Spatial Interpolation Scheme Research Articles

Finite-frequency structural sensitivities of short-period compressional body waves

SUMMARY We present an extension of the method recently introduced by Zhao & Chevrot for calculating Frechet kernels from a precomputed database of strain Green's tensors by normal mode summation. The extension involves two aspects: (1) we compute the strain Green's tensors using the Direct Solution Method, which allows us to go up to frequencies as high as 1 Hz; and (2) we develop a spatial interpolation scheme so that the Green's tensors can be computed with a relatively coarse grid, thus improving the efficiency in the computation of the sensitivity kernels. The only requirement is that the Green's tensors be computed with a fine enough spatial sampling rate to avoid spatial aliasing. The Green's tensors can then be interpolated to any location inside the Earth, avoiding the need to store and retrieve strain Green's tensors for a fine sampling grid. The interpolation scheme not only significantly reduces the CPU time required to calculate the Green's tensor database and the disk space to store it, but also enhances the efficiency in computing the kernels by reducing the number of I/O operations needed to retrieve the Green's tensors. Our new implementation allows us to calculate sensitivity kernels for high-frequency teleseismic body waves with very modest computational resources such as a laptop. We illustrate the potential of our approach for seismic tomography by computing traveltime and amplitude sensitivity kernels for high frequency P, PKP and Pdiff phases. A comparison of our PKP kernels with those computed by asymptotic ray theory clearly shows the limits of the latter. With ray theory, it is not possible to model waves diffracted by internal discontinuities such as the core–mantle boundary, and it is also difficult to compute amplitudes for paths close to the B-caustic of the PKP phase. We also compute waveform partial derivatives for different parts of the seismic wavefield, a key ingredient for high resolution imaging by waveform inversion. Our computations of partial derivatives in the time window where PcP precursors are commonly observed show that the distribution of sensitivity is complex and counter-intuitive, with a large contribution from the mid-mantle region. This clearly emphasizes the need to use accurate and complete partial derivatives in waveform inversion.

Analysis on the stability of spatial interpolation schemes for head-related transfer function

Head-related transfer functions (HRTFs) are transfer functions from sound source to two ears. They vary as continual functions of source direction. Usually, measurement yields the HRTFs at discrete directions, and HRTFs at unmeasured directions should be estimated by spatial interpolation. There are several familiar interpolation schemes, such as adjacent linear interpolation, the global interpolation, bilinear interpolation and spherical-triangular interpolation. In practice, potential subject's head movement in HRTF measurement may result in error in measured HRTFs, which may in turn deteriorate the interpolation performance. In present work, the performances for interpolation schemes against the error caused by slight head movement in HRTF measurement are evaluated and compared. The results indicate that overall, global interpolation scheme is superior to others in terms of signal-to-distortion ratio in interpolated HRTFs when undergoing a slight head movement in HRTF measurement. Taking advantage of t...

Understanding the Dynamics of Transfer of Satellite Rainfall Error Metrics From Gauged to Ungauged Satellite Gridboxes Using Interpolation Methods

