The wavelet method as an alternative for reducing ionospheric effects from single-frequency GPS receivers

The ionospheric effect is one of the major errors in GPS data processing over long baselines. As a dispersive medium, it is possible to compute its influence on the GPS signal with the ionosphere-free linear combination of L1 and L2 observables, requiring dual-frequency receivers. In the case of single-frequency receivers, ionospheric effects are either neglected or reduced by using a model. In this paper, an alternative for single-frequency users is proposed. It involves multiresolution analysis (MRA) using a wavelet analysis of the double-difference observations to remove the short- and medium-scale ionosphere variations and disturbances, as well as some minor tropospheric effects. Experiments were carried out over three baseline lengths from 50 to 450 km, and the results provided by the proposed method were better than those from dual-frequency receivers. The horizontal root mean square was of about 0.28 m (1σ).     

Water-removed spectra increase the retrieval accuracy when estimating savanna grass nitrogen and phosphorus concentrations

Information about the distribution of grass foliar nitrogen (N) and phosphorus (P) is important for understanding rangeland vitality and for facilitating the effective management of wildlife and livestock. Water absorption effects in the near-infrared (NIR) and shortwave-infrared (SWIR) regions pose a challenge for nutrient estimation using remote sensing. The aim of this study was to test the utility of water-removed (WR) spectra in combination with partial least-squares regression (PLSR) and stepwise multiple linear regression (SMLR) to estimate foliar N and P, compared to spectral transformation techniques such as first derivative, continuum removal and log-transformed (Log(1/R)) spectra. The study was based on a greenhouse experiment with a savanna grass species (Digitaria eriantha). Spectral measurements were made using a spectrometer. The D. eriantha was cut, dried and chemically analyzed for foliar N and P concentrations. WR spectra were determined by calculating the residual from the modelled leaf water spectra using a nonlinear spectral matching technique and observed leaf spectra. Results indicated that the WR spectra yielded a higher N retrieval accuracy than a traditional first derivative transformation (R²=0.84, RMSE = 0.28) compared to R²=0.59, RMSE = 0.45 for PLSR. Similar trends were observed for SMLR. The highest P retrieval accuracy was derived from WR spectra using SMLR (R²=0.64, RMSE = 0.067), while the traditional first derivative and continuum removal resulted in lower accuracy. Only when using PLSR did the first derivative result in a higher P retrieval accuracy (R²=0.47, RMSE = 0.07) than the WR spectra (R²=0.43, RMSE = 0.070). It was concluded that the water removal technique is a promising technique to minimize the perturbing effect of foliar water content when estimating grass nutrient concentrations.     

Lunar gravity field determination using SELENE same-beam differential VLBI tracking data

A lunar gravity field model up to degree and order 100 in spherical harmonics, named SGM100i, has been determined from SELENE and historical tracking data, with an emphasis on using same-beam S-band differential VLBI data obtained in the SELENE mission between January 2008 and February 2009. Orbit consistency throughout the entire mission period of SELENE as determined from orbit overlaps for the two sub-satellites of SELENE involved in the VLBI tracking improved consistently from several hundreds of metres to several tens of metres by including differential VLBI data. Through orbits that are better determined, the gravity field model is also improved by including these data. Orbit determination performance for the new model shows improvements over earlier 100th degree and order models, especially for edge-on orbits over the deep far side. Lunar Prospector orbit determination shows an improvement of orbit consistency from 1-day predictions for 2-day arcs of 6 m in a total sense, with most improvement in the along and cross-track directions. Data fit for the types and satellites involved is also improved. Formal errors for the lower degrees are smaller, and the new model also shows increased correlations with topography over the far side. The estimated value for the lunar GM for this model equals 4902.80080±0.0009 km³/s² (10 sigma). The lunar degree 2 potential Love number k ₂ was also estimated, and has a value of 0.0255 ± 0.0016 (10 sigma as well).     

