Visualization of Big Spatial Data using Coresets for Kernel Density Estimates

The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for subsampling of spatial data suitable for creating kernel density estimates from very large data and demonstrate that it results in less error than random sampling. We also introduce a method to ensure that thresholding of low values based on sampled data does not omit any regions above the desired threshold when working with sampled data. We demonstrate the effectiveness of our approach using both, artificial and real-world large geospatial datasets

Spatial modeling of extreme snow depth

The spatial modeling of extreme snow is important for adequate risk management in Alpine and high altitude countries. A natural approach to such modeling is through the theory of max-stable processes, an infinite-dimensional extension of multivariate extreme value theory. In this paper we describe the application of such processes in modeling the spatial dependence of extreme snow depth in Switzerland, based on data for the winters 1966--2008 at 101 stations. The models we propose rely on a climate transformation that allows us to account for the presence of climate regions and for directional effects, resulting from synoptic weather patterns. Estimation is performed through pairwise likelihood inference and the models are compared using penalized likelihood criteria. The max-stable models provide a much better fit to the joint behavior of the extremes than do independence or full dependence models.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS464 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Data assimilation of in situ soil moisture measurements in hydrological models: third annual doctoral progress report, work plan and achievements

Efficient water utilization and optimal water supply/distribution to increase food and fodder productivity are of utmost importance in confronting worldwide water scarcity, climate change, growing populations and increasing water demands. In this respect, irrigation efficiency, which is influenced by the type of irrigation and irrigation scheduling, is an essential issue for achieving higher productivity. To improve irrigation strategies in precision agriculture, soil water status can be more accurately described using a combination of advanced monitoring and modeling. Our study focuses on the combination of high resolution hydrological data with hydrological models that predict water flow and solute (pollutants and salts) transport and water redistribution in agricultural soils under irrigation. Field plots of a potato farmer in a sandy region in Belgium were instrumented to continuously monitor soil moisture and water potential before, during and after irrigation in dry summer periods. The aim is to optimize the irrigation process by assimilating online sensor field data into process based models. This research is part of Activity 305 ‘Precision agriculture and remote sensing’ of the VITO GWO and is also part of the strategic cooperation with UGent within the platform ‘Managing Natural Resources’. Over the past 2 years, we applied a combination of in-situ monitoring and numerical modeling -Hydrus 1D- to estimate water content fluctuations in a heterogeneous sandy grassland soil under irrigation with water table fluctuating between 80 and 155 cm. Over the last year, more sampling and analyses were carried out to further characterize the hydraulic properties over the entire field. Modeling results for the field demonstrated clearly the profound effect of the position of the GWL, and to a lesser extent, the effect of spatially variable soil hydraulic properties (Ks, n and α) on the estimated water content in the sandy two-layered soil under grass. Our results show that currently applied uniform water distribution using sprinkler irrigation seems not to be efficient since at locations with shallow groundwater, the amount of water applied will be excessive as compared to the plant requirements while in locations with a deeper GWL, requirements will not be met. To derive the optimal parameter set best describing the measured soil moisture content, 37 optimization scenarios were conducted with two to six parameters using various parameter combinations for the two soil layers. The best performing parameter optimization scenario was a 2-parameter scenario with Ks optimized for each layer. The results showed a better identifiability of the parameters (less correlations among parameters) with equal performance as compared to three, four or six parameter optimization. Model predictions using the calibrated model (with data from 2012) for an independent data set of soil moisture data in the validation period (2013) showed satisfactory performance of the model in view of irrigation management purposes. Comparing the degree of water stress for different optimization scenarios of groundwater depth, showed that grass was exposed to water stress in summer in 2013 but not for such a long period as compared to the 2012 growing season. The degree of water stress simulated with Hydrus 1D suggested to increase the irrigation amount in 2012 and 2013 and at least one or two times in the summer (June and July) and further distributing the amount of irrigation during the growing season, instead of using a huge amount of irrigation later in the season, as is common practice by the farmer. A second part of the study focused on finding a relation between measured soil hydraulic properties and apparent electrical conductivity ECa. Our measurements of hydraulic properties of the field clearly confirm that there is considerable spatial variability in the field and that this has an impact on the simulation of soil moisture content. Therefore this should be taken into account when upscaling soil hydraulic properties to the field scale in order to in understand and model flow, solute and energy fluxes in the field and develop strategies for efficient irrigation. Upscaling soil hydraulic properties to the field scale can be done by linking them to apparent electrical conductivity (ECa), which can be measured efficiently and inexpensively so a spatially dense dataset for describing within-field spatial soil variability can be generated. In this study relations between the spatial variation of soil hydraulic properties and apparent soil electrical conductivity ECa measured with EM38 and DUALEM-21S sensors at two depths of explorations (DOE) 0-50 and 0-100 cm were investigated. Two predictive modelling approaches, i.e. i) a simple regression and ii) applying Archie’s laws for saturated and unsaturated conditions in combination with MVG equations, were developed and it was compared how they were able to explain the observed values of hydraulic parameters. Results demonstrated the spatial variability and heterogeneity of ECa and soil hydraulic properties Ks, α and n. We derived a regression relationship between log Ks and ECa measured with DUALEM (r2≥0.70) and with EM38 (r2>0.46) sensors. The predicted results were tested vs measured data and confirmed that the performance of DUALEMp,100-Ks model is relatively better than that of the same sensor with lower DOE and of the EM38 sensor (RMSE = 1.31 cmh-1, R2 = 0.55). The relationships between MVG shape parameters and ECa datasets were generally poor (0.05<R2<0.26). In the second approach, we showed that the water retention curve can be translated to ECa-(h) and ECa-Se relations by combining the MVG equations and Archie’s law. Results also show that reformulating the MVG equations based on ECa-Se relationships can help to estimate unsaturated hydraulic conductivity at the field scale. In the third year, a second study site has been set up in a nearby field where potatoes are grown and has been instrumented with soil moisture sensors, tensiometers, groundwater level loggers and a weather station. Field hydraulic properties for the field will be derived using the equations developed for the first study site and the modeling approach developed for the first field will be tested here. Also quasi 3D-modelling of water flow at the field scale will be conducted. In this modeling set-up, the field will be modeled as a collection of 1D-columns representing the different field conditions (combination of soil properties, GWL, root zone depth). Combining this model with crop based models such as LINGRA-N or Aquacrop gives a direct simulation of the impact of irrigation strategies on crop yield at the field scale