The idea at the heart of the research is deceptively simple. In boreal Canada, forests are not uniform carpets of trees; they are patchworks of stands of different ages, shaped by a history of crown fires, insect outbreaks, succession, and, more recently, industrial logging. Before large-scale forestry, eastern Canadian boreal ecosystems supported far more mature and old-growth forest than they do today, and those old stands provided critical ecosystem services, from wildlife habitat and carbon storage to the regulation of surface water. Industrial harvesting has generally reduced the area of these stands and scrambled their distribution, simplifying the mosaic and threatening remnant old forests in some regions. Ontario’s response has been a policy framework that requires forest managers to emulate natural disturbance patterns, including a specific spatial configuration of mature and old-growth forest patches that the province calls texture.

Measuring that texture is straightforward in principle. Ontario’s Forest Management Guide for Boreal Landscapes instructs planners to divide a forested landscape into hexagons of 5,000 hectares, a size chosen because it matches the average footprint of natural disturbances in the province’s boreal forests and is meaningful for characterizing wildlife habitat. Within each hexagon, planners calculate the proportion of the area occupied by mature and old-growth stands, abbreviated as MOG. Those proportions are then sorted into five bins, ranging from hexagons with less than 20 percent MOG to those with more than 80 percent, producing a histogram that summarizes the landscape’s texture at a glance. A landscape shaped only by natural disturbance has a characteristic histogram, and the provincial guidelines ask managers to keep the managed landscape’s histogram as close as possible to that theoretical target.

The difficulty has always been operational. Forest harvest planning relies on mixed-integer optimization models, classic formulations known as Model I, Model II, and Model III, that find cost-effective harvest schedules under sustainability constraints. These models have been extended over the years to control connectivity between forest patches, adjacency between harvested and unharvested sites, and maximum harvest areas. But none of them could directly control landscape texture. Texture metrics, computed with moving-window statistics using tools such as Fragstats or Ontario’s own Landscape Tool, had to be calculated after the fact, as a post-assessment of a finished plan. If the texture came out wrong, there was no way to feed that information back into the harvest schedule. The provincial guidelines, in effect, demanded an outcome the planning machinery could not deliver.

Yemshanov and his colleagues closed that gap by modifying a Model I harvest scheduling formulation so that the texture histogram itself becomes part of the optimization. The landscape is covered with 5,000-hectare hexagons, and each harvestable forest site is assigned to the hexagon containing its centroid. For every possible harvest prescription at every site, and for every ten-year planning period across a century-long horizon, the model tracks whether the site will be in mature or old-growth condition. A decision variable calculates the MOG proportion within each hexagon, and a set of binary indicator variables sorts each hexagon into one of the five histogram bins. The model then computes a penalty measuring how far the resulting histogram deviates, bin by bin, from the theoretical target values that describe a landscape under natural disturbance alone, and it minimizes that penalty alongside its traditional goal of maximizing net harvest revenue.

The theoretical targets were supplied by the Ontario Ministry of Natural Resources and Forestry, based on stochastic simulations with the Boreal Forest Landscape Dynamics Simulator, which integrates the Canadian Forest Fire Behavior Prediction System with empirical forest succession rules. For the study area, the target shares of hexagons in the five MOG bins came out at roughly 0.17, 0.22, 0.20, 0.20, and 0.21. Because achieving an exact match may be impossible given a landscape’s existing age structure, the requirement is formulated as a penalty on deviations rather than a hard constraint, keeping the problem mathematically feasible even when the starting conditions are far from the ideal.

The team tested the approach in the Wabadowgang Noopming Forest, a boreal management unit in northwestern Ontario covering roughly 438,500 hectares across more than 30,000 harvestable sites, where industrial forestry operates under a forest management plan that also implements Ontario’s Dynamic Caribou Habitat Schedule. That schedule, designed to conserve threatened woodland caribou, concentrates harvesting into compact regions that rotate across the landscape over twenty-year cycles, maintaining large tracts of undisturbed habitat through time. The researchers compared a baseline scenario following the current plan against scenarios that added MOG texture control, both with and without the caribou schedule, and even a scenario in which texture control replaced the traditional area-based limits on young, mature, and old forest entirely.

