Cycle slip detection and repair for undifferenced GPS observations under high ionospheric activity

We develop a new approach for cycle slip detection and repair under high ionospheric activity using undifferenced dual-frequency GPS carrier phase observations. A forward and backward moving window averaging (FBMWA) algorithm and a second-order, time-difference phase ionospheric residual (STPIR) algorithm are integrated to jointly detect and repair cycle slips. The FBMWA algorithm is proposed to detect cycle slips from the widelane ambiguity of Melbourne–Wübbena linear combination observable. The FBMWA algorithm has the advantage of reducing the noise level of widelane ambiguities, even if the GPS data are observed under rapid ionospheric variations. Thus, the detection of slips of one cycle becomes possible. The STPIR algorithm can better remove the trend component of ionospheric variations compared to the normally used first-order, time-difference phase ionospheric residual method. The combination of STPIR and FBMWA algorithms can uniquely determine the cycle slips at both GPS L ₁ and L ₂ frequencies. The proposed approach has been tested using data collected under different levels of ionospheric activities with simulated cycle slips. The results indicate that this approach is effective even under active ionospheric conditions.     

A Directed-Line-Segment-Based Photogrammetry Method to Survey the Tunneling Working Surface of Mine Roadway

Absolute orientation is a basic technical work in digital image geologic logging of underground coal mine. Traditional control-point-based absolute orientation method requires setting object space control points of the known three-dimensional coordinates, which may lead to low efficiency. Therefore, this paper proposed a point-free close-range photogrammetry absolute orientation algorithm, which utilized direction line segments including plumb line segments and line segments with known directions and lengths to identify the dimensional orientation of a stereoscopic model. Experiment results show that the precision of the orientation results is favorable. σ _X and σ _Y are as high as 0.5 mm, and σ _Z is 0.3 mm. Finally, this paper introduced the application of the proposed algorithm in rapid geological logging of coal mine roadway, which was fast and reliable, convenient and feasible.     

Improved amplitude- and phase-scintillation indices derived from wavelet detrended high-latitude GPS data

Accuracy and validity of scintillation indices estimated using the power and phase of the GPS signal depend heavily on the detrending method used and the selection of the cutoff frequency of the associated filter. A Butterworth filter with a constant cutoff frequency of 0.1?Hz is commonly used in detrending GPS data. In this study, the performance of this commonly used filter is evaluated and compared with a new wavelet-based detrending method using GPS data from high latitudes. It was observed that in detrending high-latitude GPS data, a wavelet filter performed better than Butterworth filters as the correlation between amplitude- and phase-scintillation indices in S ₄ and ?? _? improved significantly from 0.53, when using a Butterworth filter, to 0.79, when using the wavelet filtering method. We also introduced an improved phase-scintillation index, ?? _CHAIN, which we think is comparatively a better parameter to represent phase scintillations at high latitudes as the correlation between S ₄ and ?? _CHAIN was as high as 0.90. During the analysis, we also noted that the occurrence of the ??phase scintillation without amplitude scintillation?? phenomenon was significantly reduced when scintillation indices were derived using the wavelet-based detrending method. These results seem to indicate that wavelet-based detrending is better suited for GPS scintillation signals and also that ?? _CHAIN is a better parameter for representing GPS phase scintillations at high latitudes.     

GOCE gravitational gradiometry

GOCE is the first gravitational gradiometry satellite mission. Gravitational gradiometry is the measurement of the second derivatives of the gravitational potential. The nine derivatives form a 3 × 3 matrix, which in geodesy is referred to as Marussi tensor. From the basic properties of the gravitational field, it follows that the matrix is symmetric and trace free. The latter property corresponds to Laplace equation, which gives the theoretical foundation of its representation in terms of spherical harmonic or Fourier series. At the same time, it provides the most powerful quality check of the actual measured gradients. GOCE gradiometry is based on the principle of differential accelerometry. As the satellite carries out a rotational motion in space, the accelerometer differences contain angular effects that must be removed. The GOCE gradiometer provides the components V _xx , V _yy , V _zz and V _xz with high precision, while the components V _xy and V _yz are of low precision, all expressed in the gradiometer reference frame. The best performance is achieved inside the measurement band from 5 × 10^–3 to 0.1 Hz. At lower frequencies, the noise increases with 1/f and is superimposed by cyclic distortions, which are modulated from the orbit and attitude motion into the gradient measurements. Global maps with the individual components show typical patterns related to topographic and tectonic features. The maps are separated into those for ascending and those for descending tracks as the components are expressed in the instrument frame. All results are derived from the measurements of the period from November to December 2009. While the components V _xx and V _yy reach a noise level of about \({10\;\rm{\frac{mE}{\sqrt{Hz}}}}\), that of V _zz and V _xz is about \({20\; \rm{\frac{mE}{\sqrt{Hz}}}}\). The cause of the latter’s higher noise is not yet understood. This is also the reason why the deviation from the Laplace condition is at the \({20 \;\rm{\frac{mE}{\sqrt{Hz}}}}\) level instead of the originally planned \({11\;\rm{\frac{mE}{\sqrt{Hz}}}}\). Each additional measurement cycle will improve the accuracy and to a smaller extent also the resolution of the spherical harmonic coefficients derived from the measured gradients.     

