The Role of External Variables and GIS Databases in Geostatistical Analysis

Although many geostatistical studies only study a measured attribute in relation to its spatial coordinates, this paper argues that other layers in the GIS database can be of additional use for spatial prediction purposes. They may enter the prediction equations as predictors in a regression model, or as correlated measurements. In an example we will show how this is done for predicting PCB138, a sediment pollution variable, over the North Sea floor. Issues of exploratory data analysis, required sample size, sample configuration, local versus global neighbourhoods, non‐stationarity, non‐linear transformations, change of support and conditional simulation will be discussed in the light of this example.     

Agricultural land use dynamics in the Brazilian Amazon based on remote sensing and census data

The potential impact of deforestation in the Brazilian Amazon on greenhouse gas emissions to the atmosphere calls for policies that take account of changes in forest cover. Although much research has focused on the location and effects of deforestation, little is known about the distribution and reasons for the agricultural uses that replace forest cover. We used Landsat TM-based deforestation and agricultural census data to generate maps of the distribution and proportion of four major agricultural land uses throughout the Brazilian Amazon in 1997 and 2007. We built linear and spatial regression models to assess the determinant factors of deforestation and those major agricultural land uses - pasture, temporary agriculture and permanent agriculture - for the states of Pará, Rondônia, and Mato Grosso. The data include 30 determinant factors that were grouped into two years (1996 and 2006) and in four categories: accessibility to markets, public policies, agrarian structure, and environment. We found an overall expansion of the total agricultural area between 1997 and 2007, and notable differences between the states of Pará, Rondônia, and Mato Grosso in land use changes during this period. Regression models for deforestation and pasture indicated that determinant factors such as distance to roads were more influential in 1997 than in 2007. The number of settled families played an important role in the deforestation and pasture, the effect was stronger in 2007 than 1997. Indigenous lands were significant in preventing deforestation in high-pressure areas in 2007. For temporary and permanent agricultures, our results show that in 1997 the effect of small farms was stronger than in 2007. The mapped land use time series and the models explain empirically the effects of land use changes across the region over one decade.     

Plume Tracking with a Mobile Sensor Based on Incomplete and Imprecise Information

Mobile in‐situ sensor platforms such as Unmanned Aerial Vehicles can be used in environmental monitoring. In time‐critical monitoring scenarios as for example in emergency response, and in the exploration of highly dynamic phenomena, obtaining the relevant data with one or few mobile sensors is challenging. It requires an intelligent sampling strategy that integrates prior information and adapts to the dynamics of the observed phenomenon, based on the collected sensor data. Available information about the observed phenomenon may be incomplete or imprecise and therefore insufficient for quantitative modeling. We address this problem by reasoning about the plume movement and size on a qualitative level and present an algorithm for tracking a dynamic plume that integrates this qualitative information with the collected sensor data. We evaluate our algorithm using simulated data sets of three different moving and expanding gas plumes. By means of simulations we show that the qualitative methods can be used to infer new information about the properties of a moving plume and to adapt the sensor movement for tracking the plume. Both can be done with low computational effort, without absolute positioning capability of the sensor, and with less input information than required by quantitative approaches.     

Spatio-temporal prediction of daily temperatures using time-series of MODIS LST images

A computational framework to generate daily temperature maps using time-series of publicly available MODIS MOD11A2 product Land Surface Temperature (LST) images (1 km resolution; 8-day composites) is illustrated using temperature measurements from the national network of meteorological stations (159) in Croatia. The input data set contains 57,282 ground measurements of daily temperature for the year 2008. Temperature was modeled as a function of latitude, longitude, distance from the sea, elevation, time, insolation, and the MODIS LST images. The original rasters were first converted to principal components to reduce noise and filter missing pixels in the LST images. The residual were next analyzed for spatio-temporal auto-correlation; sum-metric separable variograms were fitted to account for zonal and geometric space-time anisotropy. The final predictions were generated for time-slices of a 3D space-time cube, constructed in the R environment for statistical computing. The results show that the space-time regression model can explain a significant part of the variation in station-data (84%). MODIS LST 8-day (cloud-free) images are unbiased estimator of the daily temperature, but with relatively low precision (±4.1°C); however their added value is that they systematically improve detection of local changes in land surface temperature due to local meteorological conditions and/or active heat sources (urban areas, land cover classes). The results of 10–fold cross-validation show that use of spatio-temporal regression-kriging and incorporation of time-series of remote sensing images leads to significantly more accurate maps of temperature than if plain spatial techniques were used. The average (global) accuracy of mapping temperature was ±2.4°C. The regression-kriging explained 91% of variability in daily temperatures, compared to 44% for ordinary kriging. Further software advancement—interactive space-time variogram exploration and automated retrieval, resampling and filtering of MODIS images—are anticipated.     

