简缩极化特征值分析的溢油检测

为有效利用简缩极化SAR进行海洋溢油检测,本文基于简缩极化特征值分析,提出了3个用于简缩极化溢油检测的参数,引入了基于简缩极化特征值分解的简缩极化熵Hc(Compact Polarization Entropy)、简缩极化比参数PFc(Compact Polarization Fraction)、简缩极化基准高度PHc(Compact Polarization Pedestal Height)特征进行海洋溢油检测。海表的散射类型主要为低熵散射(小粗糙面发生的Bragg散射),为弱去极化、弱散射过程随机性状态,由于溢油会阻尼海水的Bragg散射,使其熵值变高、呈去极化、强散射过程随机性状态,故简缩极化熵、简缩极化比参数和简缩极化基准高度可以用来检测海洋溢油。本文采用C波段的Radarsat-2、SIR-C/X-SAR数据进行了实验,结果表明:简缩极化熵、简缩极化比参数和简缩极化基准高度能够有效抑制疑似溢油,使海水与疑似溢油差异变小;突出溢油区域,使海水与溢油的可区分性变大。     

Modification of fractal algorithm for oil spill detection from RADARSAT-1 SAR data

This paper introduces a modified formula for the fractal box counting dimension. The method is based on utilization of the probability distribution formula in the fractal box count. The purpose of this method is to use it for the discrimination of oil spill areas from the surrounding features, e.g., sea surface and look-alikes in RADARSAT-1 SAR Wide beam mode (W1) and Standard beam mode (S2) data have been collected under different wind speeds. The results show that the new formula of the fractal box counting dimension is able to discriminate between oil spills, look-alike areas and pixels of the size of a single ship. The W1 mode data illustrate an error standard deviation of 0.05, thus performing a better discrimination of oil spills as compared to S2 mode data. We conclude that automatic detection and discrimination of oil spill and other sea surface features can be opertionalized by using the new formula for fractal box counting.     

A note on the SG(<Emphasis Type="Italic">m</Emphasis>) test

López et al. (Reg Sci Urban Econ 40(2–3):106–115, 2010) introduce a nonparametric test of spatial dependence, called SG(m). The test is claimed to be consistent and asymptotically Chi-square distributed. Elsinger (Reg Sci Urban Econ 43(5):838–840, 2013) raises doubts about the two properties. Using a particular counterexample, he shows that the asymptotic distribution of the SG(m) test may be far from the Chi-square family; the property of consistency is also questioned. In this note, the authors want to clarify the properties of the SG(m) test. We argue that the cause of the conflict is in the specification of the symbolization map. The discrepancies can be solved by adjusting some of the definitions made in the original paper. Moreover, we introduce a permutational bootstrapped version of the SG(m) test, which is powerful and robust to the underlying statistical assumptions. This bootstrapped version may be very useful in an applied context.     

Determination of the optimized single-layer ionospheric height for electron content measurements over China

The ionosphere effective height (IEH) is a very important parameter in total electron content (TEC) measurements under the widely used single-layer model assumption. To overcome the requirement of a large amount of simultaneous vertical and slant ionospheric observations or dense “coinciding” pierce points data, a new approach comparing the converted vertical TEC (VTEC) value using mapping function based on a given IEH with the “ground truth” VTEC value provided by the combined International GNSS Service Global Ionospheric Maps is proposed for the determination of the optimal IEH. The optimal IEH in the Chinese region is determined using three different methods based on GNSS data. Based on the ionosonde data from three different locations in China, the altitude variation of the peak electron density (hmF2) is found to have clear diurnal, seasonal and latitudinal dependences, and the diurnal variation of hmF2 varies from approximately 210 to 520 km in Hainan. The determination of the optimal IEH employing the inverse method suggested by Birch et al. (Radio Sci 37, 2002. doi: 10.1029/2000rs002601) did not yield a consistent altitude in the Chinese region. Tests of the method minimizing the mapping function errors suggested by Nava et al. (Adv Space Res 39:1292–1297, 2007) indicate that the optimal IEH ranges from 400 to 600 km, and the height of 450 km is the most frequent IEH at both high and low solar activities. It is also confirmed that the IEH of 450–550 km is preferred for the Chinese region instead of the commonly adopted 350–450 km using the determination method of the optimal IEH proposed in this paper.     

