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Theoretical study of the incompressible Navier-Stokes equations by the least-squares method

Usually the theoretical analysis of the Navier-Stokes equations is conducted via the Galerkin method which leads to difficult saddle-point problems. This paper demonstrates that the least-squares method is a useful alternative tool for the theoretical study of partial differential equations since it leads to minimization problems which can often be treated by an elementary technique. The principal part of the Navier-Stokes equations in the first-order velocity-pressure-vorticity formulation consists of two div-curl systems, so the three-dimensional div-curl system is thoroughly studied at first. By introducing a dummy variable and by using the least-squares method, this paper shows that the div-curl system is properly determined and elliptic, and has a unique solution. The same technique then is employed to prove that the Stokes equations are properly determined and elliptic, and that four boundary conditions on a fixed boundary are required for three-dimensional problems. This paper also shows that under four combinations of non-standard boundary conditions the solution of the Stokes equations is unique. This paper emphasizes the application of the least-squares method and the div-curl method to derive a high-order version of differential equations and additional boundary conditions. In this paper, an elementary method (integration by parts) is used to prove Friedrichs' inequalities related to the div and curl operators which play an essential role in the analysis.

Jiang, Bo-Nan↗

Plasma and radio waves from Neptune: Source mechanisms and propagation

This report summarizes results obtained through the support of NASA Grant NAGW-2412. The objective of this project is to conduct a comprehensive investigation of the radio wave emission observed by the planetary radio astronomy (PRA) instrument on board Voyager 2 as if flew by Neptune. This study has included data analysis, theoretical and numerical calculations, ray tracing, and modeling to determine the possible source mechanism(s) and locations of the Neptune radio emissions. We have completed four papers, which are included in the appendix. The paper 'Modeling of Whistler Ray Paths in the Magnetosphere of Neptune' investigated the propagation and dispersion of lighting-generated whistler in the magnetosphere of Neptune by using three dimensional ray tracing. The two papers 'Numerical Simulations of Bursty Radio Emissions from Planetary Magnetospheres' and 'Numerical Simulations of Bursty Planetary Radio Emissions' employed numerical simulations to investigate an alternate source mechanism of bursty radio emissions in addition to the cyclotron maser instability. We have also studied the possible generation of Z and whistler mode waves by the temperature anisotropic beam instability and the result was published in 'Electron Cyclotron Wave Generation by Relativistic Electrons.' Besides the aforementioned studies, we have also collaborated with members of the PRA team to investigate various aspects of the radio wave data. Two papers have been submitted for publication and the abstracts of these papers are also listed in the appendix.

Wong, H. K.↗

Does human cognition allow Human Factors (HF) certification of advanced aircrew systems?

This paper has examined the requirements of HF specification and certification within advanced or complex aircrew systems. It suggests reasons for current inadequacies in the use of HF in the design process, giving some examples in support, and suggesting an avenue towards the improvement of the HF certification process. The importance of human cognition to the operation and performance of advanced aircrew systems has been stressed. Many of the shortfalls of advanced aircrew systems must be attributed to over automated designs that show little consideration on either the mental limits or the cognitive capabilities of the human system component. Traditional approaches to system design and HF certification are set within an over physicalistic foundation. Also, traditionally it was assumed that physicalistic system functions could be attributed to either the human or the machine on a one to one basis. Moreover, any problems associated with the parallel needs, or promoting human understanding alongside system operation and direction, were generally equated in reality by the natural flexibility and adaptability of human skills. The consideration of the human component of a complex system is seen as being primarily based on manifestations of human behavior to the almost total exclusion of any appreciation of unobservable human mental and cognitive processes. The argument of this paper is that the considered functionality of any complex human-machine system must contain functions that are purely human and purely cognitive. Human-machine system reliability ultimately depends on human reliability and dependability and, therefore, on the form and frequency of cognitive processes that have to be conducted to support system performance. The greater the demand placed by an advanced aircraft system on the human component's basic knowledge processes or cognition, rather than on skill, the more insiduous the effects the human may have on that system. This paper discusses one example of an attempt to devise an improved method of specificaiton and certification with relation to the advanced aircrew system, that of the RN Merlin helicopter. The method is realized to have limitations in practice, these mainly associated with the late production of the system specification in relation to the system development process. The need for a careful appreciation of the capabilities and support needs of human cognition within the design process of a complex man machine system has been argued, especially with relation to the concept of system functionality. Unlike the physicalistic Fitts list, a new classification of system functionality is proposed, namely: (1) equipment - system equipment related; (2) cognitive - human cognition related; and (3) associated - necessary combinatin of equipment and cognitive. This paper has not proposed a method for a fuller consideration of cognition within systems design, but has suggested the need for such a method and indicated an avenue towards its development. Finally, the HF certification of advanced aircrew systems is seen as only being possible in a qualified sense until the important functions of human cognition are considered within the system design process. (This paper contains the opinions of its authors and does not necessarily refledt the standpoint of their respective organizations).