The results were revealing. The baseline plan, constrained by the caribou schedule but blind to texture, produced a lopsided mosaic: in the first three decades, hexagons with less than 20 percent MOG fell well below the target share of 0.17, while hexagons dominated by more than 80 percent mature and old-growth forest substantially exceeded their target of 0.21. Adding texture control changed the picture dramatically. Because the target histogram demands a meaningful presence of hexagons with low MOG proportions, the optimizer dispersed harvest sites more evenly across the landscape, ensuring that every 5,000-hectare window contained some recently disturbed, young forest alongside the old. Notably, the cost of this ecological refinement was modest. Because the caribou schedule already forced harvest into compact, widely distributed regions, layering texture control on top caused only a minor increase in timber supply cost and little change in sustainable harvest levels. Without the caribou schedule, however, texture control alone allowed a higher maximum sustainable harvest of 0.323 million cubic meters per year versus 0.275 million under the combined scenario, and pushed the young-forest share up to 32.1 percent, near the plan’s upper limit.

One caution emerged clearly from the fourth scenario: texture control is not a substitute for traditional age-class management. When the researchers removed the area-based constraints on young, mature, and old-growth forest and relied on texture control plus the caribou schedule, harvested volumes rose, mean forest age fell, and the old-growth area declined substantially, with young stands exceeding the provincial maximum. Texture, in other words, governs the arrangement of the mosaic but not necessarily its total composition, and both dimensions of the landscape need explicit attention.

The study also lays bare the computational price of ecological realism. The baseline problem solved in under thirty minutes, but the texture-controlled formulations ran for seventy-two hours on a workstation with 48 processor cores and still finished with optimality gaps above 15 percent. The indirect, multi-step calculation of the histogram introduces symmetries into the data, since many different harvest configurations can produce the same histogram shape, making the problem combinatorially hard, in the formal sense of NP-hardness. The authors suggest practical workarounds, including optimizing only the most critical histogram bins, dividing large landscapes into regions solved separately, or stabilizing the coarse spatial configuration before switching penalties to hard constraints. They also note that the framework is generalizable well beyond MOG forests: the same machinery could control the texture of wildlife habitat for species such as boreal caribou at ecologically relevant scales of 10,000 hectares or more, or balance working forests, protected areas, and agricultural land in multi-use regions. As climate change alters fire regimes across the boreal zone, tools that can hold a managed landscape to a nature-like pattern, even approximately and at a computable cost, may become indispensable to keeping forestry and conservation from pulling the forest apart.

Subject of Research: Optimization of forest harvest scheduling to control the spatial texture of mature and old-growth boreal forest under competing management objectives

Article Title: Forest landscape planning with textural constraints: How to control the spatial pattern under competing management objectives

Article References: Yemshanov, D., Koch, F. H., Liu, N., & Nielsen, J. (2026). Forest landscape planning with textural constraints: How to control the spatial pattern under competing management objectives. PLOS Ecosystems, 1(2), e0000033. https://doi.org/10.1371/journal.pesy.0000033

Image Credits: AI Generated

DOI: 10.1371/journal.pesy.0000033

Keywords: boreal forest, forest management, harvest scheduling, old-growth forest, landscape texture, natural disturbance emulation, mixed-integer optimization, woodland caribou, Ontario, spatial planning, biodiversity conservation, wildfire regime

The study, led by Guiyong Wang and colleagues, addresses a bottleneck that has quietly constrained the renewable energy transition: as microgrids become richer in wind, solar, hydrogen systems, and electric vehicles, the optimization problems that keep them running efficiently become harder and slower to solve. Under a rolling-horizon scheme, the scheduler must re-optimize every fifteen minutes as forecasts and system states evolve. Commercial solvers such as CPLEX can handle these mixed-integer problems, but solution times of twenty seconds or more consume a growing share of the available decision window, leaving little computational margin for forecasting, communication, and safety checks.

