Ising Model for Interpolation of Spatial Data on Regular Grids

We apply the Ising model with nearest-neighbor correlations (INNC) in the problem of interpolation of spatially correlated data on regular grids. The correlations are captured by short-range interactions between “Ising spins”. The INNC algorithm can be used with label data (classification) as well as discrete and continuous real-valued data (regression). In the regression problem, INNC approximates continuous variables by means of a user-specified number of classes. INNC predicts the class identity at unmeasured points by using the Monte Carlo simulation conditioned on the observed data (partial sample). The algorithm locally respects the sample values and globally aims to minimize the deviation between an energy measure of the partial sample and that of the entire grid. INNC is non-parametric and, thus, is suitable for non-Gaussian data. The method is found to be very competitive with respect to interpolation accuracy and computational efficiency compared to some standard methods. Thus, this method provides a useful tool for filling gaps in gridded data such as satellite images.

It rains and then? Numerical challenges with the 1D Richards equation in kilometer-resolution land surface modelling

Over the last decade kilometer-scale weather predictions and climate projections have become established. Thereby both the representation of atmospheric processes, as well as land-surface processes need adaptions to the higher-resolution. Soil moisture is a critical variable for determining the exchange of water and energy between the atmosphere and the land surface on hourly to seasonal time scales, and a poor representation of soil processes will eventually feed back on the simulation quality of the atmosphere. Especially the partitioning between infiltration and surface runoff will feed back on the hydrological cycle. Several aspects of the coupled system are affected by a shift to kilometer-scale, convection-permitting models. First of all, the precipitation-intensity distribution changes to more intense events. Second, the time-step of the numerical integration becomes smaller. The aim of this study is to investigate the numerical convergence of the one-dimensional Richards Equation with respect to the soil hydraulic model, vertical layer thickness and time-step during the infiltration process. Both regular and non-regular (unequally spaced) grids typical in land surface modelling are considered, using a conventional semi-implicit vertical discretization. For regular grids, results from a highly idealized experiment on the infiltration process show poor numerical convergence for layer thicknesses larger than approximately 5 cm and for time steps greater than 40 s, irrespective of the soil hydraulic model. The velocity of the wetting front decreases systematically with increasing time step and decreasing vertical resolution. For non-regular grids, a new discretization based on a coordinate transform is introduced. In contrast to simpler vertical discretizations, it is able to represent the solution second-order accurate. The results for non-regular grids are qualitatively similar, as a fast increase in layer thickness with depth is equivalent to a lower vertical resolution. It is argued that the sharp gradients in soil moisture around the propagating wetting front must be resolved properly in order to achieve an acceptable numerical convergence of the Richards Equation. Furthermore, it is shown that the observed poor numerical convergence translates directly into a poor convergence of infiltration-runoff partitioning for precipitation time series characteristic of weather and climate models. As a consequence, soil simulations with low resolution in space and time may produce almost twice the amount of surface runoff within 24 hours than their high-resolution counterparts. Our analysis indicates that the problem is particularly pronounced for kilometer-resolution models.

City-Scale Mapping of Urban Façade Color Using Street-View Imagery

Precise urban façade color is the foundation of urban color planning. Nevertheless, existing research on urban colors usually relies on manual sampling due to technical limitations, which brings challenges for evaluating urban façade color with the co-existence of city-scale and fine-grained resolution. In this study, we propose a deep learning-based approach for mapping the urban façade color using street-view imagery. The dominant color of the urban façade (DCUF) is adopted as an indicator to describe the urban façade color. A case study in Shenzhen was conducted to measure the urban façade color using Baidu Street View (BSV) panoramas, with city-scale mapping of the urban façade color in both irregular geographical units and regular grids. Shenzhen’s urban façade color has a gray tone with low chroma. The results demonstrate that the proposed method has a high level of accuracy for the extraction of the urban façade color. In short, this study contributes to the development of urban color planning by efficiently analyzing the urban façade color with higher levels of validity across city-scale areas. Insights into the mapping of the urban façade color from the humanistic perspective could facilitate higher quality urban space planning and design.

Mesh-free radial-basis function-generated finite differences and its application in reverse-time migration

Compared with one-way wave equation migration and ray-based migration, reverse time migration (RTM) using the two-way wave propagation information can produce accurate imaging result for complex structures. Its computational accuracy and efficiency are mainly determined by numerical method for wavefield simulation. When using traditional regular grids for seismic modeling, scattering artifacts may occur due to the stepped approximation of layer interfaces and rugged topography. On the other hand, the irregular grids requires complex grid generation algorithm, despite having certain geometric flexibility. Mesh-free RTM can effectively reduce the scattered noise under regular grids and avoid the extra computation in the process of irregular grids generation. For the implementation of mesh-free RTM method, an algorithm with fast generation of node distributions is used to discretize the underground velocity model, and radial-basis function generated finite-difference (RBF-FD) is used to realize the numerical simulation of wave propagation, cross-correlation imaging condition is adopted for imaging. The mesh-free RTM method which has both flexibility of simulation region and abundance of wavefield information, reduces the storage required for reverse time migration, shows the potential of high-accuracy migration in the case of undulating surface and provides more accurate migration imaging results for oil and gas exploration under complex geological conditions.