Macleod, Iain S.↗

Potential future applications for the tracking and data relay satellite II (TDRS II) system

During the conceptual design phases of the tracking and data relay satellite (TDRS) II system provision was made for a future service growth (FSG) payload with an undefined mission. The intent of the FSG was to provide a resource for TDRS II applications which would be available to meet a change in requirements for the operational TDRS II system. This paper summarizes the effect of the consideration of potential FSG applications imposed on the tracking and data relay satellite (TDRS) II system. The following applications were considered as FSG candidates: An optical 650 Mbps space-to-space link (SSL) coupled to an optical or RF downlink, an RF or optical crosslink to extend the baseline TDRS II system coverage, -zone of exclusion (ZOE) closure, relay for lunar communications either RF or optically, and relay for Martian communications either RF or optically. This paper summarizes work done in the 1990 time frame on the above stated applications. Since then, NASA has sponsored several studies (during phase B of the TDRS II development cycle) of the ZOE closure application of the FSG. The purpose of this paper is to report on the efforts previously considered for the FSG. A previous paper was presented at the 1991 Congress related to the second application above. This paper extends this effort to the four stated applications.

Gibbons, Richard C.↗

Numerical investigations in the backflow region of a vacuum plume

Four tasks were completed in this period and results were published in AIAA papers. First, a Boltzmann-2D code, was developed and applied to compute MSFC-A2 nozzle/plume flow field. It solved the two-dimensional Boltzmann-BGK equation using the Finite Difference Discrete Ordinate (FDDO) numerical technique. The code was validated by experimental data for one-dimensional shock structure predictions, paper 95-2056. Successful results for nozzle/plume flow simulation using the developed Boltzmann-2D code were presented at the 1995 AIAA Aerospace Science Conference, paper 95-0627. Second, a computer code solving two-dimensional Burnett equations was developed and applied to low-density nozzle flow field calculation. Results were also published at the 1994 AIAA Thermophysics Conference, paper 94-2055. Third, the developed two-dimensional Burnett code was extended to compute axisymmetric flow field inside MSFC-A2 nozzle, paper 95-2008. The computed nozzle exit conditions are used as input data for Direct Simulation Monte Carlo (DSMC) plume calculation. Fourth, a DSMC code was modified to compute the exhausted plume near the nozzle exit and in the backflow region.

