Measuring land-use and land-cover change using the U.S. department of agriculture’s cropland data layer: Cautions and recommendations

Monitoring agricultural land is important for understanding and managing food production, environmental conservation efforts, and climate change. The United States Department of Agriculture's Cropland Data Layer (CDL), an annual satellite imagery-derived land cover map, has been increasingly used for this application since complete coverage of the conterminous United States became available in 2008. However, the CDL is designed and produced with the intent of mapping annual land cover rather than tracking changes over time, and as a result certain precautions are needed in multi-year change analyses to minimize error and misapplication. We highlight scenarios that require special considerations, suggest solutions to key challenges, and propose a set of recommended good practices and general guidelines for CDL-based land change estimation. We also characterize a problematic issue of crop area underestimation bias within the CDL that needs to be accounted for and corrected when calculating changes to crop and cropland areas. When used appropriately and in conjunction with related information, the CDL is a valuable and effective tool for detecting diverse trends in agriculture. By explicitly discussing the methods and techniques for post-classification measurement of land-cover and land-use change using the CDL, we aim to further stimulate the discourse and continued development of suitable methodologies. Recommendations generated here are intended specifically for the CDL but may be broadly applicable to additional remotely-sensed land cover datasets including the National Land Cover Database (NLCD), Moderate Resolution Imaging Spectroradiometer (MODIS)-based land cover products, and other regional, national, and global land cover classification maps.     

CODE’s new ultra-rapid orbit and ERP products for the IGS

The International GNSS Service (IGS) issues four sets of so-called ultra-rapid products per day, which are based on the contributions of the IGS Analysis Centers. The traditional (“old”) ultra-rapid orbit and earth rotation parameters (ERP) solution of the Center for Orbit Determination in Europe (CODE) was based on the output of three consecutive 3-day long-arc rapid solutions. Information from the IERS Bulletin A was required to generate the predicted part of the old CODE ultra-rapid product. The current (“new”) product, activated in November 2013, is based on the output of exactly one multi-day solution. A priori information from the IERS Bulletin A is no longer required for generating and predicting the orbits and ERPs. This article discusses the transition from the old to the new CODE ultra-rapid orbit and ERP products and the associated improvement in reliability and performance. All solutions used in this article were generated with the development version of the Bernese GNSS Software. The package was slightly extended to meet the needs of the new CODE ultra-rapid generation.     

Length-of-day and space-geodetic determination of the Earth’s variable gravity field

The temporal variations of the Earth’s gravity field, nowadays routinely determined from satellite laser ranging (SLR) and GRACE (Gravity Recovery And Climate Experiment), are related to changes in the Earth’s rotation rate through the Earth’s inertia tensor. We study this connection from actual data by comparing the traditional length-of-day (LOD) measurements provided by the International Earth Rotation and Reference Systems Service (IERS) to the variations of the degree-2 and order-0 Stokes coefficient of the gravity field determined from fitting the orbits of the LAGEOS-1 and −2 satellites since 1985. The two series show a good correlation (0.62) and similar annual and semi-annual signals, indicating that the gravity-field-derived LOD is valuable. Our analysis also provides evidence for additional signals common to both series, especially at a period near 120 days, which could be due to hydrological effects.     

Jacques Bertin’s legacy in information visualization and the reorderable matrix

ABSTRACT

Jacques Bertin’s legacy extends beyond the domain of cartography, and in particular to the field of information visualization where he continues to inspire researchers and practitioners. Although in the late twentieth century his books were out of print, their reedition around 2010 has steered a renewed interest and inspired new generations of researchers to reinterpret the principles of Semiology of Graphics and La Graphique in a time of interactive computers. In particular, the work of Jacques Bertin on the reorderable matrix has been very challenging in his time, and the quest to its automation has not been satisfactory to him. This article summarizes Bertin’s approach to the reorderable matrix, underlines the limitations of fully automated reordering methods, and introduces Bertifier, a hybrid system to reorder matrices using a combination of machine assistance and human control.     

New Solution for the Earth’s Free Wobble and Its Geophysical Implications

In this paper, the theory of the free wobble of the triaxial Earth is developed and new conclusions are drawn: the Euler period should be actually expressed by the first kind of complete elliptic integral; the trace of the free polar motion is elliptic and the orientations of its semi-minor and major axes are approximately parallel to the Earth’s principal axes A and B, respectively. In addition, the present theory shows that there is a mechanism of frequency-amplitude modulation in the Chandler wobble, whi...     

