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At least 91 records · Page 5

ISS Expeditions 16 through 20: Chemical Analysis Results for Potable Water

During the 2-year span from Expedition 16 through Expedition 20, the chemical quality of the potable water onboard the International Space Station (ISS) was verified safe for crew consumption through the return and chemical analysis of archival water samples by the Water and Food Analytical Laboratory (WAFAL) at Johnson Space Center (JSC). Reclaimed cabin humidity condensate and Russian ground-supplied water were the principal sources of potable water for Expeditions 16 through 18. During Expedition 18 the U.S. water processor assembly was delivered, installed, and tested during a 90-day checkout period. Beginning with Expedition 19, U.S. potable water recovered from a combined waste stream of humidity condensate and pretreated urine was also available for ISS crew use. A total of 74 potable water samples were collected using U.S. sampling hardware during Expeditions 16 through 20 and returned on both Shuttle and Soyuz vehicles. The results of JSC chemical analyses of these ISS potable water samples are presented in this paper. Eight potable water samples collected in flight with Russian hardware were also received for analysis, as well as 5 preflight samples of Rodnik potable water delivered to ISS on Russian Progress vehicles 28 to 34. Analytical results for these additional potable water samples are also reported and discussed.

Straub, John E., II↗

Desert Locust Cropland Damage Differentiated from Drought, with Multi-Source Remote Sensing in Ethiopia

In 2020, Ethiopia had the worst desert locust outbreak in 25 years, leading to food insecurity. Locust research has typically focused on predicting the paths and breeding grounds based on ground surveys and remote sensing of outbreak factors. In this study, we hypothesized that it is possible to detect desert locust cropland damage through the analysis of fine-scale (5–10 m) resolution satellite remote sensing datasets. We performed our analysis on 121 swarm point locations on croplands derived from the Food and Agriculture Organization (FAO) of the United Nations, and 94 ‘non-affected’ random cropland sample points generated for this study that are distributed within 20–25 km from the ‘center’ of swarm affected sample locations. Integrated Drought Condition Indices (IDCIs) and Vegetation Health Indices (VHIs) calculated for the affected sample locations for 2000–2020 were strongly correlated (R(exp 2) > 0.90) with that of the corresponding non-affected group of sample sites. Drought indices were strongly correlated with the evaluation Standardized Precipitation Evapotranspiration Indices (SPEIs) and showed that 2020 was the wettest year since 2000. In 2020, the NDVI and backscatter coefficient of cropland phenologies from the affected versus non-affected cropland sample sites showed a slightly wider, but significant gap in March (short growing season) and August-October (long growing season). Thus, slightly wider gaps in cropland phenologies between the affected and non-affected sites were likely induced from the locust damage, not drought, with fine scale data representing a larger gap.

