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At least 289 records · Page 16

Forecasting Tropical Annual Maximum Wet-Bulb Temperatures Months in Advance From the Current State of ENSO

Humid heatwaves, characterized by high temperature and humidity combinations, challenge tropical societies. Extreme wet-bulb temperatures (TW) over tropical land are coupled to the warmest sea surface temperatures by atmospheric convection and wave dynamics. Here, we harness this coupling for seasonal forecasts of the annual maximum of daily maximum TW (TW max ). We develop a multiple linear regression model that explains 80% of variance in tropical mean TW max and significant regional TW max variances. The model considers warming trends and El Niño and Southern Oscillation indices. Looking ahead, the strong-to-very-strong El Niño at the end of 2023, with an Oceanic Niño Index of ~2.0, suggests a 2024 tropical land mean TW max of 26.2°C (25.9–26.4°C), and a 68% chance (24%–94%) of breaking existing records. This method also predicts regional TW max in specific areas.

54 ENVIRONMENTAL SCIENCES↗

Wind Fields in Category 1–3 Tropical Cyclones Are Not Fully Represented in Wind Turbine Design Standards

Abstract Offshore wind energy deployment in the U.S. is expected to increase in the years to come, with proposed wind farm sites located in regions with high risk for tropical cyclones. Yet, the wind turbine design criteria outlined by the International Electrotechnical Commission for extreme events may not account for wind field characteristics unique to tropical cyclones. To evaluate if current design standards capture the extreme conditions of these storms, we perform idealized large‐eddy simulations of three tropical cyclones (one Category 1, one Category 2, and one Category 3 storms) using the Weather Research and Forecasting model. Wind conditions near the eyewall of Cat‐1, Cat‐2, and Cat‐3 storms can exceed current design standards for offshore wind turbines. Winds at 90 m can be faster than outlined in the design criteria for Class I and Class T turbines for 50‐year recurrence periods. Wind speed shear across the turbine rotor layer is also larger than assumed in design specifications. Moreover, vertical variations in wind direction across the turbine rotor layer are large for tropical cyclones of all intensity levels, suggesting design standards should include veer, which can amplify loads in wind turbines. The existence of hurricane wind field characteristics that are not represented in design standards does not imply that damage or failure will certainly occur. Engineering safety factors incorporated in the design of the turbine's blades and structural components may prevent damage from occurring.

17 WIND ENERGY↗

Modulation of Tropical Convection-Circulation Interaction by Aerosol Indirect Effects in Convective Self-Aggregation Simulations of a Gray Zone Global Model

Disentangling the response of tropical convective updrafts to enhanced aerosol concentrations has been challenging. Leading theories for explaining the influence of aerosol concentrations on tropical convection are based on the dynamical response of convection to changes in cloud microphysics, neglecting possible changes in the environment. In recent years, global convection-permitting models (GCPM) have been developed to circumvent problems arising from imposing artificial scale separation on physical processes associated with deep convection. Here, we use a global model in the convective gray zone that partially simulates deep convection to investigate how enhanced concentrations of aerosols that act as cloud condensate nuclei (CCN) impact tropical convection features by modulating the convection-circulation interaction. Results from a pair of idealized non-rotating radiative-convective equilibrium simulations show that the enhanced CCN concentration leads to weaker large-scale circulation, the closeness of deep convective systems to the moist cluster edges, and more mid-level cloud water at an equilibrium state in which convective self-aggregation occurred. Correspondingly, the enhanced CCN concentration modulates how the physical processes that support or oppose convective aggregation maintain the aggregated state at equilibrium. Overall, the enhanced CCN concentration facilitates the development of deep convection in a drier environment but reduces mean precipitation. Our results emphasize the importance of allowing atmospheric phenomena to evolve continuously across spatial and temporal scales in simulations when investigating the response of tropical convection to changes in cloud microphysics.