<Emphasis Type="Italic">C</Emphasis>/<Emphasis Type="Italic">N</Emphasis><Subscript>0</Subscript> estimators for high-sensitivity snapshot GNSS receivers

We address the problem of estimating the carrier-to-noise ratio (C/N₀) in weak signal conditions. There are several environments, such as forested areas, indoor buildings and urban canyons, where high-sensitivity global navigation satellite system (HS-GNSS) receivers are expected to work under these reception conditions. The acquisition of weak signals from the satellites requires the use of post-detection integration (PDI) techniques to accumulate enough energy to detect them. However, due to the attenuation suffered by these signals, estimating their C/N₀ becomes a challenge. Measurements of C/N₀ are important in many applications of HS-GNSS receivers such as the determination of a detection threshold or the mitigation of near-far problems. For this reason, different techniques have been proposed in the literature to estimate the C/N₀, but they only work properly in the high C/N₀ region where the coherent integration is enough to acquire the satellites. We derive four C/N₀ estimators that are specially designed for HS-GNSS snapshot receivers and only use the output of a PDI technique to perform the estimation. We consider four PDI techniques, namely non-coherent PDI, non-quadratic non-coherent PDI, differential PDI and truncated generalized PDI and we obtain the corresponding C/N₀ estimator for each of them. Our performance analysis shows a significant advantage of the proposed estimators with respect to other C/N₀ estimators available in the literature in terms of estimation accuracy and computational resources.     

Improved method for estimating the inter-frequency satellite clock bias of triple-frequency GPS

Considering the contribution of the hardware biases to the estimated clock errors, an improved method for estimating the satellite inter-frequency clock bias (IFCB) is presented, i.e., the difference in the satellite clock error as computed from ionospheric-free pseudorange and carrier phase observations using L1/L2 and P1/P2 versus L1/L5 and P1/P5. The IFCB is composed of a constant and a variable part. The constant part is the inter-frequency hardware bias (IFHB). It contains the satellite and receiver hardware delays and can be expressed as a function of the DCBs [DCB (P1 ? P2) and DCB (P1 ? P5)]. When a reference satellite is selected, the satellite IFHB can be computed but is biased by a reference satellite IFHB. This bias will not affect the utilization of IFCB in positioning since it can be absorbed by the receiver clock error. Triple-frequency observations of 30 IGS stations between June 1, 2013, and May 31, 2014, were processed to show the variations of the IFHB. The IFHB values show a long-term variation with time. When a linear and a fourth-order harmonic function are used to model the estimated IFCB, which contains contributions of the hardware delays and clock errors, the results show that 89 % of the IFCB can be corrected given the current five triple-frequency GPS satellites with the averaged fitting RMS of 1.35 cm. Five days of data are processed to test the estimated satellite clock errors using the strategy presented. The residuals of P1/P5 and L1/L5 have a STD of <0.27 m and 0.97 cm, respectively. In addition, most predicted satellite IFCBs reach an accuracy of centimeter level and its mean accuracy of 5 days is better than 7 cm.     