Desert locust↗

VEG-05 Tomato Crop Testing on the International Space Station

Production of fresh, nutritious, and tasty produce for astronauts during spaceflight may provide health-promoting, bioavailable nutrients, enhance the dietary experience, and reduce menu fatigue as we move into longer-duration missions. Growing and caring for plants may also reduce the psychological stresses associated with spaceflight and enhance connection to Earth. A diversity of crops will be required to provide nutrition, variety, and resiliency, however requirements for consistent growth under spaceflight environmental conditions remain unclear. VEG-05 is part of a series of experiments with pick-and-eat salad crops to better define best practices for crop production in space. VEG-05 and predecessor experiments VEG-04A and VEG-04B, grew salad crops in the Veggie vegetable production facilities on the International Space Station using different lighting treatments. In VEG-05 we grew ‘Red Robin’ dwarf cherry tomatoes under two different red: blue lighting spectra. Light can impact the growth habit, yield, nutritional composition, microbial levels, and even flavor attributes within crops, and our goal was to assess these characteristics in ‘Red Robin’ tomatoes during VEG-05. Considerable pre-flight verification testing was performed prior to launch in Nov. 2022. Prior to the flight and ground experiments, lighting in both Veggie units on ISS was measured and lights were standardized between flight and ground hardware. VEG-05 flight operations ran between December 2022 and March 2023, with a ground control initially 48 hours delayed. Due to environmental challenges of very low humidity during the first week of the experiment, seed germination was low for both flight and ground plants. The flight experiment ultimately had 4 - 5 plants per treatment out of the planned 6 plants, but the initial ground control had only three plants in one treatment and none in the other, so this ground control was restarted at the beginning of Feb. 2023 and ran through May, with successful growth of all 12 plants. Both flight and ground control ran 100 days, with harvests of fruit at day 83, day 90, and day 100. Flight plants had uneven growth, and following the early drying events, excess water was frequently observed, which led to a variety of plant stress responses including uneven plant growth, excess adventitious root formation, flower and fruit abortion, and visible microbial growth. In total, from the five surviving red-rich lighted plants, only 5 ripe fruit were produced, and from the four surviving blue-rich lighted plants, 10 fruit were produced with only 6 of these ripe by day 100. Because of the small fruit number and the unsatisfactory growth, crew members were not allowed to consume the tomatoes, and all fruit, as well as large branches with leaves, samples of the adventitious roots, two plant rooting pillows from each treatment, microbial sampling swabs, and some water samples were returned for analysis. Because of the small sample sizes and factors affecting growth on the ISS, objectives of assessing light quality effect (red: blue light treatments) will not be achieved. Revised objectives of this study include to compare stressed flight plants with normal ground plants to determine the impact of plant overwatering stress in space on food safety and the plant microbial community, to determine nutrient content changes in fruit and leaves from stressed plants, and to evaluate stress metabolism changes in returned tissue by transcriptomic analysis. Postflight analysis is underway with the following analyses being conducted: A. culturable microbiology and food safety as well as molecular microbial community analysis of 1. ripe fruit, 2. leaves, stems, and adventitious roots, 3. pillow components (roots, wicks, and substrates), 4. swabs, and 5. water samples from root mats before and after growth. B. transcriptomics of leaf tissue and adventitious roots, and C. elemental analysis of leaf tissue. If sufficient tissue remains elemental analyses will also be conducted on fruit. While not generating the desired information on spaceflight growth responses of healthy crops, our team is hopeful that these analyses will shed light on tomato responses to stress in this environment as plant overwatering stress is a mission-relevant condition that could occur in future space crop growth systems. This research was co-funded by the Human Research Program and Space Biology (MTL#1075) in the ILSRA 2015 NRA call.

Gioia D. Massa↗

VEG-04: the Effects of Light Quality on Mizuna Mustard Growth, Nutritional Composition, and Organoleptic Acceptability for a Space Diet

Space crop production will be important in future long duration exploration missions to supplement the packaged diet with fresh bioactive nutrients. Plant care and the addition of fresh veggies to the diet may also have a role in astronaut well-being. Pick-and-eat salad crops are the best candidates for this near-term supplementation since they require minimal processing or preparation to add to meals. While light quality can strongly influence plant responses on Earth, the impacts of light quality on plant growth and composition in spaceflight remain unclear. The VEG-04 experiment uses two Veggie plant growth chambers on the International Space Station to simultaneously test different red: blue light ratios on the growth of Mizuna mustard, a leafy green salad crop. In addition to plant health and yield, the composition of key nutrients is assessed. Astronauts conduct on-board organoleptic evaluation of the fresh produce. Microbial food safety of returned produce is examined, and a Hazard Analysis Critical Control Point (HACCP) plan has been developed for this crop. VEG-04 consists of two experiments, one lasting 28 days with a single harvest, and the second lasting 56 days, with three cut-and-come-again harvests. These different scenarios provide an opportunity to test two production concepts, examine different fertilizers, monitor microbial changes over time for this crop, and assess potential impacts of interacting with plants on crew behavioral health and performance in spaceflight operations. In ground testing, plant growth was not significantly different across the different light treatments, however nutrient composition did differ significantly. Flight test results will be compared with ground data. This research was co-funded by NASA's Human Research Program and Space Biology in the ILSRA 2015 NRA call.