54 ENVIRONMENTAL SCIENCES↗

Tropical Cyclone Super Resolution using conditional diffusion denoising probabilistic model from mesoscale simulation to LES

Accurate modeling of tropical cyclone wind fields is essential for the design, risk assessment, and operational planning of offshore energy infrastructure. While mesoscale simulations are widely used thanks to their computational efficiency, they lack the necessary resolution to capture key features such as wind shear and veer profiles as well as the distribution turbulent kinetic energy (TKE). High-fidelity large-eddy simulation (LES) models on the other hand, can resolve turbulent structures and provide a more accurate representation of the complex wind field, albeit at a higher computational cost. To address this modeling gap, we introduce a two-part generative framework to enhance the resolution and physics-capturing ability of mesoscale simulations. First, a reduced-order model based on Karhunen–Loève (KL) decomposition is used to extract dominant spatial modes from one-dimensional mean wind profiles. A multilayer perceptron (MLP) is trained to map mesoscale mode weights to their LES counterparts, enabling accurate reconstruction of vertical velocity profiles. Second, a conditional Diffusion Denoising Probabilistic Model (DDPM) is developed to super-resolve coarse and low-fidelity mesoscale velocity fields, recovering fine-scale turbulence structures and stress distributions. The framework is evaluated across different tropical cyclone intensity categories defined by the Saffir–Simpson scale and demonstrates strong performance in both interpolation and extrapolation tasks. The generated fields accurately reproduce spatial coherence, stress distributions, and spectral energy characteristics observed in LES data. By bridging the fidelity gap between mesoscale and LES outputs, this approach offers a scalable, data-driven solution for enhancing the representation of tropical cyclone wind fields, enabling more robust offshore energy infrastructure systems design in tropical-cyclone-prone areas.

17 WIND ENERGY↗

δ 13 C methane source signatures from tropical wetland and rice field emissions

The atmospheric methane (CH 4 ) burden is rising sharply, but the causes are still not well understood. One factor of uncertainty is the importance of tropical CH 4 emissions into the global mix. Isotopic signatures of major sources remain poorly constrained, despite their usefulness in constraining the global methane budget. Here, a collection of new δ 13 C CH 4 signatures is presented for a range of tropical wetlands and rice fields determined from air samples collected during campaigns from 2016 to 2020. Long-term monitoring of δ 13 C CH 4 in ambient air has been conducted at the Chacaltaya observatory, Bolivia and Southern Botswana. Both long-term records are dominated by biogenic CH 4 sources, with isotopic signatures expected from wetland sources. From the longer-term Bolivian record, a seasonal isotopic shift is observed corresponding to wetland extent suggesting that there is input of relatively isotopically light CH 4 to the atmosphere during periods of reduced wetland extent. This new data expands the geographical extent and range of measurements of tropical wetland and rice δ 13 C CH 4 sources and hints at significant seasonal variation in tropical wetland δ 13 C CH 4 signatures which may be important to capture in future global and regional models.

54 ENVIRONMENTAL SCIENCES↗

Above-ground net primary productivity in regenerating seasonally dry tropical forest: Contributions of rainfall, forest age and soil

Identifying factors controlling forest productivity is critical to understanding forest-climate change feedbacks, modelling vegetation dynamics and carbon finance schemes. However, little research has focused on productivity in regenerating tropical forests which are expanding in their fraction of global area have an order of magnitude larger carbon uptake rates relative to older forest. Here We examined above-ground net primary productivity (ANPP) and its components (wood production and litterfall) over 10 years in forest plots that vary in successional age, soil characteristics and species composition using band dendrometers and litterfall traps in regenerating seasonally dry tropical forests in northwestern Costa Rica. We show that the components of ANPP are differentially driven by age and annual rainfall and that local soil variation is important. Total ANPP was explained by a combination of age, annual rainfall and soil variation. Wood production comprised 35% of ANPP on average across sites and years, and was explained by annual rainfall but not forest age. Conversely, litterfall increased with forest age and soil fertility yet was not affected by annual rainfall. In this region, edaphic variability is highly correlated with plant community composition. Thus, variation in ecosystem processes explained by soil may also be partially explained by species composition. These results suggest that future changes in annual rainfall can alter the secondary forest carbon sink, but this effect will be buffered by the litterfall flux which varies little among years. In determining the long-term strength of the secondary forest carbon sink, both rainfall and forest age will be critical variables to track. We also conclude that detailed understanding of local site variation in soils and plant community may be required to accurately predict the impact of changing rainfall on forest carbon uptake. Synthesis. We show that in seasonally dry tropical forest, annual rainfall has a positive relationship with the growth of above-ground woody tissues of trees and that droughts lead to significant reductions in above-ground productivity. These results provide evidence for climate change—carbon cycle feedbacks in the seasonal tropics and highlight the value of longitudinal data on forest regeneration.

