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We introduce the concept of \emph{expected exposure} as the average attention ranked items receive from users over repeated samples of the same query. Furthermore, we advocate for the adoption of the principle of equal expected exposure: given a fixed information need, no item should receive more or less expected exposure than any other item of the same relevance grade. We argue that this principle is desirable for many retrieval objectives and scenarios, including topical diversity and fair ranking. Leveraging user models from existing retrieval metrics, we propose a general evaluation methodology based on expected exposure and draw connections to related metrics in information retrieval evaluation. Importantly, this methodology relaxes classic information retrieval assumptions, allowing a system, in response to a query, to produce a \emph{distribution over rankings} instead of a single fixed ranking. We study the behavior of the expected exposure metric and stochastic rankers across a variety of information access conditions, including \emph{ad hoc} retrieval and recommendation. We believe that measuring and optimizing expected exposure metrics using randomization opens a new area for retrieval algorithm development and progress. 

Abstract Wetland methane (CH 4 ) emissions ( $${F}_{{{CH}}_{4}}$$ F C H 4 ) are important in global carbon budgets and climate change assessments. Currently, $${F}_{{{CH}}_{4}}$$ F C H 4 projections rely on prescribed static temperature sensitivity that varies among biogeochemical models. Meta-analyses have proposed a consistent $${F}_{{{CH}}_{4}}$$ F C H 4 temperature dependence across spatial scales for use in models; however, site-level studies demonstrate that $${F}_{{{CH}}_{4}}$$ F C H 4 are often controlled by factors beyond temperature. Here, we evaluate the relationship between $${F}_{{{CH}}_{4}}$$ F C H 4 and temperature using observations from the FLUXNET-CH 4 database. Measurements collected across the globe show substantial seasonal hysteresis between $${F}_{{{CH}}_{4}}$$ F C H 4 and temperature, suggesting larger $${F}_{{{CH}}_{4}}$$ F C H 4 sensitivity to temperature later in the frost-free season (about 77% of site-years). Results derived from a machine-learning model and several regression models highlight the importance of representing the large spatial and temporal variability within site-years and ecosystem types. Mechanistic advancements in biogeochemical model parameterization and detailed measurements in factors modulating CH 4 production are thus needed to improve global CH 4 budget assessments. 

This paper describes the formation of, and initial results for, a new FLUXNET coordination network for ecosystem-scale methane (CH 4 ) measurements at 60 sites globally, organized by the Global Carbon Project in partnership with other initiatives and regional flux tower networks. The objectives of the effort are presented along with an overview of the coverage of eddy covariance (EC) CH 4 flux measurements globally, initial results comparing CH 4 fluxes across the sites, and future research directions and needs. Annual estimates of net CH 4 fluxes across sites ranged from −0.2 ± 0.02 g C m –2 yr –1 for an upland forest site to 114.9 ± 13.4 g C m –2 yr –1 for an estuarine freshwater marsh, with fluxes exceeding 40 g C m –2 yr –1 at multiple sites. Average annual soil and air temperatures were found to be the strongest predictor of annual CH 4 flux across wetland sites globally. Water table position was positively correlated with annual CH 4 emissions, although only for wetland sites that were not consistently inundated throughout the year. The ratio of annual CH 4 fluxes to ecosystem respiration increased significantly with mean site temperature. Uncertainties in annual CH 4 estimates due to gap-filling and random errors were on average ±1.6 g C m –2 yr –1 at 95% confidence, with the relative error decreasing exponentially with increasing flux magnitude across sites. Through the analysis and synthesis of a growing EC CH 4 flux database, the controls on ecosystem CH 4 fluxes can be better understood, used to inform and validate Earth system models, and reconcile differences between land surface model- and atmospheric-based estimates of CH 4 emissions. 