The researchers’ system models a grid-connected microgrid comprising a 5-megawatt wind farm, a 2-megawatt photovoltaic station, a diesel generator, an electrolyzer and fuel cell linked by a hydrogen storage tank, a fleet of 200 electric vehicles, and a bidirectional connection to the utility grid. The objective function minimizes total operating cost, spanning electricity transactions, diesel fuel, operation and maintenance, pollutant emission penalties for carbon dioxide, sulfur dioxide, and nitrogen oxides, renewable curtailment penalties, and even battery degradation costs from excessive vehicle charging and discharging cycles.

What distinguishes the framework is its insistence that the electric vehicle fleet be treated not as a static block of demand but as a living, state-aware resource. A vehicle’s ability to charge faster or discharge power back to the grid depends directly on its state of charge, its battery capacity, its connection status, and the state of charge it must reach before departure. Rather than assuming these values, the team estimates them online using an enhanced unscented Kalman filter, which reconstructs battery states from noisy current, voltage, and temperature measurements.

The proposed filter, dubbed MI-SVD-NIS-UKF, layers three refinements onto the standard Kalman recursion. Singular value decomposition stabilizes the covariance matrix to keep long-running estimates numerically healthy. A normalized innovation squared statistic continuously compares actual measurements against predicted distributions, triggering adaptive adjustments of the process and measurement noise covariances when conditions change. Finally, a multi-innovation correction blends information from several recent time steps, weighted by a forgetting factor, to suppress the influence of single-step voltage disturbances. Together, these mechanisms cut the mean absolute state-of-charge estimation error to 0.3915 percent under a representative operating condition — a 53 percent improvement over the standard filter — and achieved the lowest mean error among seven filter variants across thirty Monte Carlo scenarios.

The practical payoff of that accuracy becomes vivid when estimation errors are translated into energy terms. An open-loop approach that ignores online state estimation misjudges each vehicle’s dispatchable energy by an average of 3.597 kilowatt-hours, which balloons to 719 kilowatt-hours across a 200-vehicle fleet. The proposed estimator reduces that misperception to 0.294 kilowatt-hours per vehicle, or just 59 kilowatt-hours fleet-wide. These continuously updated per-vehicle flexibility boundaries are then aggregated and handed to the scheduling layer, giving the optimizer a truthful, time-varying picture of how much flexibility the fleet actually offers at every fifteen-minute interval.

With state perception in place, the second half of the framework tackles computation. The team trained a long short-term memory network — a recurrent neural architecture well suited to capturing temporal dependencies — to imitate the optimal decisions produced by CPLEX across three years of fifteen-minute operational data. The network takes nineteen inputs, including wind, solar, and load forecasts, time-of-use electricity prices, system states, and the dynamic electric vehicle flexibility boundaries, and outputs thirteen scheduling variables over a four-step prediction horizon. Training combined imitation loss with feasibility and objective-deviation terms, encouraging the network to respect power balance, device limits, and hydrogen inventory constraints rather than merely mimic surface patterns.

Because neural networks can occasionally produce infeasible outputs, the framework wraps its inference in a layered safety net. Raw network predictions are first projected onto the continuous feasible region through a quadratic program, then binary operating states — such as whether the electrolyzer or fuel cell runs, or whether the microgrid imports or exports power — are repaired to resolve mutually exclusive logic. A final feasibility check gates every action, and any rejected prediction triggers a hard-constrained recovery optimization. In testing, this pipeline achieved a 99.8 percent final feasibility rate, with the long short-term memory architecture outperforming gated recurrent unit and multilayer perceptron alternatives on violation rate, repair success, and economic fidelity.

The speed gains are striking. On fifty unseen testing days, the neural surrogate required a median of 67.9 milliseconds per scheduling decision, compared with 22.33 seconds for CPLEX — a median speedup of 323-fold and a mean of 326-fold. On a representative day, the learned schedule cost 46,920 yuan, only 2.49 percent above the exact optimizer’s 45,780 yuan benchmark, with average root-mean-square and mean absolute errors of just 0.0579 and 0.0349 megawatts across key scheduling variables. Under deliberately harsh generalization tests — continuous rainy days and severe generation fluctuations drawn from a different year — the coefficient of determination for step-cost predictions remained above 0.984.