Liaw, Goang-Shin↗

MACH 3: Past and future approaches to intelligent tutoring

In 1986, the U.S. Army Research Institute created an intelligent tutoring system as a proof-of-concept for artificial intelligence applications in Army training. The Maintenance Aid Computer HAWK Intelligent Institutional Instructor (MACH 3) taught student mechanics to maintain and troubleshoot the AN/MPQ-57 High Power Illuminator Radar (HPIR) of the HAWK Air Defense Missile System. In 1989, TRADOC Analysis Command compared the effectiveness of MACH 3 to traditional paper-based troubleshooting drills. For the study, all students received lecture and hands-on training as usual. However, during troubleshooting drills, students traced faults using either MACH 3 or the traditional paper-based method. Class records showed that the MACH 3 group completed significantly more troubleshooting tasks and progressed through tasks of greater difficulty than the paper-based group. Upon completion of training, students took written, practical, and oral essay tests. Mean test scores showed that students performed similarly regardless of the drill method used. However, significantly different standard deviations showed that the MACH 3 group performed more consistently than the paper-based group. Furthermore, significantly different time measures showed that the MACH 3 group reached faster troubleshooting solutions on the actual radar transmitter than the paper-based group. We will present the study results and discuss how updating the design of the MACH 3 can include desktop computing in a virtual environment.

Acchione-Noel, Sylvia↗

Generalizing Atoms in Constraint Logic

This paper studies the generalization of atomic formulas, or atoms, that are augmented with constraints on or among their terms. The atoms may also be viewed as definite clauses whose antecedents express the constraints. Atoms are generalized relative to a body of background information about the constraints. This paper first examines generalization of atoms with only monadic constraints. The paper develops an algorithm for the generalization task and discusses algorithm complexity. It then extends the algorithm to apply to atoms with constraints of arbitrary arity. The paper also presents semantic properties of the generalizations computed by the algorithms, making the algorithms applicable to such problems as abduction, induction, and knowledge base verification. The paper emphasizes the application to induction and presents a pac-learning result for constrained atoms.

Page, C. David, Jr.↗

Observational and Model Studies of Large-Scale Mixing Processes in the Stratosphere

The following is the final technical report for grant NAGW-3442, 'Observational and Model Studies of Large-Scale Mixing Processes in the Stratosphere'. Research efforts in the first year concentrated on transport and mixing processes in the polar vortices. Three papers on mixing in the Antarctic were published. The first was a numerical modeling study of wavebreaking and mixing and their relationship to the period of observed stratospheric waves (Bowman). The second paper presented evidence from TOMS for wavebreaking in the Antarctic (Bowman and Mangus 1993). The third paper used Lagrangian trajectory calculations from analyzed winds to show that there is very little transport into the Antarctic polar vortex prior to the vortex breakdown (Bowman). Mixing is significantly greater at lower levels. This research helped to confirm theoretical arguments for vortex isolation and data from the Antarctic field experiments that were interpreted as indicating isolation. A Ph.D. student, Steve Dahlberg, used the trajectory approach to investigate mixing and transport in the Arctic. While the Arctic vortex is much more disturbed than the Antarctic, there still appears to be relatively little transport across the vortex boundary at 450 K prior to the vortex breakdown. The primary reason for the absence of an ozone hole in the Arctic is the earlier warming and breakdown of the vortex compared to the Antarctic, not replenishment of ozone by greater transport. Two papers describing these results have appeared (Dahlberg and Bowman; Dahlberg and Bowman). Steve Dahlberg completed his Ph.D. thesis (Dahlberg and Bowman) and is now teaching in the Physics Department at Concordia College. We also prepared an analysis of the QBO in SBUV ozone data (Hollandsworth et al.). A numerical study in collaboration with Dr. Ping Chen investigated mixing by barotropic instability, which is the probable origin of the 4-day wave in the upper stratosphere (Bowman and Chen). The important result from this paper is that even in the presence of growing, unstable waves, the mixing barriers around

Bowman, Kenneth P.↗

Spectra of High-Ionization Seyfert 1 Galaxies: Implications for the Narrow-Line Region