Catchment‐scale response functions, such as transit time distribution (TTD) and evapotranspiration time distribution (ETTD), are considered fundamental descriptors of a catchment's hydrologic and ecohydrologic responses to spatially and temporally varying precipitation inputs. Yet, estimating these functions is challenging, especially in headwater catchments where data collection is complicated by rugged terrain, or in semi‐arid or sub‐humid areas where precipitation is infrequent. Hence, we developed practical approaches for estimating both TTD and ETTD from commonly available tracer flux data in hydrologic inflows and outflows without requiring continuous observations. Using the weighted wavelet spectral analysis method of Kirchner and Neal [2013] for δ¹⁸O in precipitation and stream water, we calculated TTDs that contribute to streamflow via spatially and temporally variable flow paths in a sub‐humid mountain headwater catchment in Arizona, United States. Our results indicate that composite TTDs (a combination of Piston Flow and Gamma TTDs) most accurately represented this system for periods up to approximately 1 month, and that a Gamma TTD was most appropriate thereafter during both winter and summer seasons and for the overall time‐weighted TTD; a Gamma TTD type was applicable for all periods during the dry season. The TTD results also suggested that old waters, i.e., beyond the applicable tracer range, represented approximately 3% of subsurface contributions to streamflow. For ETTD and using δ¹⁸O as a tracer in precipitation and xylem waters, a Gamma ETTD type best matched the observations for all seasons and for the overall time‐weighted pattern, and stable water isotopes were effective tracers for the majority of vegetation source waters. This study addresses a fundamental question in mountain catchment hydrology; namely, how do the spatially and temporally varying subsurface flow paths that support catchment evapotranspiration and streamflow modulate water quantity and quality over space and time.

 

Abstract. Methane (CH4) emissions from natural landscapes constituteroughly half of global CH4 contributions to the atmosphere, yet largeuncertainties remain in the absolute magnitude and the seasonality ofemission quantities and drivers. Eddy covariance (EC) measurements ofCH4 flux are ideal for constraining ecosystem-scale CH4emissions due to quasi-continuous and high-temporal-resolution CH4flux measurements, coincident carbon dioxide, water, and energy fluxmeasurements, lack of ecosystem disturbance, and increased availability ofdatasets over the last decade. Here, we (1) describe the newly publisheddataset, FLUXNET-CH4 Version 1.0, the first open-source global dataset ofCH4 EC measurements (available athttps://fluxnet.org/data/fluxnet-ch4-community-product/, last access: 7 April 2021). FLUXNET-CH4includes half-hourly and daily gap-filled and non-gap-filled aggregatedCH4 fluxes and meteorological data from 79 sites globally: 42freshwater wetlands, 6 brackish and saline wetlands, 7 formerly drainedecosystems, 7 rice paddy sites, 2 lakes, and 15 uplands. Then, we (2) evaluate FLUXNET-CH4 representativeness for freshwater wetland coverageglobally because the majority of sites in FLUXNET-CH4 Version 1.0 arefreshwater wetlands which are a substantial source of total atmosphericCH4 emissions; and (3) we provide the first global estimates of theseasonal variability and seasonality predictors of freshwater wetlandCH4 fluxes. Our representativeness analysis suggests that thefreshwater wetland sites in the dataset cover global wetland bioclimaticattributes (encompassing energy, moisture, and vegetation-relatedparameters) in arctic, boreal, and temperate regions but only sparselycover humid tropical regions. Seasonality metrics of wetland CH4emissions vary considerably across latitudinal bands. In freshwater wetlands(except those between 20∘ S to 20∘ N) the spring onsetof elevated CH4 emissions starts 3 d earlier, and the CH4emission season lasts 4 d longer, for each degree Celsius increase in meanannual air temperature. On average, the spring onset of increasing CH4emissions lags behind soil warming by 1 month, with very few sites experiencingincreased CH4 emissions prior to the onset of soil warming. Incontrast, roughly half of these sites experience the spring onset of risingCH4 emissions prior to the spring increase in gross primaryproductivity (GPP). The timing of peak summer CH4 emissions does notcorrelate with the timing for either peak summer temperature or peak GPP.Our results provide seasonality parameters for CH4 modeling andhighlight seasonality metrics that cannot be predicted by temperature or GPP(i.e., seasonality of CH4 peak). FLUXNET-CH4 is a powerful new resourcefor diagnosing and understanding the role of terrestrial ecosystems andclimate drivers in the global CH4 cycle, and future additions of sitesin tropical ecosystems and site years of data collection will provide addedvalue to this database. All seasonality parameters are available athttps://doi.org/10.5281/zenodo.4672601 (Delwiche et al., 2021).Additionally, raw FLUXNET-CH4 data used to extract seasonality parameterscan be downloaded from https://fluxnet.org/data/fluxnet-ch4-community-product/ (last access: 7 April 2021), and a completelist of the 79 individual site data DOIs is provided in Table 2 of this paper.