Quality assessment of sub-Nyquist recovery from future gravity satellite missions

Drawing on experience from Gravity Recovery and Climate Experiment (GRACE) data analysis, the scientific challenges were already identified in several studies. Any future mission should focus on improvement in both precision and resolution in space and time. For future gravity missions which use high quality sensors, aliasing of high frequency time-variable geophysical signals to the lower frequency signals is one of the most serious problems. The aliasing problem and the spatio-temporal resolution are mainly restricted by two sampling theorems describing the space-time sampling of satellite missions: (i) a Heisenberg-like uncertainty theorem which states that the product of spatial resolution and time resolution is constant, and (ii) the Colombo–Nyquist rule (CNR), which requires the number of satellite revolutions in a repeat period to be at least twice a given maximum spherical harmonic degree. The CNR holds under the assumption of equal ground-track spacing, and limits the spatial resolution of the gravity solution.     

Long-wavelength lunar gravity field recovery from simulated orbit and inter-satellite tracking data

As has been demonstrated recently, inter-satellite Ka-band tracking data collected by the GRAIL (Gravity Recovery And Interior Laboratory) spacecraft have the potential to improve the resolution and accuracy of the lunar gravity field by several orders of magnitude compared to previous models. By means of a series of simulation studies, here we investigate the contribution of inter-satellite ranging for the recovery of the Moon’s gravitational features; the evaluation of results is made against findings from ground-based Doppler tracking. For this purpose we make use of classical dynamic orbit determination, supported by the analysis of satellite-to-satellite tracking observations. This study sheds particularly light on the influence of the angular distance between the two satellites, solar radiation modeling and the co-estimation of the lunar Love number k₂. The quality of the obtained results is assessed by gravity field power spectra, gravity anomalies and precision orbit determination. We expect our simulation results to be supportive for the processing of real GRAIL data.     

Regional gravity field model in Pakistan area from the combination of CHAMP,GRACE and ground data using least squares collocation: A case study

This study describes a methodology of recovery of the Earth’s gravity field from CHAMP and GRACE satellites data in Pakistan using least squares collocation (LSC) based downward continuation technique. The CHAMP height anomalies and GRACE gravity disturbances derived from the observed satellite data have been used in combination solution using LSC with observed gravity values at the Earth surface. The combined covariance functions of height anomalies and/or gravity disturbances at satellite altitudes and observed gravity anomalies at Earth surface have been used as the basis for combination and downward continuation solution. The variance of predicted gravity anomalies from GRACE gravity disturbances is relatively lower than the corresponding results of gravity anomalies from CHAMP height anomalies. This fact may be attributed partly to the amplification of noise and partly to the unstable inverse transformation process of height anomalies to gravity anomalies. The impact of data error variance has been studied in the context of smoothing and noise reduction in the final solution of downward continuation using least squares collocation. The raising of data error suppresses the noise and as a result a smooth final solution is obtained. The prediction results appear to be dependent on the quality of data and goodness of combined covariance function, which are fairly comparable for the CHAMP and GRACE data. The recovered gravity field from satellite data appears to contribute mainly to medium and long wavelength parts of total gravity field spectrum. Due to flexibility of data handling in least squares collocation, this procedure is applicable to any observable of gravity field being at different altitudes and with different data spacing.     

Recovery of the Earth’s gravity field from formation-flying satellites: Temporal aliasing issues

Temporal and mean gravity field models derived from the twin-satellite, leader–follower mission GRACE have provided a new type of information for Earth sciences. In this contribution, we study the potential of various alternative satellite formations for gravity field determination in the post-GRACE era in a simulation environment. In particular, the effects of spherical harmonic truncation and of temporal aliasing in the processing of gravity products from such future formations are investigated.     

High precision subsurface structural mapping of the Trompsburg complex (South Africa) from gravity and magnetic data

Trompsburg Complex, South Africa, is obscured by the Karoo sediments, and it is not observed on the surface. Knowledge of the boundaries of the subsurface geological bodies in the region is of main interest in many applications of the Earth Sciences. There are many methods developed to delineate boundaries of subsurface geological sources such as the curvature-based method and parabola-based methods. In this study, we applied an improved approach based on parabolic curve fitting to the gradient amplitudes of gravity and magnetic data for extracting geological structures of the Trompsburg Complex. The results showed ring structures with a diameter of about 50 km, that include granitic rocks in the central part of the Trompsburg Complex. The results also demonstrated the existence of boundaries of the other structures in the south-eastern region of the Complex, which were not determined in previous studies. The result provides new information for a better understanding of the structural and tectonic features of the Trompsburg Complex. The success of this study suggests that the improved technique based on parabolic curve, is helpful in outlining the edge locations of subsurface geologic structures.     