Knowledge of error characteristics of high resolution satellite rainfall data at different spatial/temporal scales is useful, especially when the scheduled Global Precipitation Mission (GPM) plans to provide High Resolution Precipitation Products (HRPPs) at global scales. Satellite rainfall data contain errors which need ground validation (GV) data for characterization, while satellite rainfall data will be most useful in the regions that are lacking in GV data. Therefore, a critical step to bridge this gap is to assess spatial interpolation schemes for transfer of the error characteristics from GV regions to non-GV regions. In this study, a comprehensive assessment of kriging methods for spatial transfer (interpolation) of error metrics is performed. Three kriging methods for spatial interpolation are compared, which are: ordinary kriging (OK), indicator kriging (IK) and disjunctive kriging (DK). Additional comparison with the simple inverse distance weighting (IDW) method is also performed to quantify the added benefit (if any) of using geostatistical methods. Four commonly used satellite rainfall error metrics are assessed for transfer to non-GV satellite gridboxes: Probability of Detection (POD) for rain, False Alarm Ratio (FAR), bias (BIAS), and Root Mean Squared Error (RMSE). Results show that performance of a kriging scheme is strongly sensitive to the timescale for which the errors are interpolated (monthly and weekly) wherein the extent of coverage by GV data plays an equally sensitive role. While most kriging techniques perform well according to correlation measure at climatologic timescales for a range of GV data coverage, only DK and OK appear to retain accuracy at the shorter timescales (monthly and weekly). However, scalar assessment metrics such as mean and standard deviation of error (i.e., difference between true and interpolated errors) reveal a completely different picture of accuracy of each interpolation method. In terms of such assessment measures, the overall performance ranking of the kriging methods is as follows: OK=DK >; IDW >; IK. Assessment of kriging methods also revealed that the transfer accuracy is sensitive to error metric type. The ranking of error metrics with highest accuracy in transfer is: POD >; FAR >; RMSE >; BIAS. Overall, the assessment of kriging methods revealed that these best linear unbiased spatial estimators may not be appropriate transfer methods for transfer of satellite rainfall error metrics at time scales shorter than a week. It is worthwhile now to pursue more non-linear transfer methods (such as neural networks) and other kriging methods that use additional spatial information on the rainfall process (such as co-kriging) to further constrain the interpolation uncertainty.

Spatial interpolation schemes of daily precipitation for hydrologic modeling

Distributed hydrologic models typically require spatial estimates of precipitation interpolated from sparsely located observational points to the specific grid points. We compare and contrast the performance of regression-based statistical methods for the spatial estimation of precipitation in two hydrologically different basins and confirmed that widely used regression-based estimation schemes fail to describe the realistic spatial variability of daily precipitation field. The methods assessed are: (1) inverse distance weighted average; (2) multiple linear regression (MLR); (3) climatological MLR; and (4) locally weighted polynomial regression (LWP). In order to improve the performance of the interpolations, the authors propose a two-step regression technique for effective daily precipitation estimation. In this simple two-step estimation process, precipitation occurrence is first generated via a logistic regression model before estimate the amount of precipitation separately on wet days. This process generated the precipitation occurrence, amount, and spatial correlation effectively. A distributed hydrologic model (PRMS) was used for the impact analysis in daily time step simulation. Multiple simulations suggested noticeable differences between the input alternatives generated by three different interpolation schemes. Differences are shown in overall simulation error against the observations, degree of explained variability, and seasonal volumes. Simulated streamflows also showed different characteristics in mean, maximum, minimum, and peak flows. Given the same parameter optimization technique, LWP input showed least streamflow error in Alapaha basin and CMLR input showed least error (still very close to LWP) in Animas basin. All of the two-step interpolation inputs resulted in lower streamflow error compared to the directly interpolated inputs.

Using satellite altimetry to correct mean temperature and salinity fields derived from Argo floats in the ocean regions around Australia

We present results from a suite of methods using in situ temperature and salinity data, and satellite altimetric observations to obtain an enhanced set of mean fields of temperature, salinity (down to 2000-m depth) and steric height (0/2000 m) for a time-specific period (1992–2007). Firstly, the improved global sampling resulting from the introduction of the Argo program, enables a representative determination of the large-scale mean oceanic structure. However, shortcomings in the coverage remain. High variability western boundary current eddy fields, continental slope and shelf boundaries may all be below their optimal sampling requirements. We describe a simple method to supplement and improve standard spatial interpolation schemes and apply them to the available data within the waters surrounding Australia (100°E–180°W; 50°S–10°N). This region includes a major current system, the East Australian Current (EAC), complex topography, unique boundary currents such as the Leeuwin Current, and large ENSO related interannual variability in the southwest Pacific. We use satellite altimetry sea level anomalies (SLA) to directly correct sampling errors in in situ derived mean surface steric height and subsurface temperature and salinity fields. The surface correction is projected through the water column (using an empirical model) to modify the mean subsurface temperature and salinity fields. The errors inherent in all these calculations are examined. The spatial distribution of the barotropic–baroclinic balance is obtained for the region and a ‘baroclinic factor’ to convert the altimetry SLA into an equivalent in situ height is determined. The mean fields in the EAC region are compared with independent estimates on repeated XBT sections, a mooring array and full-depth CTD transects.