54 ENVIRONMENTAL SCIENCES↗

Diurnal MCSs Precede the Genesis of Tropical Cyclone Mora (2017): The Role of Convectively Forced Gravity Waves

In this work, a novel high-resolution regional reanalysis is used to investigate the mesoscale processes that preceded the formation of Tropical Cyclone (TC) Mora (2017). Both satellite observations and the regional reanalysis show early morning mesoscale convective systems (MCSs) persistently initiated and organized in the downshear quadrant of the preexisting tropical disturbance a few days prior to the genesis of TC Mora. The diurnal MCSs gradually enhanced the meso-α-scale vortex near the center of the preexisting tropical disturbance through vortex stretching, providing a vorticity-rich and moist environment for the following burst of deep convection and enhancement of the meso-β-scale vortex. The regional reanalysis shows that the gravity waves that radiated from afternoon convection over the northern coast of the Bay of Bengal might play an important role in modulating the diurnal cycle of pregenesis MCSs. The diurnal convectively forced gravity waves increased the tropospheric stability, reduced the column saturation fraction, and suppressed deep convection within the preexisting tropical disturbance from noon to evening. A similar quasi-diurnal cycle of organized deep convection prior to TC genesis has also been observed over other basins. However, modeling studies are needed to conclusively demonstrate the relationships between the gravity waves and pregenesis diurnal MCSs. Also, whether diurnal gravity waves play a similar role in modulating the pregenesis deep convection in other TCs is worth future investigations.

54 ENVIRONMENTAL SCIENCES↗

Impact of Model Resolution on Tropical Cyclone Simulation Using the HighResMIP–PRIMAVERA Multimodel Ensemble

A multimodel, multiresolution set of simulations over the period 1950–2014 using a common forcing protocol from CMIP6 HighResMIP have been completed by six modeling groups. Analysis of tropical cyclone performance using two different tracking algorithms suggests that enhanced resolution toward 25 km typically leads to more frequent and stronger tropical cyclones, together with improvements in spatial distribution and storm structure. Both of these factors reduce typical GCM biases seen at lower resolution. Using single ensemble members of each model, there is little evidence of systematic improvement in interannual variability in either storm frequency or accumulated cyclone energy as compared with observations when resolution is increased. Changes in the relationships between large-scale drivers of climate variability and tropical cyclone variability in the Atlantic Ocean are also not robust to model resolution. However, using a larger ensemble of simulations (of up to 14 members) with one model at different resolutions does show evidence of increased skill at higher resolution. The ensemble mean correlation of Atlantic interannual tropical cyclone variability increases from ~0.5 to ~0.65 when resolution increases from 250 to 100 km. In the northwestern Pacific Ocean the skill keeps increasing with 50-km resolution to 0.7. These calculations also suggest that more than six members are required to adequately distinguish the impact of resolution within the forced signal from the weather noise.

54 ENVIRONMENTAL SCIENCES↗

An Extratropical Pathway for the Madden–Julian Oscillation’s Influence on North Atlantic Tropical Cyclones

Abstract This study investigates the combined impacts of the Madden–Julian oscillation (MJO) and extratropical anticyclonic Rossby wave breaking (AWB) on subseasonal Atlantic tropical cyclone (TC) activity and their physical connections. Our results show that during MJO phases 2–3 (enhanced Indian Ocean convection) and 6–7 (enhanced tropical Pacific convection), there are significant changes in basinwide TC activity. The MJO and AWB collaborate to suppress basinwide TC activity during phases 6–7 but not during phases 2–3. During phases 6–7, when AWB occurs, various TC metrics including hurricanes, accumulated cyclone energy, and rapid intensification probability decrease by ∼50%–80%. Simultaneously, large-scale environmental variables, like vertical wind shear, precipitable water, and sea surface temperatures become extremely unfavorable for TC formation and intensification, compared to periods characterized by suppressed AWB activity during the same MJO phases. Further investigation reveals that AWB events during phases 6–7 occur in concert with the development of a stronger anticyclone in the lower troposphere, which transports more dry, stable extratropical air equatorward, and drives enhanced tropical SST cooling. As a result, individual AWB events in phases 6–7 can disturb the development of surrounding TCs to a greater extent than their phases 2–3 counterparts. The influence of the MJO on AWB over the western subtropical Atlantic can be attributed to the modulation of the convectively forced Rossby wave source over the tropical eastern Pacific. A significant number of Rossby waves initiating from this region during phases 5–6 propagate into the subtropical North Atlantic, preceding the occurrence of AWB events in phases 6–7.

