scholarly journals Dealing with spatial heterogeneity in pointwise-to-gridded- data comparisons

2022 ◽  
Vol 15 (1) ◽  
pp. 41-59
Author(s):  
Amir H. Souri ◽  
Kelly Chance ◽  
Kang Sun ◽  
Xiong Liu ◽  
Matthew S. Johnson
Keyword(s):  
Spatial Heterogeneity ◽  
Linear Prediction ◽  
Spatial Information ◽  
Spatial Scales ◽  
Systematic Bias ◽  
Gridded Data ◽  
Paired Data ◽  
Spatial Homogeneity ◽  
Geostatistical Approach ◽  
Least Squares Fit

Abstract. Most studies on validation of satellite trace gas retrievals or atmospheric chemical transport models assume that pointwise measurements, which roughly represent the element of space, should compare well with satellite (model) pixels (grid box). This assumption implies that the field of interest must possess a high degree of spatial homogeneity within the pixels (grid box), which may not hold true for species with short atmospheric lifetimes or in the proximity of plumes. Results of this assumption often lead to a perception of a nonphysical discrepancy between data, resulting from different spatial scales, potentially making the comparisons prone to overinterpretation. Semivariogram is a mathematical expression of spatial variability in discrete data. Modeling the semivariogram behavior permits carrying out spatial optimal linear prediction of a random process field using kriging. Kriging can extract the spatial information (variance) pertaining to a specific scale, which in turn translates pointwise data to a gridded space with quantified uncertainty such that a grid-to-grid comparison can be made. Here, using both theoretical and real-world experiments, we demonstrate that this classical geostatistical approach can be well adapted to solving problems in evaluating model-predicted or satellite-derived atmospheric trace gases. This study suggests that satellite validation procedures using the present method must take kriging variance and satellite spatial response functions into account. We present the comparison of Ozone Monitoring Instrument (OMI) tropospheric NO2 columns against 11 Pandora spectrometer instrument (PSI) systems during the DISCOVER-AQ campaign over Houston. The least-squares fit to the paired data shows a low slope (OMI=0.76×PSI+1.18×1015 molecules cm−2, r2=0.66), which is indicative of varying biases in OMI. This perceived slope, induced by the problem of spatial scale, disappears in the comparison of the convolved kriged PSI and OMI (0.96×PSI+0.66×1015 molecules cm−2, r2=0.72), illustrating that OMI possibly has a constant systematic bias over the area. To avoid gross errors in comparisons made between gridded data vs. pointwise measurements, we argue that the concept of semivariogram (or spatial autocorrelation) should be taken into consideration, particularly if the field exhibits a strong degree of spatial heterogeneity at the scale of satellite and/or model footprints.

scholarly journals Dealing with Spatial Heterogeneity in Pointwise to Gridded Data Comparisons

2021 ◽  
Author(s):  
Amir H. Souri ◽  
Kelly Chance ◽  
Kang Sun ◽  
Xiong Liu ◽  
Matthew S. Johnson
Keyword(s):  
Spatial Heterogeneity ◽  
Linear Prediction ◽  
Spatial Information ◽  
Spatial Scales ◽  
Systematic Bias ◽  
Gridded Data ◽  
Paired Data ◽  
Spatial Homogeneity ◽  
Geostatistical Approach ◽  
Least Squares Fit