Calibration for the shear strain of 3-component borehole strainmeters in eastern Taiwan through Earth and ocean tidal waveform modeling

We propose an approach for calibrating the horizontal tidal shear components [(differential extension (\(\gamma _1\)) and engineering shear (\(\gamma _2\))] of two Sacks–Evertson (in Pap Meteorol Geophys 22:195–208, 1971) SES-3 borehole strainmeters installed in the Longitudinal Valley in eastern Taiwan. The method is based on the waveform reconstruction of the Earth and ocean tidal shear signals through linear regressions on strain gauge signals, with variable sensor azimuth. This method allows us to derive the orientation of the sensor without any initial constraints and to calibrate the shear strain components \(\gamma _1\) and \(\gamma _2\) against \(M_2\) tidal constituent. The results illustrate the potential of tensor strainmeters for recording horizontal tidal shear strain.     

Automatic Building Extraction from Image and LiDAR Data with Active Contour Segmentation

Automatic building extraction is an important topic for many applications such as urban planning, disaster management, 3D building modeling and updating GIS databases. Its approaches mainly depend on two data sources: light detection and ranging (LiDAR) point cloud and aerial imagery both of which have advantages and disadvantages of their own. In this study, in order to benefit from the advantages of each data sources, LiDAR and image data combined together. And then, the building boundaries were extracted with the automated active contour algorithm implemented in MATLAB. Active contour algorithm uses initial contour positions to segment an object in the image. Initial contour positions were detected without user interaction by a series of image enhancements, band ratio and morphological operations. Four test areas with varying building and background levels of detail were selected from ISPRS’s benchmark Vaihingen and Istanbul datasets. Vegetation and shadows were removed from all the datasets by band ratio to improve segmentation quality. Subsequently, LiDAR point cloud data was converted to raster format and added to the aerial imagery as an extra band. Resulting merged image and initial contour positions were given to the active contour algorithm to extract building boundaries. In order to compare the contribution of LiDAR to the proposed method, the boundaries of the buildings were extracted from the input image before and after adding LiDAR data to the image as a layer. Finally extracted building boundaries were smoothed by the Awrangjeb (Int J Remote Sen 37(3): 551–579.  https://doi.org/10.1080/01431161.2015.1131868, 2016) boundary regularization algorithm. Correctness (Corr), completeness (Comp) and accuracy (Q) metrics were used to assess accuracy of segmented building boundaries by comparing extracted building boundaries with manually digitized building boundaries. Proposed approach shows the promising results with over 93% correctness, 92% completeness and 89% quality.     

Geology of the area around Katta,sindhudurg district,Maharashtra. Based on aerospace data

Geological studies of the area around Katta, in the southern part of the Ratnagiri District of Maharashtra, were carried out with the help of visual remote sensing techniques using LANDSAT imageries on 1:250,000 scale and aerial photographs on 1:60,000 scale. The major stratigraphic units represented in the area under study are the Archean Complex, Kaladgi Supergroup, Deccan Trap, Laterite and Alluvium. The Kaladgis unconformably overlie the Archean metasediments and also at places exhibit faulted contacts with the latter. The major part of the area is covered by a thick evergreen vegetation. The interpretation followed by field work and laboratory work revealed the following:

1. The different lithologic units could be delineated on the aerial photographs.
2. Different lineaments marked on the imagery were found to be due either to faults or fracture zones. Some of the older faults appear to have been rejuvenated after the formation of the laterites.
3. Some of the lithologic horizons can be identified on the Landsat imagery by virtue of their spatial signatures.

These studies indicate that even in the area covered with thick vegetation, aerospace imagery in appropriate band and data scale can provide significant geological information.     

Simple Approaches to Oil Spill Detection Using Sentinel Application Platform (SNAP)-Ocean Application Tools and Texture Analysis: A Comparative Study

Effective and efficient monitoring of oil spills that originate from ships, offshore platforms and any accidents are of immense importance from the viewpoint of public safety and environmental protection. Detection of spilled oil is also essential to estimate the potential spread and drift from the source to the nearby coastal areas. In this regard, utilization of SAR data for the detection and monitoring of oil spills has received considerable attention in recent times, due to their wide area coverage, day-night and all-weather capabilities. In this paper, two oil spills incidents along the coast of Mumbai, India are investigated; (1) The 2010 oil spill that occurred after the MV MSC Chitra and MV Khalijia-3 collided and (2) the oil spill caused due to sinking of MV RAK carrier in 2011. Two simple and relatively quick approaches for oil spill detection have been applied to VV polarized Radarsat-2 imagery of the incidents and a comparison is made of the results obtained. The first approach utilizes the oil spill detection tool of Sentinel Application Platform (SNAP) and the second explores texture analysis using Grey Level co-occurrence matrix (GLCM). The results of the study show that texture analysis proves to be an efficient method for oil spill detection as compared to the SNAP oil spill detection tool. Nevertheless, both the proposed methodologies are useful for detection of oil spills and for subsequent utilization of the results, timely and cost effectively, for the calibration and validation of numerical models that predict oil spill dispersion trajectories.     

