Near real-time water vapor distribution surface rendering using Ordinary KrigingThis article is one of a series of papers published in this Special Issue on the theme GEODESY.

2009 ◽  
Vol 46 (8) ◽  
pp. 611-625
Author(s):  
Wenyou Tao ◽  
Yang Gao
Keyword(s):  
Water Vapor ◽  
Real Time ◽  
Ordinary Kriging ◽  
Weighted Least Squares ◽  
Gaussian Model ◽  
Spherical Model ◽  
Precipitable Water ◽  
Kriging Interpolation ◽  
Surface Rendering ◽  
The University

Based on the near real-time Global Positioning System (GPS) precise pointing positioning (PPP)-inferred water vapor system recently developed at the University of Calgary, Calgary, Alberta, an Ordinary Kriging procedure has been developed to predict the local and regional precipitable water vapor (PWV) and describe its distribution over Canada using limited available data. The Ordinary Kriging procedure includes five steps: (1) quantifying PWV spatial structure by calculating an experimental semivariogram; (2) fitting semivariogram models (spherical, exponential, and Gaussian) with nonlinear, weighted least squares; (3) determining the best-fitted model with cross-validation analysis; (4) estimating whole PWV maps by Ordinary Kriging interpolation; and (5) outputting kriging standard error maps. The 24 h variogram analysis shows that the correctly calculated experimental semivariogram is essential to the accuracy of the kriged maps, which depends on the configuration of the sites, lag step, and lag tolerance. The optimal lag step and lag tolerance for the current Canadian GPS network configuration are 5° and 2.5°, respectively. Among the three semivariogram models, the spherical model fails in its performance most of the time, and the best hourly fitted semivariogram model is either the exponential (90%) or the Gaussian (10%) model. The Gaussian-model-based Ordinary Kriging process produces more detailed maps. The surface maps of the kriging standard errors indicate that the area between longitudes –125° and –60° and latitudes 44° and 54° has higher accuracy due to higher availability of data.

scholarly journals HGPT2: An ERA5-Based Global Model to Estimate Relative Humidity

2021 ◽  
Vol 13 (11) ◽  
pp. 2179
Author(s):  
Pedro Mateus ◽  
Virgílio B. Mendes ◽  
Sandra M. Plecha
Keyword(s):  
Water Vapor ◽  
Relative Humidity ◽  
Real Time ◽  
Prediction Models ◽  
Weather Prediction ◽  
Precipitable Water ◽  
Precipitable Water Vapor ◽  
Global Navigation Satellite Systems ◽  
International Gnss Service ◽  
Weighted Mean Temperature

The neutral atmospheric delay is one of the major error sources in Space Geodesy techniques such as Global Navigation Satellite Systems (GNSS), and its modeling for high accuracy applications can be challenging. Improving the modeling of the atmospheric delays (hydrostatic and non-hydrostatic) also leads to a more accurate and precise precipitable water vapor estimation (PWV), mostly in real-time applications, where models play an important role, since numerical weather prediction models cannot be used for real-time processing or forecasting. This study developed an improved version of the Hourly Global Pressure and Temperature (HGPT) model, the HGPT2. It is based on 20 years of ERA5 reanalysis data at full spatial (0.25° × 0.25°) and temporal resolution (1-h). Apart from surface air temperature, surface pressure, zenith hydrostatic delay, and weighted mean temperature, the updated model also provides information regarding the relative humidity, zenith non-hydrostatic delay, and precipitable water vapor. The HGPT2 is based on the time-segmentation concept and uses the annual, semi-annual, and quarterly periodicities to calculate the relative humidity anywhere on the Earth’s surface. Data from 282 moisture sensors located close to GNSS stations during 1 year (2020) were used to assess the model coefficients. The HGPT2 meteorological parameters were used to process 35 GNSS sites belonging to the International GNSS Service (IGS) using the GAMIT/GLOBK software package. Results show a decreased root-mean-square error (RMSE) and bias values relative to the most used zenith delay models, with a significant impact on the height component. The HGPT2 was developed to be applied in the most diverse areas that can significantly benefit from an ERA5 full-resolution model.

scholarly journals Geostatistical interpolation of daily rainfall at catchment scale: the use of several variogram models in the Ourthe and Ambleve catchments, Belgium

2011 ◽  
Vol 15 (7) ◽  
pp. 2259-2274 ◽  
Author(s):  
S. Ly ◽  
C. Charles ◽  
A. Degré
Keyword(s):  
Ordinary Kriging ◽  
Spatial Interpolation ◽  
Gaussian Model ◽  
Daily Rainfall ◽  
Spherical Model ◽  
Daily Basis ◽  
Catchment Scale ◽  
Multivariate Geostatistics ◽  
Variogram Models ◽  
Thiessen Polygon