A gravity wave analysis near to the Andes Range from GPS radio occultation data and mesoscale numerical simulations: Two case studies

Global maps of potential wave energy per unit mass, recently performed with the Global Positioning System (GPS) Radio Occultation (RO) technique and different satellite missions (CHAMP and SAC-C since 2001, GRACE and COSMIC since 2006) revealed in Argentina, at the eastern side of the highest Andes Mountains, a considerable wave activity (WA) in comparison with other extra-tropical regions. The main gravity wave (GW) sources in this natural laboratory are deep convection (mainly during late Spring and Summer), topographic forcing and geostrophic adjustment.     

The accuracy of data from ionosondes for the estimation of hmF2 and the identification of global change in the ionosphere

A long temporal series of simulated ionograms was generated with a superimposed secular variation of −14 km/century on the h_mF2 parameter. These ionograms were interpreted by the automatic scaling program Autoscala. By applying four different empirical formulas, four artificial series of h_mF2 were generated and then processed with the same methods used by other authors for real data sets. Data analysis of the simulated ionograms revealed the artificially imposed long-term trend. These results lead to the conclusion, that regardless of the empirical formula used, the accuracy of h_mF2 from ionosonde measurements would be adequate to observe a long-term trend of −14 km/century.     

The water cycle in closed ecological systems: Perspectives from the Biosphere 2 and Laboratory Biosphere systems

To achieve sustainable, healthy closed ecological systems requires solutions to challenges of closing the water cycle – recycling wastewater/irrigation water/soil medium leachate and evaporated water and supplying water of required quality as needed for different needs within the facility. Engineering Biosphere 2, the first multi-biome closed ecological system within a total airtight footprint of 12,700 m² with a combined volume of 200,000 m³ with a total water capacity of some 6 × 10⁶ L of water was especially challenging because it included human inhabitants, their agricultural and technical systems, as well as five analogue ecosystems ranging from rainforest to desert, freshwater ecologies to saltwater systems like mangrove and mini-ocean coral reef ecosystems. By contrast, the Laboratory Biosphere – a small (40 m³ volume) soil-based plant growth facility with a footprint of 15 m² – is a very simplified system, but with similar challenges re salinity management and provision of water quality suitable for plant growth. In Biosphere 2, water needs included supplying potable water for people and domestic animals, irrigation water for a wide variety of food crops, and recycling and recovering soil nutrients from wastewater. In the wilderness biomes, providing adequately low salinity freshwater terrestrial ecosystems and maintaining appropriate salinity and pH in aquatic/marine ecosystems were challenges. The largest reservoirs in Biosphere 2 were the ocean/marsh with some 4 × 10⁶ L, soil with 1 to 2 × 10⁶ l, primary storage tank with 0 to 8 × 10⁵ L and storage tanks for condensate and soil leachate collection and mixing tanks with a capacity of 1.6 × 10⁵ L to supply irrigation for farm and wilderness ecosystems. Other reservoirs were far smaller – humidity in the atmosphere (2 × 10³ L), streams in the rainforest and savannah, and seasonal pools in the desert were orders of magnitude smaller (8 × 10⁴ L). Key technologies included condensation from humidity in the air handlers and from the glass space frame to produce high quality freshwater, wastewater treatment with constructed wetlands and desalination through reverse osmosis and flash evaporation were key to recycling water with appropriate quality throughout the Biosphere 2 facility. Wastewater from all human uses and the domestic animals in Biosphere 2 was treated and recycled through a series of constructed wetlands, which had hydraulic loading of 0.9–1.1 m³ day⁻¹ (240–290 gal d⁻¹). Plant production in the wetland treatment system produced 1210 kg dry weight of emergent and floating aquatic plant wetland which was used as fodder for the domestic animals while remaining nutrients/water was reused as part of the agricultural irrigation supply. There were pools of water with recycling times of days to weeks and others with far longer cycling times within Biosphere 2. By contrast, the Laboratory Biosphere with a total water reservoir of less than 500 L has far quicker cycling rapidity: for example, atmospheric residence time for water vapor was 5–20 min in the Laboratory Biosphere vs. 1–4 h in Biosphere 2, as compared with 9 days in the Earth’s biosphere. Just as in Biosphere 2, humidity in the Laboratory Biosphere amounts to a very small reservoir of water. The amount of water passing through the air in the course of a 12-h operational day is two orders of magnitude greater than the amount stored in the air. Thus, evaporation and condensation collection are vital parts of the recycle system just as in Biosphere 2. The water cycle and sustainable water recycling in closed ecological systems presents problems requiring further research – such as how to control buildup of salinity in materially closed ecosystems and effective ways to retain nutrients in optimal quantity and useable form for plant growth. These issues are common to all closed ecological systems of whatever size, including planet Earth’s biosphere and are relevant to a global environment facing increasing water shortages while maintaining water quality for human and ecosystem health. Modular biospheres offer a test bed where technical methods of resolving these problems can be tested for feasibility.