Error analysis for the evaluation of model performance: rainfall–runoff event time series data

This paper provides a procedure for evaluating model performance where model predictions and observations are given as time series data. The procedure focuses on the analysis of error time series by graphing them, summarizing them, and predicting their variability through available information (recalibration). We analysed two rainfall–runoff events from the R‐5 data set, and evaluated 12 distinct model simulation scenarios for these events, of which 10 were conducted with the quasi‐physically‐based rainfall–runoff model (QPBRRM) and two with the integrated hydrology model (InHM). The QPBRRM simulation scenarios differ in their representation of saturated hydraulic conductivity. Two InHM simulation scenarios differ with respect to the inclusion of the roads at R‐5. The two models, QPBRRM and InHM, differ strongly in the complexity and number of processes included. For all model simulations we found that errors could be predicted fairly well to very well, based on model output, or based on smooth functions of lagged rainfall data. The errors remaining after recalibration are much more alike in terms of variability than those without recalibration. In this paper, recalibration is not meant to fix models, but merely as a diagnostic tool that exhibits the magnitude and direction of model errors and indicates whether these model errors are related to model inputs such as rainfall. Copyright © 2004 John Wiley & Sons, Ltd.     

Error analysis for the evaluation of model performance: rainfall–runoff event summary variables

This paper provides a procedure for the evaluation of model performance for rainfall–runoff event summary variables, such as total discharge or peak runoff. The procedure is based on the analysis of model errors, defined as the differences between observed values and values predicted by a simulation model. Model errors can (i) indicate whether and where the model can be improved, (ii) be used to measure the performance of a model, and (iii) be used to compare model simulations. In this paper, both statistical and graphical methods are used to characterize model errors. We explore model recalibration by relating model errors to the model predictions, and to external, independent variables. The R‐5 catchment data sets that we used in this study include summary variables for 72 rainfall–runoff events. The simulations used in this study were previously conducted with the quasi‐physically based rainfall–runoff model QPBRRM for 11 different characterizations of the R‐5 catchment, each with increasing information or a refined spatial discretization of the overland flow planes. This paper is about proposing model diagnostics and not about procedures for using diagnostics for model modification. Copyright © 2007 John Wiley & Sons, Ltd.     

The GRASS GIS temporal framework

The availability of continental and global-scale spatio-temporal geographical data sets and the requirement to efficiently process, analyse and manage them led to the development of the temporally enabled Geographic Resources Analysis Support System (GRASS GIS). We present the temporal framework that extends GRASS GIS with spatio-temporal capabilities. The framework provides comprehensive functionality to implement a full-featured temporal geographic information system (GIS) based on a combined field and object-based approach. A significantly improved snapshot approach is used to manage spatial fields of raster, three-dimensional raster and vector type in time. The resulting timestamped spatial fields are organised in spatio-temporal fields referred to as space-time data sets. Both types of fields are handled as objects in our framework. The spatio-temporal extent of the objects and related metadata is stored in relational databases, thus providing additional functionalities to perform SQL-based analysis. We present our combined field and object-based approach in detail and show the management, analysis and processing of spatio-temporal data sets with complex spatio-temporal topologies. A key feature is the hierarchical processing of spatio-temporal data ranging from topological analysis of spatio-temporal fields over boolean operations on spatio-temporal extents, to single pixel, voxel and vector feature access. The linear scalability of our approach is demonstrated by handling up to 1,000,000 raster layers in a single space-time data set. We provide several code examples to show the capabilities of the GRASS GIS Temporal Framework and present the spatio-temporal intersection of trajectory data which demonstrates the object-based ability of our framework.     

Using geostatistical simulation to disaggregate air quality model results for individual exposure estimation on GPS tracks

In this work, we address the mismatch in spatio-temporal resolution between individual, point-location based exposure and grid cell based air quality model predictions by disaggregating the grid model results. Variability of PM₁₀ point measurements was modelled within each grid cell by the exponential variogram, using point support concentration measurements. Variogram parameters were estimated over the study area globally using constant estimates, and locally by multiple regression models using traffic, weather and land use data. Model predictions of spatio-temporal variability were used for geostatistical unconditional simulation, estimating the deviation of point values from grid cell averages on GPS tracks. The distribution of deviations can be used as an estimate of uncertainty for individual exposure. Results showed a relevant impact of the disaggregation uncertainties compared to other uncertainty sources, dependent of the model used for spatio-temporal variability. Depending on individual behaviour and variability of the pollutant, these uncertainties average out again over time.     

Assessment of the prediction error in a large-scale application of a dynamic soil acidification model

 The prediction error of a relatively simple soil acidification model (SMART2) was assessed before and after calibration, focussing on the Al and NO₃ concentrations on a block scale. Although SMART2 is especially developed for application on a national to European scale, it still runs at a point support. A 5×5 km² grid was used for application on the European scale. Block characteristic values were obtained simply by taking the median value of the point support values within the corresponding grid cell. In order to increase confidence in model predictions on large spatial scales, the model was calibrated and validated for the Netherlands, using a resolution that is feasible for Europe as a whole. Because observations are available only at the point support, it was necessary to transfer them to the block support of the model results. For this purpose, about 250 point observations of soil solution concentrations in forest soils were upscaled to a 5×5 km² grid map, using multiple linear regression analysis combined with block kriging. The resulting map with upscaled observations was used for both validation and calibration. A comparison of the map with model predictions using nominal parameter values and the map with the upscaled observations showed that the model overestimated the predicted Al and NO₃ concentrations. The nominal model results were still in the 95% confidence interval of the upscaled observations, but calibration improved the model predictions and strongly reduced the model error. However, the model error after calibration remains rather large.