Avoiding numerical stability problems of long duration DGPS/INS Kalman filters

A current pursuit of the geodetic community is the optimal integration of differential GPS (DGPS) and inertial navigation system (INS) data streams for precise and efficient position and gravity vector surveying. Therein a complete INS and multiple-antenna GPS receiver payload, mounted on a moving platform, is used in conjunction with a network of ground-fixed single antenna GPS receivers. This paper presents a complete, GPS-based, external updating measurement model for the applicable Kalman filter. The model utilizes four external observation types for every GPS satellite in-view: DGPS range differences, single phase differences, and single phase-rate differences; as well as the mobile, multipleantenna GPS receiver's measurement of theerrors in the INS's estimate of the phase difference between any two vehicle-borne GPS antennae. Although not widely conveyed in the geodetic world, the inertial navigation community has long known that traditional Kalman filter covariance propagation recurrences are inherently unstable when such highly accurate external updates are repeatedly applied (every 1 second) over long time durations. A hybrid square root covariance/U — D covariance factorization approach is a numerically stable alternative and is reviewed herein. The hybrid makeup of the algorithm is necessitated by the correlated nature of the fourth type of GPS external measurement listed above (each vehicle-borne GPS antenna formstwo baselines). Such measurement correlations require a functional transformation of the overall external updating model to permit the multiple updates (simultaneously available at each updating epoch) to be sequentially (and efficiently) processed. An appropriate transformation is given. Stable covariance propagation relationships are presented and the transformed Kalman gain is also furnished and its use in the determination of the externally updated error states is discussed. Specific DGPS/INS instabilities produced by the traditional recurrences are displayed. The stable alternative method requires about 25% more CPU time than the traditional Kalman recurrences. With the ever-increasing computational speeds of microprocessors, this added CPU time is of no real concern.     

The influence of silicate melt composition on distribution of siderophile elements among metal and silicate liquids

Liquid metal-liquid silicate partitioning of Fe, Ni, Co, P, Ge, W and Mo among a carbon-saturated metal and a variety of silicate melts (magnesian-tholeiitic-siliceous-aluminous-aluminosiliceous basalts) depends modestly to strongly upon silicate melt structure and composition. Low valency siderophile elements, Fe, Ni and Co, show a modest influence of silicate melt composition on partitioning. Germanium shows a moderate but consistent preference for the depolymerized magnesian melt. High valency siderophile elements, P, Mo, and W, show more than an order of magnitude decrease in metal-silicate partition coefficients as the silicate melt becomes more depolymerized. Detailed inspection of our and other published W data shows that polymerization state, temperature and pressure are more important controls on W partitioning than oxidation state. For this to be true for a high and variable valence element implies a secondary role in general for oxidation state, even though some role must be present. Equilibrium core segregation through a magma ocean of ‘ultrabasic’ composition can provide a resolution to the ‘excess’ abundances of Ge, P, W and Mo in the mantle, but the mantle composition alone cannot explain the excess abundances of nickel and cobalt in chondritic proportions.     

Comparative study of activation energies of conductance and desiccation rates of some marine algae

Measurements of the activation energy of electrical conductance and desiccation rates on subtidal marine algae from Florida were compared to similar data from the Bay of Fundy, Nova Scotia, on intertidal marine algae frequently subjected to long periods of exposure to air. We have developed a method for calculating the reaction rate constant of desiccation of fully hydrated marine algae. Values of activation energies and desiccation rate constants are consistent with the requirements for survival of these algae under widely different environmental conditions.     

BIFoR FACE: Water–soil–vegetation–atmosphere data from a temperate deciduous forest catchment,including under elevated CO2

The ecosystem services provided by forests modulate runoff generation processes, nutrient cycling and water and energy exchange between soils, vegetation and atmosphere. Increasing atmospheric CO₂ affects many linked aspects of forest and catchment function in ways we do not adequately understand. Global levels of atmospheric CO₂ will be around 40% higher in 2050 than current levels, yet estimates of how water and solute fluxes in forested catchments will respond to increased CO₂ are highly uncertain. The Free Air CO₂ Enrichment (FACE) facility of the University of Birmingham's Institute of Forest Research (BIFoR) is the only FACE in mature deciduous forest. The site specializes in fundamental studies of the response of whole ecosystem patches of mature, deciduous, temperate woodland to elevated CO₂ (eCO₂). Here, we describe a dataset of hydrological parameters – seven weather parameters at each of three heights and four locations, shallow soil moisture and temperature, stream hydrology and CO₂ enrichment – retrieved at high frequency from the BIFoR FACE catchment.     