On the equivalence of spherical splines with least-squares collocation and Stokes’s formula for regional geoid computation

This work is an investigation of three methods for regional geoid computation: Stokes’s formula, least-squares collocation (LSC), and spherical radial base functions (RBFs) using the spline kernel (SK). It is a first attempt to compare the three methods theoretically and numerically in a unified framework. While Stokes integration and LSC may be regarded as classic methods for regional geoid computation, RBFs may still be regarded as a modern approach. All methods are theoretically equal when applied globally, and we therefore expect them to give comparable results in regional applications. However, it has been shown by de Min (Bull Géod 69:223–232, 1995. doi: 10.1007/BF00806734) that the equivalence of Stokes’s formula and LSC does not hold in regional applications without modifying the cross-covariance function. In order to make all methods comparable in regional applications, the corresponding modification has been introduced also in the SK. Ultimately, we present numerical examples comparing Stokes’s formula, LSC, and SKs in a closed-loop environment using synthetic noise-free data, to verify their equivalence. All agree on the millimeter level.     

Implications of allometric model selection for county-level biomass mapping

Background

Carbon accounting in forests remains a large area of uncertainty in the global carbon cycle. Forest aboveground biomass is therefore an attribute of great interest for the forest management community, but the accuracy of aboveground biomass maps depends on the accuracy of the underlying field estimates used to calibrate models. These field estimates depend on the application of allometric models, which often have unknown and unreported uncertainties outside of the size class or environment in which they were developed.

Results

Here, we test three popular allometric approaches to field biomass estimation, and explore the implications of allometric model selection for county-level biomass mapping in Sonoma County, California. We test three allometric models: Jenkins et al. (For Sci 49(1): 12–35, 2003), Chojnacky et al. (Forestry 87(1): 129–151, 2014) and the US Forest Service’s Component Ratio Method (CRM). We found that Jenkins and Chojnacky models perform comparably, but that at both a field plot level and a total county level there was a ~ 20% difference between these estimates and the CRM estimates. Further, we show that discrepancies are greater in high biomass areas with high canopy covers and relatively moderate heights (25–45 m). The CRM models, although on average ~ 20% lower than Jenkins and Chojnacky, produce higher estimates in the tallest forests samples (> 60 m), while Jenkins generally produces higher estimates of biomass in forests < 50 m tall. Discrepancies do not continually increase with increasing forest height, suggesting that inclusion of height in allometric models is not primarily driving discrepancies. Models developed using all three allometric models underestimate high biomass and overestimate low biomass, as expected with random forest biomass modeling. However, these deviations were generally larger using the Jenkins and Chojnacky allometries, suggesting that the CRM approach may be more appropriate for biomass mapping with lidar.

Conclusions

These results confirm that allometric model selection considerably impacts biomass maps and estimates, and that allometric model errors remain poorly understood. Our findings that allometric model discrepancies are not explained by lidar heights suggests that allometric model form does not drive these discrepancies. A better understanding of the sources of allometric model errors, particularly in high biomass systems, is essential for improved forest biomass mapping.

     

Exploring the spatially varying innovation capacity of the US counties in the framework of Griliches’ knowledge production function: a mixed GWR approach

Griliches’ knowledge production function has been increasingly adopted at the regional level where location-specific conditions drive the spatial differences in knowledge creation dynamics. However, the large majority of such studies rely on a traditional regression approach that assumes spatially homogenous marginal effects of knowledge input factors. This paper extends the authors’ previous work (Kang and Dall’erba in Int Reg Sci Rev, 2015. doi: 10.1177/0160017615572888) to investigate the spatial heterogeneity in the marginal effects by using nonparametric local modeling approaches such as geographically weighted regression (GWR) and mixed GWR with two distinct samples of the US Metropolitan Statistical Area (MSA) and non-MSA counties. The results indicate a high degree of spatial heterogeneity in the marginal effects of the knowledge input variables, more specifically for the local and distant spillovers of private knowledge measured across MSA counties. On the other hand, local academic knowledge spillovers are found to display spatially homogenous elasticities in both MSA and non-MSA counties. Our results highlight the strengths and weaknesses of each county’s innovation capacity and suggest policy implications for regional innovation strategies.     

