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At least 595 records · Page 33

Enhancing Short-Range Weather Forecasts through Temporal Variation Encoding: A Multiperiod Embedding Approach

Machine learning (ML) techniques have emerged as promising approaches to improve regional weather forecast accuracy and reliability through data-driven methods. We propose a novel ML-based weather forecasting model, the Multiperiod Embed Net (MPENet). A key distinguishing feature of MPENet is its explicit utilization of the inherent cyclic nature in weather dynamics, unlike the autoregressive strategies commonly used in other ML weather forecasting approaches. Critical cyclic structures are identified via Fourier analyses of dynamic time series. Cyclicity in the convolutional representation is achieved by transforming one-dimensional time series of meteorological variables into two-dimensional tensors based on identified periods. This approach enables the model to leverage intrinsic weather patterns, enhancing regional forecast performance. To demonstrate the effectiveness of MPENet, we conduct a comparative analysis with Nvidia’s FourCastNet. Both models are trained on High-Resolution Rapid Refresh (HRRR) data from 2015 to 2022, over a 192 km × 192 km region in Tennessee. The comparisons are performed locally at two specific locations known to have different weather dynamics due to orographic effects: Crossville, on the relatively flat Cumberland Plateau with fewer topographic airflow disruptions, and Oak Ridge, in the ridge-and-valley region, where airflow is heavily influenced by surrounding valleys and mountains. Our results indicate that FourCastNet achieves strong accuracy at very short lead times, while MPENet maintains competitive skill and shows advantages in capturing temporal evolution over longer periods. Cross-correlation analyses of MPENet and FourCastNet predictions with the HRRR data suggest that encoding critical cyclicity into the network architecture leads to improvements in the forecasting skill.

Artificial intelligence↗

On the structure of cellular solutions in Rayleigh-Benard-Marangoni flows in small-aspect-ratio containers

Multiple steady flow patterns occur in surface-tension/buoyancy-driven convection in a liquid layer heated from below (Rayleigh-Benard-Marangoni flows). Techniques of numerical bifurcation theory are used to study the multiplicity and stability of two-dimensional steady flow patterns (rolls) in rectangular small-aspect-ratio containers as the aspect ratio is varied. For pure Marangoni flows at moderate Biot and Prandtl number, the transitions occurring when paths of codimension 1 singularities intersect determine to a large extent the multiplicity of stable patterns. These transitions also lead, for example, to Hopf bifurcations and stable periodic flows for a small range in aspect ratio. The influence of the type of lateral walls on the multiplicity of steady states is considered. 'No-slip' lateral walls lead to hysteresis effects and typically restrict the number of stable flow patterns (with respect to 'slippery' sidewalls) through the occurrence of saddle node bifurcations. In this way 'no-slip' sidewalls induce a selection of certain patterns, which typically have the largest Nusselt number, through secondary bifurcation.

Dijkstra, Henk A.↗

Poly(dimethylsiloxane- b -methyl methacrylate): A Promising Candidate for Sub-10 nm Patterning

We report herein the modular synthesis and nanolithographic potential of poly(dimethylsiloxane-block-methyl methacrylate) (PDMS-b-PMMA) with self-assembled domains approaching sub-10 nm periods. A straightforward and modular coupling strategy, optimized for low molecular weight diblocks and using copper-catalyzed azide–alkyne “click” cycloaddition, was employed to obtain a library of PDMS-b-PMMA and poly(dimethylsiloxane-block-styrene) (PDMS-b-PS) diblock copolymers. Flory–Huggins interaction parameters, determined from small-angle X-ray scattering experiments, were high for PDMS-b-PMMA (χ ~ 0.2 at 150 °C), suggesting this diblock copolymer system has promise for sub-10 nm lithographic applications when compared to the corresponding PDMS-b-PS diblock copolymers (χ ~ 0.1 at 150 °C). Furthermore, performance evaluation in thin film self-assembly experiments allowed domain periods as small as 12.1 nm to be obtained, which is among the smallest highly ordered nanoscale patterns reported hitherto for thermally annealed materials.

