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Spatial interpolation for real-time rainfall field estimation in areas with complex topography
Published in María Carolina Rogelis Prada, Operational Flood Forecasting, Warning and Response for Multi-Scale Flood Risks in Developing Cities, 2020
The geostatistical interpolation technique of Kriging groups different methods: Simple Kriging, Ordinary Kriging, Universal Kriging, Kriging with External Drift, Regression Kriging, Intrinsic Kriging etc, depending on the underlying model [Chiles and Delfiner, 1999]. The variogram is a key tool in Kriging methods to represent spatial structure by describing how the spatial continuity changes with distance and direction [Isaaks and Srivastava, 1989].
Spatial averages of in situ measurements versus remote sensing observations: a soil moisture analysis
Published in Journal of Spatial Science, 2022
Nilda Sanchez, Laura Almendra, Javier Plaza, Ángel González-Zamora, José Martínez-Fernández
Regression kriging models are a hybrid of ordinary least-squares regression and simple kriging. Among them, EBK (Krivoruchko 2012; Gribov and Krivoruchko , 2012) is an interpolating method based in the Bayesian rules that differs from classical kriging by accounting for the error using many semivariograms models estimated and applied iteratively from the data. With each repetition, the estimated semivariogram is used to simulate a new set of values at the input locations, which in turn allows new semivariogram estimations, together with their weights (Krivoruchko 2012). This procedure is especially suitable for extremely variable characteristics such as the soil moisture. In EBK interpolation, the explanatory variables improve the results. In the ArcGIS Geostatistical Analyst tool used for this EBK application, all explanatory variables must be supplied as rasters maps, and the regression kriging model is constructed by extracting their values for each input point. After several tests with the input data, an exponential semivariogram model was chosen, together with a logarithmic transformation, which is recommended when the dependent variable cannot be negative, such as soil moisture or rainfall measurements (Ly et al. 2011). Similarly to the other methods, the spatial resolution of the resulting maps was set to 20 × 20 km.
Spatial prediction based on Third Law of Geography
Published in Annals of GIS, 2018
A‐Xing Zhu, Guonian Lu, Jing Liu, Cheng‐Zhi Qin, Chenghu Zhou
The third method is regression Kriging (RK) which represents the combination of the statistical principle and the First Law of Geography. RK is a widely used technique for spatial prediction due to its ability to utilize both the spatial relationship and the covariate relationship(s) (Hengl, Heuvelink, and Stein 2004). In this case study, the regression component of RK was that constructed for the MLR method as described above. The regression residuals at the 10 sample points on the transect were then used to construct a semivariogram to describe the spatial autocorrelation of the residuals and used in the Kriging component (e.g. ordinary Kriging) of RK. The regression component and the Kriging component are added together as the final RK model (Hengl, Heuvelink, and Rossiter 2007). For this model both the SOM value and the error variance for each location were computed. The error variance was regarded as the prediction uncertainty at each location.
Estimation of VMT using heteroskedastic log-linear regression models
Published in Transportation Letters, 2023
Asif Mahmud, Ian Hamilton, Vikash V. Gayah, Richard J. Porter
Several forecasting methods have been proposed in the literature that make use of previous VMT estimates to predict future VMT values. Trend analysis, regression models, and machine learning (ML) models have been some of the most widely used forecasting methods in the literature. Trend or time-series analyses use historic traffic count data to forecast change in VMT (either growth or decline) in the future based only on previous VMT values in the study area. At the simplest level, VMT can be assumed to grow or decline at a constant rate annually. However, regression-based methods incorporate other data sources (in addition to previous VMT values) to provide insight into the relationship between VMT and other external factors. Regression models are extremely common in the literature and have been used to establish relationships between either AADT, VMT, or the change in VMT and various explanatory variables. VMT has been found to depend on a wide range of variables including age, gender, mode of travel, trip purpose, occupation, and income (Weerasekera and Amarasingha 2017) and regression methods can accommodate these relationships. As an example, Kweon and Kockelman (2004) developed a non-parametric regression method using data on vehicle ownership, household-level information, area type, and public transit availability. Kim et al. (2016) implemented a regression kriging method – a combination of linear regression and kriging – to estimate VMT in urban areas. Musunuru, Wei, and Porter (2017) developed kriging interpolation techniques to estimate traffic volume (or AADT) on rural two-lane highway locations. Musunuru and Porter (2019) developed a regression-based correction strategy to investigate the impact of measurement error, resulting from the extrapolation of short-term traffic count to estimate AADT. Several studies applied regression methods to first estimate AADTs on different roadways and then subsequently used these AADT estimates to estimate VMT. Most of these developed multiple regression models using socioeconomic data, demographic data, household data, education, and employment data to estimate AADT (Mohamad et al. 1998; Neveu 1983; Zhao and Chung 2001). Wang, Bai, and Bao (2011) used regression to analyze the relationship between the number of households and the total AADT at the entrances of associated communities.