Proximal Remote Sensing of Herbicide and Drought Stress in Field Grown Colocasia and Sweet Potato Plants by Sunlight-Induced Chlorophyll Fluorescence Imaging

Chlorophyll fluorescence is an indicator of plant photosynthetic activity and has been used to monitor the health status of vegetation. Several studies have exploited the application of red/far-red chlorophyll fluorescence ratio in detecting the impact of various types of stresses in plants. Recently, sunlight-induced chlorophyll fluorescence imaging has been used to detect and discriminate different stages of mosaic virus infection in potted cassava plants with a multi-spectral imaging system (MSIS). In this study, the MSIS is used to investigate the impact of drought and herbicide stress in field grown crop plants. Towards this control and treatment groups of colocasia and sweet potato plants were grown in laterite soil beds and the reflectance images of these crop plants were recorded up to 14-days of treatment at the Fraunhofer lines of O₂ B at 687 nm and O₂ A at 759.5 nm and the off-lines at 684 and 757.5 nm. The recorded images were analyzed using the Fraunhofer Line Discrimination technique to extract the sunlight-induced chlorophyll fluorescence component from the reflectance images of the plant leaves. As compared to the control group, the chlorophyll fluorescence image ratio (F ₆₈₇/F ₇₆₀) in the treatment groups of both the plant varieties shows an increasing trend with increase in the extent of stress. Further, the F ₆₈₇/F ₇₆₀ ratio was found to correlate with the net photosynthetic rate (Pn) and stomatal conductance (g_s) of leaves. The correlation coefficient (R ²) for the relationship of F ₆₈₇/F ₇₆₀ ratio with Pn were found to be 0.78, 0.79 and 0.78, respectively for the control, herbicide treated and drought treated colocasia plants, while these were 0.77, 0.86 and 0.88, respectively for sweet potato plants. The results presented show the potential of proximal remote sensing and the application F ₆₈₇/F ₇₆₀ fluorescence image ratio for effective monitoring of stress-induced changes in field grown plants.     

Monitoring of <Emphasis Type="Italic">Aphis gossypii</Emphasis> Using Greenseeker and SPAD Meter

Cotton aphid (Aphis gossypii) is considered as one of the most important agriculture pest for the cotton production. However, it is generally labor-intensive and time-consuming to obtain some information of Cotton aphid with conventional methods through direct measurement by sampling in the field. This study explores the potential of using a new method to obtain information of the Cotton aphid rapidly. In our study, the cotton canopy spectral indices (NDVI, VI_2, REDrefc, NIRrefc) and chlorophyll concentration, obtained from hand-held high spectrometer GreenSeeker and chlorophyll meter SPAD-502 and Cotton aphid amount derived from the artificial field-based survey were used to uncover the relationship between Cotton aphid amount and canopy spectral index and SPAD value of the cotton in city of Shihezi, China. The results showed that NDVI and NIRrefc were negatively related to Cotton aphid amount. VI_2 content had a significant and positive relationship with its amount. The non-linear three cubic models with alate Aphid amount as independent variables have been established between VI_2 value and alatae Aphid amount, which could explain 92.37 % of VI_2 value variance. SPAD values were also significantly and negatively correlated to the Aphid amount. The non-linear logarithm model with wingless Aphid amount as independent variables was the best for uncovering the relationship between SPAD value and wingless Aphid amount, which could explain 85.48 % of SPAD value variance. The results demonstrate the establishment of the function model provides a theoretical basis and techniques for indirect and rapid monitoring and management of Cotton aphid.     

Global morphology of ionospheric sporadic E layer from the FormoSat-3/COSMIC GPS radio occultation experiment

Ionospheric sporadic-E (Es) activity and global morphology were studied using the 50 Hz signal-to-noise ratio amplitude and excess phase measurements from the FormoSat-3/Constellation Observing System for Meteorology, Ionosphere and Climate (FS3/COSMIC) GPS radio occultation (RO) observations. The results are presented for data collected during the last sunspot cycle from mid-2006 to the end of 2017. The FS3/COSMIC generally performed more than 1000 complete E-region GPS RO observations per day, which were used to retrieve normalized L1-band amplitude standard deviation (SDL1) and relative electron density (N_e) profiles successfully. More or less 31% of those observations were identified as Es events based on SDL1 and peak SDL1 altitude criteria. We found that the peak Es-event i values are approximately proportional to the logarithms of the corresponding peak N_e differences. Five major geographical zones were identified, in which the seasonal and diurnal Es occurrence patterns are markedly different. These five zones include the geomagnetic equatorial zone (??5°?<?magnetic latitude (ML)?<?5°), two extended geomagnetic mid-latitude zones (15°?<?ML?<?55°, and ??55°?<?ML < ??15°), and two auroral zones (70°?<?ML, and ML < ??70°). The Es climatology, namely its variations with each identified zone, altitude, season, and local time has been documented.     