36 MATERIALS SCIENCE↗

Ionospheric convection response to changing IMF direction

By combining ground-based and satellite-based measurements of ionospheric electric fields, conductivities and magnetic perturbations, it was possible to examine the characteristics of instantaneous, ionospheric convection patterns associated with changing directions of the interplanetary magnetic field (IMF). In response to a rapid southward-to-northward turning of the IMF on July 23, 1983, the ionospheric convection reconfigured over a period of 40 minutes. The configuration changed from a conventional two-cell pattern to a contracted four-cell pattern, with reversed convection cells in the high-latitude dayside, associated with a strong potential drop of about 75 kV. Later, in response to a gradual rotation of the IMF from the +Z through the -Y toward the -Z direction, the nightside cells disappeared and the dawn cell in the reversed pair wrapped around and displaced the dusk cell until a conventional two-cell pattern was reestablished, largely in accord with the qualitative model of Crooker (1988). The results suggest that multiple cells can arise as a result of strong southward to northward transitions in the IMF. They appear to persist for sometime thereafter.

Knipp, D. J.↗

Climate and atmospheric deposition drive the inter-annual variability and long-term trend of dissolved organic carbon flux in the conterminous United States

The lateral flux of dissolved organic carbon (DOC) from soils to inland waters and ultimately to the ocean represents a fundamental component of the global carbon cycle. To estimate the DOC flux, we developed an empirical terrestrial-aquatic DOC fluxes model (TAF-DOC). TAF-DOC incorporates various environmental factors (e.g., meteorology, sulfur, and nitrogen deposition) that to-date have not been comprehensively considered or well-represented in existing modeling frameworks. TAF-DOC was applied to estimate spatial-temporal patterns of DOC flux and potential fates across the conterminous United States during the 1985 to 2018 time period. Our results suggest that TAF-DOC successfully characterized spatial-temporal of DOC flux. As expected, the interannual pattern of DOC flux was strongly regulated by precipitation, but the long-term trend was significantly influenced by the rate of atmospheric wet sulfur deposition. From 1985 to 2018, TAF-DOC estimated DOC loading from terrestrial to aquatic ecosystems in the conterminous United States to be 33.5 ± 2.2 TgC per year, which was roughly 0.39–0.49% of total soil organic carbon stock estimates. The dominant fate of terrestrially-derived DOC was delivery to the coastal ocean in riverine export (41%), with another 21% buried in sediment and the remaining 12.8 ± 0.4 TgC per year (38%) returned to the atmosphere through outgassing from inland waters. Finally, assuming the quantities of DOC sediment burial and export to the ocean as an annual sink of terrestrially-derived carbon, budget inventories and models that do not account for DOC flux in the conterminous United States will underestimate the net annual carbon sink by as much as 5.5–6.4%.

54 ENVIRONMENTAL SCIENCES↗

The influence of differential rotation on the equatorial component of the sun's magnetic dipole field

This paper examines the effect that solar differential rotation would have on a hypothetical large-scale equatorial dipole field. The evolving large-scale field pattern is expressed as a series of non-axisymmetric moments. As time increases, power is transferred to progressively higher order moments. In the 27d rotating coordinate system, each moment undergoes a small retrograde drift which remains nearly uniform until that mode begins to fade. The synodic rotation periods of the first few moments are comparable to the observed 28.5d period of the sun's large-scale field near sunspot maximum. Differential rotation may be the source of this 28.5d period, but the eruption of new flux is necessary to keep the pattern going.

Sheeley, N. R., Jr.↗

Clouds, precipitation, and the global heat and moisture budgets during SOP-1, FGGE

Two sets of precipitation estimates are derived using the budget method equations: one is based on the apparent heat source or Q1-budget technique, the other is based on the apparent moisture sink or Q2-budget technique. Both techniques and application results are presented for the period of January 10 to February 13, 1979 which was part of SOP-1, FGGE. Maps of time-averaged outgoing longwave radiation (OLR) are shown for two periods running from January 10 to January 24, 1979 and from January 26 to February 7, 1979. The present study of estimating precipitation was initiated because of agreement between OLR and circulation patterns, and the noted regional differences and similarities in deep convections between these two periods.