Rectangular rotation of spherical harmonic expansion of arbitrary high degree and order

In order to move the polar singularity of arbitrary spherical harmonic expansion to a point on the equator, we rotate the expansion around the y-axis by \(90^{\circ }\) such that the x-axis becomes a new pole. The expansion coefficients are transformed by multiplying a special value of Wigner D-matrix and a normalization factor. The transformation matrix is unchanged whether the coefficients are \(4 \pi \) fully normalized or Schmidt quasi-normalized. The matrix is recursively computed by the so-called X-number formulation (Fukushima in J Geodesy 86: 271–285, 2012a). As an example, we obtained \(2190\times 2190\) coefficients of the rectangular rotated spherical harmonic expansion of EGM2008. A proper combination of the original and the rotated expansions will be useful in (i) integrating the polar orbits of artificial satellites precisely and (ii) synthesizing/analyzing the gravitational/geomagnetic potentials and their derivatives accurately in the high latitude regions including the arctic and antarctic area.     

On the degree of polarization for SAR sea oil slick observation

A polarimetric model to relate the degree of polarization, DoP, to the sea surface scattering with and without oil slicks, under low-to-moderate wind conditions, is proposed. DoP, measured directly from the Mueller scattering matrix, is shown to be a reliable measure of the departure from Bragg scattering; a phenomenon that, under low-to-moderate wind conditions, occurs when an oil slick is present. Following this theoretical rationale, a simple filter is developed to observe oil slicks in quad-polarimetric full-resolution Synthetic Aperture Radar (SAR) data. Experiments, undertaken on a meaningful set of quad-polarization Single Look Complex (SLC) C-band RADARSAT-2 SAR data, where both well-known oil slicks and a weak-damping look-alike are in place, demonstrate the soundness of the model and its effectiveness from an operational viewpoint.     

PSO-Based Optimal Selection of Zernike Moments for Target Discrimination in High-Resolution SAR Imagery

Target discrimination is the key step of automatic target detection in synthetic aperture radar (SAR) images. In this paper, a new algorithm, effective and robust feature sets for target discrimination in high resolution SAR images has been proposed. Two main steps in target discrimination of SAR images have been developed, the feature extraction based on Zernike moments (ZMs) having linear transformation invariance properties and the PSO based feature selection to select the optimal feature subset of Zernike moments for decreasing computational complexity of feature extraction step. The input regions of interest (ROIs) have been segmented and passed to a number of preprocessing stages such as histogram equalization, position and size normalization. Two groups of Zernike moments (shape and margin (intensity) characteristic) have been extracted from the preprocessed images and they have been applied to the feature selection step. Each group includes 34 moments with different orders and iterations. The selected moments have been applied to a SVM classifier. The proposed scheme has been tested on the MSTAR database. The Receiver Operational Characteristics (ROC) curve and the performance of proposed method using some measured data have been analyzed. Experimental results demonstrate the efficiency of the proposed approach in target discrimination of SAR imagery.     

Tsallis熵和改进CV模型的海面溢油SAR图像分割

为了解决海洋表面溢油监测中合成孔径雷达(SAR)图像分割精度不高的难题,提出一种基于Tsallis熵多阈值分割与改进CV(ChanVese)模型相结合的海面溢油图像分割方法。首先采用基于Tsallis熵的多阈值选取算法对海面溢油图像进行粗分割;然后分别将得到的溢油区域和溢油粗略轮廓作为CV模型的局部区域和初始轮廓,以降低CV模型的场景复杂度及其对初始条件的敏感性。CV模型仅考虑了图像各区域的均值信息而没有考虑图像的局部信息,尽管能够得到渐进型边界图像,但其分割结果存在误差。本文采用了加入移动因子的改进CV模型降低分割误差,提高收敛速度。实验结果表明,提出的海面溢油SAR图像分割方法具有分割边界定位准确、运行高效和无需设置初始条件等优点。     