CODE’s five-system orbit and clock solution—the challenges of multi-GNSS data analysis

This article describes the processing strategy and the validation results of CODE’s MGEX (COM) orbit and satellite clock solution, including the satellite systems GPS, GLONASS, Galileo, BeiDou, and QZSS. The validation with orbit misclosures and SLR residuals shows that the orbits of the new systems Galileo, BeiDou, and QZSS are affected by modelling deficiencies with impact on the orbit scale (e.g., antenna calibration, Earth albedo, and transmitter antenna thrust). Another weakness is the attitude and solar radiation pressure (SRP) modelling of satellites moving in the orbit normal mode—which is not yet correctly considered in the COM solution. Due to these issues, we consider the current state COM solution as preliminary. We, however, use the long-time series of COM products for identifying the challenges and for the assessment of model-improvements. The latter is demonstrated on the example of the solar radiation pressure (SRP) model, which has been replaced by a more generalized model. The SLR validation shows that the new SRP model significantly improves the orbit determination of Galileo and QZSS satellites at times when the satellite’s attitude is maintained by yaw-steering. The impact of this orbit improvement is also visible in the estimated satellite clocks—demonstrating the potential use of the new generation satellite clocks for orbit validation. Finally, we point out further challenges and open issues affecting multi-GNSS data processing that deserves dedicated studies.     

Surface gravitational field and topography changes induced by the Earth’s fluid core motions

Using a Love number formalism, the elastic deformations of the mantle and the mass redistribution gravitational potential within the Earth induced by the fluid pressure acting at the core–mantle boundary (CMB) are computed. This pressure field changes at a decadal time scale and may be estimated from observations of the surface magnetic field and its secular variation. First, using a spherical harmonic expansion, the poloidal and toroidal part of the fluid velocity field at the CMB for the last 40 years is computed, under the hypothesis of tangential geostrophy. Then the associated geostrophic pressure, whose order of magnitude is about 1000 Pa, is computed. The surface topography induced by this pressure field is computed using Love numbers, and is a few millimetres. The mass redistribution gravitational potential induced by these deformations and, in particular, the zonal components of the related surface gravitational potential perturbation (J₂, J₃ and J₄ coefficients), are calculated. Overall perturbations for the J₂ coefficient of about 10^–10, for J₃ of about 10^–11 and for J₄ are found of about 0.3×10^–11. Finally, these theoretical results are compared with recent observations of the decadal variation of J₂ from satellite laser ranging. Results concerning J₂ can be described as follows: first, they are one order of magnitude too small to explain the observed decadal variation of J₂ and, second, they show a significant linear trend over the last 40 years, whose rate of decrease amounts to 7% of the observed value.     

Exploring the spatiotemporal behavior of Helsinki’s housing prices with fractal geometry and co-integration

Fractal geometry and co-integration are combined for exploring spatial morphological aspects of quarterly dwelling prices in Helsinki’s region from 1977 to 2011. Curves of fractal scaling behavior are first employed to measure the fractal dimensions of high- and low-price/m² spatial clusters at multiple scales. Subsequently, the fractal dimensions at indicative neighborhood and citywide scales are modeled with vector error correction specifications. The results identify long-run joint equilibria between the fractal geometries of high- and low-price/m² clusters at both spatial scales. High-price/m² clusters exhibit consistently higher fractal dimensions than their low-value counterparts at the neighborhood scale, while this long-run relation is reversed at the citywide scale. Short-run disequilibria and subsequent adjustments are also scale sensitive. The fractal geometry of high-price/m² clusters leads the dynamics at the neighborhood scale, while low-price/m² clusters lead at the citywide scale. The system’s responses to exogenous shocks take longer time to stabilize at the neighborhood scale compared to the citywide scale, but in both scales the non-stationary nature of fractal behavior is evident. These elements indicate that a closer look on spatial economic behavior at more than one spatial and temporal scale at a time can reveal non-trivial information in the context of urban research and policy analysis.     

Recovery of Bennu’s orientation for the OSIRIS-REx mission: implications for the spin state accuracy and geolocation errors

