HCMM energy budget data as a model input for assessing regions of high potential groundwater pollution

The author has identified the following significant results. In early April 1978, heavy spring runoff from snowmelt caused significant flooding along a portion of the Big Sioux River Basin in southeastern South Dakota. The flooded area was visible from surrounding areas on a May 15 HCMM IR test image. On May 15, the flood waters had receded but an area of anomalous residual high soil moisture remained. The high soil moisture area was not visible on a HCMM day visible test image of the same scene, or on LANDSAT imagery. To evaluate the effect of water table depth on surface temperatures, thermal scanner data collected on September 5 and 6, 1978 at approximate HCMM overpass times at an altitude of 3650 m were analyzed. Apparent surface temperatures measured by the scanner included emittance contributions from soil surface and the land cover. Results indicated that the shallow water tables produced a damping of the amplitude of the diurnal surface temperature wave

Sensitivity of GPS and GLONASS orbits with respect to resonant geopotential parameters

The Center for Orbit Determination in Europe (CODE) has been involved in the processing of combined GPS/GLONASS data during the International GLONASS Experiment (IGEX). The resulting precise orbits were analyzed using the program SORBDT. Introducing one satellite's positions as pseudo-observations, the program is capable of fitting orbital arcs through these positions using an orbit improvement procedure based on the numerical integration of the satellite's orbit and its partial derivative with respect to the orbit parameters. For this study, the program was enhanced to estimate selected parameters of the Earth's gravity field. The orbital periods of the GPS satellites are —in contrast to those of the GLONASS satellites - 2:1 commensurable (P Sid:P GPS) with the rotation period of the Earth. Therefore, resonance effects of the satellite motion with terms of the geopotential occur and they influence the estimation of these parameters. A sensitivity study of the GPS and GLONASS orbits with respect to the geopotential coefficients reveals that the correlations between different geopotential coefficients and the correlations of geopotential coefficients with other orbit parameters, in particular with solar radiation pressure parameters, are the crucial issues in this context. The estimation of the resonant geopotential terms is, in the case of GPS, hindered by correlations with the simultaneously estimated radiation pressure parameters. In the GLONASS case, arc lengths of several days allow the decorrelation of the two parameter types. The formal errors of the estimates based on the GLONASS orbits are a factor of 5 to 10 smaller for all resonant term

Pseudo-Stochastic Orbit Modeling Techniques for Low-Earth Orbiters

The Earth's non-spherical mass distribution and atmospheric drag cause the strongest perturbations on very low-Earth orbiting satellites (LEOs). Models of gravitational and non-gravitational accelerations are utilized in dynamic precise orbit determination (POD) with GPS data, but it is also possible to derive LEO positions based on GPS precise point positioning without dynamical information. We use the reduced-dynamic technique for LEO POD, which combines the geometric strength of the GPS observations with the force models, and investigate the performance of different pseudo-stochastic orbit parametrizations, such as instantaneous velocity changes (pulses), piecewise constant accelerations, and continuous piecewise linear accelerations. The estimation of such empirical orbit parameters in a standard least-squares adjustment process of GPS observations, together with other relevant parameters, strives for the highest precision in the computation of LEO trajectories. We used the procedures for the CHAMP satellite and found that the orbits may be validated by means of independent SLR measurements at the level of 3.2cm RMS. Validations with independent accelerometer data revealed correlations at the level of 95% in the along-track direction. As expected, the empirical parameters compensate to a certain extent for deficiencies in the dynamic models. We analyzed the capability of pseudo-stochastic parameters for deriving information about the mismodeled part of the force field and found evidence that the resulting orbits may be used to recover force field parameters, if the number of pseudo-stochastic parameters is large enough. Results based on simulations showed a significantly better performance of acceleration-based orbits for gravity field recovery than for pulse-based orbits, with a quality comparable to a direct estimation if unconstrained accelerations are set up every 30