Effects of pipe outlet blocking on hydrological functioning in a degraded blanket peatland

Peatland restoration practitioners are keen to understand the role of drainage via natural soil pipes, especially where erosion has released large quantities of fluvial carbon in stream waters. However, little is known about pipe-to-stream connectivity and whether blocking methods used to impede flow in open ditch networks and gullies also work on pipe networks. Two streams in a heavily degraded blanket bog (southern Pennines, UK) were used to assess whether impeding drainage from pipe networks alters the streamflow responses to storm events, and how such intervention affects the hydrological functioning of the pipe network and the surrounding peat. Pipeflow was impeded in half of the pipe outlets in one stream, either by inserting a plug-like structure in the pipe-end or by the insertion of a vertical screen at the pipe outlet perpendicular to the direction of the predicted pipe course. Statistical response variable η² showed the overall effects of pipe outlet blocking on stream responses were small with η² = 0.022 for total storm runoff, η² = 0.097 for peak discharge, η² = 0.014 for peak lag, and η² = 0.207 for response index. Both trialled blocking methods either led to new pipe outlets appearing or seepage occurring around blocks within 90 days of blocking. Discharge from four individual pipe outlets was monitored for 17 months before blocking and contributed 11.3% of streamflow. Pipe outlets on streambanks with headward retreat produced significantly larger peak flows and storm contributions to streamflow compared to pipe outlets that issued onto straight streambank sections. We found a distinctive distance-decay effect of the water table around pipe outlets, with deeper water tables around pipe outlets that issued onto straight streambanks sections. We suggest that impeding pipeflow at pipe outlets would exacerbate pipe development in the gully edge zone, and propose that future pipe blocking efforts in peatlands prioritize increasing the residence time of pipe water by forming surface storage higher up the pipe network.     

New snow metrics for a warming world

Snow is Earth's most climatically sensitive land cover type. Traditional snow metrics may not be able to adequately capture the changing nature of snow cover. For example, April 1 snow water equivalent (SWE) has been an effective index for streamflow forecasting, but it cannot express the effects of midwinter melt events, now expected in warming snow climates, nor can we assume that station-based measurements will be representative of snow conditions in future decades. Remote sensing and climate model data provide capacity for a suite of multi-use snow metrics from local to global scales. Such indicators need to be simple enough to “tell the story” of snowpack changes over space and time, but not overly simplistic or overly complicated in their interpretation. We describe a suite of spatially explicit, multi-temporal snow metrics based on global satellite data from NASA's Moderate Resolution Imaging Spectroradiometer (MODIS) and downscaled climate model output for the U.S. We describe and provide examples for Snow Cover Frequency (SCF), Snow Disappearance Date (SDD), At-Risk Snow (ARS), and Frequency of a Warm Winter (FWW). Using these retrospective and prospective snow metrics, we assess the current and future snow-related conditions in three hydroclimatically different U.S. watersheds: the Truckee, Colorado Headwaters, and Upper Connecticut. In the two western U.S. watersheds, SCF and SDD show greater sensitivity to annual differences in snow cover compared with data from the ground-based Snow Telemetry (SNOTEL) network. The eastern U.S. watershed does not have a ground-based network of data, so these MODIS-derived metrics provide uniquely valuable snow information. The ARS and FWW metrics show that the Truckee Watershed is highly vulnerable to conversion from snowfall to rainfall (ARS) and midwinter melt events (FWW) throughout the seasonal snow zone. In comparison, the Colorado Headwaters and Upper Connecticut Watersheds are colder and much less vulnerable through mid- and late-century.     

