Detrended Kriging Research Articles

High-Resolution Mapping of Air Pollution in Delhi Using Detrended Kriging Model

High-Resolution Mapping of Air Pollution in Delhi Using Detrended Kriging Model

31 years of hourly spatially distributed air temperature, humidity, and precipitation amount and phase from Reynolds Critical Zone Observatory

Thirty one years of spatially distributed air temperature, relative humidity, dew point temperature, precipitation amount, and precipitation phase data are presented for the Reynolds Creek Experimental Watershed, which is part of the Critical Zone Observatory network. The air temperature, relative humidity, and precipitation amount data are spatially distributed over a 10 m Lidar-derived digital elevation model at an hourly time step using a detrended kriging algorithm. This dataset covers a wide range of weather extremes in a mesoscale basin (237 km<sup>2</sup>) that encompasses the rain-snow transition zone and should find widespread application in earth science modeling communities. Spatial data allows for a more holistic analysis of basin means and elevation gradients, compared to weather station data measured at specific locations. Files are stored in the NetCDF file format, which allows for easy spatiotemporal averaging and/or subsetting. Data are made publicly available through an OPeNDAP-enabled THREDDS server hosted by Boise State University Libraries in support of the Reynolds Creek Critical Zone Observatory (<a href="https://doi.org/doi:10.18122/B2B59V" target ="_blank">https://doi.org/10.18122/B2B59V</a>).

Geostatistical mapping of real estate prices: an empirical comparison of kriging and cokriging

Small-sized housing samples and price predictions at nonobserved locations require geostatistical approaches, particularly the kriging estimator. Nevertheless, geostatistics has thus far received little attention in real estate economics. The article’s objective is to empirically compare the prediction accuracy of univariate kriging variants, namely detrended kriging (DK) and universal kriging (UK), and multivariate extensions, including detrended cokriging (DCK) and universal cokriging (UCK). Both latter methods consider structural and neighborhood characteristics as auxiliary variables. While the price surfaces of DK and UK show nearly identical cross-validated accuracies, the cross-validation-based prediction accuracy of DCK and UCK differ in favor of the latter. If real estate agencies are faced with a univariate sample of property prices, either DK or UK can be used, while in the multivariate case, UCK is recommended, although numerically more complex.

Use of past precipitation data for regionalisation of hourly rainfall in the low mountain ranges of Saxony, Germany

Abstract. Within the context of flood forecasting we deal with the improvement of regionalisation methods for the generation of highly resolved (1 h, 1×1km2) precipitation fields, which can be used as input for rainfall-runoff models or for verification of weather forecasts. Although radar observations of precipitation are available in many regions, it might be necessary to apply regionalisation methods near real-time for the cases that radar is not available or observations are of low quality. The aim of this paper is to investigate whether past precipitation information can be used to improve regionalisation of rainfall. Within a case study we determined typical precipitation Background-Fields (BGF) for the mountainous and hilly regions of Saxony using hourly and daily rain gauge data. Additionally, calibrated radar data served as past information for the BGF generation. For regionalisation of precipitation we used de-trended kriging and compared the results with another kriging based regionalisation method and with Inverse Distance Weighting (IDW). The performance of the methods was assessed by applying cross-validation, by inspection and by evaluation with rainfall-runoff simulations. The regionalisation of rainfall yielded better results in case of advective events than in case of convective events. The performance of the applied regionalisation methods showed no significant disagreement for different precipitation types. Cross-validation results were rather similar in most cases. Subjectively judged, the BGF-method reproduced best the structures of rain cells. Precipitation input derived from radar or kriging resulted in a better matching between observed and simulated flood hydrographs. Simple techniques like IDW also deliver satisfying results in some occasions. Implementation of past radar data into the BGF-method rendered no improvement, because of data shortages. Thus, no method proved to outperform the others generally. The decision, which method is appropriate for an event, should be made objectively using cross-validation, but also subjectively, using the expert knowledge of the forecaster.

Spatial interpolation of air pollution measurements using CORINE land cover data

Real-time assessment of the ambient air quality has gained an increased interest in recent years. To give support to this evolution, the statistical air pollution interpolation model RIO is developed. Due to the very low computational cost, this interpolation model is an efficient tool for an environment agency when performing real-time air quality assessment. Beside this, a reliable interpolation model can be used to produce analysed maps of historical data records as well. Such maps are essential for correctly checking compliance with population exposure limit values as foreseen by the new EU Air Quality Directive. RIO is an interpolation model that can be classified as a detrended Kriging model. In a first step, the local character of the air pollution sampling values is removed in a detrending procedure. Subsequently, the site-independent data is interpolated by an Ordinary Kriging scheme. Finally, in a re-trending step, a local bias is added to the Kriging interpolation results. As spatially resolved driving force in the detrending process, a land use indicator is developed based on the CORINE land cover data set. The indicator is optimized independently for the three pollutants O 3, NO 2 and PM 10. As a result, the RIO model is able to account for the local character of the air pollution phenomenon at locations where no monitoring stations are available. Through a cross-validation procedure the superiority of the RIO model over standard interpolation techniques, such as the Ordinary Kriging is demonstrated. Air quality maps are presented for the three pollutants mentioned and compared to maps based on standard interpolation techniques.