Massa, Gioia D.↗

Reserves and Trade Jointly Determine Exposure to Food Supply Shocks

While a growing proportion of global food consumption is obtained through international trade, there is an ongoing debate on whether this increased reliance on trade benefits or hinders food security, and specifically, the ability of global food systems to absorb shocks due to local or regional losses of production. This paper introduces a model that simulates the short-term response to a food supply shock originating in a single country, which is partly absorbed through decreases in domestic reserves and consumption, and partly transmitted through the adjustment of trade flows. By applying the model to publicly-available data for the cereals commodity group over a 17 year period, we find that differential outcomes of supply shocks simulated through this time period are driven not only by the intensification of trade, but as importantly by changes in the distribution of reserves. Our analysis also identifies countries where trade dependency may accentuate the risk of food shortages from foreign production shocks; such risk could be reduced by increasing domestic reserves or importing food from a diversity of suppliers that possess their own reserves. This simulation-based model provides a framework to study the short-term, nonlinear and out-of-equilibrium response of trade networks to supply shocks, and could be applied to specific scenarios of environmental or economic perturbations.

supply↗

Food Fortification Stability Study

NASA has established the goal of traveling beyond low-Earth orbit and extending manned exploration to Mars. The extended length of a Mars mission, along with the lack of resupply missions increases the importance of nutritional content in the food system. The purpose of this research is to assess the stability of vitamin supplementation in traditionally processed spaceflight foods. It is expected that commercially available fortificants will remain stable through long-duration missions if proper formulation, processing, and storage temperatures are all achieved. Five vitamins (vitamin E, vitamin K, pantothenic acid, folic acid, and thiamin) were blended into a vitamin premix (DSM, Freeport, TX); premixes were formulated to be compatible with current processing techniques (retort or freeze-dried), varied water activities (high or low), and packaging material. The overall goal of this process is to provide 25% of the recommended daily intake of each vitamin (per serving), following processing and two years of ambient storage. Four freeze-dried foods (Scrambled Eggs, Italian Vegetables, Potatoes Au Gratin, Noodles and Chicken) and four thermostabilized foods (Curry Sauce with Vegetables, Chicken Noodle Soup, Grilled Pork Chop, Rice with Butter) were produced (with and without the vitamin premix), to assess the impact of the added fortificant on color and taste, and to determine the stability of supplemental vitamins in spaceflight foods. The use of fortification in spaceflight foods appears to be a plausible mitigation step to inadequate nutrition. This is due to the ease of vitamin addition as well as the sustainability of the premixes through initial processing steps. Postprocessing analysis indicated that vitamin fortification with this premix did not immediately impact organoleptic properties of the food. At this stage, the largest hurdle to fortification is the preciseness to which vitamins can be added; the total amount of vitamins required for production is 10 - 20 grams, a minor percentage of the formulation. As demonstrated by the over-fortification measured in Italian Vegetables and Grilled Pork Chop, homogeneity may be difficult to achieve with such small amounts. Thus, pouch-to-pouch variability, over-fortification, and underfortification may ensue if a method for precise addition is not identified. Stability will continue to be evaluated over two years of storage at three temperatures, and future analysis should reveal the extent to which this issue should be a concern

Abdulmalik, T. O.↗

Mathematical Modeling of Food Supply for Long Term Space Missions Using Advanced Life Support

A habitat for long duration missions which utilizes Advanced Life Support (ALS), the Bioregenerative Planetary Life Support Systems Test Complex (BIO-Plex), is currently being built at JSC. In this system all consumables will be recycled and reused. In support of this effort, a menu is being planned utilizing ALS crops that will meet nutritional and psychological requirements. The need exists in the food system to identify specific physical quantities that define life support systems from an analysis and modeling perspective. Once these quantities are defined, they need to be fed into a mathematical model that takes into consideration other systems in the BIO-Plex. This model, if successful, will be used to understand the impacts of changes in the food system on the other systems and vice versa. The Equivalent System Mass (ESM) metric has been used to describe systems and subsystems, including the food system options, in terms of the single parameter, mass. There is concern that this approach might not adequately address the important issues of food quality and psychological impact on crew morale of a supply of fiesh food items. In fact, the mass of food can also depend on the quality of the food. This summer faculty fellow project will involve creating an appropriate mathematical model for the food plan developed by the Food Processing System for BIO-Plex. The desired outcome of this work will be a quantitative model that can be applied to the various options of supplying food on long-term space missions.

Cruthirds, John E.↗

Two new advanced forms of spectrometry for space and commercial applications

Reagentless ultraviolet absorption spectrometry (UVAS) and Liquid Atomic Emission Spectrometry (LAES) represent new forms of spectrometry with extensive potential in both space and commercial applications. Originally developed under KSC sponsorship for monitoring nutrient solutions for the Controlled Ecological Life Support System (CELSS), both UVAS and LAES have extensive analytical capabilities for both organic and inorganic chemical compounds. Both forms of instrumentation involve the use of remote fiber optic probes and real-time measurements for on-line process monitoring. Commercial applications exist primarily in environmental analysis and for process control in the chemical, pulp and paper, food processing, metal plating, and water/wastewater treatment industries.