Scalability results reinforce the approach’s promise. When the vehicle fleet grew from 200 to 400, the exact solver’s runtime climbed from 22.33 to 30.15 seconds, while the surrogate’s inference-and-repair time rose only from 67.9 to 86.4 milliseconds, staying below a tenth of a second throughout. That leaves an enormous computational margin within each fifteen-minute interval for state updating, forecast processing, and communication — margin that future grids, with larger and more heterogeneous fleets and tighter coupling among energy carriers, will likely need. The authors position the framework as a transferable foundation for small- and medium-scale grid-connected microgrids, with extensions toward stronger uncertainty, multi-microgrid coordination, and multi-timescale scheduling on the horizon. If such state-aware surrogate methods mature, the real-time nervous system of a decarbonized energy network may one day think in milliseconds rather than minutes.

Subject of Research: State-aware surrogate learning for fast rolling scheduling of multi-energy microgrids

Article Title: State-aware surrogate learning for fast rolling scheduling of multi-energy microgrids

Article References: Wang, G., He, J., Luo, Z., Chuan, Z., Li, J., & Li, Y. (2026). State-aware surrogate learning for fast rolling scheduling of multi-energy microgrids. Results in Engineering, 32, Article 113317. https://doi.org/10.1016/j.rineng.2026.113317

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113317

Keywords: microgrid, rolling scheduling, state of charge, unscented Kalman filter, LSTM, surrogate model, electric vehicles, hydrogen energy, renewable energy, CPLEX, mixed-integer optimization, energy management

A new study published in Nature Water by Sinan Abi Farraj, Akshay K. Rao and Meagan S. Mauter of Stanford University argues that the way utilities plan these upgrades is fundamentally inefficient. Most treatment plants make capital decisions in isolation, each sizing and scheduling its own improvements based on its own projected loads and regulatory deadlines. The researchers show that when facilities sharing a single regulated watershed coordinate their investment and operating decisions, the total cost of meeting nutrient targets can fall dramatically. In a case study of three treatment facilities in the San Francisco Bay, coordinated planning reduced the cost of subembayment nutrient removal by up to 48 percent, a saving of roughly US$268 million.

The heart of the work is a decision support tool the authors call CLEANRWastewater, short for Coordination for Lean Effective Affordable Nutrient Removal for Wastewater. It is formulated as a multi-period, mixed-integer optimization framework, a class of mathematical model that can handle both continuous decisions, such as how much flow to send through a given process each year, and discrete choices, such as whether to build a particular treatment module at all. Because the model runs across multiple time periods, it can capture the timing of investments, not just their magnitude. That temporal dimension matters enormously in infrastructure planning, where the difference between building a facility in 2027 and 2035 can be measured in hundreds of millions of dollars of avoided or deferred capital expenditure.

Technically, the framework represents each treatment plant as a set of candidate upgrade pathways, each with its own capital cost, operating cost, removal efficiency and construction lead time. Binary variables encode whether and when a facility commits to a given technology, while continuous variables track flows, loads and effluent concentrations through each period. Constraints enforce permit limits at the subembayment level, meaning the model can satisfy a collective nitrogen target for a body of water rather than forcing every individual plant to hit the same stringent effluent concentration. This flexibility is precisely where the savings come from: instead of every plant paying for deep removal, the optimizer can concentrate treatment where it is cheapest per kilogram of nitrogen removed and let other facilities do less, as long as the aggregate load stays within the regulatory envelope.

The San Francisco Bay case study is a natural testing ground for this approach. The bay receives treated effluent from dozens of municipal dischargers, and regional authorities have been wrestling with how to respond to growing evidence that nitrogen loading threatens the estuary. Recent regulatory developments, including a nutrient watershed permit for the region, have pushed utilities to consider both facility-level upgrades and novel strategies such as nutrient trading, in which a plant that removes nitrogen cheaply can sell credits to a plant for whom removal is expensive. The Stanford team applied their optimization framework to three facilities in the Lower South Bay, comparing a business-as-usual scenario in which each plant plans independently against scenarios with staged deployment and varying degrees of regional coordination.