A geostatistical approach to mapping site response spectral amplifications

If quantitative estimates of the seismic properties do not exist at a location of interest then the site response spectral amplifications must be estimated from data collected at other locations. Currently, the most common approach employs correlations of site class with maps of surficial geology. Analogously, correlations of site class with topographic slope can be employed where the surficial geology is unknown. Our goal is to identify and validate a method to estimate site response with greater spatial resolution and accuracy for regions where additional effort is warranted. This method consists of three components: region-specific data collection, a spatial model for interpolating seismic properties, and a theoretical method for computing spectral amplifications from the interpolated seismic properties. We consider three spatial interpolation schemes: correlations with surficial geology, termed the geologic trend (GT), ordinary kriging (OK), and kriging with a trend (KT). We estimate the spectral amplifications from seismic properties using the square root of impedance method, thereby linking the frequency-dependent spectral amplifications to the depth-dependent seismic properties. Thus, the range of periods for which this method is applicable is limited by the depth of exploration. A dense survey of near-surface S-wave slowness ( S s ) throughout Kobe, Japan shows that the geostatistical methods give more accurate estimates of S s than the topographic slope and GT methods, and the OK and KT methods perform equally well. We prefer the KT model because it can be seamlessly integrated with geologic maps that cover larger regions. Empirical spectral amplifications show that the region-specific data achieve more accurate estimates of observed median short-period amplifications than the topographic slope method.

Dipping-interface Mapping Using Mode-separated Rayleigh Waves

Multichannel analysis of surface waves (MASW) method is a non-invasive geophysical technique that uses the dispersive characteristic of Rayleigh waves to estimate a vertical shear (S)-wave velocity profile. A pseudo-2D S-wave velocity section is constructed by aligning 1D S-wave velocity profiles at the midpoint of each receiver spread that are contoured using a spatial interpolation scheme. The horizontal resolution of the section is therefore most influenced by the receiver spread length and the source interval. Based on the assumption that a dipping-layer model can be regarded as stepped flat layers, high-resolution linear Radon transform (LRT) has been proposed to image Rayleigh-wave dispersive energy and separate modes of Rayleigh waves from a multichannel record. With the mode-separation technique, therefore, a dispersion curve that possesses satisfactory accuracy can be calculated using a pair of consecutive traces within a mode-separated shot gather. In this study, using synthetic models containing a dipping layer with a slope of 5, 10, 15, 20, or 30 degrees and a real-world example, we assess the ability of using high-resolution LRT to image and separate fundamental-mode Rayleigh waves from raw surface-wave data and accuracy of dispersion curves generated by a pair of consecutive traces within a mode-separated shot gather. Results of synthetic and real-world examples demonstrate that a dipping interface with a slope smaller than 15 degrees can be successfully mapped by separated fundamental waves using high-resolution LRT.

Spatial interpolation in wireless sensor networks: localized algorithms for variogram modeling and Kriging

Wireless sensor networks (WSNs) are rapidly emerging as the prominent technology for monitoring physical phenomena. However, large scale WSNs are known to suffer from coverage holes, i.e., large regions of deployment area where no sensing coverage can be provided. Such holes are the result of hardware failures, extensive costs for redeployment or the hostility of deployment areas. Coverage holes can adversely affect the accurate representation of natural phenomena that are monitored by a WSN. In this work, we propose to exploit the spatial correlation of physical phenomena to make monitoring systems more resilient to coverage holes. We show that a phenomenon can be interpolated inside a coverage hole with a high level of accuracy from the available nodal data given a model of its spatial correlation. However, due to energy limitations of sensor nodes it is imperative to perform this interpolation in an energy efficient manner that minimizes communication among nodes. In this paper, we present highly energy efficient methods for spatial interpolation in WSNs. First, we build a correlation model of the phenomenon being monitored in a distributed manner. Then, a purely localized and distributed spatial interpolation scheme based on Kriging interpolates the phenomenon inside coverage holes. We test the cost and accuracy of our scheme with extensive simulations and show that it is significantly more energy efficient than global interpolations and remarkably more accurate than simple averaging.