Application of ray-traced tropospheric slant delays to geodetic VLBI analysis

The correction of tropospheric influences via so-called path delays is critical for the analysis of observations from space geodetic techniques like the very long baseline interferometry (VLBI). In standard VLBI analysis, the a priori slant path delays are determined using the concept of zenith delays, mapping functions and gradients. The a priori use of ray-traced delays, i.e., tropospheric slant path delays determined with the technique of ray-tracing through the meteorological data of numerical weather models (NWM), serves as an alternative way of correcting the influences of the troposphere on the VLBI observations within the analysis. In the presented research, the application of ray-traced delays to the VLBI analysis of sessions in a time span of 16.5 years is investigated. Ray-traced delays have been determined with program RADIATE (see Hofmeister in Ph.D. thesis, Department of Geodesy and Geophysics, Faculty of Mathematics and Geoinformation, Technische Universität Wien. http://resolver.obvsg.at/urn:nbn:at:at-ubtuw:1-3444, 2016) utilizing meteorological data provided by NWM of the European Centre for Medium-Range Weather Forecasts (ECMWF). In comparison with a standard VLBI analysis, which includes the tropospheric gradient estimation, the application of the ray-traced delays to an analysis, which uses the same parameterization except for the a priori slant path delay handling and the used wet mapping factors for the zenith wet delay (ZWD) estimation, improves the baseline length repeatability (BLR) at 55.9% of the baselines at sub-mm level. If no tropospheric gradients are estimated within the compared analyses, 90.6% of all baselines benefit from the application of the ray-traced delays, which leads to an average improvement of the BLR of 1 mm. The effects of the ray-traced delays on the terrestrial reference frame are also investigated. A separate assessment of the RADIATE ray-traced delays is carried out by comparison to the ray-traced delays from the National Aeronautics and Space Administration Goddard Space Flight Center (NASA GSFC) (Eriksson and MacMillan in http://lacerta.gsfc.nasa.gov/tropodelays, 2016) with respect to the analysis performances in terms of BLR results. If tropospheric gradient estimation is included in the analysis, 51.3% of the baselines benefit from the RADIATE ray-traced delays at sub-mm difference level. If no tropospheric gradients are estimated within the analysis, the RADIATE ray-traced delays deliver a better BLR at 63% of the baselines compared to the NASA GSFC ray-traced delays.     

Refined discrete and empirical horizontal gradients in VLBI analysis

Missing or incorrect consideration of azimuthal asymmetry of troposphere delays is a considerable error source in space geodetic techniques such as Global Navigation Satellite Systems (GNSS) or Very Long Baseline Interferometry (VLBI). So-called horizontal troposphere gradients are generally utilized for modeling such azimuthal variations and are particularly required for observations at low elevation angles. Apart from estimating the gradients within the data analysis, which has become common practice in space geodetic techniques, there is also the possibility to determine the gradients beforehand from different data sources than the actual observations. Using ray-tracing through Numerical Weather Models (NWMs), we determined discrete gradient values referred to as GRAD for VLBI observations, based on the standard gradient model by Chen and Herring (J Geophys Res 102(B9):20489–20502, 1997.  https://doi.org/10.1029/97JB01739) and also for new, higher-order gradient models. These gradients are produced on the same data basis as the Vienna Mapping Functions 3 (VMF3) (Landskron and Böhm in J Geod, 2017.  https://doi.org/10.1007/s00190-017-1066-2), so they can also be regarded as the VMF3 gradients as they are fully consistent with each other. From VLBI analyses of the Vienna VLBI and Satellite Software (VieVS), it becomes evident that baseline length repeatabilities (BLRs) are improved on average by 5% when using a priori gradients GRAD instead of estimating the gradients. The reason for this improvement is that the gradient estimation yields poor results for VLBI sessions with a small number of observations, while the GRAD a priori gradients are unaffected from this. We also developed a new empirical gradient model applicable for any time and location on Earth, which is included in the Global Pressure and Temperature 3 (GPT3) model. Although being able to describe only the systematic component of azimuthal asymmetry and no short-term variations at all, even these empirical a priori gradients slightly reduce (improve) the BLRs with respect to the estimation of gradients. In general, this paper addresses that a priori horizontal gradients are actually more important for VLBI analysis than previously assumed, as particularly the discrete model GRAD as well as the empirical model GPT3 are indeed able to refine and improve the results.     

Entropy Econometrics for combining regional economic forecasts: A Data-Weighted Prior Estimator

Forecast combination has been studied in econometrics for a long time, and the literature has shown the superior performance of forecast combination over individual predictions. However, there is still controversy on which is the best procedure to specify the forecast weights. This paper explores the possibility of using a procedure based on Entropy Econometrics, which allows setting the weights for the individual forecasts as a mixture of different alternatives. In particular, we examine the ability of the Data-Weighted Prior Estimator proposed by Golan (J Econom 101(1):165–193, 2001) to combine forecasting models in a context of small sample sizes, a relative common scenario when dealing with time series for regional economies. We test the validity of the proposed approach using a simulation exercise and a real-world example that aims at predicting gross regional product growth rates for a regional economy. The forecasting performance of the Data-Weighted Prior Estimator proposed is compared with other combining methods. The simulation results indicate that in scenarios of heavily ill-conditioned datasets the approach suggested dominates other forecast combination strategies. The empirical results are consistent with the conclusions found in the numerical experiment.     