Abstract. Atmospheric modelers and the trace gas retrieval community typically presuppose that pointwise measurements, which roughly represent the element of space, should compare well with satellite (model) pixels (grids). This assumption implies that the field of interest must possess a high degree of spatial homogeneity within the pixels (grids), which may not hold true for species with short atmospheric lifetimes or in the proximity of plumes. Results of this assumption often lead to a perception of a nonphysical discrepancy between data, resulting from different spatial scales, potentially making the comparisons prone to overinterpretation. Semivariogram is a mathematical expression of spatial variability in discrete data. Modeling the semivariogram behavior permits carrying out spatial optimal linear prediction of a random process field using kriging. Kriging can extract the spatial information (variance) pertaining to a specific scale, which in turn translating pointwise data to a grid space with quantified uncertainty such that a grid-to-grid comparison can be made. Here, using both theoretical and real-world experiments, we demonstrate that this classical geostatistical approach can be well adapted to solving problems in evaluating model-predicted or satellite-derived atmospheric trace gases. This study demonstrates that satellite validation procedures must take kriging variance and satellite spatial response functions into account. We present the comparison of Ozone Monitoring Instrument (OMI) tropospheric NO2 columns against 11 Pandora Spectrometer Instrument (PSI) systems during the DISCOVER-AQ campaign over Houston. The least-squares fit to the paired data shows a low slope (OMI=0.76×PSI+1.18×1015 molecules cm−2, r2=0.67) which is indicative of varying biases in OMI. This perceived slope, induced by the problem of spatial scale, disappears in the comparison of the convolved kriged PSI and OMI (0.96×PSI+0.66×1015 molecules cm−2, r2=0.72) illustrating that OMI possibly has a constant systematic bias over the area. To avoid gross errors in comparisons made between gridded data versus pointwise measurements, we argue that the concept of semivariogram (or spatial auto-correlation) should be taken into consideration, particularly if the field exhibits a strong degree of spatial heterogeneity at the scale of satellite and/or model footprints.

Using spatial information for evaluating the quality of prediction maps from hyperspectral images: A geostatistical approach

2019 ◽  
Vol 1077 ◽  
pp. 116-128 ◽  
Author(s):  
Ana Herrero-Langreo ◽  
Nathalie Gorretta ◽  
Bruno Tisseyre ◽  
Aoife Gowen ◽  
Jun-Li Xu ◽  
...  
Keyword(s):  
Spatial Information ◽  
Hyperspectral Images ◽  
Geostatistical Approach

scholarly journals MAX-DOAS observations of aerosols, formaldehyde and nitrogen dioxide in the Beijing area: comparison of two profile retrieval approaches

2015 ◽  
Vol 8 (2) ◽  
pp. 941-963 ◽  
Author(s):  
T. Vlemmix ◽  
F. Hendrick ◽  
G. Pinardi ◽  
I. De Smedt ◽  
C. Fayt ◽  
...  
Keyword(s):  
Standard Deviation ◽  
A Priori ◽  
Systematic Bias ◽  
Aerosol Extinction ◽  
Data Set ◽  
Near Surface ◽  
Beijing Area ◽  
Least Squares Fit ◽  
Relative Differences ◽  
Good Agreement

Abstract. A 4-year data set of MAX-DOAS observations in the Beijing area (2008–2012) is analysed with a focus on NO2, HCHO and aerosols. Two very different retrieval methods are applied. Method A describes the tropospheric profile with 13 layers and makes use of the optimal estimation method. Method B uses 2–4 parameters to describe the tropospheric profile and an inversion based on a least-squares fit. For each constituent (NO2, HCHO and aerosols) the retrieval outcomes are compared in terms of tropospheric column densities, surface concentrations and "characteristic profile heights" (i.e. the height below which 75% of the vertically integrated tropospheric column density resides). We find best agreement between the two methods for tropospheric NO2 column densities, with a standard deviation of relative differences below 10%, a correlation of 0.99 and a linear regression with a slope of 1.03. For tropospheric HCHO column densities we find a similar slope, but also a systematic bias of almost 10% which is likely related to differences in profile height. Aerosol optical depths (AODs) retrieved with method B are 20% high compared to method A. They are more in agreement with AERONET measurements, which are on average only 5% lower, however with considerable relative differences (standard deviation ~ 25%). With respect to near-surface volume mixing ratios and aerosol extinction we find considerably larger relative differences: 10 ± 30, −23 ± 28 and −8 ± 33% for aerosols, HCHO and NO2 respectively. The frequency distributions of these near-surface concentrations show however a quite good agreement, and this indicates that near-surface concentrations derived from MAX-DOAS are certainly useful in a climatological sense. A major difference between the two methods is the dynamic range of retrieved characteristic profile heights which is larger for method B than for method A. This effect is most pronounced for HCHO, where retrieved profile shapes with method A are very close to the a priori, and moderate for NO2 and aerosol extinction which on average show quite good agreement for characteristic profile heights below 1.5 km. One of the main advantages of method A is the stability, even under suboptimal conditions (e.g. in the presence of clouds). Method B is generally more unstable and this explains probably a substantial part of the quite large relative differences between the two methods. However, despite a relatively low precision for individual profile retrievals it appears as if seasonally averaged profile heights retrieved with method B are less biased towards a priori assumptions than those retrieved with method A. This gives confidence in the result obtained with method B, namely that aerosol extinction profiles tend on average to be higher than NO2 profiles in spring and summer, whereas they seem on average to be of the same height in winter, a result which is especially relevant in relation to the validation of satellite retrievals.

