A new Bayesian hierarchical geostatistical model based on two spatial fields with case studies with short records of annual runoff in Norway

2020 ◽  
Author(s):  
Ingelin Steinsland ◽  
Thea Roksvåg ◽  
Kolbjørn Engeland
Keyword(s):  
Missing Values ◽  
Interpolation Method ◽  
Gaussian Random Fields ◽  
Annual Runoff ◽  
Kriging Interpolation ◽  
Linear Regression Method ◽  
Geostatistical Model ◽  
Model Framework ◽  
Kriging Interpolation Method ◽  
Over Time

<p>We present a new Bayesian geostatistical hierarchical model that is particularly suitable for interpolation of hydrological data when the available dataset has short records, for including overlapping catchments consistently and for combining areal (runoff) and point (precipitation) observations. A key feature of the proposed framework is that several years of runoff are modeled simultaneously with two Gaussian random fields (GRFs): One that is common for all years under study and represents the runoff generation due to long-term climatic conditions, and one that is year specific. The framework is demonstrated by filling in missing values of annual runoff and by predicting mean annual runoff for about 200 catchments in Norway. The predictive performance is compared to Top-Kriging (interpolation method) and simple linear regression (method for exploiting short records). The results show that if the runoff is driven by weather patterns that are repeated over time, the value of including short records is large, and that we for partially gauged catchments perform better than comparable methods for both annual spatial interpolation and mean annual runoff. We also find that short records, even of length one year, can safely be included in the model.</p><p>In a smaller case study of ten years of annual runoff in Voss in Norway it is demonstrated that by combining runoff and precipitation data in the model framework that includes consistently modelling of overlapping catchments on average preforms better compared to using only one of the data sources. Further, the interaction between nested areal data and point data gives a geostatistical model that takes us beyond smoothing: The model can give predictions that are higher (or lower) than any of the observations.</p><p>A finding is that in Norway the climatic effects dominates over annual effects for annual runoff. Through a simulation study we demonstrate that in this case systematic under- and overestimation of runoff over time can be expected. On the other hand, a strong climate implies that short records of runoff from an otherwise ungauged catchment can lead to large improvements in the predictability of runoff.</p>

scholarly journals A geostatistical framework for estimating flow indices by exploiting short records and long-term spatial averages – Application to annual and monthly runoff

2019 ◽  
Author(s):  
Thea Roksvåg ◽  
Ingelin Steinsland ◽  
Kolbjørn Engeland
Keyword(s):  
Missing Values ◽  
Interpolation Method ◽  
Gaussian Random Fields ◽  
Climatic Conditions ◽  
Kriging Interpolation ◽  
Linear Regression Method ◽  
Runoff Generation ◽  
Kriging Interpolation Method ◽  
Monthly Runoff

Abstract. In this article, we present a Bayesian geostatistical framework that is particularly suitable for interpolation of hydrological data when the available dataset is sparse and includes missing values and short records of data. A key feature of the proposed framework is that several years of runoff is modeled simultaneously with two Gaussian random fields (GRFs): One that is common for all years under study and represents the runoff generation due to long-term climatic conditions, and one that is year specific. The climatic GRF learns how short records of runoff from partially gauged catchments vary relatively to longer time series from other catchments, and transfers this information across years. Another property, is that the model takes the nested structure of catchments into account such that the water balance is preserved for any point in the landscape. The framework is demonstrated by interpolation of annual and monthly runoff from around 200 catchments in Norway, and we compare it to Top-Kriging (interpolation method) and simple linear regression (method for exploiting short records). The results show that if the correlation between neighboring catchments is high, a model that considers several years of runoff simultaneously is considerably better at capturing large spatial variability than a model that treats each year of data separately.

scholarly journals Estimation of annual runoff by exploiting long-term spatial patterns and short records within a geostatistical framework