ITRF2008: an improved solution of the international terrestrial reference frame

ITRF2008 is a refined version of the International Terrestrial Reference Frame based on reprocessed solutions of the four space geodetic techniques: VLBI, SLR, GPS and DORIS, spanning 29, 26, 12.5 and 16?years of observations, respectively. The input data used in its elaboration are time series (weekly from satellite techniques and 24-h session-wise from VLBI) of station positions and daily Earth Orientation Parameters (EOPs). The ITRF2008 origin is defined in such a way that it has zero translations and translation rates with respect to the mean Earth center of mass, averaged by the SLR time series. Its scale is defined by nullifying the scale factor and its rate with respect to the mean of VLBI and SLR long-term solutions as obtained by stacking their respective time series. The scale agreement between these two technique solutions is estimated to be 1.05 ± 0.13 ppb at epoch 2005.0 and 0.049 ± 0.010?ppb/yr. The ITRF2008 orientation (at epoch 2005.0) and its rate are aligned to the ITRF2005 using 179 stations of high geodetic quality. An estimate of the origin components from ITRF2008 to ITRF2005 (both origins are defined by SLR) indicates differences at epoch 2005.0, namely: ?0.5, ?0.9 and ?4.7?mm along X, Y and Z-axis, respectively. The translation rate differences between the two frames are zero for Y and Z, while we observe an X-translation rate of 0.3?mm/yr. The estimated formal errors of these parameters are 0.2?mm and 0.2?mm/yr, respectively. The high level of origin agreement between ITRF2008 and ITRF2005 is an indication of an imprecise ITRF2000 origin that exhibits a Z-translation drift of 1.8?mm/yr with respect to ITRF2005. An evaluation of the ITRF2008 origin accuracy based on the level of its agreement with ITRF2005 is believed to be at the level of 1?cm over the time-span of the SLR observations. Considering the level of scale consistency between VLBI and SLR, the ITRF2008 scale accuracy is evaluated to be at the level of 1.2?ppb (8?mm at the equator) over the common time-span of the observations of both techniques. Although the performance of the ITRF2008 is demonstrated to be higher than ITRF2005, future ITRF improvement resides in improving the consistency between local ties in co-location sites and space geodesy estimates.     

VLBI-derived troposphere parameters during CONT08

Time-series of zenith wet and total troposphere delays as well as north and east gradients are compared, and zenith total delays (ZTD) are combined on the level of parameter estimates. Input data sets are provided by ten Analysis Centers (ACs) of the International VLBI Service for Geodesy and Astrometry (IVS) for the CONT08 campaign (12?C26 August 2008). The inconsistent usage of meteorological data and models, such as mapping functions, causes systematics among the ACs, and differing parameterizations and constraints add noise to the troposphere parameter estimates. The empirical standard deviation of ZTD among the ACs with regard to an unweighted mean is 4.6?mm. The ratio of the analysis noise to the observation noise assessed by the operator/software impact (OSI) model is about 2.5. These and other effects have to be accounted for to improve the intra-technique combination of VLBI-derived troposphere parameters. While the largest systematics caused by inconsistent usage of meteorological data can be avoided and the application of different mapping functions can be considered by applying empirical corrections, the noise has to be modeled in the stochastic model of intra-technique combination. The application of different stochastic models shows no significant effects on the combined parameters but results in different mean formal errors: the mean formal errors of the combined ZTD are 2.3?mm (unweighted), 4.4?mm (diagonal), 8.6?mm [variance component (VC) estimation], and 8.6?mm (operator/software impact, OSI). On the one hand, the OSI model, i.e. the inclusion of off-diagonal elements in the cofactor-matrix, considers the reapplication of observations yielding a factor of about two for mean formal errors as compared to the diagonal approach. On the other hand, the combination based on VC estimation shows large differences among the VCs and exhibits a comparable scaling of formal errors. Thus, for the combination of troposphere parameters a combination of the two extensions of the stochastic model is recommended.     

Quality assessment of GPS reprocessed terrestrial reference frame

The International GNSS Service (IGS) contributes to the construction of the International Terrestrial Reference Frame (ITRF) by submitting time series of station positions and Earth Rotation Parameters (ERP). For the first time, its submission to the ITRF2008 construction is based on a combination of entirely reprocessed GPS solutions delivered by 11 Analysis Centers (ACs). We analyze the IGS submission and four of the individual AC contributions in terms of the GNSS frame origin and scale, station position repeatability and time series seasonal variations. We show here that the GPS Terrestrial Reference Frame (TRF) origin is consistent with Satellite laser Ranging (SLR) at the centimeter level with a drift lower than 1 mm/year. Although the scale drift compared to Very Long baseline Interferometry (VLBI) and SLR mean scale is smaller than 0.4 mm/year, we think that it would be premature to use that information in the ITRF scale definition due to its strong dependence on the GPS satellite and ground antenna phase center variations. The new position time series also show a better repeatability compared to past IGS combined products and their annual variations are shown to be more consistent with loading models. The comparison of GPS station positions and velocities to those of VLBI via local ties in co-located sites demonstrates that the IGS reprocessed solution submitted to the ITRF2008 is more reliable and precise than any of the past submissions. However, we show that some of the remaining inconsistencies between GPS and VLBI positioning may be caused by uncalibrated GNSS radomes.     