The goal of the OSIRIS-REx mission is to return a sample of asteroid material from near-Earth asteroid (101955) Bennu. The role of the navigation and flight dynamics team is critical for the spacecraft to execute a precisely planned sampling maneuver over a specifically selected landing site. In particular, the orientation of Bennu needs to be recovered with good accuracy during orbital operations to contribute as small an error as possible to the landing error budget. Although Bennu is well characterized from Earth-based radar observations, its orientation dynamics are not sufficiently known to exclude the presence of a small wobble. To better understand this contingency and evaluate how well the orientation can be recovered in the presence of a large 1\(^{\circ }\) wobble, we conduct a comprehensive simulation with the NASA GSFC GEODYN orbit determination and geodetic parameter estimation software. We describe the dynamic orientation modeling implemented in GEODYN in support of OSIRIS-REx operations and show how both altimetry and imagery data can be used as either undifferenced (landmark, direct altimetry) or differenced (image crossover, altimetry crossover) measurements. We find that these two different types of data contribute differently to the recovery of instrument pointing or planetary orientation. When upweighted, the absolute measurements help reduce the geolocation errors, despite poorer astrometric (inertial) performance. We find that with no wobble present, all the geolocation requirements are met. While the presence of a large wobble is detrimental, the recovery is still reliable thanks to the combined use of altimetry and imagery data.     

Forecasting China’s GDP at the pixel level using nighttime lights time series and population images

China’s rapid economic development greatly affected not only the global economy but also the entire environment of the Earth. Forecasting China’s economic growth has become a popular and essential issue but at present, such forecasts are nearly all conducted at the national scale. In this study, we use nighttime light images and the gridded Landscan population dataset to disaggregate gross domestic product (GDP) reported at the province scale on a per pixel level for 2000–2013. Using the disaggregated GDP time series data and the statistical tool of Holt–Winters smoothing, we predict changes of GDP at each 1 km × 1 km grid area from 2014 to 2020 and then aggregate the pixel-level GDP to forecast economic growth in 23 major urban agglomerations of China. We elaborate and demonstrate that lit population (brightness of nighttime lights × population) is a better indicator than brightness of nighttime lights to estimate and disaggregate GDP. We also show that our forecast GDP has high agreement with the National Bureau of Statistics of China’s demographic data and the International Monetary Fund’s predictions. Finally, we display uncertainties and analyze potential errors of this disaggregation and forecast method.     

Efficient and accurate high-degree spherical harmonic synthesis of gravity field functionals at the Earth’s surface using the gradient approach

Spherical harmonic synthesis (SHS) of gravity field functionals at the Earth’s surface requires the use of heights. The present study investigates the gradient approach as an efficient yet accurate strategy to incorporate height information in SHS at densely spaced multiple points. Taylor series expansions of commonly used functionals quasigeoid heights, gravity disturbances and vertical deflections are formulated, and expressions of their radial derivatives are presented to arbitrary order. Numerical tests show that first-order gradients, as introduced by Rapp (J Geod 71(5):282–289, 1997) for degree 360 models, produce cm- to dm-level RMS approximation errors over rugged terrain when applied with EGM2008 to degree 2190. Instead, higher-order Taylor expansions are recommended that are capable of reducing approximation errors to insignificance for practical applications. Because the height information is separated from the actual synthesis, the gradient approach can be applied along with existing highly efficient SHS routines to compute surface functionals at arbitrarily dense grid points. This confers considerable computational savings (above or well above one order of magnitude) over conventional point-by-point SHS. As an application example, an ultra-high resolution model of surface gravity functionals (EurAlpGM2011) is constructed over the entire European Alps that incorporates height information in the SHS at 12,000,000 surface points. Based on EGM2008 and residual topography data, quasigeoid heights, gravity disturbances and vertical deflections are estimated at ~200m resolution. As a conclusion, the gradient approach is efficient and accurate for high-degree SHS at multiple points at the Earth’s surface.     

Effects of topographic–isostatic masses on gravitational functionals at the Earth’s surface and at airborne and satellite altitudes

Topographic–isostatic masses represent an important source of gravity field information, especially in the high-frequency band, even if the detailed mass-density distribution inside the topographic masses is unknown. If this information is used within a remove-restore procedure, then the instability problems in downward continuation of gravity observations from aircraft or satellite altitudes can be reduced. In this article, integral formulae are derived for determination of gravitational effects of topographic–isostatic masses on the first- and second-order derivatives of the gravitational potential for three topographic–isostatic models. The application of these formulas is useful for airborne gravimetry/gradiometry and satellite gravity gradiometry. The formulas are presented in spherical approximation by separating the 3D integration in an analytical integration in the radial direction and 2D integration over the mean sphere. Therefore, spherical volume elements can be considered as being approximated by mass-lines located at the centre of the discretization compartments (the mass of the tesseroid is condensed mathematically along its vertical axis). The errors of this approximation are investigated for the second-order derivatives of the topographic–isostatic gravitational potential in the vicinity of the Earth’s surface. The formulas are then applied to various scenarios of airborne gravimetry/gradiometry and satellite gradiometry. The components of the gravitational vector at aircraft altitudes of 4 and 10 km have been determined, as well as the gravitational tensor components at a satellite altitude of 250 km envisaged for the forthcoming GOCE (gravity field and steady-state ocean-circulation explorer) mission. The numerical computations are based on digital elevation models with a 5-arc-minute resolution for satellite gravity gradiometry and 1-arc-minute resolution for airborne gravity/gradiometry.     