Pedigo, Catherine B.↗

Classifying Multi-Model Wheat Yield Impact Response Surfaces Showing Sensitivity to Temperature and Precipitation Change

Crop growth simulation models can differ greatly in their treatment of key processes and hence in their response to environmental conditions. Here, we used an ensemble of 26 process-based wheat models applied at sites across a European transect to compare their sensitivity to changes in temperature (minus 2 to plus 9 degrees Centigrade) and precipitation (minus 50 to plus 50 percent). Model results were analysed by plotting them as impact response surfaces (IRSs), classifying the IRS patterns of individual model simulations, describing these classes and analysing factors that may explain the major differences in model responses. The model ensemble was used to simulate yields of winter and spring wheat at four sites in Finland, Germany and Spain. Results were plotted as IRSs that show changes in yields relative to the baseline with respect to temperature and precipitation. IRSs of 30-year means and selected extreme years were classified using two approaches describing their pattern. The expert diagnostic approach (EDA) combines two aspects of IRS patterns: location of the maximum yield (nine classes) and strength of the yield response with respect to climate (four classes), resulting in a total of 36 combined classes defined using criteria pre-specified by experts. The statistical diagnostic approach (SDA) groups IRSs by comparing their pattern and magnitude, without attempting to interpret these features. It applies a hierarchical clustering method, grouping response patterns using a distance metric that combines the spatial correlation and Euclidian distance between IRS pairs. The two approaches were used to investigate whether different patterns of yield response could be related to different properties of the crop models, specifically their genealogy, calibration and process description. Although no single model property across a large model ensemble was found to explain the integrated yield response to temperature and precipitation perturbations, the application of the EDA and SDA approaches revealed their capability to distinguish: (i) stronger yield responses to precipitation for winter wheat than spring wheat; (ii) differing strengths of response to climate changes for years with anomalous weather conditions compared to period-average conditions; (iii) the influence of site conditions on yield patterns; (iv) similarities in IRS patterns among models with related genealogy; (v) similarities in IRS patterns for models with simpler process descriptions of root growth and water uptake compared to those with more complex descriptions; and (vi) a closer correspondence of IRS patterns in models using partitioning schemes to represent yield formation than in those using a harvest index. Such results can inform future crop modelling studies that seek to exploit the diversity of multi-model ensembles, by distinguishing ensemble members that span a wide range of responses as well as those that display implausible behaviour or strong mutual similarities.

Classification; Climate change; Crop model; Ensemb↗

Linear trends in Northern Hemisphere tropospheric geopotential height and temperature patterns

Gridded National Meteorological Center data for 500 mb geopotential height and 300-500 mb and 500-700 mb thickness for the period 1951-1978 are subjected to linear trend analyses. The analyses are carried out for each calendar month. Significant geographical and seasonal distributions of cooling and warming patterns are found. An atmospheric cooling trend over the North Pacific during the winter months is seen in a region where oceanic cooling has also been observed, but planetary-wave adjustments rather than ocean-atmosphere feedback mechanisms appear to be dominant in the atmospheric cooling on climatic time scales. Consistently large temperature trends are also seen over the continent of Asia. Comparisons between thickness trends in the layer 300-500 mb and those in the layer 500-700 mb reveal pronounced patterns of stabilization and destabilization.

Reiter, E. R.↗

Investigation of the environmental change pattern of Japan

The author has identified the following significant results. ERTS-1 imagery clearly identifies the relationships between the status of erosion, effluent patterns affected by the coastal current, and the cultural construction activities. Simple photographic techniques can be used for detecting water mass distribution separately from cloud cover and also noise caused by reflected sunlight from wave surfaces. Polluted water does not diffuse continuously into the oceanic water, but forms masses in the water in the Kuroshio area. The polluted or turbid water in the area just north of the Tomogashima Channel, the south outlet of the Osaka Bay, shows that the northward tidal current runs in a clockwise eddy at the tidal period when the imagery was taken. Such an eddy-like pattern of tidal current had never been revealed by conventional oceanographic data. A front between an oceanic water mass and a polluted water mass runs in a NW-SE direction in the central part of the Osaka Bay. The patterns of turbid water discharged from the Kii River and Yoshino River show a northward tidal current in the North Kii Straits. The pattern of lighter turbid or polluted water located in the northwest region of the North Kii straits suggests the existence of a clockwise eddy in the straits.

