The hierarchical tessellation model and its use in spatial analysis

The hierarchid tessellation model belongs to a class of spatial data models based on the recursive decomposition of space. The quadtree is one such tessellation and is characterized by square cells and a 1:4 decomposition ratio. To relax these constraints in the tessellation, a generalized hierarchical tessellation data model, called Adaptive Recursive Tessellations (ART), has been proposed. ART increases flexibility in the tessellation by the use of rectangular cells and variable decomposition ratios. In ART, users can specify cell sizes which are intuitively meaningful to their applications, or which can reflect the scales of data. ART is implemented in a data structure called Adaptive Recursive Run-Encoding (ARRE), which is a variant of two-dimensional run-encoding whose running path can vary with the different tessellation structures incorporated in an ART model. Given the recognition of the benefits of implementing statistical spatial analysis in GIS, the use of hierarchical tessellation models such as ART in spatial analysis is discussed. Three examples are introduced to show how ART can: (1) be applied to solve the quadrat size problem in quadrat analysis of point patterns; (2) act as the data model in the variable resolution block kriging technique for geostatistical data to reduce variation in kriging error; and (3) facilitate the evaluation of spatial autocorrelation for area data at multiple map resolutions via the construction of a connectivity matrix for calculating spatial autocorrelation indices based on ARRE.     

MAP MAKING FOR PROFIT AND PLEASURE

Some of the economic and operational aspects of mapping are discussed, including the conditions that may offer air survey a competitive advantage over other methods. The financing of national mapping programmes around the world is increasingly market oriented, driven by the need to provide the end users with information that they can turn into sustainable economic growth and social progress. Despite these economic pressures, map makers seem to find their work more enjoyable and rewarding than most professionals.     

Response of GPS occultation signals to atmospheric gravity waves and retrieval of gravity wave parameters

We show that the amplitude of the Global Positioning System (GPS) signals in the radio occultation (RO) experiments is an indicator of the activity of the gravity waves (GW) in the atmosphere. The amplitude of the GPS RO signals is more sensitive to the atmospheric wave structures than is the phase. Early investigations used only the phase of the GPS occultation signals for statistical investigation of the GW activity in the height interval 10–40 km on a global scale. In this study, we use the polarization equations and Hilbert transform to find the 1-D GW radio image in the atmosphere by analyzing the amplitude of the RO signal. The radio image, also called the GW portrait, consists of the phase and amplitude of the GW as functions of height. We demonstrate the potential of this method using the amplitude data from GPS/Meteorology (GPS/MET) and satellite mission Challenge Mini-satellite Payload (CHAMP) RO events. The GW activity is nonuniformly distributed with the main contribution associated with the tropopause and the secondary maximums related to the GW breaking regions. Using our method we find the vertical profiles of the horizontal wind perturbations and its vertical gradient associated with the GW influence. The estimated values of the horizontal wind perturbations are in fairly good agreement with radiosonde data. The horizontal wind perturbations v(h) are ±1 to ±5 m s with vertical gradients dv/dh ±0.5 to ±15 m s km at height 10–40 km. The height dependence of the GW vertical wavelength was inferred through the differentiation of the GW phase. Analysis of this dependence using the dispersion relationship for the GW gives the estimation of the projection of the horizontal background wind velocity on the direction of the GW propagation. For the event considered, the magnitude of this projection changes between 1.5 and 10 m s at heights of 10–40 km. We conclude that the amplitude of the GPS occultation signals contain important information about the wave processes in the atmosphere on a global scale.     

Improved relativistic transformations in GPS

For GPS satellite clocks, a nominal (hardware) frequency offset and a conventional periodic relativistic correction derived as a dot product of the satellite position and velocity vectors, are used to compensate the relativistic effects. The conventional hardware clock rate offset of 38,575.008 ns/day corresponds to a nominal orbit semi-major axis of about 26,561,400 m. For some of the GPS satellites, the departures from the nominal semi-major axis can cause an apparent clock rate up to 10 ns/day. GPS orbit perturbations, together with the earth gravity field oblateness, which is largely responsible for the orbit perturbations, cause the standard GPS relativistic transformations to depart from the rigorous relativity transformation by up to 0.2 ns/day. In addition, the conventional periodic relativistic correction exhibits periodic errors with amplitudes of about 0.1 and 0.2 ns, with periods of about 6 h and 14 days, respectively. Using an analytical integration of the gravity oblateness term (J₂), a simple analytical approximation was derived for the apparent clock rate and the 6-h periodic errors of the standard GPS gravity correction. For daily linear representations of GPS satellite clocks, the improved relativistic formula was found to agree with the precise numerical integration of the GPS relativistic effects within about 0.015 ns. For most of the Block IIR satellites, the 6-h periodical errors of the GPS conventional relativistic correction are already detectable in the recent IGS final clock combinations.     