54 ENVIRONMENTAL SCIENCES↗

The Influence of ENSO Diversity on Future Atlantic Tropical Cyclone Activity

El Niño–Southern Oscillation (ENSO) influences seasonal Atlantic tropical cyclone (TC) activity by impacting environmental conditions important for TC genesis. However, the influence of future climate change on the teleconnection between ENSO and Atlantic TCs is uncertain, as climate change is expected to impact both ENSO and the mean climate state. We used the Weather Research and Forecasting Model on a tropical channel domain to simulate 5-member ensembles of Atlantic TC seasons in historical and future climates under different ENSO conditions. Experiments were forced with idealized sea surface temperature configurations based on the Community Earth System Model (CESM) Large Ensemble representing: a monthly varying climatology, eastern Pacific El Niño, central Pacific El Niño, and La Niña. The historical simulations produced fewer Atlantic TCs during eastern Pacific El Niño compared to central Pacific El Niño, consistent with observations and other modeling studies. For each ENSO state, the future simulations produced a similar teleconnection with Atlantic TCs as in the historical simulations. Specifically, La Niña continues to enhance Atlantic TC activity, and El Niño continues to suppress Atlantic TCs, with greater suppression during eastern Pacific El Niño compared to central Pacific El Niño. In addition, we found a decrease in the Atlantic TC frequency in the future relative to historical regardless of ENSO state, which was associated with a future increase in northern tropical Atlantic vertical wind shear and a future decrease in the zonal tropical Pacific sea surface temperature (SST) gradient, corresponding to a more El Niño–like mean climate state. Our results indicate that ENSO will remain useful for seasonal Atlantic TC prediction in the future.

54 ENVIRONMENTAL SCIENCES↗

Tropical Tree Crop Simulation with a Process-Based, Daily Timestep Simulation Model (ALMANAC): Description of Model Adaptation and Examples with Coffee and Cocoa Simulations

Coffee (Coffea species) and Cocoa (Theobroma cacao) are important cash crops grown in the tropics but traded globally. This study was conducted to apply the ALMANAC model to these crops for the first time, and to test its ability to simulate them under agroforestry management schemes and varying precipitation amounts. To create this simulation, coffee was grown on a site in Kaua’i, Hawai’i, USA, and cocoa was grown on a site in Sefwi Bekwai, Ghana. A stand-in for a tropical overstory tree was created for agroforestry simulations using altered parameters for carob, a common taller tropical tree for these regions. For both crops, ALMANAC was able to realistically simulate yields when compared to the collected total yield data. On Kaua’i, the mean simulated yield was 2% different from the mean measured yield, and in all three years, the simulated values were within 10% of the measured values. For cocoa, the mean simulated yield was 3% different from the mean measured yield and the simulated yield was within 10% of measured yields for all four available years. When precipitation patterns were altered, in Ghana, the wetter site showed lower percent changes in yield than the drier site in Hawai’i. When agroforestry-style management was simulated, a low Leaf Area Index (LAI) of the overstory showed positive or no effect on yields, but when LAI climbed too high, the simulation was able to show the detrimental effect this competition had on crop yields. These simulation results are supported by other literature documenting the effects of agroforestry on tropical crops. This research has applied ALMANAC to new crops and demonstrated its simulation of different management and environmental conditions. The results show promise for ALMANAC’s applicability to these scenarios as well as its potential to be further tested and utilized in new circumstances.

60 APPLIED LIFE SCIENCES↗

Human Influence on Tropical Cyclone Intensity

Recent assessments agree that tropical cyclone intensity should increase as the climate warms. Less agreement exists on the detection of recent historical trends in tropical cyclone intensity.We interpret future and recent historical trends by using the theory of potential intensity, which predicts the maximum intensity achievable by a tropical cyclone in a given local environment. Although greenhouse gas-driven warming increases potential intensity, climate model simulations suggest that aerosol cooling has largely canceled that effect over the historical record. Large natural variability complicates analysis of trends, as do poleward shifts in the latitude of maximum intensity. In the absence of strong reductions in greenhouse gas emissions, future greenhouse gas forcing of potential intensity will increasingly dominate over aerosol forcing, leading to substantially larger increases in tropical cyclone intensities.