We present line profiles and profile parameters for the Narrow-Line Regions (NLRs) of six Seyfert 1 galaxies with high-ionization lines: MCG 8-11-11, Mrk 79, Mrk 704, Mrk 841, NGC 4151, and NGC 5548. The sample was chosen primarily with the goal of obtaining high-quality [Fe VII] lambda6087 and, when possible, [Fe X] lambda6374 profiles to determine if these lines are more likely formed in a physically distinct 'coronal line region' or are formed throughout the NLR along with lines of lower critical density (n(sub cr)) and/or Ionization Potential (IP). We discuss correlations of velocity shift and width with n(sub cr) and IP. In some objects, lines of high IP and/or n(sub cr) are systematically broader than those of low IP/n(sub cr). Of particular interest, however, are objects that show no correlations of line width with either IP or n(sub cr). In these objects, lines of high and low IP/n(sub cr), are remarkably similar, which is difficult to reconcile with the classical picture of the NLR, in which lines of high and low IP/n(sub cr) are formed in physically distinct regions. We argue for similar spatial extents for the flux in lines with similar profiles. Here, as well as in a modeling-oriented companion paper, we develop further an idea suggested by Moore & Cohen that objects that do and do not show line width correlations with IP/n(sub cr) can both be explained in terms of a single NLR model with only a small difference in the cloud column density distinguishing the two types of object. Overall, our objects do not show correlations between the Full Width at Half-Maximum (FWHM) and IP and/or n(sub cr). The width must be defined by a parameter that is sensitive to extended profile wings in order for the correlations to result. We present models in which FWHM correlations with IP and/or n(sub cr) result only after simulating the lower spectral resolution used in previous observational studies. The models that simulate the higher spectral resolution of our observational study produce line width correlations only if the width is defined by a parameter that is more sensitive to extended profile wings than is the FWHM. Our sample of six objects is in effect augmented by incorporating the larger sample (16 objects) of Veilleux into some of our discussion. This paper focuses on new interpretations of NLR emission-line spectra and line profiles that stem directly from the observations. Paper 2 focuses on modeling and complements this paper by illustrating explicitly the effects that spatial variations in electron density, ionization parameter, and column density have on model profiles. By comparing model profiles with the observed profiles presented here, as well as with those presented by Veilleux, Paper 2 yields insight into how the electron density, ionization parameter, and column density likely vary throughout the NLR.

Moore, David↗

Analysis of Data from the Energetic Gamma-ray Experiment on the Gamma Ray Observatory

The work under the Grant has involved participation with the Compton Gamma Ray Observatory Energetic Gamma-Ray Experiment Telescope (EGRET) Team in the analysis of data obtained during instrument operations and the preparation of scientific papers and proposals for future observations. The Principal Investigator (PI) has been a co-author on a total of 90 papers published in refereed professional journals since the beginning of 1991, plus many other non-refereed publications, and contributed and invited papers at professional meetings and IAU telegrams. On seven of these papers he was the lead author. The EGRET team continues to submit IAU Astronomical telegrams and present many papers at scientific meetings. The effort by the PI has involved working remotely by internet connection on the Goddard Space Flight Center Computers where the EGRET data are archived. Students have monitored instrument performance, performed Viewing Period Analyses and analyzed data remotely. The PI has completed the detailed analysis of over 20 viewing periods to search for point sources and this work has been used in developing the first and second EGRET catalog of sources, published in Supplements to the Astrophysical Journal.

Kniffen, Donald A.↗

Diurnal Forcing of Planetary Atmospheres

Much progress has been made on calculations of the Martian seasonal water cycle using the Mars Climate Model developed for this purpose. Two papers, documenting the model and the water transport results obtained with it have been published in the Journal of Geophysical Research - Planets. An additional paper describing results related to the evolution of the seasonal water cycle as a result of orbital changes was published in Advances in Space Research. Since that time, further studies have concentrated on the consequences of the soil adsorption required to match the observed water cycle and its relation to the stability of ground ice and other potential water reservoirs. Earth-related studies have concentrated on incorporating an efficient and realistic microphysical model into the Ames Stratospheric General Circulation Model used to simulate the spread of the ML Pinatubo and other volcanic clouds in the stratosphere. In addition, visualizations of the simulations are being incorporated into a video describing the UARS mission. A paper describing the new stratospheric aerosol microphysics package (and its consequences for volcanic cloud evolution) will be submitted in the near future. The paper will discuss the relative importance of condensation and coagulation to early particle growth and the separation of the cloud by sedimentation of the larger particles. A more general paper which highlights the observation that particle number densities did not increase dramatically after the ML Pinatubo eruption is planned. Simulations of atmospheric transport will be extended to include studies of terrestrial tropospheric tracers using the Fifth-Generation Penn State/NCAR Mesoscale Model.