Maruyasu, T.↗

Enhancement of Optical Emission and Ion Currents in a Laser Produced Silicon Plasma by Femtosecond Laser-Induced Periodic Surface Structuring

Laser-induced periodic surface structuring is a powerful technique for modifying the surface properties of solids. Using ultrashort pulses from a Ti:Sapphire laser (800 nm, 100 fs) we have fabricated nanoscale order laser-induced periodic surface structures (LIPSS) on a silicon (100) surface. The LIPSS patterns are found to be strongly dependent on the laser pulse energy, state of polarization, number of shots delivered on the target, and the ambient pressure. The role of laser wavelength is studied by using the second harmonic output (400 nm) also for fabrication. Large area (5x4 mm2) surface structuring has been carried out at atmospheric pressure after optimizing the laser parameters at 800 nm. The patterned silicon surface shows a substantial reduction in the reflection of incident light over a wide range of wavelengths, in comparison to plain silicon. Moreover, when used for laser induced breakdown spectroscopy (LIBS) experiments, enhanced optical emission and ion current have been observed from the patterned surface. This indicates that coupling of laser energy to the surface is enhanced in the case of patterned silicon. While spectral lines emitted by doubly ionized silicon have been observed from the patterned surface, the plain surface gives lines from singly ionized silicon only. A discernible enhancement has been measured in both optical (50-90%) and electrical (34%) signals from the plasma generated on the patterned surface. These results confirm that LIPSS is a versatile method for enhancing the coupling of laser energy on to irradiated solid surfaces.

ion currents, optical emission, laser produced sil↗

Smart Ventilation Controls for Occupancy and Auxiliary Fan Use Across U.S. Climates

Smart Ventilation has been developed as a way to reduce the energy associated with ventilation by changing when ventilation happens and how much ventilation occurs at any given time. In high performance buildings with low envelope and appliance related loads, ventilation is becoming a bigger part of the total building energy use and needs to be addressed if performance targets are to be met. This work explores the development and performance of smart ventilation controls based on occupancy and auxiliary fan operation that provide annual dwelling unit ventilation equivalence to ASHRAE Standard 62.2-2016. A prototype high performance home compliant with U.S. DOE Building America Zero Energy Ready program requirements was simulated using the REGCAP tool with and without smart controls across 15 U.S. DOE climate zones. Balanced and unbalanced IAQ fans were independently simulated, and all smart controlled fans had airflows double the reference 62.2-2016 airflow. Three idealized occupancy patterns were examined: 1st shift (a typical daily work/school absence), an extended 1st shift with more time spent out of the home evenings and weekends and 3rd shift (night work). The Occupancy controller turns the IAQ fan off during unoccupied periods, and it resumes ventilation upon their return. While unoccupied, contaminants are allowed to accumulate in the space, because occupants are not exposed to these contaminants. When occupants return home, they are exposed to these higher contaminant concentrations, and the controller increases the ventilation rate sufficiently to ensure equivalence with a continuous IAQ fan. Accounting for pollutant emissions that occur during unoccupied periods (as required by ASHRAE 62.2-2016), sharply distinguishes our occupancy controls from past Demand Controlled Ventilation systems. This new accounting method results in equivalent contaminant exposure, as well as lower reductions in average ventilation rates and lower energy savings. Smart controls were demonstrated that saved HVAC energy (i.e., avoided heating/cooling load, as well as fan energy)—averaging between 6 and 46% of ventilation-related energy use depending on the control strategy and occupancy pattern assumptions. The greatest savings were in the combined Auxiliary Fan + Occupancy control. Energy savings increased with climate heating demand and longer unoccupied time periods. The 3rd shift occupancy pattern had better performance, due to the thermal benefit of reducing the ventilation rate during the cold nighttime hours. This same effect provided a cooling energy benefit in hotter locations for the 1st shift. Overall, savings from occupancy-based smart controls were low, because of the recovery period required after occupants return home, during which the airflow is double the 62.2 reference. This recovery is required to maintain equivalence with the ASHRAE standard. Occupancy-based control performance was improved when combined with sensing auxiliary fans and when providing a pre-occupancy flush out of one- or two-hours. Performance was similarly improved if the ASHRAE Standard were to recognize that pollutant emissions are lower during unoccupied periods, iii allowing a lower target ventilation rate during unoccupied periods (not currently in the standard) (see Full vs. Half AEQ in this report). Finally, over-sized unbalanced fans that are cycled on-and-off by a smart controller (or timer) were found to substantially increase annual average air exchange and energy use relative to a continuous unbalanced fan due to the effects of superposition with natural infiltration.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Evidence for a fundamental period of the sun and its relation to the 154 day complex of periodicities