Generation of a pseudo-2D shear-wave velocity section by inversion of a series of 1D dispersion curves

Multichannel Analysis of Surface Waves utilizes a multichannel recording system to estimate near-surface shear (S)-wave velocities from high-frequency Rayleigh waves. A pseudo-2D S-wave velocity ( v S) section is constructed by aligning 1D models at the midpoint of each receiver spread and using a spatial interpolation scheme. The horizontal resolution of the section is therefore most influenced by the receiver spread length and the source interval. The receiver spread length sets the theoretical lower limit and any v S structure with its lateral dimension smaller than this length will not be properly resolved in the final v S section. A source interval smaller than the spread length will not improve the horizontal resolution because spatial smearing has already been introduced by the receiver spread. In this paper, we first analyze the horizontal resolution of a pair of synthetic traces. Resolution analysis shows that (1) a pair of traces with a smaller receiver spacing achieves higher horizontal resolution of inverted S-wave velocities but results in a larger relative error; (2) the relative error of the phase velocity at a high frequency is smaller than at a low frequency; and (3) a relative error of the inverted S-wave velocity is affected by the signal-to-noise ratio of data. These results provide us with a guideline to balance the trade-off between receiver spacing (horizontal resolution) and accuracy of the inverted S-wave velocity. We then present a scheme to generate a pseudo-2D S-wave velocity section with high horizontal resolution using multichannel records by inverting high-frequency surface-wave dispersion curves calculated through cross-correlation combined with a phase-shift scanning method. This method chooses only a pair of consecutive traces within a shot gather to calculate a dispersion curve. We finally invert surface-wave dispersion curves of synthetic and real-world data. Inversion results of both synthetic and real-world data demonstrate that inverting high-frequency surface-wave dispersion curves – by a pair of traces through cross-correlation with phase-shift scanning method and with the damped least-square method and the singular-value decomposition technique – can feasibly achieve a reliable pseudo-2D S-wave velocity section with relatively high horizontal resolution.

A New Spatial Interpolation Algorithm to Reduce the Matrix Fill Time in the Method of Moments Analysis of Planar Microstrip Structures

A new spatial interpolation scheme is proposed to reduce the matrix fill time in the method of moments implementation of planar microstrip structures. The approach is based on the division of the distance between the basis and the testing functions into three, namely near, intermediate and far regions. The matrix entries in the near region are computed directly. The entries corresponding to both intermediate and far regions are evaluated in two steps: (1) choosing an adequate number of sampling points in these regions and computing the associated entries directly and (2) interpolating the remaining entries by using cubic spline or bicubic spline algorithms. To demonstrate the efficiency and accuracy, the technique is applied to a planar microstrip low-pass filter and a microstrip-line fed patch antenna problems. It is shown that the interpolation scheme can result in significant savings with high accuracy.

Short-pulsed laser transport in absorbing and scattering media: time-based versus frequency-based approaches