scholarly journals Spatial scale-dependent land–atmospheric methane exchanges in the northern high latitudes from 1993 to 2004

2014 ◽  
Vol 11 (7) ◽  
pp. 1693-1704 ◽  
Author(s):  
X. Zhu ◽  
Q. Zhuang ◽  
X. Lu ◽  
L. Song
Keyword(s):  
Spatial Heterogeneity ◽  
Spatial Scale ◽  
Water Table ◽  
Spatial Scales ◽  
Grid Cell ◽  
High Latitudes ◽  
Atmospheric Methane ◽  
Ch4 Emissions ◽  
Biogeochemical Models ◽  
Macro Scale

Abstract. Effects of various spatial scales of water table dynamics on land–atmospheric methane (CH4) exchanges have not yet been assessed for large regions. Here we used a coupled hydrology–biogeochemistry model to quantify daily CH4 exchanges over the pan-Arctic from 1993 to 2004 at two spatial scales of 100 km and 5 km. The effects of sub-grid spatial variability of the water table depth (WTD) on CH4 emissions were examined with a TOPMODEL-based parameterization scheme for the northern high latitudes. We found that both WTD and CH4 emissions are better simulated at a 5 km spatial resolution. By considering the spatial heterogeneity of WTD, net regional CH4 emissions at a 5 km resolution are 38.1–55.4 Tg CH4 yr−1 from 1993 to 2004, which are on average 42% larger than those simulated at a 100 km resolution using a grid-cell-mean WTD scheme. The difference in annual CH4 emissions is attributed to the increased emitting area and enhanced flux density with finer resolution for WTD. Further, the inclusion of sub-grid WTD spatial heterogeneity also influences the inter-annual variability of CH4 emissions. Soil temperature plays an important role in the 100 km estimates, while the 5 km estimates are mainly influenced by WTD. This study suggests that previous macro-scale biogeochemical models using a grid-cell-mean WTD scheme might have underestimated the regional CH4 emissions. The spatial scale-dependent effects of WTD should be considered in future quantification of regional CH4 emissions.

scholarly journals A new uncertainty estimation approach with multiple datasets and implementation for various precipitation products

2020 ◽  
Vol 24 (4) ◽  
pp. 2061-2081 ◽  
Author(s):  
Xudong Zhou ◽  
Jan Polcher ◽  
Tao Yang ◽  
Ching-Sheng Huang
Keyword(s):  
Spatial Heterogeneity ◽  
Spatial Scales ◽  
Three Dimensional ◽  
Variance Partitioning ◽  
Uncertainty Estimation ◽  
The Other ◽  
New Approach ◽  
Multiple Datasets ◽  
Uncertainty Estimates ◽  
Spatiotemporal Scales

Abstract. Ensemble estimates based on multiple datasets are frequently applied once many datasets are available for the same climatic variable. An uncertainty estimate based on the difference between the ensemble datasets is always provided along with the ensemble mean estimate to show to what extent the ensemble members are consistent with each other. However, one fundamental flaw of classic uncertainty estimates is that only the uncertainty in one dimension (either the temporal variability or the spatial heterogeneity) can be considered, whereas the variation along the other dimension is dismissed due to limitations in algorithms for classic uncertainty estimates, resulting in an incomplete assessment of the uncertainties. This study introduces a three-dimensional variance partitioning approach and proposes a new uncertainty estimation (Ue) that includes the data uncertainties in both spatiotemporal scales. The new approach avoids pre-averaging in either of the spatiotemporal dimensions and, as a result, the Ue estimate is around 20 % higher than the classic uncertainty metrics. The deviation of Ue from the classic metrics is apparent for regions with strong spatial heterogeneity and where the variations significantly differ in temporal and spatial scales. This shows that classic metrics underestimate the uncertainty through averaging, which means a loss of information in the variations across spatiotemporal scales. Decomposing the formula for Ue shows that Ue has integrated four different variations across the ensemble dataset members, while only two of the components are represented in the classic uncertainty estimates. This analysis of the decomposition explains the correlation as well as the differences between the newly proposed Ue and the two classic uncertainty metrics. The new approach is implemented and analysed with multiple precipitation products of different types (e.g. gauge-based products, merged products and GCMs) which contain different sources of uncertainties with different magnitudes. Ue of the gauge-based precipitation products is the smallest, while Ue of the other products is generally larger because other uncertainty sources are included and the constraints of the observations are not as strong as in gauge-based products. This new three-dimensional approach is flexible in its structure and particularly suitable for a comprehensive assessment of multiple datasets over large regions within any given period.

