A posteriori pointwise error computation for 2-D transport equations based on the variational multiscale method

This article presents a general framework to estimate the pointwise error of linear partial differential equations. The error estimator is based on the variational multiscale theory, in which the error is decomposed in two components according to the nature of the residuals: element interior residuals and inter-element jumps. The relationship between the residuals (coarse scales) and the error components (fine scales) is established, yielding to a very simple model. In particular, the pointwise error is modeled as a linear combination of bubble functions and Green’s functions. If residual-free bubbles and the classical Green’s function are employed, the technology leads to an exact explicit method for the pointwise error. If bubble functions and free-space Green’s functions are employed, then a local projection problem must be solved within each element and a global boundary integral equation must be solved on the domain boundary. As a consequence, this gives a model for the so-called fine-scale Green’s functions. The numerical error is studied for the standard Galerkin and SUPG methods with application to the heat equation, the reaction–diffusion equation and the convection–diffusion equation. Numerical results show that stabilized methods minimize the propagation of pollution errors, which stay mostly locally

Trends of Aboveground Net Primary Productivity of Patagonian Meadows, the Omitted Ecosystem in Desertification Studies

The United Nations defines desertification as the loss of productivity in arid and semiarid environments. The extended steppes of Patagonia harbor small meadows whose compounded area is comparatively small, but their aboveground net primary production (ANPP) is up to ten times higher than their surroundings. These meadows then represent a key ecosystem for cattle grazing systems, but there are no descriptions of the trends in their ANPP and, consequently, their carrying capacity, and, as a result, their degradation syndromes. Our objectives were as follows: (1) analyze the trends of mean and spatial heterogeneity of annual ANPP in meadows and neighboring steppes and relate them with precipitation and temperature, (2) evaluate the impact on the livestock carrying capacity of meadows in the region, and (3) evaluate the degradation trends of these meadows, based on a novel description proposed to characterize the trend syndromes of these type of ecosystems. We identified meadow areas across a subcontinental scale in Patagonia, covering a mean annual precipitation range from 129 to 936 mm. We estimated ANPP on a monthly basis from 2000 to 2019 via regional calibrated remote sensing information. In the last two decades, ANPP decreased in 74% of the studied meadow areas, while remaining relatively stable in the nearby steppes. This decrease was relatively higher in the arid end of the analyzed precipitation gradient. Hence, the global carrying capacity for all the studied meadow areas decreased by 8%. Finally, we identified four trend syndromes based on the combination of the ANPP trend and its spatial heterogeneity, calculated as the spatial standard deviation. The predominant trend syndrome, in 55% of the area, was associated with a negative trend of both ANPP and spatial heterogeneity. These results could help prioritize areas where specific management decisions, given the different trend syndromes, could help revert ANPP negative trends

Generating the Best Stacking Sequence Table for the Design of Blended Composite Structures

In order to improve the ability of a large-scale light-weight composite structure to carry tensile or compressive loads, stiffeners are added to the structure. The stiffeners divide the structure into several smaller panels. For a composite structure to be manufacturable, it is necessary that plies are continuous in multiple adjacent panels. To be able to prescribe a manufacturable design, an optimization algorithm can be coupled with a reference table for the stacking sequences (SST). As long as the ply stacks are selected from the SST, it is guaranteed that the design is manufacturable and all strength related guidelines associated with the design of composite structures are satisfied. An SST is made only based on strength related guidelines. Therefore, there exist a large number of possibilities for SSTs. Minimized mass is a typical goal in the design of aircraft structures. Different SSTs result in different values for the minimized mass. Thus it is crucial to perform optimization based on the SST which results in the lowest mass. This paper aims to introduce an approach to generate a unique SST resulting in the lowest mass. The proposed method is applied to the optimization problem of a stiffened composite structure resembling the skin of an aircraft wing box

Comparing Forage Biomass Estimation Between Forager-Mounted Near Infrared Spectroscopy (NIRS) and Rising Plate-Meter (RPM) Techniques