Propagation of atmospheric model errors to gravity potential harmonics—impact on GRACE de-aliasing

High-frequency, time-varying mass redistributions in the ocean and atmosphere have an impact on GRACE gravity field solutions due to the space-time sampling characteristics of signal and orbit. Consequently, aliasing of these signals into the GRACE observations is present and needs to be taken into account during data analysis by applying atmospheric and oceanic model data (de-aliasing). As the accuracy predicted prior to launch could not yet be achieved in the analysis of real GRACE data, the de-aliasing process and related geophysical model uncertainties are regarded as a potential error source in GRACE gravity field determination. Therefore, this study aims to improve the de-aliasing process in order to obtain a more accurate GRACE gravity field time-series. As these time-series provide estimates for the integrated mass transport in the Earth system, like the global water cycle and solid Earth geophysical processes, any increase in accuracy will lead to improvements in the geophysical interpretation of the results. So in conclusion, improving the de-aliasing is of relevance for a better understanding of geophysical processes. By no longer regarding the atmosphere and ocean model output as error-free, deeper insight into the impact of such uncertainties on the de-aliasing and on the resulting GRACE gravity field models can be obtained. For this purpose, in a first step, a full error propagation of the atmospheric and oceanic model parameters up to the de-aliasing gravity field coefficients is performed and the GRACE K-Band-Satellite-to-Satellite Tracking (KBR-SST) residuals, as an intermediate gravity field result, are analysed. The paper reviews the standard GRACE de-aliasing process and presents the mathematical model applied for the error propagation. Specifically, the effect of uncertainties in the atmospheric input parameters (temperature, surface pressure, specific humidity, geopotential) on the gravity field potential coefficients used for de-aliasing is shown in several scenarios. Finally, the impact of de-aliasing products (with and without error propagation) on a GRACE gravity field solution is investigated on the level of observation residuals. From the results obtained in this study it can be concluded that with respect to the current GRACE error budget, atmospheric model uncertainties do not play a prominent role in the error budget of current GRACE gravity field solutions. Nevertheless, in order to fully exploit the GRACE measurements towards the baseline accuracy, an optimized de-aliasing is needed. In this case, GRACE gravity field solutions are sensitive to uncertainties in atmospheric and oceanic models. Thus, the associated geophysical model errors shall be taken into account in the de-aliasing proces

High-rate GPS clock corrections from CODE: support of 1Hz applications

GPS zero-difference applications with a sampling rate up to 1Hz require corresponding high-rate GPS clock corrections. The determination of the clock corrections in a full network solution is a time-consuming task. The Center for Orbit Determination in Europe (CODE) has developed an efficient algorithm based on epoch-differenced phase observations, which allows to generate high-rate clock corrections within reasonably short time (<2h) and with sufficient accuracy (on the same level as the CODE rapid or final clock corrections, respectively). The clock determination procedure at CODE and the new algorithm is described in detail. It is shown that the simplifications to speed up the processing are not causing a significant loss of accuracy for the clock corrections. The high-rate clock corrections have in essence the same quality as clock corrections determined in a full network solution. In order to support 1Hz applications 1-s clock corrections would be needed. The computation time, even for the efficient algorithm, is not negligible, however. Therefore, we studied whether a reduced sampling is sufficient for the GPS satellite clock corrections to reach the same or only slightly inferior level of accuracy as for the full 1-s clock correction set. We show that high-rate satellite clock corrections with a spacing of 5s may be linearly interpolated resulting in less than 2% degradation of accurac