Abstract. Spatial interpolation of precipitation data is of great importance for hydrological modelling. Geostatistical methods (kriging) are widely applied in spatial interpolation from point measurement to continuous surfaces. The first step in kriging computation is the semi-variogram modelling which usually used only one variogram model for all-moment data. The objective of this paper was to develop different algorithms of spatial interpolation for daily rainfall on 1 km2 regular grids in the catchment area and to compare the results of geostatistical and deterministic approaches. This study leaned on 30-yr daily rainfall data of 70 raingages in the hilly landscape of the Ourthe and Ambleve catchments in Belgium (2908 km2). This area lies between 35 and 693 m in elevation and consists of river networks, which are tributaries of the Meuse River. For geostatistical algorithms, seven semi-variogram models (logarithmic, power, exponential, Gaussian, rational quadratic, spherical and penta-spherical) were fitted to daily sample semi-variogram on a daily basis. These seven variogram models were also adopted to avoid negative interpolated rainfall. The elevation, extracted from a digital elevation model, was incorporated into multivariate geostatistics. Seven validation raingages and cross validation were used to compare the interpolation performance of these algorithms applied to different densities of raingages. We found that between the seven variogram models used, the Gaussian model was the most frequently best fit. Using seven variogram models can avoid negative daily rainfall in ordinary kriging. The negative estimates of kriging were observed for convective more than stratiform rain. The performance of the different methods varied slightly according to the density of raingages, particularly between 8 and 70 raingages but it was much different for interpolation using 4 raingages. Spatial interpolation with the geostatistical and Inverse Distance Weighting (IDW) algorithms outperformed considerably the interpolation with the Thiessen polygon, commonly used in various hydrological models. Integrating elevation into Kriging with an External Drift (KED) and Ordinary Cokriging (OCK) did not improve the interpolation accuracy for daily rainfall. Ordinary Kriging (ORK) and IDW were considered to be the best methods, as they provided smallest RMSE value for nearly all cases. Care should be taken in applying UNK and KED when interpolating daily rainfall with very few neighbourhood sample points. These recommendations complement the results reported in the literature. ORK, UNK and KED using only spherical model offered a slightly better result whereas OCK using seven variogram models achieved better result.

scholarly journals PROCESSING STRATEGY FOR NEAR REAL TIME GPS PRECIPITABLE WATER VAPOR RETRIEVAL

2007 ◽  
Vol 24 (4) ◽  
pp. 275-284
Author(s):  
Jeong-Ho Baek ◽  
Jae-Won Lee ◽  
Byung-Kyu Choi ◽  
Jung-Ho Cho
Keyword(s):  
Water Vapor ◽  
Real Time ◽  
Precipitable Water ◽  
Precipitable Water Vapor ◽  
Processing Strategy

The atmospheric water vapor retrieved by OH(8-3) band airglow from astronomical observations

2020 ◽  
Author(s):  
Weijun Liu ◽  
Jiyao Xu ◽  
Jianchun Bian ◽  
Xiao Liu ◽  
Wei Yuan ◽  
...  
Keyword(s):  
Water Vapor ◽  
Real Time ◽  
Emission Spectra ◽  
Precipitable Water ◽  
Line Of Sight ◽  
Regression Result ◽  
Absorption Cross ◽  
Standard Star ◽  
Astronomical Observations ◽  
Effective Absorption

<p>Water vapor in the atmosphere is an important trace gas, and seriously affects the ground-based astronomical observations due to water vapor attenuation and emission. It is significant to correct the effects of water vapor along the line-of-sight of astronomical target in real time. Here, we discuss a method to retrieve the precipitable water vapor (PWV) from the OH(8-3) band airglow spectrum. The pressure, temperature and water vapor profiles determine the effective absorption cross-section in PWV retrieval, so a simple and effective method of the effective absorption cross-sections using profiles from a standard atmosphere model is discussed. The Monte Carlo simulations are used to estimate the PWV retrieval. Besides, the PWV is calculated using the sky nightglows from UVES and is compared to that from the standard star spectra of UVES observed from 2000 to 2016. The results indicate that The PWV derived from OH(8-3) spectra is in good agreement with that retrieved from UVES standard star equivalent width and the averaged difference between the two is 0.66 mm. The regression result indicates that the slope α=1.06 +/-0.03 and the correlation coefficient is r=0.87. Because the sky emission spectra and the astronomical target are observed at the same time and along the same line-of-sight, the method of PWV retrieved by OH(8-3) band spectra provides a quick and economical means of correcting the effects if water vapor on ground-based astronomical observations locally, in real-time, and along the line-of-sight of astronomical observations.</p>

Real-time retrieval of precipitable water vapor from GPS and BeiDou observations

2015 ◽  
Vol 89 (9) ◽  
pp. 843-856 ◽  
Author(s):  
Cuixian Lu ◽  
Xingxing Li ◽  
Tobias Nilsson ◽  
Tong Ning ◽  
Robert Heinkelmann ◽  
...  
Keyword(s):  
Water Vapor ◽  
Real Time ◽  
Precipitable Water ◽  
Precipitable Water Vapor

scholarly journals Efficiency of Ni Content in Laterite Nickel Deposits through The Least Square Method Approach on Semivariogram

2021 ◽  
Vol 2123 (1) ◽  
pp. 012015
Author(s):  
F Usman ◽  
G M Tinungki ◽  
E T Herdiani
Keyword(s):  
Ordinary Kriging ◽  
Gaussian Model ◽  
Spherical Model ◽  
Least Square Method ◽  
Spatial Prediction ◽  
Least Square ◽  
Minimization Method ◽  
Semivariogram Model ◽  
Ni Content ◽  
Nickel Deposits

Abstract Ordinary kriging is one of the geostatistical techniques used for spatial prediction on a spatially distributed random plane. Ordinary kriging is a linear unbiased estimator which is part of a semivariogram system of equations that minimizes errors of variance in estimating mineral resources. The semivariogram model shows optimal results in the estimation using the least square method, the effective minimization method smoothes the data points against the curve on a semivariogram graph, the least square makes the size error efficient in the semivariogram model and has been proven to be effective in reducing errors in the semivariogram model in the case of laterite nickel deposits. at PT. Vale Indonesia Tbk. Thus, conclusively the prediction of unsampled Ni content results is very accurate. This is indicated by the lowest root mean square error (RMSE) in limonite in the exponential model, saprolite in the spherical model, and bedrock in the gaussian model. The greatest value of Ni content in this study was in the saprolite layer.

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