Houben, Howard C.↗

The Implementation of Satellite Attitude Control System Software Using Object Oriented Design

NASA established the Small Explorer (SNMX) program in 1988 to provide frequent opportunities for highly focused and relatively inexpensive space science missions. The SMEX program has produced five satellites, three of which have been successfully launched. The remaining two spacecraft are scheduled for launch within the coming year. NASA has recently developed a prototype for the next generation Small Explorer spacecraft (SMEX-Lite). This paper describes the object-oriented design (OOD) of the SMEX-Lite Attitude Control System (ACS) software. The SMEX-Lite ACS is three-axis controlled and is capable of performing sub-arc-minute pointing. This paper first describes high level requirements governing the SMEX-Lite ACS software architecture. Next, the context in which the software resides is explained. The paper describes the principles of encapsulation, inheritance, and polymorphism with respect to the implementation of an ACS software system. This paper will also discuss the design of several ACS software components. Specifically, object-oriented designs are presented for sensor data processing, attitude determination, attitude control, and failure detection. Finally, this paper will address the establishment of the ACS Foundation Class (AFC) Library. The AFC is a large software repository, requiring a minimal amount of code modifications to produce ACS software for future projects.

Reid, W. Mark↗

Studies of the Martian Magnetic Field

This report covers two awards: the first NAGW-2573 was awarded to enable participation in the Mars 94 mission that slipped to become the Mars 96 mission. Upon the unfortunate failure of Mars 96 to achieve its intended trajectory, the second grant was awarded to closeout the Mars 96 activities. Our initial efforts concentrated on assisting our colleagues: W. Riedler, K. Schwingenschuh, K. Gringanz, M. Verigin and Ye. Yeroshenko with advice on the development of the magnetic field portion of the investigation and to help them with test activities. We also worked with them to properly analyze the Phobos magnetic field and plasma data in order to optimize the return from the Mars 94/96 mission. This activity resulted in 18 papers on Mars scientific topics, and two on the instrumentation. One of these latter two papers was the last of the papers written, and speaks to the value of the closeout award. These 20 papers are listed in the attached bibliography. Because we had previously studied Venus and Titan and since it was becoming evident that the magnetic field was very weak, we compared the various properties of the Martian interaction with those of the analogous interactions at Venus and Titan while other papers simply analyzed the properties of the interaction as Phobos 2 observed them. One very interesting observation was the identification of ions picked up in the solar wind, originating in Mars neutral atmosphere. These had been predicted by our earlier observation of cyclotron waves at the proton gyrofrequency in the region upstream from Mars in the solar wind. Of course, the key question we addressed was that of the intrinsic or induced nature of the Martian magnetic field. We found little evidence for the former and much for the latter point of view. We also discussed the instrumentation planned for the Mars balloon and the instrumentation on the orbiter. In all these studies were very rewarding despite the short span of the Phobos data. Although they did not affect the eventual analysis of the Mars 96 data, these studies did pave the way for the Mars Global Surveyor and have been fully confirmed by the measurements at much closer distances than Phobos 2 ever reached. No patents or inventions resulted from the work.