Optical tomography (OT) is a promising non-intrusive characterization technique of absorbing and scattering media that uses transmitted and/or reflected signals of samples irradiated with visible or near-infrared light. The quality of OT techniques is directly related to the accuracy of their forward models due to the use of inversion algorithms. In this paper, forward models for transient OT approaches are investigated. The system under study involves a one-dimensional absorbing and scattering medium illuminated by a short laser pulse; this problem is solved using a discrete ordinates–finite volume (DO–FV) method in both time and frequency domain. Previous works have shown that time-domain approaches coupled with first order spatial interpolation schemes cannot represent the physics of the problem adequately as transmitted fluxes emerge before the minimal physical time required to leave the medium. In this work, the Van Leer and Superbee flux limiters, combined with the second order Lax–Wendroff scheme, are used in an attempt to prevent this. Results show that despite significant improvement, flux limiters fail to completely eliminate the physically unrealistic behaviour. On the other hand, results for transmittance obtained from the frequency-based method are accurate, without physically unrealistic behaviours at early time periods. The frequency-dependent approach is however computationally expensive, since it requires approximately five times more computational time than its temporal counterpart when used as a forward model for transient OT. On the other hand, the great advantages of the frequency-based approach is that limited windows of temporal signals can be calculated efficiently (in transient OT), and it can also be used as a forward model for steady-state, frequency-based and transient OT techniques.

Numerical predictions of short-pulsed laser transport in absorbing and scattering media. I—A time-based approach with flux limiters

A one-dimensional transient radiative transfer problem in the Cartesian coordinate system involving an absorbing and scattering medium illuminated by a short laser pulse has computationally been solved by use of a finite volume method (FVM). Previous works have shown that first order spatial interpolation schemes cannot represent the physics of the problem adequately as transmitted fluxes emerge before the minimal physical time required to leave the medium. In this paper, the Van Leer and Superbee flux limiters, combined with the second order Lax–Wendroff scheme, are used in an attempt to prevent this. Results presented in this work show that, despite significant improvement, flux limiters fail to completely eliminate the physically unrealistic behaviour. Therefore, a numerical approach into which temporal variables are transformed into frequency-dependent variables is presented in the companion paper to this work.

Multi-site precipitation downscaling via an expanded conditional density network

AbstractStatistical downscaling models are used to estimate weather data at a station or stations based on atmospheric circulation data defined at a coarser resolution, for example gridded outputs from a Global Climate Model (GCM). Downscaled data can be used as inputs to environmental models that require finer-scale climate fields than are currently available from GCMs. Maintaining realistic downscaling relationships between sites and variables is particularly important in hydrological models, as streamflow depends strongly on the spatial distribution of precipitation in a watershed and on interactions with temperature that determine whether precipitation falls as rain or snow. More generally, precipitation is a difficult variable to downscale because of its non-normal distribution and its spatial and temporal patchiness.A downscaling algorithm for daily precipitation series at multiple stations is presented. The expanded conditional density network (ECDN) models the conditional density of the Poisson-gamma distribution via an artificial neural network. ECDN is capable of (1) specifying the conditional distribution of precipitation at each site; (2) modeling occurrence and amount of precipitation simultaneously; (3) reproducing observed spatial relationships between sites; (4) randomly generating synthetic precipitation series; and (5) predicting precipitation amounts in excess of those in the observational record. The ECDN model is applied to two downscaling problems: the first is a benchmark precipitation downscaling task previously evaluated by other modeling groups; the second is a multi-site precipitation dataset from British Columbia, Canada. Results suggest that the ECDN approach is capable of generating spatially and temporally realistic precipitation series that are suitable for use as inputs to hydrological models or to spatial interpolation schemes.