Schlager, Kenneth J.↗

Heat Melt Compaction as an Effective Treatment for Eliminating Microorganisms from Solid Waste

One of the technologies being tested at Ames Research Center as part of the logistics and repurposing project is heat melt compaction (HMC) of solid waste to reduce volume, remove water and render a biologically stable and safe product. Studies at Kennedy Space Center have focused on the efficacy of the heat melt compaction process for killing microorganisms in waste and specific compacter operation protocols, i.e., time and temperature, required to achieve a sterile, stable product. The work reported here includes a controlled study to examine the survival and potential re-growth of specific microorganisms over a 6-month period of storage after heating and compaction. Before heating and compaction, ersatz solid wastes were inoculated with Bacillus amyloliquefaciens and Rhodotorula mucilaginosa, previously isolated from recovered space shuttle mission food and packaging waste. Compacted HMC tiles were sampled for microbiological analysis at time points between 0 and 180 days of storage in a controlled environment chamber. In addition, biological indicator strips containing spores of Bacillus atrophaeus and Ceo bacillus stearothermophilus were imbedded in trash to assess the efficacy of the HMC process to achieve sterilization. Analysis of several tiles compacted at 180 C for times of 40 minutes to over 2 hours detected organisms in all tile samples with the exception of one exposed to 180 C for approximately 2 hours. Neither of the inoculated organisms was recovered, and the biological indicator strips were negative for growth in all tiles indicating at least local sterilization of tile areas. The findings suggest that minimum time/temperature combination is required for complete sterilization. Microbial analysis of tiles processed at lower temperatures from 130 C-150 C at varying times will be discussed, as well as analysis of the bacteria and fungi present on the compactor hardware as a result of exposure to the waste and the surrounding environment. The two organisms inoculated into the waste were among those isolated and identified from the HMC surfaces indicating the possibility of cross contamination.

Hummerick, Mary P.↗

Heat Melt Compaction as an Effective Treatment for Eliminating Microorganisms from Solid Waste

One of the technologies being tested at Ames Research Center as part of the logistics and repurposing project is heat melt compaction (HMC) of solid waste to reduce volume, remove water and render a biologically stable and safe product. Studies at Kennedy Space Center have focused on the efficacy of the heat melt compaction process for killing microorganisms in waste and specific compacter operation protocols, i.e., time and temperature required to achieve a sterile, stable product. The work. reported here includes a controlled study to examine the survival and potential re-growth of specific microorganisms over a 6-month period of storage after heating and compaction. Before heating and compaction, ersatz solid wastes were inoculated with Bacillus amyloliquefaciens and Rhodotorula mucilaginosa, previously isolated from recovered space shuttle mission food and packaging waste. Compacted HMC tiles were sampled for microbiological analysis at time points between 0 and 180 days of storage in a controlled environment chamber. In addition, biological indicator strips containing spores of Bacillus atrophaeus and Geobacillus stearothermophilus were imbedded in trash to assess the efficacy of the HMC process to achieve sterilization. Analysis of several tiles compacted at 180deg C for times of 40 minutes to over 2 hours detected organisms in all tile samples with the exception of one exposed to 180deg C for approximately 2 hours. Neither of the inoculated organisms was recovered, and the biological indicator strips were negative for growth in all tiles indicating at least local sterilization of tile areas. The findings suggest that minimum time/temperature combination is required for complete sterilization. Microbial analysis of tiles processed at lower temperatures from 130deg C-150deg C at varying times will be discussed, as well as analysis of the bacteria and fungi present on the compactor hardware as a result of exposure to the waste and the surrounding environment. The two organisms inoculated into the waste were among those isolated and identified from the HMC surfaces indicating the possibility of cross contamination.