We have analyzed the longitude distributions of major flares observed in the 1955-1991 interval, referring them to coordinate systems rotating about axes tilted with respect to the rotation axis of the solar envelope. We find that the longitude distribution exhibits the largest modulation in the coordinate system with the following parameters: rotation period, 25.50 days; tilt angle of the rotation axis, 40 deg; tilt direction, toward the position of the earth on December 4 in its orbit around the sun. We interpret this as being due to an obliquely rotating structure (or a wave pattern rotating about an oblique axis) which has two exciters. We identify the period of 25.50 days as the fundamental period of the hypothetical 'clock' proposed by Bai and Sturrock (1991). The periods of the subharmonics are 51.0, 76.5, 102.0, 127.5, and 153.0 days, in agreement with periodicities found from analysis of flare occurrence times.

Bai, T.↗

Self-organization of nanoparticles and molecules in periodic Liesegang-type structures

Chemical organization in reaction-diffusion systems offers a strategy for the generation of materials with ordered morphologies and structural hierarchy. Periodic structures are formed by either molecules or nanoparticles. On the premise of new directing factors and materials, an emerging frontier is the design of systems in which the precipitation partners are nanoparticles and molecules. We show that solvent evaporation from a suspension of cellulose nanocrystals (CNCs) and L -(+)-tartaric acid [ L -(+)-TA] causes phase separation and precipitation, which, being coupled with a reaction/diffusion, results in rhythmic alternation of CNC-rich and L -(+)-TA–rich rings. The CNC-rich regions have a cholesteric structure, while the L -(+)-TA–rich bands are formed by radially aligned elongated bundles. The moving edge of the pattern propagates with a finite constant velocity, which enables control of periodicity by varying film preparation conditions. This work expands knowledge about self-organizing reaction-diffusion systems and offers a strategy for the design of self-organizing materials.

36 MATERIALS SCIENCE↗

Impact of decadal cloud variations on the Earth’s energy budget

Feedbacks of clouds on climate change strongly influence the magnitude of global warming. Cloud feedbacks, in turn, depend on the spatial patterns of surface warming, which vary on decadal timescales. Therefore, the magnitude of the decadal cloud feedback could deviate from the long-term cloud feedback. We present climate model simulations to show that the global mean cloud feedback in response to decadal temperature fluctuations varies dramatically due to time variations in the spatial pattern of sea surface temperature. Here, we find that cloud anomalies associated with these patterns significantly modify the Earth’s energy budget. Specifically, the decadal cloud feedback between the 1980s and 2000s is substantially more negative than the long-term cloud feedback. This is a result of cooling in tropical regions where air descends, relative to warming in tropical ascent regions, which strengthens low-level atmospheric stability. Under these conditions, low-level cloud cover and its reflection of solar radiation increase, despite an increase in global mean surface temperature. Our results suggest that sea surface temperature pattern-induced low cloud anomalies could have contributed to the period of reduced warming between 1998 and 2013, and o er a physical explanation of why climate sensitivities estimated from recently observed trends are probably biased low.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Non-contact magnetically coupled rectilinear-rotary oscillations to exploit low-frequency broadband energy harvesting with frequency up-conversion

Ambient vibrations have a rectilinear and broadband nature and are particularly rich in the low-frequency regions. This letter reports an electromagnetic energy harvester to transform low-frequency broadband rectilinear vibrations into electricity with frequency up-conversion. The harvester consists of a rectilinear oscillator and a rotary oscillator coupled through magnetic force induced by four arc permanent magnets centrosymmetrically distributed on each oscillator. The rotary oscillator also includes two repulsive magnets and six stationary coils with steel screws inside to obtain and maintain four equilibrium positions with shallowed potential wells. The magnetic interaction between the rectilinear oscillator and the rotary oscillator is formulated using a magnetic dipole model. The restoring torque induced by the steel screws on the rotor is experimentally measured. Magnetically coupled governing equations are derived and their numerical solutions are used to characterize the dynamic response of the harvester under chirp excitations. Experimental results demonstrate its excellent harvesting capability of scavenging low-frequency wideband vibrational energy under slow-frequency-drifted excitations, simple harmonic excitations, and mixed-frequency excitations. Under harmonic excitations, the rectilinear oscillator vibrates non-harmonically but approximately periodically, while the rotary counterpart oscillates in a more complex pattern varying with the excitation frequency, which leads to the frequency up-conversion (up to 10 times increase) and broadened bandwidth (25% increase from its resonant frequency). Experiments show an output voltage of 5 V (RMS)/40 V (Peak to Peak) and an output power of 55 mW (RMS)/950 mW (Peak) at an optimal load of 465 Ω under harmonic excitation of 4 Hz at 0.7 g.