Russell, C. T.↗

Atmospheric Aerosol Chemical Composition Measurements for the Subsonic Aircraft: Contrail and Cloud Effects Special Study (SUCCESS)

We received funding to provide measurements of the chemical composition of aerosols aboard the NASA Ames DC-8 research aircraft during the SUCCESS mission. These measurements were successfully completed and the final data resides in the Cloud I computer archive at NASA Ames Research Center. The interpretation of the data obtained on this mission over the central United States has been published in special issues of Geophysical Research Letters. The papers with the University of New Hampshire as first author constitute this report and summarize the salient features of our data. The paper by Talbot et al. discusses the impact of vertical transport on free tropospheric chemistry over the the central USA in springtime. This transport was a dominant feature of the aerosol chemistry during SUCCESS. The paper by Dibb et al. discusses aerosol chemistry specifically as it related to free tropospheric sulfate related to jet exhaust and surface sources. Somewhat surprisingly, we found that surface sources appeared to dominant the distribution of aerosol sulfate in the free troposphere. In addition to these first authored papers, researchers from the University of New Hampshire were co-authors on numerous other companion papers in the special issues.

Talbot, Robert W.↗

Autonomous Formation Flying from the Ground to Flight

The cost of on-orbit operations remains a significant and increasingly visible concern in the support of satellite missions. Headway has been made in automating some ground operations; however, increased mission complexity and more precise orbital constraints have compelled continuing human involvement in mission design and maneuver planning operations. AI Solutions, Inc. in cooperation with the National Aeronautics and Space Administration's (NASA) Goddard Space Flight Center (GSFC) has tackled these more complex problems through the development of AutoCon(TM) as a tool for an automated solution. NASA is using AutoCon(TM) to automate the maneuver planning for the Earth Orbiter-1 (EO-1) mission. AutoCon(TM) was developed originally as a ground system tool. The EO-1 mission will be using a scaled version of AutoCon(TM) on-board the EO-1 satellite to command orbit adjustment maneuvers. The flight version of AutoCon(TM) plans maneuvers based on formation flying algorithms developed by GSFC, JPL, and other industry partners. In its fully autonomous mode, an AutoCon(TM) planned maneuver will be executed on-board the satellite without intervention from the ground. This paper describes how AutoCon(TM) automates maneuver planning for the formation flying constraints of the EO-1 mission. AutoCon(TM) was modified in a number of ways to automate the maneuver planning on-board the satellite. This paper describes how the interface and functionality of AutoCon(TM) were modified to support the on-board system. A significant component of this modification was the implementation of a data smoother, based on a Kalman filter, that ensures that the spacecraft states estimated by an on-board GPS receiver are as accurate as possible for maneuver planning. This paper also presents the methodology used to scale the AutoCon(TM) functionality to fit and execute on the flight hardware. This paper also presents the modes built into the system that allow the incremental phasing in of autonomy. New technologies for autonomous operations are usually received with significant, and probably appropriate, trepidation. A number of safeguards have been designed in both AutoCon(TM) and the interfacing systems to alleviate the potential of mission-impacting anomalies from the on-board autonomous system. This paper describes the error checking, input data integrity validation, and limits set on maneuvers in AutoCon(TM) and the on-board system.

Chapman, Keith B.↗

Autonomous Formation Flying from Ground to Flight

The cost of on-orbit operations remains a significant and increasingly visible concern in the support of satellite missions. Headway has been made in automating some ground operations; however, increased mission complexity and more precise orbital constraints have compelled continuing human involvement in mission design and maneuver planning operations. AI Solutions, Inc. in cooperation with the National Aeronautics and Space Administration's (NASA) Goddard Space Flight Center (GSFC) has tackled these more complex problems through the development of AutoCon as a tool for an automated solution. NASA is using AutoCon to automate the maneuver planning for the Earth Orbiter-1 (EO-1) mission. AutoCon was developed originally as a ground system tool. The EO-1 mission will be using a scaled version of AutoCon on-board the EO-1 satellite to command orbit adjustment maneuvers. The flight version of AutoCon plans maneuvers based on formation flying algorithms developed by GSFC, JPL, and other industry partners. In its fully autonomous mode, an AutoCon planned maneuver will be executed on-board the satellite without intervention from the ground. This paper describes how AutoCon automates maneuver planning for the formation flying constraints of the EO-1 mission. AutoCon was modified in a number of ways to automate the maneuver planning on-board the satellite. This paper describes how the interface and functionality of AutoCon were modified to support the on-board system. A significant component of this modification was the implementation of a data smoother, based on a Kalman filter, that ensures that the spacecraft states estimated by an on-board GPS receiver are as accurate as possible for maneuver planning. This paper also presents the methodology use to scale the AutoCon functionality to fit and execute on the flight hardware. This paper also presents the modes built that allow the incremental phasing in of autonomy. New technologies for autonomous operations are usually received with significant, and probably appropriate trepidation. A number of safeguards have been designed in both AutoCon and the interfacing systems to alleviate the potential of mission-impacting anomalies from the on-board autonomous system. This paper describes the error checking, input data integrity validation and limits set on maneuvers in AutoCon and the on-board system.