Human influence on climate↗

NASA Global Satellite and Model Data Products and Services for Tropical Meteorology and Climatology

Satellite remote sensing and model data play an important role in research and applications of tropical meteorology and climatology over vast, data sparse oceans and remote continents. Since the first weather satellite was launched by NASA in 1960, a large collection of NASA's Earth science data is freely available to the research and application communities around the world, significantly improving our overall understanding of the Earth system and environment. Established in the mid-80s, the NASA Goddard Earth Sciences Data and Information Services Center (GES DISC), located in Maryland, USA, is a data archive center for multidisciplinary, satellite and model assimilation data products. As one of the 12 NASA data centers in Earth Sciences, GES DISC hosts several important NASA satellite missions for tropical meteorology and climatology such as the Tropical Rainfall Measuring Mission (TRMM), the Global Precipitation Measurement (GPM) mission and the Modern-Era Retrospective analysis for Research and Applications (MERRA). Over the years, GES DISC has developed data services to facilitate data discovery, access, distribution, analysis and visualization, including Giovanni, an online analysis and visualization tool without the need to download data and software. Despite many efforts for improving data access, still quite a number of challenges remain, such as finding datasets and services for a specific research topic or project, especially for inexperienced users or users outside the remote sensing community. In this article, we list and describe major NASA satellite remote sensing and model datasets and services for tropical meteorology and climatology along with examples of using the data and services, in hope that may help users better utilize the information in their research and applications.

tropical meteorology and climatology, data, servic↗

Impact of Assimilating Adaptively Thinned AIRS Cloud-Cleared Radiances on the Analysis of Polar Lows and Mediterranean Sea Tropical-Like Cyclone in a Global Modeling and Data Assimilation Framework

Polar lows, and mesoscale convective cyclones bearing resemblance to tropical cyclones but originating outside of the tropics, are storms that are challenging to represent accurately in global analyses and models because of their small size, rapid growth at subsynoptic scales, occurrence in data poor oceanic regions, and difficulties in objectively validating them in analysis. Building on previous positive results obtained with respect to the representation of tropical cyclones (TCs) in a global model, a set of observing system experiments (OSEs) performed using the NASA Goddard Earth Observing System (GEOS, version 5) are investigated, focusing on three case studies—a polar low in the Sea of Okhotsk, a polar low in the Southern Ocean, and a Mediterranean Sea tropical-like cyclone that occurred during the boreal fall season of 2014. Experiments assimilating adaptively thinned cloud-cleared hyperspectral infrared radiances from the Atmospheric Infrared Sounder (AIRS) instrument on board the NASA Aqua satellite, with higher density in the vicinity of each storm and its pre-cyclogenesis environment, and lower density elsewhere, demonstrate a positive impact on the analyzed representation of each storm. The adaptive thinning experiments improve the storm intensity and structure, including vertical alignment, depth, symmetry, strength, and compactness of warm core compared to the reference experiments. The results suggest that jet-level processes associated with extremely strong horizontal velocity gradients as represented in the model analysis can be useful to locate dynamically active regions of the extratropical atmosphere where denser data coverage is likely to improve the analyzed representation of polar lows and other similar marine mesoscale convective cyclones.

global modeling↗

Microbial community data from throughfall exclusion experiment: Metadata, SI, community composition, LefSe, and FunGuilR data tables from PARCHED Panama tropical forest soils, 2024-2025

Soil contains more carbon (C) than terrestrial vegetation and the atmosphere combined, with some of the largest terrestrial C stocks in tropical rainforests. Soil microbes decompose organic matter, playing a vital role in the storage or loss of soil C. With climate change, drought conditions are predicted to increase in many tropical regions, including both chronic drying and extended drought, potentially influencing these processes. This project explored the effects of chronic and seasonal drying on soil microbial communities across four distinct tropical forests in a long-term drying experiment. We investigated the effects of a chronic drying manipulation on soil microbial community abundance and variation across different forests and seasons. We also compared findings with previously published data from these forests after short-term drying. This project used soils from a long-term drying experiment established in 2018 across four seasonal lowland forests in Panama. Soils were collected from 0 – 10 cm depths during three seasonal periods in control and drying plots in 2024 and 2025 from a total of 32 plots (n = 4 per forest per treatment). The forests varied in baseline rainfall and soil fertility. We calculated alpha and beta diversity indices and compared taxonomic community composition. We found significant biogeographic variation in microbial diversity and taxonomy, with significant differences across the forests and significant effects of the drying treatment. Metadata and sample IDs are within Metadata_16S.csv and Metadata_ITS.csv. Relative abundance tables of every sample at every season are shown in the Excel workbooks 16S Relative Abundance.xlsx and ITS Relative Abundance.xlsx. They are then also shown in CSV files by each taxonomic level. Linear discriminant analysis effect size (LefSe) tables are shown for the full 16S and ITS datasets (n = 96), subsets for every site at every season (n = 8), and then for the forests with each plot merged by season (n = 8). FunGuildR data table of ITS data is uploaded.