Seasonal low-degree changes in terrestrial water mass load from global GNSS measurements

Large-scale mass redistribution in the terrestrial water storage (TWS) leads to changes in the low-degree spherical harmonic coefficients of the Earth’s surface mass density field. Studying these low-degree fluctuations is an important task that contributes to our understanding of continental hydrology. In this study, we use global GNSS measurements of vertical and horizontal crustal displacements that we correct for atmospheric and oceanic effects, and use a set of modified basis functions similar to Clarke et al. (Geophys J Int 171:1–10, 2007) to perform an inversion of the corrected measurements in order to recover changes in the coefficients of degree-0 (hydrological mass change), degree-1 (centre of mass shift) and degree-2 (flattening of the Earth) caused by variations in the TWS over the period January 2003–January 2015. We infer from the GNSS-derived degree-0 estimate an annual variation in total continental water mass with an amplitude of \((3.49 \pm 0.19) \times 10^{3}\) Gt and a phase of \(70^{\circ } \pm 3^{\circ }\) (implying a peak in early March), in excellent agreement with corresponding values derived from the Global Land Data Assimilation System (GLDAS) water storage model that amount to \((3.39 \pm 0.10) \times 10^{3}\) Gt and \(71^{\circ } \pm 2^{\circ }\), respectively. The degree-1 coefficients we recover from GNSS predict annual geocentre motion (i.e. the offset change between the centre of common mass and the centre of figure) caused by changes in TWS with amplitudes of \(0.69 \pm 0.07\) mm for GX, \(1.31 \pm 0.08\) mm for GY and \(2.60 \pm 0.13\) mm for GZ. These values agree with GLDAS and estimates obtained from the combination of GRACE and the output of an ocean model using the approach of Swenson et al. (J Geophys Res 113(B8), 2008) at the level of about 0.5, 0.3 and 0.9 mm for GX, GY and GZ, respectively. Corresponding degree-1 coefficients from SLR, however, generally show higher variability and predict larger amplitudes for GX and GZ. The results we obtain for the degree-2 coefficients from GNSS are slightly mixed, and the level of agreement with the other sources heavily depends on the individual coefficient being investigated. The best agreement is observed for \(T_{20}^C\) and \(T_{22}^S\), which contain the most prominent annual signals among the degree-2 coefficients, with amplitudes amounting to \((5.47 \pm 0.44) \times 10^{-3}\) and \((4.52 \pm 0.31) \times 10^{-3}\) m of equivalent water height (EWH), respectively, as inferred from GNSS. Corresponding agreement with values from SLR and GRACE is at the level of or better than \(0.4 \times 10^{-3}\) and \(0.9 \times 10^{-3}\) m of EWH for \(T_{20}^C\) and \(T_{22}^S\), respectively, while for both coefficients, GLDAS predicts smaller amplitudes. Somewhat lower agreement is obtained for the order-1 coefficients, \(T_{21}^C\) and \(T_{21}^S\), while our GNSS inversion seems unable to reliably recover \(T_{22}^C\). For all the coefficients we consider, the GNSS-derived estimates from the modified inversion approach are more consistent with the solutions from the other sources than corresponding estimates obtained from an unconstrained standard inversion.     

Retrograde diurnal motion of the instantaneous rotation axis observed by a large ring laser gyroscope

Ring laser gyroscope technique directly senses the Earth’s instantaneous rotation pole (IRP), whose polar motion contains strong retrograde diurnal components induced by external torques due to the gravitational attraction of the Moon and Sun. The first direct measurement of this retrograde diurnal motion with three large ring lasers was reported by Schreiber et al. (J Geophys Res 109(B18):B06405, 2004). Since then many technical improvements led to a significant increase in precision and stability of ring laser gyroscopes; however, precise determination of amplitude and phase at main partial waves has not been given in the literature. In this paper, I will report on determination of the retrograde diurnal motion of the IRP at main partial waves (\(Oo_1, J_1, K_1, M_1, O_1, Q_1\)) by the ring laser “G”, located in Wettzell, Germany, which is the most stable one amongst the currently running large ring laser gyroscopes.