoir nodes, or a very large spatial embedding (i.e., high-dimensional spatial embedding) per reservoir node, or both, to achieve acceptable imitation and prediction accuracy. These requirements reduce the practical feasibility of such PNA reservoir systems. To address this shortcoming, we present a mixed delay/nondelay embeddings-based PNA reservoir system. Our system uses a single PNA reservoir node with the ability to obtain a mixture of delay/nondelay embeddings of the dynamical information of the time-series data applied at the input of a single PNA reservoir node. Our analysis shows that when these mixed delay/nondelay embeddings are used to train a perceptron at the output layer, our reservoir system outperforms existing PNA-based reservoir systems for the imitation of NARMA 2, NARMA 5, NARMA 7, and NARMA 10 time series data, and for the short-term and long-term prediction of the Mackey Glass time series data.