2020 ◽  
Vol 24 (8) ◽  
pp. 4109-4133
Author(s):  
Thea Roksvåg ◽  
Ingelin Steinsland ◽  
Kolbjørn Engeland
Keyword(s):  
Missing Values ◽  
Mean Squared Error ◽  
Interpolation Method ◽  
Predictive Performance ◽  
Annual Runoff ◽  
Climatic Conditions ◽  
Kriging Interpolation ◽  
Runoff Generation ◽  
Kriging Interpolation Method

Abstract. In this article, we present a Bayesian geostatistical framework that is particularly suitable for interpolation of hydrological data when the available dataset is sparse and includes both long and short records of runoff. A key feature of the proposed framework is that several years of runoff are modelled simultaneously with two spatial fields: one that is common for all years under study that represents the runoff generation due to long-term (climatic) conditions and one that is year-specific. The climatic spatial field captures how short records of runoff from partially gauged catchments vary relative to longer time series from other catchments, and transfers this information across years. To make the Bayesian model computationally feasible and fast, we use integrated nested Laplace approximations (INLAs) and the stochastic partial differential equation (SPDE) approach to spatial modelling. The geostatistical framework is demonstrated by filling in missing values of annual runoff and by predicting mean annual runoff for around 200 catchments in Norway. The predictive performance is compared to top-kriging (interpolation method) and simple linear regression (record augmentation method). The results show that if the runoff is driven by processes that are repeated over time (e.g. orographic precipitation patterns), the value of including short records in the suggested model is large. For partially gauged catchments the suggested framework performs better than comparable methods, and one annual observation from the target catchment can lead to a 50 % reduction in root mean squared error (RMSE) compared to when no observations are available from the target catchment. We also find that short records safely can be included in the framework regardless of the spatial characteristics of the underlying climate, and down to record lengths of 1 year.

Numerical Investigation of the Identifiability of Elastomer Mechanical Properties by Nano-Indentation and Shape-Manifold Approach

2021 ◽  
Author(s):  
Oumaima Ezzaamari ◽  
Guénhaël Le Quilliec ◽  
Florian Lacroix ◽  
Stéphane Méo
Keyword(s):  
Numerical Study ◽  
Interpolation Method ◽  
Structural Characteristics ◽  
Numerical Approach ◽  
Kriging Interpolation ◽  
Nano Indentation ◽  
Kriging Interpolation Method ◽  
Elastomeric Materials ◽  
Hyper Elastic ◽  
Characterization Test

ABSTRACT Various research is covering instrumented nano-indentation in the literature. However, studies on this characterization test remain limited when it comes to the local mechanical behavior of elastomeric materials. The application of nano-indentation on these materials is a difficult task given their complex mechanical and structural characteristics. We try to overcome these experimental limitations and find an effective numerical approach for local mechanical characterization of hyper-elastic materials. For such needs, we carried out a numerical study based on model reduction and shape manifold approach to investigate the parameters identification of different hyper-elastic constitutive laws by using instrumented indentation. Similarly, we studied the influence of the indenter geometry, the friction coefficient variation, and finally the indented material height effect. To this end, we constructed a reduced order model through a design of experiments by proper orthogonal decomposition combined with the kriging interpolation method.

scholarly journals Estimation of Ice Thickness and the Features of Subglacial Media Detected by Ground Penetrating Radar at the Baishui River Glacier No. 1 in Mt. Yulong, China

2020 ◽  
Vol 12 (24) ◽  
pp. 4105
Author(s):  
Jing Liu ◽  
Shijin Wang ◽  
Yuanqing He ◽  
Yuqiang Li ◽  
Yuzhe Wang ◽  
...  
Keyword(s):  
Ground Penetrating Radar ◽  
Interpolation Method ◽  
Kriging Interpolation ◽  
Ice Thickness ◽  
Grid Data ◽  
Differential Gps ◽  
Landsat Images ◽  
Kriging Interpolation Method ◽  
Bedrock Surface ◽  
Ground Penetrating