Forced motion near black holes

We present two methods for integrating forced geodesic equations in the Kerr spacetime, which can accommodate arbitrary forces. As a test case, we compute inspirals under a simple drag force, mimicking the presence of gas. We verify that both methods give the same results for this simple force. We find that drag generally causes eccentricity to increase throughout the inspiral. This is a relativistic effect qualitatively opposite to what is seen in gravitational-radiation-driven inspirals, and similar to what is observed in hydrodynamic simulations of gaseous binaries. We provide an analytic explanation by deriving the leading order relativistic correction to the Newtonian dynamics. If observed, an increasing eccentricity would provide clear evidence that the inspiral was occurring in a non-vacuum environment. Our two methods are especially useful for evolving orbits in the adiabatic regime. Both use the method of osculating orbits, in which each point on the orbit is characterized by the parameters of the geodesic with the same instantaneous position and velocity. Both methods describe the orbit in terms of the geodesic energy, axial angular momentum, Carter constant, azimuthal phase, and two angular variables that increase monotonically and are relativistic generalizations of the eccentric anomaly. The two methods differ in their treatment of the orbital phases and the representation of the force. In one method the geodesic phase and phase constant are evolved together as a single orbital phase parameter, and the force is expressed in terms of its components on the Kinnersley orthonormal tetrad. In the second method, the phase constants of the geodesic motion are evolved separately and the force is expressed in terms of its Boyer-Lindquist components. This second approach is a generalization of earlier work by Pound and Poisson for planar forces in a Schwarzschild background.Comment: 28 pages, 2 figures, submitted to Phys. Rev. D; v2 has minor changes for consistency with published version, plus a new section discussing the relative advantages of the two approache

Efficient satellite orbit modelling using pseudo-stochastic parameters

If the force field acting on an artificial Earth satellite is not known a priori with sufficient accuracy to represent its observations on their accuracy level, one may introduce so-called pseudo-stochastic parameters into an orbit determination process, e.g. instantaneous velocity changes at user-defined epochs or piecewise constant accelerations in user-defined adjacent time subintervals or piecewise linear and continuous accelerations in adjacent time subintervals. The procedures, based on standard least-squares, associated with such parameterizations are well established, but they become inefficient (slow) if the number of pseudo-stochastic parameters becomes large. We develop two efficient methods to solve the orbit determination problem in the presence of pseudo-stochastic parameters. The results of the methods are identical to those obtained with conventional least-squares algorithms. The first efficient algorithm also provides the full variance-covariance matrix; the second, even more efficient algorithm, only parts of i

Evaluation of HCMM data for assessing soil moisture and water table depth

Soil moisture in the 0-cm to 4-cm layer could be estimated with 1-mm soil temperatures throughout the growing season of a rainfed barley crop in eastern South Dakota. Empirical equations were developed to reduce the effect of canopy cover when radiometrically estimating the soil temperature. Corrective equations were applied to an aircraft simulation of HCMM data for a diversity of crop types and land cover conditions to estimate the soil moisture. The average difference between observed and measured soil moisture was 1.6% of field capacity. Shallow alluvial aquifers were located with HCMM predawn data. After correcting the data for vegetation differences, equations were developed for predicting water table depths within the aquifer. A finite difference code simulating soil moisture and soil temperature shows that soils with different moisture profiles differed in soil temperatures in a well defined functional manner. A significant surface thermal anomaly was found to be associated with shallow water tables

Evaluation of HCMM data for assessing soil moisture and water table depth

Data were analyzed for variations in eastern South Dakota. Soil moisture in the 0-4 cm layer could be estimated with 1-mm soil temperatures throughout the growing season of a rainfed barley crop (% cover ranging from 30% to 90%) with an r squared = 0.81. Empirical equations were developed to reduce the effect of canopy cover when radiometrically estimating the 1-mm soil temperature, r squared = 0.88. The corrective equations were applied to an aircraft simulation of HCMM data for a diversity of crop types and land cover conditions to estimate the 0-4 cm soil moisture. The average difference between observed and measured soil moisture was 1.6% of field capacity. HCMM data were used to estimate the soil moisture for four dates with an r squared = 0.55 after correction for crop conditions. Location of shallow alluvial aquifers could be accomplished with HCMM predawn data. After correction of HCMM day data for vegetation differences, equations were developed for predicting water table depths within the aquifer (r=0.8)