Hummerick, Mary P.↗

Identifying Climate-Smart Agriculture Research Needs

Climate-smart agriculture (CSA) is an approach to help agricultural systems worldwide, concurrently addressing three challenge areas: increased adaptation to climate change, mitigation of climate change, and ensuring global food security - through innovative policies, practices, and financing. It involves a set of objectives and multiple transformative transitions for which there are newly identified knowledge gaps. We address these questions raised by CSA within three areas: conceptualization, implementation, and implications for policy and decision-makers. We also draw up scenarios on the future of the CSA concept in relation to the 4 per 1000 Initiative (Soils for Food Security and Climate) launched at UNFCCC 21st Conference of the Parties (COP 21). Our analysis shows that there is still a need for further interdisciplinary research on the theoretical foundation of the CSA concept and on the necessary transformations of agriculture and land use systems. Contrasting views about implementation indicate that CSA focus on the ''triple win'' (adaptation, mitigation, food security) needs to be assessed in terms of science-based practices. CSA policy tools need to incorporate an integrated set of measures supported by reliable metrics. Environmental and social safeguards are necessary to make sure that CSA initiatives conform to the principles of sustainability, both at the agriculture and food system levels.

mitigation↗

Microbiological Quality and Food Safety of Plants Grown on ISS Project

The goal of this project is to select and advance methods to enable real-time sampling, microbiological analysis, and sanitation of crops grown on the International Space Station (ISS). These methods would validate the microbiological quality of crops grown for consumption to ensure safe and palatable fresh foods. This would be achieved through the development / advancement of microbiological sample collection, rapid pathogen detection and effective sanitation methods that are compatible with a microgravity environment.

Technology Portfolio System↗

A Dividend in Food Safety

When NASA faced the problem of how and what to feed an astronaut in a sealed capsule under weightless conditions while planning for manned space mission, they enlisted the aid of The Pillsbury Company. There were two principal concerns: barring crumbs of food that might contaminate the spacecraft's atmosphere or float their way into sensitive instruments; and assuring absolute freedom from potentially catastrophic disease-producing bacteria and toxins. Pillsbury quickly solved the first concern, but the other part of the problem was not as easy. They found that with using standard methods, there was no way to be assured there would not be any bacteria. It was concluded that the only way to succeed was to establish control over the entire process, the raw materials, the processing environment and the people involved. Pillsbury developed the Hazard Analysis and Critical Control Point (HACCP) concept. The HACCP is designed to prevent food safety problems rather than to catch them after they have occurred. Three other government agencies are taking preliminary steps toward extending HACCP to meat/poultry and seafood inspection operations. Today, Pillsbury plants are still operating under HACCP.

Source record↗

Importance of Trade Dependencies for Agricultural Inputs: A Case Study of Finland

Approximately 80% of the world's population lives in countries that are dependent on food imports to sustain an adequate food supply. Besides these food imports, further dependencies also arise due to the requirements for agricultural inputs, including energy, fertilisers, feed and agricultural machinery. While the trade of agricultural inputs is relatively well represented in economic analysis, the quantification is often in terms of monetary values, and thus the assessments of the actual input quantities are very limited. In this paper, we develop a framework for analysis of the traded input quantities at the country-level and demonstrate its utility through an in-depth analysis of Finland's dependency on agricultural inputs. Further, we assess the importance of these inputs for domestic food production from a resilience perspective. We find that Finland, a country with relatively high food self-sufficiency but also a great dependency on imported agricultural inputs, experienced an increase in its dependency over the period 1996-2016. In case of trading partners, the story is more mixed: while trading partners for soybeans increased, those decreased in case of electricity while no significant change was observed in other commodities. In Finland, the rapeseed dependency on imports (ratio of net imports and consumption) grew from around 0% to almost 50% between the years 1987-2013. Changes for electricity remained substantially smaller, with dependency only slightly growing during the study period. Crude oil and soybean supplies are totally dependent on imports as neither is produced in Finland. Interestingly, the highest dependencies for agricultural inputs were on different countries than that for foodstuff imports. Thus, when identifying and assessing approaches to increase resilience to trade-related shocks, it is essential to understand both foodstuff and agricultural input dependencies within the global food system.

trade dependencies↗

Preparing for Veg-04 and Veg-05: Improving Pick-And-Eat Food Capabilities for the International Space Station