Transformation of amplitudes and frequencies of precession and nutation of the earth’s rotation vector to amplitudes and frequencies of diurnal polar motion

The temporal change of the rotation vector of a rotating body is, in the first order, identical in a space-fixed system and in a body-fixed system. Therefore, if the motion of the rotation axis of the earth relative to a space-fixed system is given as a function of time, it should be possible to compute its motion relative to an earth-fixed system, and vice versa. This paper presents such a transformation. Two models of motion of the rotation axis in the space-fixed system are considered: one consisting only of a regular (i.e., strictly conical) precession and one extended by circular nutation components, which are superimposed upon the regular precession. The Euler angles describing the orientation of the earth-fixed system with respect to the space-fixed system are derived by an analytical solution of the kinematical Eulerian differential equations. In the first case (precession only), this is directly possible, and in the second case (precession and nutation), a solution is achieved by a perturbation approach, where the result of the first case serves as an approximation and nutation is regarded as a small perturbation, which is treated in a linearized form. The transformation by means of these Euler angles shows that the rotation axis performs in the earth-fixed system retrograde conical revolutions with small amplitudes, namely one revolution with a period of one sidereal day corresponding to precession and one revolution with a period which is slightly smaller or larger than one sidereal day corresponding to each (prograde or retrograde) circular nutation component. The peculiar feature of the derivation presented here is the analytical solution of the Eulerian differential equations.     

Landsat-8 vs. Sentinel-2: examining the added value of sentinel-2’s red-edge bands to land-use and land-cover mapping in Burkina Faso

The availability of freely available moderate-to-high spatial resolution (10–30 m) satellite imagery received a major boost with the recent launch of the Sentinel-2 sensor by the European Space Agency. Together with Landsat, these sensors provide the scientific community with a wide range of spatial, spectral, and temporal properties. This study compared and explored the synergistic use of Landsat-8 and Sentinel-2 data in mapping land use and land cover (LULC) in rural Burkina Faso. Specifically, contribution of the red-edge bands of Sentinel-2 in improving LULC mapping was examined. Three machine-learning algorithms – random forest, stochastic gradient boosting, and support vector machines – were employed to classify different data configurations. Classification of all Sentinel-2 bands as well as Sentinel-2 bands common to Landsat-8 produced an overall accuracy, that is 5% and 4% better than Landsat-8. The combination of Landsat-8 and Sentinel-2 red-edge bands resulted in a 4% accuracy improvement over that of Landsat-8. It was found that classification of the Sentinel-2 red-edge bands alone produced better and comparable results to Landsat-8 and the other Sentinel-2 bands, respectively. Results of this study demonstrate the added value of the Sentinel-2 red-edge bands and encourage multi-sensoral approaches to LULC mapping in West Africa.     

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.     

Horizontal and vertical accuracy of Google Earth®: comment on ‘Positional accuracy of the Google Earth terrain model derived from stratigraphic unconformities in the Big Bend region,Texas, USA’ by S.C. Benker,R.P. Langford and T.L. Pavlis

Comment on ‘Positional accuracy of the Google Earth terrain model derived from stratigraphic unconformities in the Big Bend region, Texas, USA’ by S.C. Benker, R.P. Langford and T.L. Pavlis (Geocarto Int. 26:291–303, doi: 10.1080/10106049.2011.568125).     

The First Depiction of Two Superimposed Geographical Surfaces in One Autostereoscopic Map: Antarctica’s Topography and the Southern Ocean Seafloor

Within the past 10–15 years true-3D lenticular cartography has experienced a remarkable boost. In the course of this development, besides studies into its potential for thematic-cartographic representations, the synoptic depiction of physical surfaces (‘geo[graphical] surfaces’) has been playing a significant role. In this context the innovative holistic display of complex morphological and topographical conditions is of particular interest. The simultaneous representation of various cartographic parameters at different depths will deliver an enormous surplus of information transfer in the field of thematic cartography as well as in physical/topographic cartography. This paper describes the methodological development and generation of an autostereoscopic hardcopy display of Antarctic topography. The purpose was the simultaneous depiction of the two superimposed surfaces of both the ice-sheet and the rock-bed and, in addition, of the surrounding seafloor, thus displaying a vertical drop of more than 12,000?m.