Hydrological modelling for assessing spatio-temporal groundwater recharge variations in the water-stressed Amathole Water Supply System,Eastern Cape,South Africa

To increase the resilience of regional water supply systems in South Africa in the face of anticipated climatic changes and a constant increase in water demand, water supply sources require diversification. Many water-stressed metropolitan regions in South Africa depend largely on surface water to cover their water demand. While climatic and river discharge data is widely available in these regions, information on groundwater resources – which could support supply source diversification – is scarce. Groundwater recharge is a key parameter that is used to estimate groundwater amounts that can be sustainably exploited at a sub-watershed level. Therefore, the objective of this study was to develop a reliable hydrological modelling routine that enables the assessment of regional spatio-temporal variations of groundwater recharge to discern the most promising areas for groundwater development. Accordingly, we present a semi-distributed hydrological modelling approach that incorporates water balance routines coupled with baseflow modelling techniques to yield spatio-temporal variations of groundwater recharge on a regional level. The approach is demonstrated for the actively managed catchment areas of the Amathole Water Supply System situated in a semi-arid part of the Eastern Cape of South Africa. In the investigated study area, annual groundwater recharge exhibits a high spatio-temporal heterogeneity and is estimated to vary between ~0.5% and 8% of annual rainfall. Despite some uncertainties induced by limited data availability, calibration and validation of the model were found to be satisfactory and yielded model results similar to (point) data of annual groundwater recharge reported in earlier studies. Our approach is therefore found to derive crucial information for efficiently targeting more detailed groundwater exploration studies and could work as a blueprint for orientating groundwater potential exploration in similar environments.     

Little River Experimental Watershed,a keystone in understanding of coastal plain watersheds

The US Department of Agriculture-Agricultural Research Service Southeast Watershed Research Laboratory (SEWRL) initiated a hydrologic research program on the Little River Experimental Watershed (LREW) in 1967. Long-term (52 years) streamflow data are available for nine sites, including rainfall-runoff relationships and hydrograph characteristics regularly used in research on interactive effects of climate, vegetation, soils, and land-use in low-gradient streams of the US EPA Level III Southeastern Plains ecoregion. A summary of prior research on the LREW illustrates the impact of the watershed on building a regional understanding of hydrology and water quality. Climatic and streamflow data were used to make comparisons of scale across the nine nested LREW watersheds (LRB, LRF, LRI, LRJ, LRK, LRO, LRN, LRM, and LRO3) and two regional watersheds (Alapaha and Little River at Adel). Annual rainfall for the largest LREW, LRB, was 1200 mm while average annual streamflow was 320 mm. Annual rainfall, streamflow, and the ratio between annual streamflow and rainfall (Sratio) were similar (α = 0.05) across LREWs LRB, LRF, LRI, LRJ, LRK, and LRO. While annual rainfall within the 275 ha LRO3 was found to be similar to LRO and LRM (α = 0.05), annual streamflow and Sratio were significantly different (α = 0.05). Comparisons of annual rainfall, streamflow, and Sratio between LRB and the regional watersheds indicated no differences (α = 0.05). Based upon this analysis, most regional watersheds shared similar hydrologic characteristics. LRO3 was an exception, where increases in row crops and decreases in forest coverage resulted in increased streamflow. LREW data have been instrumental in building considerable scientific understanding of flow and transport processes for these stream systems. Continued operation of the LREW hydrologic network will support hydrologic research as well as environmental quality and riparian research programs that address emerging and high priority natural resource and environmental issues.     

Water source dynamics of high Arctic river basins

Arctic river basins are amongst the most vulnerable to climate change. However, there is currently limited knowledge of the hydrological processes that govern flow dynamics in Arctic river basins. We address this research gap using natural hydrochemical and isotopic tracers to identify water sources that contributed to runoff in river basins spanning a gradient of glacierization (0–61%) in Svalbard during summer 2010 and 2011. Spatially distinct hydrological processes operating over diurnal, weekly and seasonal timescales were characterized by river hydrochemistry and isotopic composition. Two conceptual water sources (‘meltwater’ and ‘groundwater’) were identified and used as a basis for end‐member mixing analyses to assess seasonal and year‐to‐year variability in water source dynamics. In glacier‐fed rivers, meltwater dominated flows at all sites (typically >80%) with the highest contributions observed at the beginning of each study period in early July when snow cover was most extensive. Rivers in non‐glacierized basins were sourced initially from snowmelt but became increasingly dependent on groundwater inputs (up to 100% of total flow volume) by late summer. These hydrological changes were attributed to the depletion of snowpacks and enhanced soil water storage capacity as the active layer expanded throughout each melt season. These findings provide insight into the processes that underpin water source dynamics in Arctic river systems and potential future changes in Arctic hydrology that might be expected under a changing climate. Copyright © 2013 John Wiley & Sons, Ltd.