The capability to grow nutritious, palatable food for crew consumption during spaceflight has the potential to provide health-promoting, bioavailable nutrients, enhance the dietary experience, and reduce launch mass as we move toward longer-duration missions. Studies of edible produce during spaceflight have been limited, leaving a significant knowledge gap in the methods required to grow safe, acceptable, nutritious crops for consumption in space. Researchers from Kennedy Space Center, Johnson Space Center, Purdue University and ORBITEC have teamed up to explore the potential for plant growth and food production on the International Space Station (ISS) and future exploration missions. Ground testing of Chinese cabbage and dwarf tomato crops under different LED lighting and fertilizer conditions is being conducted to allow for a preliminary down selection of the two best lighting recipes and the best fertilizer treatment. Two trials of Chinese cabbage and one trial on dwarf tomato have been completed in on-going ground tests. Horticultural data on crop growth and productivity and chemical data on specific nutrients have been collected and are being analyzed to allow preliminary down selection. Taste test evaluations are planned on the preliminary down selection treatments to allow a final down selection for flight testing. Microbial assessment for hazard analysis critical control points (HACCP) evaluation is also underway to enable implementation of food consumption. Following down selection flight preparation will commence for testing these crops in the Veggie vegetable-production system on the ISS. A crew questionnaire has been developed to better understand the impact of crop growth in Veggie on crew behavioral health. A single Veggie plant growth chamber is currently installed on ISS, and preparations are underway to launch a second Veggie, allowing side-by-side testing under different lighting conditions. Veg-04 will be the first mission that will use this dual-Veggie capability, where the selected cultivar of Tokyo bekana Chinese cabbage will be grown under two different red-to-blue light ratios. ORBITEC has developed custom lighting software allowing independent selection of red and blue light levels. The VEG-05 experiment will test similar light treatments using Red Robin dwarf tomato. These tests offer an opportunity to develop a pick-and-eat fresh vegetable component to the ISS food system as a first step to regular supplemental food production. Our work will help define light colors, levels, and horticultural best practices to achieve high yields of safe, nutritious leafy greens and tomatoes to supplement a space diet of prepackaged food. With this work we will continue the synergistic research to help close gaps in the human research roadmap, and enable humans to venture to Mars and beyond. This research was co-funded by the Human Research Program and Space Biology (MTL1075) in the ILSRA 2015 NRA call.

International Space Station↗

Developing a Community of Practice for Applied Uses of Future PACE Data to Address Food Security Challenges

Ocean color satellite measurements have yielded valuable information about the base of the marine food web for over 20 years. The Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission is building an advanced spectrometer to further refine ecosystem monitoring. Higher spectral resolution data from PACE will enable identification of additional marine biological indicators and their response to multiple stressors to guide sustainable management. Seafood is an important source of protein for a significant number of people. Wild catches cannot match increasing demand and their sustainability is in question. Aquaculture is an ever more important industry to feed the world's population. We share early efforts to engage a community of practice around food security to increase satellite data product use in support of resource management, business decisions, and policy analysis. Understanding the needs of applied scientists as well as non-traditional users of satellite data early in the PACE mission process will improve planning and preparation for a broader user base and hopefully help to mitigate food insecurity.

Schollaert Uz, Stephanie↗

Chemical Analysis Results for Potable Water from ISS Expeditions 21 to 25

The Johnson Space Center Water and Food Analytical Laboratory (WAFAL) performed detailed ground-based analyses of archival water samples for verification of the chemical quality of the International Space Station (ISS) potable water supplies for Expeditions 21 to 25. Over a 14-month period, the Space Shuttle visited the ISS on five occasions to complete construction and deliver supplies. The onboard supplies of potable water available for consumption by the Expeditions 21 to 25 crews consisted of Russian ground-supplied potable water, Russian potable water regenerated from humidity condensate, and US potable water recovered from urine distillate and condensate. Chemical archival water samples that were collected with U.S. hardware during Expeditions 21 to 25 were returned on Shuttle flights STS-129 (ULF3), STS-130 (20A), STS-131 (19A), STS-132 (ULF4) and STS-133 (ULF5), as well as on Soyuz flights 19-22. This paper reports the analytical results for the returned archival water samples and evaluates their compliance with ISS water quality standards. The WAFAL also received and analyzed aliquots of some Russian potable water samples collected in-flight and pre-flight samples of Rodnik potable water delivered to the Station on the Russian Progress vehicle during Expeditions 21 to 25. These additional analytical results are also reported and discussed in this paper.

Straub, John E., II↗