Deng, Wei (ORCID:0000000194598151)↗

High-precision phase control of an optical lattice with up to 50 dB noise suppression

An optical lattice is a periodic light crystal constructed from the standing-wave interference patterns of laser beams. It can be used to store and manipulate quantum degenerate atoms and is an ideal platform for the quantum simulation of many-body physics. A principal feature is that optical lattices are flexible and possess a variety of multidimensional geometries with modifiable band structure. An even richer landscape emerges when control functions can be applied to the lattice by modulation of the position or amplitude with Floquet driving. However, the desire of realizing high-modulation bandwidths while preserving extreme lattice stability has been difficult to achieve. In this paper, we demonstrate an effective solution that consists of overlapping two counterpropagating lattice beams and controlling the phase and intensity of each with independent acousto-optic modulators. Our phase controller mixes sampled light from both lattice beams with a common optical reference. This dual heterodyne locking method allows exquisite determination of the lattice position, while also removing parasitic phase noise accrued as the beams travel along separate paths. Here, we report up to 50 dB suppression in lattice phase noise in the 0.1–1 Hz band, along with significant suppression spanning more than 4 decades of frequency. The absolute phase diffusion of the lattice position is only 10 Å when integrated over 10 s. This method permits precise, high-bandwidth modulation (greater than 50 kHz) of the optical lattice intensity and phase. We demonstrate the efficacy of this approach by executing intricate time-varying phase profiles for atom interferometry.

Atom interferometry↗

Successional trajectories of rhizosphere bacterial communities over consecutive seasons

It is well known that rhizosphere microbiomes differ from those of surrounding soil, and yet we know little about how these root-associated microbial communities change through the growing season and between seasons. We analyzed the response of soil bacteria to roots of the common annual grass Avena fatua over two growing seasons using high-throughput sequencing of 16S rRNA genes. Over the two periods of growth, the rhizosphere bacterial communities followed consistent successional patterns as plants grew, although the starting communities were distinct. Succession in the rhizosphere was characterized by a significant decrease in both taxonomic and phylogenetic diversity relative to background soil communities, driven by reductions in both richness and evenness of the bacterial communities. Plant roots selectively stimulated the relative abundance of Alphaproteobacteria , Betaproteobacteria , and Bacteroidetes but reduced the abundance of Acidobacteria , Actinobacteria , and Firmicutes . Taxa that increased in relative abundance in the rhizosphere soil displayed phylogenetic clustering, suggesting some conservation and an evolutionary basis for the response of complex soil bacterial communities to the presence of plant roots. The reproducibility of rhizosphere succession and the apparent phylogenetic conservation of rhizosphere competence traits suggest adaptation of the indigenous bacterial community to this common grass over the many decades of its presence. We document the successional patterns of rhizosphere bacterial communities associated with a “wild” annual grass, Avena fatua , which is commonly a dominant plant in Mediterranean-type annual grasslands around the world; the plant was grown in its grassland soil. Most studies documenting rhizosphere microbiomes address “domesticated” plants growing in soils to which they are introduced. Rhizosphere bacterial communities exhibited a pattern of temporal succession that was consistent and repeatable over two growing seasons. There are few studies assessing the reproducibility over multiple seasons. Through the growing season, the rhizosphere community became progressively less diverse, likely reflecting root homogenization of soil microniches. Phylogenetic clustering of the rhizosphere dynamic taxa suggests evolutionary adaptation to Avena roots. The reproducibility of rhizosphere succession and the apparent phylogenetic conservation of rhizosphere competence traits suggest adaptation of the indigenous bacterial community to this common grass over the many decades of its presence.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