Chapman, Keith B.↗

A Cybernetic Approach to the Modeling of Agent Communities

In an earlier paper [1] examples of agent technology in a NASA context were presented. Both groundbased and space-based applications were addressed. This paper continues the discussion of one aspect of the Goddard Space Flight Center's continuing efforts to develop a community of agents that can support both ground-based and space-based systems autonomy. The paper focuses on an approach to agent-community modeling based on the theory of viable systems developed by Stafford Beer. It gives the status of an initial attempt to capture some of the agent-community behaviors in a viable system context. This paper is expository in nature and focuses on a discussion of the modeling of some of the underlying concepts and infrastructure that will serve as the basis of more detailed investigative work into the behavior of agent communities. The paper is organized as follows. First, a general introduction to agent community requirements is presented. Secondly, a brief introduction to the cybernetic concept of a viable system is given. This concept forms the foundation of the modeling approach. Then the concept of an agent community is modeled in the cybernetic context.

Truszkowski, Walt↗

Introduction to This Special Issue on Geostatistics and Geospatial Techniques in Remote Sensing

The germination of this special Computers & Geosciences (C&G) issue began at the Royal Geographical Society (with the Institute of British Geographers) (RGS-IBG) annual meeting in January 1997 held at the University of Exeter, UK. The snow and cold of the English winter were tempered greatly by warm and cordial discussion of how to stimulate and enhance cooperation on geostatistical and geospatial research in remote sensing 'across the big pond' between UK and US researchers. It was decided that one way forward would be to hold parallel sessions in 1998 on geostatistical and geospatial research in remote sensing at appropriate venues in both the UK and the US. Selected papers given at these sessions would be published as special issues of C&G on the UK side and Photogrammetric Engineering and Remote Sensing (PE&RS) on the US side. These issues would highlight the commonality in research on geostatistical and geospatial research in remote sensing on both sides of the Atlantic Ocean. As a consequence, a session on "Geostatistics and Geospatial Techniques for Remote Sensing of Land Surface Processes" was held at the RGS-IBG annual meeting in Guildford, Surrey, UK in January 1998, organized by the Modeling and Advanced Techniques Special Interest Group (MAT SIG) of the Remote Sensing Society (RSS). A similar session was held at the Association of American Geographers (AAG) annual meeting in Boston, Massachusetts in March 1998, sponsored by the AAG's Remote Sensing Specialty Group (RSSG). The 10 papers that make up this issue of C&G, comprise 7 papers from the UK and 3 papers from the LIS. We are both co-editors of each of the journal special issues, with the lead editor of each journal issue being from their respective side of the Atlantic. The special issue of PE&RS (vol. 65) that constitutes the other half of this co-edited journal series was published in early 1999, comprising 6 papers by US authors. We are indebted to the International Association for Mathematical Geology for allowing us to use C&G as a vehicle to convey how geostatistics and geospatial techniques can be used to analyze remote sensing and other types of spatial data. We see this special issue of C&G. and its complementary issue of PE&RS. as a testament to the vitality and interest in the application of geostatistical and geospatial techniques in remote sensing. We also see these special journal issues as the beginning of a fruitful. and hopefully long-term relationship, between American and British geographers and other researchers interested in geostatistical and geospatial techniques applied to remote sensing and other spatial data.

Atkinson, Peter↗