Bacteria↗

Tropical understory herbaceous community responds more strongly to hurricane disturbance than to experimental warming

The effects of climate change on tropical forests may have global consequences due to the forests’ high biodiversity and major role in the global carbon cycle. In this study, we document the effects of experimental warming on the abundance and composition of a tropical forest floor herbaceous plant community in the Luquillo Experimental Forest, Puerto Rico. This study was conducted within Tropical Responses to Altered Climate Experiment (TRACE) plots, which use infrared heaters under free-air, open-field conditions, to warm understory vegetation and soils + 4°C above nearby control plots. Hurricanes Irma and María damaged the heating infrastructure in the second year of warming, therefore, the study included one pretreatment year, one year of warming, and one year of hurricane response with no warming. We measured percent leaf cover of individual herbaceous species, fern population dynamics, and species richness and diversity within three warmed and three control plots. Results showed that one year of experimental warming did not significantly affect the cover of individual herbaceous species, fern population dynamics, species richness, or species diversity. In contrast, herbaceous cover increased from 20% to 70%, bare ground decreased from 70% to 6%, and species composition shifted pre to posthurricane. The negligible effects of warming may have been due to the short duration of the warming treatment or an understory that is somewhat resistant to higher temperatures. Our results suggest that climate extremes that are predicted to increase with climate change, such as hurricanes and droughts, may cause more abrupt changes in tropical forest understories than longer-term sustained warming.

54 ENVIRONMENTAL SCIENCES↗

Fast redox switches lead to rapid transformation of goethite in humid tropical soils: A Mössbauer spectroscopy study

Abstract Humid tropical forest soils experience frequent rainfall, which limits oxygen diffusion and creates redox heterogeneity in upland soils. In this study we gauged the effect of short‐term anoxic conditions on Fe mineralogy of relatively Fe‐ and C‐rich surface soils (C/Fe mole ratio ∼5) from a humid tropical forest in Puerto Rico. Soils subjected to 4‐d oxic/anoxic oscillation were characterized by selective chemical extractions, Mössbauer spectroscopy (MBS), and X‐ray diffraction. Chemical extraction data suggested that rapidly switching redox conditions had subtle effects on bulk Fe mineralogy. Mössbauer, on the other hand, indicated that (a) the soil Fe is a mixture of goethites of varying characteristics with minor contributions from ferrihydrite (<5%) and Fe(III)‐organic matter (OM) phases (∼10%), and (b) anoxic conditions rapidly transformed all forms of goethite to relatively stable Fe oxides. Such fast changes in goethite features could be due to rapid depletion and sorption of bio‐released structural Al or sorbed OM onto residual soil components. The rapid temporal changes in MBS parameters and corresponding pore water nominal oxidation state of C values suggest that Fe‐C transformations in these upland tropical soils are complex and intricately coupled. A comprehensive understanding of the fate of Fe, Al, and OM (Fe‐organic moieties) during redox switches and concurrent changes in pore water chemistry is critical for development of robust transport models in humid tropical soils, which are subject to episodic low‐redox events.

54 ENVIRONMENTAL SCIENCES↗

Tropical amplitudes for colored Lagrangians

Recently a new formulation for scattering amplitudes in Tr(Φ 3 ) theory has been given based on simple combinatorial ideas in the space of kinematic data. This allows all-loop integrated amplitudes to be expressed as “curve integrals” defined using tropical building blocks — the “headlight functions”. This paper shows how the formulation extends to the amplitudes of more general Lagrangians. We will present a number of different ways of introducing tropical “numerator functions” that allow us to describe general Lagrangian interactions. The simplest family of these “tropical numerators” computes the amplitudes of interesting Lagrangians with infinitely many interactions. We also describe methods for tropically formulating the amplitudes for general Lagrangians. One uses a variant of “Wick contraction” to glue together numerator factors for general interaction vertices. Another uses a natural characterization of polygons on surfaces to give a novel combinatorial description of all possible diagrams associated with arbitrary valence interactions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