Multi-site precipitation downscaling via an expanded conditional density network

Statistical downscaling models are used to estimate weather data at a station or stations based on atmospheric circulation data defined at a coarser resolution, for example gridded outputs from a Global Climate Model (GCM). Downscaled data can be used as inputs to environmental models that require finer-scale climate fields than are currently available from GCMs. Maintaining realistic downscaling relationships between sites and variables is particularly important in hydrological models, as streamflow depends strongly on the spatial distribution of precipitation in a watershed and on interactions with temperature that determine whether precipitation falls as rain or snow. More generally, precipitation is a difficult variable to downscale because of its non-normal distribution and its spatial and temporal patchiness.A downscaling algorithm for daily precipitation series at multiple stations is presented. The expanded conditional density network (ECDN) models the conditional density of the Poisson-gamma distribution via an artificial neural network. ECDN is capable of (1) specifying the conditional distribution of precipitation at each site; (2) modeling occurrence and amount of precipitation simultaneously; (3) reproducing observed spatial relationships between sites; (4) randomly generating synthetic precipitation series; and (5) predicting precipitation amounts in excess of those in the observational record. The ECDN model is applied to two downscaling problems: the first is a benchmark precipitation downscaling task previously evaluated by other modeling groups; the second is a multi-site precipitation dataset from British Columbia, Canada. Results suggest that the ECDN approach is capable of generating spatially and temporally realistic precipitation series that are suitable for use as inputs to hydrological models or to spatial interpolation schemes.

Equatorial spread F modeling: Multiple bifurcated structures, secondary instabilities, large density ‘bite‐outs,’ and supersonic flows

The Naval Research Laboratory has recently developed a new two‐dimensional code to study equatorial spread F (ESF): NRLESF2. The code uses an 8th order spatial interpolation scheme and the partial donor cell method. This allows the model to capture very sharp gradients over ∼ 4 grid cells and to assess the impact of numerical diffusion on the dynamics of ‘bubble’ evolution. Simulation results are presented that show new and complex ESF bubble dynamics: multiple bifurcations, secondary instabilities, density ‘bite‐outs’ of over three orders of magnitude, and supersonic flows within low density channels (V ≃ few km/s). These results are consistent with radar and satellite observations, as well as optical images. It is also shown that numerical diffusion can inhibit bubble bifurcation and the development of small‐scale structure.

On the prediction error variance of three common spatial interpolation schemes

Three forms of linear interpolation are routinely implemented in geographical information science, by interpolating between measurements made at the endpoints of a line, the vertices of a triangle, and the vertices of a rectangle (bilinear interpolation). Assuming the linear form of interpolation to be correct, we study the propagation of error when measurement error variances and covariances are known for the samples at the vertices of these geometric objects. We derive prediction error variances associated with interpolated values at generic points in the above objects, as well as expected (average) prediction error variances over random locations in these objects. We also place all the three variants of linear interpolation mentioned above within a geostatistical framework, and illustrate that they can be seen as particular cases of Universal Kriging (UK). We demonstrate that different definitions of measurement error in UK lead to different UK variants that, for particular expected profiles or surfaces (drift models), yield weights and predictions identical with the interpolation methods considered above, but produce fundamentally different (yet equally plausible from a pure data standpoint) prediction error variances.

Minimum temperature mapping over complex terrain by estimating cold air accumulation potential

Nocturnal cold air pools, which frequently form in complex terrain under anticyclonic systems, are a hazard to flowering buds of temperate fruit trees, but the spatial resolution to anticipate them exceeds the current weather forecast scale. To supplement the insufficient spatial resolution of official minimum temperature forecasts, a spatial interpolation scheme was developed by incorporating local geographic potential for cold air accumulation. Air temperature was measured at 10-min intervals at eight locations within a 2.1 km × 2.1 km hilly orchard area in South Korea from September 2002 to August 2003. Minimum temperature data for suspected radiative cooling nights were collected, and deviations from estimations by a conventional spatial interpolation were calculated. A digital elevation model with a 10 m cell size was used to calculate the cold air accumulation at eight locations. Zonal averages of the cold air accumulation were computed for each location by increasing the cell radius from 1 to 10. Temperature deviations were regressed to a common logarithm of the smoothed averages of cold air accumulation to derive a linear relationship between the local temperature deviation and the site topography. The highest coefficient of determination was found at a cell radius of 5, which corresponds to an approximately 1 ha boundary surrounding the point of interest. Nocturnal temperature profiles were observed and the inversion cap height was determined using a tethered balloon system. Empirical equations describing the potential effects of cold air accumulation and of the inversion profile on minimum temperature were combined with a conventional lapse rate-corrected inverse distance weighting interpolation scheme. This new interpolation scheme was successfully validated with an independent data set, showing a strong feasibility for development of a site-specific frost warning system for mountainous areas.