Application of Remotely-Sensed Data to Estimate a Water Budget for Data-Scarce Endorheic Basins: A Case Study of Lake Urmia basin,Iran

Estimating the water budgets of large basins is a challenge because of the lack of data and information. It becomes more complicated in endorheic basins that consist of separate land and water phases. The application of remotely-sensed data is one solution in this regard. The present study addresses this issue and develops a modeling framework to evaluate a water budget based on remotely-sensed data for endorheic basins. To explore the methodology, Lake Urmia basin was selected as a case study. The lake water level has declined steeply since 1995 and stakeholders have agreed to allocate 3100 MCM of water per year to the lake. This makes it necessary to monitor river inflow into the lake to fulfill the agreement. Gauging stations have been employed around the lake, but they could not account for shortages such as water uptake below the stations. To do this, separate water budgets for the water body and the land were required. More specifically, it was necessary to estimate actual evapotranspiration (ET _a ) from freshwater (E _f ) and saltwater (E _s ) estimated using the SEBAL model. Different methods were applied to estimate soil moisture, groundwater exploitation, and surface-groundwater inflow into the lake. A comparison of the observed and estimated amounts showed good agreement. For instance, the coefficient of determination for the observed/reported and estimated ET _a and E _f were 0.83 and 0.84, respectively. The average annual inflow was estimated to be 2.2 BCM/year for 2002–2008 using the RS model, which is about 84 % of the total inflow from the last recording stations before the lake and shows influence of water exploitation after these stations. Future study should focus on increasing temporal and spatial resolution of the method     

A Terrestrial Reference Frame realised on the observation level using a GPS-LEO satellite constellation

Applying a one-step integrated process, i.e. by simultaneously processing all data and determining all satellite orbits involved, a Terrestrial Reference Frame (TRF) consisting of a geometric as well as a dynamic part has been determined at the observation level using the EPOS-OC software of Deutsches GeoForschungsZentrum. The satellite systems involved comprise the Global Positioning System (GPS) as well as the twin GRACE spacecrafts. Applying a novel approach, the inherent datum defect has been overcome empirically. In order not to rely on theoretical assumptions this is done by carrying out the TRF estimation based on simulated observations and using the associated satellite orbits as background truth. The datum defect is identified here as the total of all three translations as well as the rotation about the z-axis of the ground station network leading to a rank-deficient estimation problem. To rectify this singularity, datum constraints comprising no-net translation (NNT) conditions in x, y, and z as well as a no-net rotation (NNR) condition about the z-axis are imposed. Thus minimally constrained, the TRF solution covers a time span of roughly a year with daily resolution. For the geometric part the focus is put on Helmert transformations between the a priori and the estimated sets of ground station positions, and the dynamic part is represented by gravity field coefficients of degree one and two. The results of a reference solution reveal the TRF parameters to be estimated reliably with high precision. Moreover, carrying out a comparable two-step approach using the same data and models leads to parameters and observational residuals of worse quality. A validation w.r.t. external sources shows the dynamic origin to coincide at a level of 5 mm or better in x and y, and mostly better than 15 mm in z. Comparing the derived GPS orbits to IGS final orbits as well as analysing the SLR residuals for the GRACE satellites reveals an orbit quality on the few cm level. Additional TRF test solutions demonstrate that K-Band Range-Rate observations between both GRACE spacecrafts are crucial for accurately estimating the dynamic frame’s orientation, and reveal the importance of the NNT- and NNR-conditions imposed for estimating the components of the dynamic geocenter.     

Multi-Index Soil Moisture Estimation from Satellite Earth Observations: Comparative Evaluation of the Topographic Wetness Index (TWI), the Temperature Vegetation Dryness Index (TVDI) and the Improved TVDI (iTVDI)