Evaluating a thermal image sharpening model over a mixed agricultural landscape in India

Fine spatial resolution (e.g., <300 m) thermal data are needed regularly to characterise the temporal pattern of surface moisture status, water stress, and to forecast agriculture drought and famine. However, current optical sensors do not provide frequent thermal data at a fine spatial resolution. The TsHARP model provides a possibility to generate fine spatial resolution thermal data from coarse spatial resolution (≥1 km) data on the basis of an anticipated inverse linear relationship between the normalised difference vegetation index (NDVI) at fine spatial resolution and land surface temperature at coarse spatial resolution. The current study utilised the TsHARP model over a mixed agricultural landscape in the northern part of India. Five variants of the model were analysed, including the original model, for their efficiency. Those five variants were the global model (original); the resolution-adjusted global model; the piecewise regression model; the stratified model; and the local model. The models were first evaluated using Advanced Space-borne Thermal Emission Reflection Radiometer (ASTER) thermal data (90 m) aggregated to the following spatial resolutions: 180 m, 270 m, 450 m, 630 m, 810 m and 990 m. Although sharpening was undertaken for spatial resolutions from 990 m to 90 m, root mean square error (RMSE) of <2 K could, on average, be achieved only for 990–270 m in the ASTER data. The RMSE of the sharpened images at 270 m, using ASTER data, from the global, resolution-adjusted global, piecewise regression, stratification and local models were 1.91, 1.89, 1.96, 1.91, 1.70 K, respectively. The global model, resolution-adjusted global model and local model yielded higher accuracy, and were applied to sharpen MODIS thermal data (1 km) to the target spatial resolutions. Aggregated ASTER thermal data were considered as a reference at the respective target spatial resolutions to assess the prediction results from MODIS data. The RMSE of the predicted sharpened image from MODIS using the global, resolution-adjusted global and local models at 250 m were 3.08, 2.92 and 1.98 K, respectively. The local model consistently led to more accurate sharpened predictions by comparison to other variants.     

Normalized algorithm for mapping and dating forest disturbances and regrowth for the United States

Forest disturbances such as harvesting, wildfire and insect infestation are critical ecosystem processes affecting the carbon cycle. Because carbon dynamics are related to time since disturbance, forest stand age that can be used as a surrogate for major clear-cut/fire disturbance information has recently been recognized as an important input to forest carbon cycle models for improving prediction accuracy. In this study, forest disturbances in the USA for the period of ∼1990–2000 were mapped using 400+ pairs of re-sampled Landsat TM/ETM scenes in 500m resolution, which were provided by the Landsat Ecosystem Disturbance Adaptive Processing System project. The detected disturbances were then separated into two five-year age groups, facilitated by Forest Inventory and Analysis (FIA) data, which was used to calculate the area of forest regeneration for each county in the USA.     

The relation between rigorous and Helmert’s definitions of orthometric heights

Following our earlier definition of the rigorous orthometric height [J Geod 79(1-3):82–92 (2005)] we present the derivation and calculation of the differences between this and the Helmert orthometric height, which is embedded in the vertical datums used in numerous countries. By way of comparison, we also consider Mader and Niethammer’s refinements to the Helmert orthometric height. For a profile across the Canadian Rocky Mountains (maximum height of ~2,800 m), the rigorous correction to Helmert’s height reaches ~13 cm, whereas the Mader and Niethammer corrections only reach ~3 cm. The discrepancy is due mostly to the rigorous correction’s consideration of the geoid-generated gravity disturbance. We also point out that several of the terms derived here are the same as those used in regional gravimetric geoid models, thus simplifying their implementation. This will enable those who currently use Helmert orthometric heights to upgrade them to a more rigorous height system based on the Earth’s gravity field and one that is more compatible with a regional geoid model.