Statistical Estimation of Daily Maximum and Minimum Air Temperatures from MODIS LST Data over the State of Mississippi

Recent studies have shown that the Land Surface Temperature (LST) data measured by Moderate Resolution Imaging Spectro-Radiometer (MODIS) from both the Terra and Aqua platforms can be successfully used for linear regression estimates of daily maximum and minimum air temperatures at a local scale. Incorporation of these estimates into spatial interpolation schemes results in accuracy improvement of the surface air temperature, provided that the correlation coefficient (R) between the air temperature and LST is rather high. The purpose of this work was to examine the importance of pixel resolution (1.0 and 5.0 km2), satellite overpass time, season, land cover type, and the vegetation fraction (depending on the view zenith angle of the MODIS instrument) in controlling the observed level of R. The relative contribution of these factors in producing R variations has been assessed over the state of Mississippi during 2000-2004. Similarly, the sensitivity analysis of the difference between daily maximum and minimum air temperatures and LST to the same factors was performed. Results from these analyses have shown that R and the average difference between temperatures exhibited rather consistent variations depending on the above factors. The difference between maximum air temperature and LST increased linearly with the view angle (having typical range of 1-2°C for angle changes from 0° to ±65°) and remained constant or slightly decreased for daily air minimum temperatures. Both Terra and Aqua 1.0 km2 LST exhibited a small but persistent increase of R between the air temperature and LST as compared with that of using 5.0 km2 LST. Changing from Terra to Aqua LST did not alter significantly estimated values of R. This result suggested that the time difference between the moment of the satellite overpass and the time when maximum or minimum air temperature was observed was not critical for controlling the R value between the air temperature and LST at the involved spatial scales.

A GIS‐based agro‐ecological decision system based on gridded climatology

AbstractThe introduction of GIS has opened up new possibilities in combining different sources of geographical information. In Norway, an agro‐meteorological decision system is under development which combines gridded weather information with soil and crop development data. The system is based on a daily scale soil moisture model driven by meteorological inputs. Weather information is based on in‐situ observations, and spatial interpolation schemes are used to establish fine‐mesh grids of these variables over the model domain. These interpolation schemes take advantage of geographical co‐variables such as terrain information. The soil moisture model is used to estimate the soil water content, which is the determinant of soil suitability for tillage and sowing. The system also includes a phenological model for identification of suitable days when combine‐harvesting of cereals can be satisfactorily undertaken.Spatial interpolation of the meteorological elements is based upon all available in‐situ observations. The different elements are interpolated by different interpolation techniques. Snow depth, cloud cover, relative humidity and wind are in this first version, interpolated by using inverse distance weighting. Precipitation is determined by triangulation with elevation adjustment. Temperature is interpolated by using a residual kriging approach that includes five independent predictors in the trend equation. Evaporation is estimated by using the Penman2 formula based on the estimates of the meteorological elements.This approach is a good demonstration of the benefits of applying GIS and distributed geo‐data in cross‐disciplinary situations. The application is a valuable contribution to soil capability assessments. Copyright © 2005 Royal Meteorological Society.

Meta‐analysis of tropical surface temperatures during the Last Glacial Maximum

The magnitude of tropical cooling during the Last Glacial Maximum (LGM) has been the subject of uncertainty for over 25 years. We use principles of meta‐analysis as an objective approach to reconcile estimates from different proxies. This approach treats each observation as a random estimate of the true mean and weights estimates by their reported precision. We assigned global uncertainties to proxies and derived a new regional standard deviation for temperatures calculated from the Sr/Ca ratio in tropical corals (σ = 1.4°C). Using a Bayesian spatial interpolation scheme, we estimate a mean cooling of LGM tropical sea surface temperatures of −2.7 ±0.5°C (±σ) and surface air temperatures of −5.4 ±0.3°C (±σ).