The results quantify, in dollars, what many planners have suspected qualitatively. Full coordination across the facilities allowed them to delay capital-intensive upgrades and deploy the lowest-cost treatment options at the subembayment level first, deferring expensive construction until it was genuinely needed. The multi-period structure of the model is what makes this possible: it can weigh the present value of spending now against the risk of spending more later, and it can sequence investments so that cheap operational optimizations, such as tweaking existing biological processes, are exhausted before new concrete is poured. The authors also built in the ability to accommodate uncertainty analysis around future nutrient loads, testing how sensitive the optimal plans are to changes in projected flows and nitrogen arriving at the plants.

That uncertainty component deserves emphasis, because it addresses a chronic weakness in infrastructure planning. Population growth, water conservation, climate-driven changes in wastewater strength and shifting regulatory timelines all make future loads genuinely uncertain, and a plan optimized for a single deterministic forecast can fail badly when reality diverges. By incorporating time-varying constraints and allowing sensitivity analysis across load scenarios, the framework gives utility managers a way to see how robust a given sequencing of investments is before committing ratepayer money. The published model code and data are openly available through GitHub and Figshare, built on the Pyomo optimization modeling language and solved with commercial mixed-integer solvers, which lowers the barrier for other regions to adapt the approach to their own watersheds.

The broader significance of the study lies in how it could reshape the economics of water quality regulation. Nutrient trading programs exist in several US watersheds, most notably Connecticut’s Long Island Sound nitrogen exchange and the Chesapeake Bay program, but adoption has been limited, in part because utilities lack a rigorous way to value participation before joining. By attaching a concrete dollar figure to coordination, the Stanford framework gives utility managers and regulators a quantitative argument for establishing trading markets and joint infrastructure investments. The authors suggest that quantifying these financial benefits may be the missing incentive that motivates utilities to move from voluntary cooperation to formalized regional institutions, such as interlocal agreements or structured credit markets.

There are, of course, institutional hurdles that mathematics alone cannot dissolve. Treatment plants are owned by different municipalities with different bond capacities, governance structures and political constituencies, and sharing costs and credits across jurisdictional lines requires legal agreements and trust that take years to build. Prior research on water quality trading has documented how transaction costs, monitoring requirements and liability questions can stall otherwise economically attractive exchanges. The optimization framework does not eliminate these frictions, but it changes the conversation: instead of debating coordination in the abstract, stakeholders can negotiate over a quantified surplus of hundreds of millions of dollars, which is a far more compelling basis for agreement than an appeal to regional goodwill.

For the San Francisco Bay, the findings arrive at a pivotal moment, as regional permits begin to mandate nutrient reductions and utilities weigh rate increases against environmental obligations. For the wider world of water management, the study offers a template for a shift from plant-by-plant compliance to watershed-scale optimization, mirroring transitions already seen in air pollution trading and electricity system planning. If the 48 percent savings observed in the Lower South Bay case are even roughly representative of other nutrient-impaired estuaries, the aggregate opportunity across the hundreds of US watersheds facing nutrient limits could run to tens of billions of dollars. Turning that theoretical surplus into real savings will require regulators to write permits that reward collective performance, and utilities to plan together what they have always planned alone, but the mathematics of the opportunity is now on the table.

Subject of Research: Regional coordination and optimization of wastewater treatment plant nutrient discharge management

Article Title: Valuing regional coordination of nutrient discharge management

Article References: Abi Farraj, S., Rao, A. K., & Mauter, M. S. (2026). Valuing regional coordination of nutrient discharge management. Nature Water. https://doi.org/10.1038/s44221-026-00717-7

Image Credits: AI Generated

DOI: 10.1038/s44221-026-00717-7

Keywords: wastewater treatment, nutrient removal, nitrogen pollution, San Francisco Bay, mixed-integer optimization, nutrient trading, water infrastructure, watershed management, Nature Water, decision support tool, algal blooms, water affordability