Robustness of Kriging when interpolating in random simulation with heterogeneous variances: Some experiments

This paper investigates the use of Kriging in random simulation when the simulation output variances are not constant. Kriging gives a response surface or metamodel that can be used for interpolation. Because Ordinary Kriging assumes constant variances, this paper also applies Detrended Kriging to estimate a non-constant signal function, and then standardizes the residual noise through the heterogeneous variances estimated from replicated simulation runs. Numerical examples, however, suggest that Ordinary Kriging is a robust interpolation method.

Kriging for interpolation in random simulation

Whenever simulation requires much computer time, interpolation is needed. Simulationists use different interpolation techniques (eg linear regression), but this paper focuses on Kriging. This technique was originally developed in geostatistics by DG Krige, and has recently been widely applied in deterministic simulation. This paper, however, focuses on random or stochastic simulation. Essentially, Kriging gives more weight to ‘neighbouring’ observations. There are several types of Kriging; this paper discusses—besides Ordinary Kriging—a novel type, which ‘detrends’ data through the use of linear regression. Results are presented for two examples of input/output behaviour of the underlying random simulation model: Ordinary and Detrended Kriging give quite acceptable predictions; traditional linear regression gives the worst results.

Spatial interpolation of climatic Normals: test of a new method in the Canadian boreal forest

Spatial interpolation of climatic data is frequently required to provide input for plant growth models. As no single method is optimal for all regions, it is important to compare the results obtained using alternative methods applied to each data set. For estimating 30-year averages (Normals) of monthly temperature and precipitation at specific sites in western Canada, we examined four forms of kriging and three simple alternatives. One of the alternatives was a novel technique, termed `gradient-plus-inverse distance squared' (GIDS), which combines multiple linear regression and distance-weighting. Based on the mean absolute errors from cross-validation tests, the methods were ranked GIDS > detrended kriging > nearest neighbour >co-kriging > inverse distance squared > universal kriging > ordinary kriging for interpolating monthly temperature, and GIDS > co-kriging>inverse distance squared > nearest neighbour > ordinary kriging > detrended kriging > universal kriging for interpolating monthly precipitation. GIDS gave the lowest errors, which averaged 0.5°C for monthly temperature and 3.6 mm, or 11%, for monthly precipitation. These errors were comparable with those from optimal methods in other studies. GIDS errors were also more consistent for a wide range of data variability than the other methods. The performance of kriging may have been constrained by the limited number of stations (32) in the study region, but if so, this is an unavoidable limitation in regions with sparse coverage of climate stations. Compared with kriging, GIDS was simple to apply and avoided the subjectivity involved in defining variogram models and neighbourhoods. We conclude that GIDS is a simple, robust and accurate interpolation method for use in our region, and that it should be applicable elsewhere, subject to careful comparison with other methods.

MEAN AREAL PRECIPITATION FOR DAILY HYDROLOGIC MODELING IN MOUNTAINOUS REGIONS1

ABSTRACT: A procedure using detrended kriging has been developed to calculate daily values of mean areal precipitation (MAP) for input to hydrologic models. The important features of this procedure that overcome weaknesses in existing MAP procedures are: (1) specific precipitation‐elevation relationships are determined for each time period as opposed to using relationships based on climatological averages, (2) spatial variability is incorporated by estimating precipitation for each grid cell over a watershed, (3) the spatial correlation structure of precipitation is explicitly modeled, and (4) station weights for precipitation estimates are determined objectively and optimally. Detailed cross‐validation testing of the procedure was done for the Reynolds Creek research watershed in southwestern Idaho. The procedure is suitable for use in operational streamflow forecasting.

A comparison of geostatistical procedures for spatial analysis of precipitation in mountainous terrain

Spatially distributed measurements or estimates of precipitation over a region are required for modelling of hydrologic processes and soil moisture for agricultural and natural resource management. Simple interpolation methods fail to consider the effects of topography on precipitation and may be in considerable error in mountainous regions. The performance of three geostatistical methods for making mean annual precipitation estimates on a regular grid of points in mountainous terrain was evaluated. The methods were: (1) kriging; (2) kriging elevation-detrended data; and (3) cokriging with elevation as an auxiliary variable. The study area was the Willamette River basin, a 2.9 million hectare region spanning the area between the Coast Range and the Cascade Range in western Oregon. Compared with kriging, detrended kriging and cokriging both exhibited better precision (as indicated by estimation coefficients of variation of 16 and 17% vs. 21%; and average absolute errors of 19 and 20 cm vs. 26 cm) and accuracy (as indicated by average errors of −1.4 and −2.0 cm vs. −5.2 cm) in the estimation of mean annual precipitation. Contour diagrams for kriging and detrended kriging exhibited smooth zonation following general elevation trends, while cokriging showed a patchier pattern more closely corresponding to local topographic features. Detrended kriging and cokriging offer improved spatially distributed precipitation estimates in mountainous terrain on the scale of a few million hectares. Application of these methods for a larger region, the Columbia River drainage in the USA (57 million hectares), was unsuccessful due to the lack of a consistent precipitation-elevation relationship at this scale. Precipitation estimation incorporating the effects of topography at larger scales will require either piecewise estimation using the methods described here or development of a physically based orographic model.