Soil moisture estimation from satellite earth observation has emerged effectively advantageous due to the high temporal resolution, spatial resolution, coverage, and processing convenience it affords. In this paper, we present a study carried out to estimate soil moisture level at every location within Enugu State Nigeria from satellite earth observation. Comparative analysis of multiple indices for soil moisture estimation was carried out with a view to evaluating the robustness, correlation, appropriateness and accuracy of the indices in estimating the spatial distribution of soil moisture level in Enugu State. Results were correlated and validated with In-Situ soil moisture observations from multi-sample points. To achieve this, the Topographic Wetness Index (TWI), based on digital elevation data, the Temperature Vegetation Dryness Index (TVDI) and an improved TVDI (iTVDI) incorporating air temperature and a Digital Elevation Model (DEM) were calculated from ASTER global DEM and Landsat images. Possible dependencies of the indices on land cover type, topography, and precipitation were explored. In-Situ soil moisture data were used to validate the derived indices. The results showed that there was a positive significant relationship between iTVDI versus TVDI (R = 0.53, P value < 0.05), while in iTVDI versus TWI (R = 0.00, P value > 0.05) and TVDI versus TWI (R = ?0.01, P value > 0.05) no significant relationship existed. There was a strong relationship between iTVDI and topography, land cover type, and precipitation than other indices (TVDI, TWI). In situ measured soil moisture values showed negative significant relationship with TVDI (R = ?0.52, P value < 0.05) and iTVDI (R = ?0.63, P value < 0.05) but not with TWI (R = ?0.10, P value > 0.05). The iTVDI outperformed the other two index; having a stronger relationship with topography, precipitation, land cover classes and soil moisture. It concludes that although iTVDI outperformed other indices (TVDI, TWI) in soil moisture estimation, the decision of which index to apply is dependent on available data, the intent of usage and spatial scale.     

A low-complexity algorithm for fast acquisition of weak DSSS signal in high dynamic environment

The initial acquisition of direct-sequence spread-spectrum (DSSS) signal transmitted in bursts by ground terminals at satellite-borne receiver poses an engineering challenge. We propose a low-complexity acquisition algorithm that is capable of capturing extremely weak DSSS signal in the presence of large Doppler dynamics. The algorithm uses fast Fourier transform (FFT)-based frequency-domain techniques to implement circular correlations between the received signal and the local pseudo-random noise (PRN) code, and it coherently accumulates the correlation results across multiple PRN code periods, to achieve a sufficient signal–noise ratio for reliable acquisition. We invoke another FFT procedure to perform the coherent accumulation and the fine compensation for the residual Doppler frequency offset. To highlight the advantage of the proposed algorithm, we make a complexity comparison among the proposed algorithm and two other benchmark strategies, namely the modified double block zero padding (MDBZP) and two-dimensional exhaustive search (2D-ES). It is shown that the proposed algorithm has the lowest complexity, which is particularly desirable for satellite-borne receivers where the computational resource is limited. The acquisition performance of the proposed algorithm is verified by theoretical analysis and Monte Carlo simulations and compared with that of MDBZP and 2D-ES. Moreover, we have carried out extensive tests on a hardware verification system, and we show the claimed tradeoff between performance and cost is indeed attainable with the suggested algorithm. Numerically, it is found the proposed algorithm can achieve a detection rate of 0.9 and a false alarm rate of \(10^{ - 5}\) at C/N ₀ = 29.5 dBHz over a Doppler frequency offset range of \(\left[ { - 7.5\,{\text{kHz}},7.5\,{\text{kHz}}} \right]\) in floating-point simulation, which coincides with the analytical results. The same performance is achieved at C/N ₀ = 31 dBHz in fixed-point simulation and at C/N ₀ = 31.5 dBHz on a hardware system.     

Estimation of satellite position,clock and phase bias corrections

Precise point positioning with integer ambiguity resolution requires precise knowledge of satellite position, clock and phase bias corrections. In this paper, a method for the estimation of these parameters with a global network of reference stations is presented. The method processes uncombined and undifferenced measurements of an arbitrary number of frequencies such that the obtained satellite position, clock and bias corrections can be used for any type of differenced and/or combined measurements. We perform a clustering of reference stations. The clustering enables a common satellite visibility within each cluster and an efficient fixing of the double difference ambiguities within each cluster. Additionally, the double difference ambiguities between the reference stations of different clusters are fixed. We use an integer decorrelation for ambiguity fixing in dense global networks. The performance of the proposed method is analysed with both simulated Galileo measurements on E1 and E5a and real GPS measurements of the IGS network. We defined 16 clusters and obtained satellite position, clock and phase bias corrections with a precision of better than 2 cm.     