Using ground-penetrating radar (GPR), we measured and estimated the ice thickness of the Baishui River Glacier No. 1 of Yulong Snow Mountain. According to the position of the reflected media from the GPR image, combined with the radar waveform amplitude and polarity change information, the ice thickness and the changing medium position at the bottom of this temperate glacier were identified. Water paths were found in the measured ice, including ice caves and crevasses. A debris-rich ice layer was found at the bottom of the glacier, which produces strong abrasion and ploughing action at the bedrock surface. This results in the formation of different detrital layers stagnated at the ice-bedrock interface and numerous crevasses on the bedrock surface. Based on the obtained ice thickness and differential GPS data, combined with Landsat images, the kriging interpolation method was used to obtain grid data. The average ice thickness was 52.48 m and between 4740 and 4890 m above sea level, with a maximum depth of 92.83 m. The bedrock topography map of this area was drawn using digital elevation model from the Shuttle Radar Topography Mission. The central part of the glacier was characterized by small ice basins with distributed ice steps and ice ridges at the upper and lower parts.

Numerical Modeling of Fracture Process Using Element-Free Method

2013 ◽  
Vol 427-429 ◽  
pp. 146-149
Author(s):  
Cheng Fan
Keyword(s):  
Interpolation Method ◽  
Kriging Interpolation ◽  
Computational Accuracy ◽  
Simple Method ◽  
Solution Domain ◽  
Kriging Interpolation Method ◽  
Finite Covers ◽  
Crack Problems ◽  
Cover Systems ◽  
Element Free

A new element-free formulation of Kriging interpolation procedure based on finite covers technique and Kriging interpolation method which integrates the flexibilities of the manifold method in dealing with discontinuity and the element-free features of the moving Kriging interpolation. Two cover systems are employed in this method. Mathematical cover of the solution domain under consideration are used to construct shape function and physical cover is used to reproduce the geometry of the solution domain. The mathematical covers can take any types of shape and is much easily formed compared with those in the conventional MM. The presented method can overcome some difficulties in conventional element-free Galerkin methods in treating discontinuous crack problems. The fundamental theory of this procedure is illustrated and numerical analyses of examples show that the proposed procedure is an effective and simple method with higher computational accuracy.

Integration of statistical and spatial methods for distributing precipitation in tropical areas

2012 ◽  
Vol 44 (6) ◽  
pp. 982-994 ◽  
Author(s):  
Mandana Abedini ◽  
Md Azlin Md Said ◽  
Fauziah Ahmad
Keyword(s):  
Multivariate Regression ◽  
Interpolation Method ◽  
Rainfall Data ◽  
Environmental Research ◽  
Kriging Interpolation ◽  
Slope Aspect ◽  
Annual Average ◽  
Rain Gauges ◽  
Kriging Interpolation Method ◽  
Topographical Factors

The high spatial resolution of precipitation distribution is a major concern for experts in environmental research and planning. This paper establishes a combination of multivariate regression algorithm and spatial analysis to predict distribution of precipitation, considering the four topographical factors of altitude, slope, aspect and location. Annual average and seasonal rainfall data were collected in nine rain gauges in Ulu Kinta Catchment in East Malaysia from 1974 to 2010. To examine records and fill gaps from long-term rain gauges, homogeneity analysis was performed using the double-mass curve method. Estimated missing rainfall data were also tested using index gauges from network rainfall stations. Multivariate regression analysis was conducted to propose an empirical equation for the study area. Topographical factors were considered from a 90 m resolution digital elevation model. The multivariate regression model was found to clarify 74% of spatial variability of precipitation on annual average and 78% during wet season. However, the correlation coefficient for the dry season decreased sharply to 63%. By using the kriging interpolation method, the estimated annual average improved to 78.4%; the average improved to 65.2 and 80.3% in the dry and wet seasons, respectively. This confirms the efficiency and significance of the model and its potential for use in other tropical catchments.

Sign in / Sign up

Export Citation Format

Share Document