Quantifying the forage mass harvested per paddock is essential for informing late-season management decisions on grazing livestock farms. This information can be used to calculate winter feed budgets and thus support decisions such as area of land to defer for autumn grazing, and head of stock to sell before winter housing. However, there are practical limitations associated with existing measurement methods, which can influence the accuracy of forage biomass estimates. The purpose of the current study was therefore to compare biomass estimation from two alternative precision farming methods — near infrared spectroscopy (NIRS) integrated within-spout of a self-propelled forage harvester, against a rising plate meter (RPM). Data were collected from the North Wyke Farm Platform (NWFP) in South- West England. RPM readings were taken within seven days preceding harvest, and Harvester measurements taken at the point of harvest. Data from two paddocks were collected during 2021 (figure 2, points a and b) and two from 2020 (points c and d). Three of the sampled paddocks (a, c and d) contained permanent pasture and one (b) contained reseeded white clover and perennial ryegrass. Paddocks c and d in figure 2 suggest a good correspondence between methods, demonstrated by proximity to the 1:1 line which passes through the origin. However, points a and b lie parallel to the 1:1 line, suggesting a systematic underestimation from the RPM. This underestimation could be linked to the tendency of grass to lodge at high yields, or due to an unquantified factor linked to the year of harvest, such as weather conditions which are known to indirectly influence RPM readings. With suitable calibration and consideration of practical limitations, forager mounted NIRS technology can provide valuable farm management data quickly, and at a relatively low cost compared to manual methods of biomass estimation

Winter Herbage Mass Accumulation and Animals Grazing Days of Set Stocking or Cell Grazing Dairy x Beef Systems in Southwest England

Cell grazing (CG) has shown to increase the production per hectare by allowing higher stocking rates, greater grass production and higher herbage utilisation throughout the grazing season compared to set stocking (SS). Our objective was to compare the herbage growth rate during winter resting (WHGR, October/November to April) and the animals grazing days per ha (AGD-ha) of CG and SS systems grazed by dairy x beef steers. Three 1.75ha (1.5ha in 2018) plots and three 1.0ha were used for the SS and CG, respectively. Forty-two and 48 autumn born dairy x beef steer calves were split into six equal groups and randomly allocated to treatments in April 2018 and April 2020, respectively. In the second grazing seasons (2019 and 2021), the number of animals was reduced to keep stocking rates comparative to the prior year, and steers remained in the plots until finishing (October/November). Herbage mass (HM) was recorded weekly with a rising plate meter. The WHGR was estimated by subtracting the HM recorded at the end of the previous grazing season to the HM recorded at the beginning of the following season and divided by the number of days between readings. The AGD-ha was calculated by summing the days each animal grazed each area and divided by the size of the study enclosure. In three of the four years, the CG had fewer days of winter resting (157-175) than the SS (157-182), whereas the WHGR was greater in three of the four winters (average across years: 5.77 vs. 4.05 kg DM/ha per d, for CG and SS respectively). Despite the shorter winter rest, overall, the CG accumulated 37% more HM (average across years: 976 vs. 710 kg DM/ha) and had 78% more AGD-ha (1102 vs. 620 animal.d/ha) than SS. These differences do not seem to be driven by the herbage residual at the end of the grazing season but by the change in botanical composition across time

Biophysical, Grazing-Season Management, and Animal Traits Effects on Individual Animal Performance of Cow-Calf Systems: Insights from a Long-Term Experiment in the US Western Great Plains

Beef grazing systems require information on management, biophysical, and individual animal influences on performance metrics. However, long-term controlled experiments are lacking to comprehensively ascertain these individual and likely interacting influences. We used a legacy data set from the USDA Agricultural Research Service where individual weight gains were determined from on and off weights of Hereford cows and calves grazing native northern mixed-grass prairie, during the June through September season, from 1975-2001 near Cheyenne, Wyoming, USA. The herd size varied from a minimum of 10 to a maximum of 48 pairs across years. Management (on and off grazing dates and stocking rate, kg BW/ha), biophysical (forage production estimated through NDVI LANDSAT time series, temperature, and precipitation variability), and individual animal (cow age, cow body weight at beginning of grazing season, and calf gender) influences were evaluated for effects on calf weight gain (WG, kg/head). Linear mixed models were used for analyses where the above mentioned were fixed factors, and year and individual cow were random ones. Calf performance was influenced by three animal traits: gender with steer WG 4 kg more than heifer, cow body weight with calf WG increased 2kg for each 100kg of cow body weight, and cow age as optimum calf WG occurred with 5-year-old cows. Management influenced calf WG through the on and off dates. Delaying the start of a grazing season decreased calf WG by 0.80 kg per delayed day. On the contrary, extending the grazing season increased calf WG by about the same amount. Biophysical effects on calf WG were not significant suggesting that the cow performance was mitigating these effects of variability. Results suggest that calf individual performance in this resilient rangeland ecosystem relies on cows’ body weight at beginning of the grazing, their age, and the timing to enter and remove animals from pastures