A new GPS/BDS tropospheric delay resolution approach for monitoring deformation in super high-rise buildings

A new approach for deformation monitoring of super high-rise building using GPS/BDS technology is proposed for the case when prior coordinates are known and the baseline is short but has a large height difference. The approach is based on the ambiguity function method (AFM). Considering that the double-differenced (DD) troposphere delay residual error cannot be ignored, the relative zenith tropospheric delay (RZTD) parameter is introduced into the original AFM equation. Thus, the RZTD and 3D coordinate parameters are together obtained through the modified AFM (MAFM). Due to the low computational efficiency of conventional AFM, an improved particle swarm optimization (IPSO) algorithm is used to search the four optimal parameters X/Y/Z/RZTD and replaces the grid search method. In this study, GPS/BDS deformation monitoring data for buildings with approximately 290 m height difference were used to verify the feasibility of the proposed MAFM. Numerical results show a single-epoch average computation time of approximately 0.3 s, which meets the requirements of near-real-time dynamic monitoring. The average accuracy of the GPS single-epoch RZTD solution is better than 1 cm, the combined GPS/BDS MAFM performance outperforms the GPS-only system, and using multi-epoch observations can further improve the accuracy of the RZTD solution. After RZTD correction, GPS/BDS monitoring precision can be improved, particularly the height dimension, whose precision is improved by approximately 6 cm.     

GPS scintillation over the European Arctic during the November 2004 storms

Small-scale irregularities in the background electron density of the ionosphere can cause rapid fluctuations in the amplitude and phase of radio signals passing through it. These rapid fluctuations are known as scintillation and can cause a Global Positioning System (GPS) receiver to lose lock on a signal. This could compromise the integrity of a safety of life system based on GPS, operating in auroral regions. In this paper, the relationship between the loss of lock on GPS signals and ionospheric scintillation in auroral regions is explored. The period from 8 to 14 November 2004 is selected for this study, as it includes both geomagnetically quiet and disturbed conditions. Phase and amplitude scintillation are measured by GPS receivers located at three sites in Northern Scandinavia, and correlated with losses of signal lock in receivers at varying distances from the scintillation receivers. Local multi-path effects are screened out by rejection of low-elevation data from the analysis. The results indicate that losses of lock are more closely related to rapid fluctuations in the phase rather than the amplitude of the received signal. This supports the idea, suggested by Humphreys et al. (2005) (performance of GPS carrier tracking loops during ionospheric scintillations. Proceedings Internationsl Ionospheric Effects Symposium 3–5 May 2005), that a wide loop bandwidth may be preferred for receivers operating at auroral latitudes. Evidence from the Imaging Riometer for Ionospheric Studies (IRIS) appears to suggest that, for this particular storm, precipitation of particles in the D/E regions may be the mechanism that drives the rapid phase fluctuations in the signal.

Generation of a consistent absolute phase-center correction model for GPS receiver and satellite antennas

The development and numerical values of the new absolute phase-center correction model for GPS receiver and satellite antennas, as adopted by the International GNSS (global navigation satellite systems) Service, are presented. Fixing absolute receiver antenna phase-center corrections to robot-based calibrations, the GeoForschungsZentrum Potsdam (GFZ) and the Technische Universität München reprocessed more than 10 years of GPS data in order to generate a consistent set of nadir-dependent phase-center variations (PCVs) and offsets in the z-direction pointing toward the Earth for all GPS satellites in orbit during that period. The agreement between the two solutions estimated by independent software packages is better than 1 mm for the PCVs and about 4 cm for the z-offsets. In addition, the long time-series facilitates the study of correlations of the satellite antenna corrections with several other parameters such as the global terrestrial scale or the orientation of the orbital planes with respect to the Sun. Finally, completely reprocessed GPS solutions using different phase-center correction models demonstrate the benefits from switching from relative to absolute antenna phase-center corrections. For example, tropospheric zenith delay biases between GPS and very long baseline interferometry (VLBI), as well as the drift of the terrestrial scale, are reduced and the GPS orbit consistency is improved.     