Uniting space, ground, and underwater measurements for improved estimates of rain rate

Global precipitation is monitored from a variety of platforms including spaceborne, ground-, and ocean-based platforms. Intercomparisons of these observations are crucial to validating the measurements and providing confidence for each measurement technique. Probability distribution functions of rain rates are used to compare satellite and ground-based radar observations. A preferred adjustment technique for improving rain rate distribution estimates is identified using measurements from ground-based radar and rain gauges within the coverage area of the radar. The underwater measurement of rainfall shows similarities to radar measurements, but with intermediate spatial resolution and high temporal resolution. Reconciling these different measurement techniques provides understanding and confidence for all of the methods.     

Boreal forest coherence-based measures of interferometric pair suitability for operational stem volume retrieval

The performance of interferometric synthetic aperture radar (INSAR)-based boreal forest stem volume retrieval is strongly affected by weather conditions around the time of the SAR image acquisitions. Since weather conditions cannot be controlled, the suitability of a particular interferometric pair for stem volume retrieval can only be assessed afterward. In this letter, four objective measures based on observed forest coherence were compared in assessing the suitability of interferometric pairs for stem volume retrieval. These suitability measures can be used to identify the best and worst pairs, i.e., the ones with the most and least favorable weather conditions. Stem volume retrievals were performed using single European Remote Sensing (ERS-1/2) Tandem interferometric pairs by inverting a backscattering-coherence model for boreal forests. A total of 14 ERS Tandem image pairs acquired in varying weather conditions were studied, and the stem volume retrieval performance was assessed against ground-based stem volume estimates on 134 boreal forest stands. Stem volume retrieval performance as measured by R/sup 2/-values between INSAR-estimated stem volumes and ground truth was found to be directly proportional to boreal forest coherence. The interferometric coherence-contrast (ICC), i.e., the difference in coherence between sparsest and densest boreal forest stands was found to be the best of the four studied suitability measures. The ICC could be used as a suitability parameter in the selection of the best interferometric pairs for operational boreal forest stem volume retrieval.     

Internet teaching foundation for the Remote Sensing Core Curriculum program

The Remote Sensing Core Curriculum (RSCC) was initiated in 1993 to meet the demands for a college-level set of resources to enhance the quality of education across national and international campuses. The American Society of Photogrammetry and Remote Sensing adopted the RSCC in 1996 to sustain support of this educational initiative for its membership and collegiate community. A series of volumes, containing lectures, exercises, and data, is being created by expert contributors to address the different technical fields of remote sensing. The RSCC program is designed to operate on the Internet taking full advantage of the World Wide Web (WWW) technology for distance learning. The issues of curriculum development related to the educational setting, with demands on faculty, students, and facilities, is considered to understand the new paradigms for WW-influenced computer-aided learning. The WWW is shown to be especially appropriate for facilitating remote sensing education with requirements for addressing image data sets and multimedia learning tools. The RSCC is located at http://www.umbc.edu/rscc     

Spatially explicit models for exploring COVID‐19 lockdown strategies

This article describes two spatially explicit models created to allow experimentation with different societal responses to the COVID‐19 pandemic. We outline the work to date on modeling spatially explicit infective diseases and show that there are gaps that remain important to fill. We demonstrate how geographical regions, rather than a single, national approach, are likely to lead to better outcomes for the population. We provide a full account of how our models function, and how they can be used to explore many different aspects of contagion, including: experimenting with different lockdown measures, with connectivity between places, with the tracing of disease clusters, and the use of improved contact tracing and isolation. We provide comprehensive results showing the use of these models in given scenarios, and conclude that explicitly regionalized models for mitigation provide significant advantages over a “one‐size‐fits‐all” approach. We have made our models, and their data, publicly available for others to use in their own locales, with the hope of providing the tools needed for geographers to have a voice during this difficult time.