Prediction of UT1–UTC,LOD and AAM χ<Subscript>3</Subscript> by combination of least-squares and multivariate stochastic methods

This article presents the application of a multivariate prediction technique for predicting universal time (UT1–UTC), length of day (LOD) and the axial component of atmospheric angular momentum (AAM χ ₃). The multivariate predictions of LOD and UT1–UTC are generated by means of the combination of (1) least-squares (LS) extrapolation of models for annual, semiannual, 18.6-year, 9.3-year oscillations and for the linear trend, and (2) multivariate autoregressive (MAR) stochastic prediction of LS residuals (LS + MAR). The MAR technique enables the use of the AAM χ ₃ time-series as the explanatory variable for the computation of LOD or UT1–UTC predictions. In order to evaluate the performance of this approach, two other prediction schemes are also applied: (1) LS extrapolation, (2) combination of LS extrapolation and univariate autoregressive (AR) prediction of LS residuals (LS + AR). The multivariate predictions of AAM χ ₃ data, however, are computed as a combination of the extrapolation of the LS model for annual and semiannual oscillations and the LS + MAR. The AAM χ ₃ predictions are also compared with LS extrapolation and LS + AR prediction. It is shown that the predictions of LOD and UT1–UTC based on LS + MAR taking into account the axial component of AAM are more accurate than the predictions of LOD and UT1–UTC based on LS extrapolation or on LS + AR. In particular, the UT1–UTC predictions based on LS + MAR during El Niño/La Niña events exhibit considerably smaller prediction errors than those calculated by means of LS or LS + AR. The AAM χ ₃ time-series is predicted using LS + MAR with higher accuracy than applying LS extrapolation itself in the case of medium-term predictions (up to 100 days in the future). However, the predictions of AAM χ ₃ reveal the best accuracy for LS + AR.     

Enriching the semantics of the directed polyline–polygon topological relationships: the $$\mathcal {}$$-intersection matrix

In this paper, we define an intersection matrix for enriching the semantics of the topological relationships between a directed polyline and a polygon. In particular, we propose the \(\mathcal {DLP}\)-intersection matrix which enables us to model the origin and destination points, as well as the right- and left-hand sides of the directed polyline. This matrix overcomes the limitation of the well-known DE-9IM, because it allows the representation of the different dimensions of the intersection results at the same time. Accordingly, the geo-operators have been revised and extended in order to address the notions of right- and left-hand sides of a directed polyline, as well as additional notions related to the orientation of the polyline. The \(\mathcal {DLP}\)-intersection matrix has been implemented by extending the Java Topology Suite methods in order to address the new geo-operators based on the notion of orientation.     

Estimation of geometric route distance from its topological distance: application to narrow road networks in Tokyo

The structure of road networks has been investigated in accordance with the development of GIScience. By classifying road networks into wide and narrow ones, we can define the route as the path from the route’s origin (also called the root) on a wide road network to a narrow road segment which consists of the sequence of narrow road segments arranged by ascending order of the number of steps of adjacency to its root. The length of the route can be defined with the following geometric and topological terms: the route distance, measuring the length along the route and the depth, counting the number of road segments on the route. The depth plays the important role of being a substitute for the route distance in modelling road networks as a planar graph. Since road networks clearly exhibit irregular patterns and road segment lengths are non-uniform, it is considered appropriate to adopt a stochastic approach rather than a deterministic one to analyse the route distance. However, the relationship between the route distance and its depth has not been sufficiently investigated stochastically. Therefore, the research question is how can we estimate the route distance from its depth? Based on an empirical study in the Tokyo metropolitan region, it was found that (1) the statistical distribution of the route distance can be formulated as an Erlang distribution whose parameters are its depth and the inverse of the mean length of narrow road segments, and (2) this length is constant and close to 40 m. Therefore, we can estimate the route distance from only one parameter, the depth. Also, as a practical application, accessibility to the kth depth link in terms of firefighting was evaluated because the maximum length of the extension of fire hoses is approximately 200 m. It was found that (1) even if k?≤?5, the probability that the route distance to the kth depth link is equal to or longer than 200 m ranges from 0 to 0.45; and (2) if k?≥?8, the probability is approximately 1. These indicate the limitation of the deterministic approach because, on the basis of complete grid patterns (with intervals of 40 m between intersections), k?=?5 corresponds to a distance of 200 m from wide road networks and the route to the 5th depth link can be covered with fire hoses. Moreover, it was found that the connectivity of wide road networks is higher than that of narrow ones in terms of the smaller ratio of cul-de-sacs and the larger ratio of four-way intersections. These answers contribute substantially not only to constructing a science of cities that provides a simple model and specifies the most important parameter, but also to our understanding of the structure of narrow road networks within several hundred metres of wide road networks.