scholarly journals Scale Characterization and Correction of Diurnal Cycle Errors in MAPLE

2017 ◽  
Vol 56 (9) ◽  
pp. 2561-2575 ◽  
Author(s):  
Aitor Atencia ◽  
Isztar Zawadzki ◽  
Marc Berenguer
Keyword(s):  
Diurnal Cycle ◽  
Spatial Scales ◽  
Time Of Day ◽  
Precipitation Forecast ◽  
Systematic Bias ◽  
Correction Scheme ◽  
Average Rainfall ◽  
The Mean ◽  
Scale Characterization ◽  
Composite Data

AbstractThe most widely used technique for nowcasting of quantitative precipitation in operational and research centers is the Lagrangian extrapolation of the latest radar observations. However, this technique has a limited forecast skill because of the assumption made on its formulation, such as the fact that the motion vectors do not change and, even more important for convective events, neglect any growth or decay in the precipitation field. In this work, the McGill Algorithm for Precipitation Nowcasting by Lagrangian Extrapolation (MAPLE) errors have been computed for 10 yr of radar composite data over the continental United States. The study of these errors shows systematic bias depending on the time of day. This effect is related to the solar cycle, whose heating energy results in an increase in the average rainfall in the afternoon. This external forcing interacts with the atmospheric system, creating local initiation and dissipation of convection depending on orography, land use, cloud coverage, etc. The signal of the diurnal cycle in MAPLE precipitation forecast has been studied in different locations and spatial scales as a function of lead time in order to recognize where, when, and for which spatial scales the signal is significant. This information has been used in the development of a scaling correction scheme where the mean errors due to the diurnal cycle are adjusted. The results show that the developed methodology improves the forecast for the spatial scales and locations where the diurnal cycle signal is significant.

scholarly journals Unique spatial integration in mouse primary visual cortex and higher visual areas

2019 ◽  
Author(s):  
Kevin A. Murgas ◽  
Ashley M. Wilson ◽  
Valerie Michael ◽  
Lindsey L. Glickfeld
Keyword(s):  
Visual Cortex ◽  
Visual System ◽  
Primary Visual Cortex ◽  
Spatial Information ◽  
Spatial Scales ◽  
Spatial Integration ◽  
Global Features ◽  
Wide Range ◽  
Visual Areas ◽  
Higher Visual Areas

AbstractNeurons in the visual system integrate over a wide range of spatial scales. This diversity is thought to enable both local and global computations. To understand how spatial information is encoded across the mouse visual system, we use two-photon imaging to measure receptive fields in primary visual cortex (V1) and three downstream higher visual areas (HVAs): LM (lateromedial), AL (anterolateral) and PM (posteromedial). We find significantly larger receptive field sizes and less surround suppression in PM than in V1 or the other HVAs. Unlike other visual features studied in this system, specialization of spatial integration in PM cannot be explained by specific projections from V1 to the HVAs. Instead, our data suggests that distinct connectivity within PM may support the area’s unique ability to encode global features of the visual scene, whereas V1, LM and AL may be more specialized for processing local features.

scholarly journals Biases in object location estimation: the role of camera rotations and translation

2021 ◽  
Author(s):  
Vladislava Segen
Keyword(s):  
Older Adults ◽  
Spatial Memory ◽  
Spatial Information ◽  
Location Estimation ◽  
Object Location ◽  
Systematic Bias ◽  
Accurate Representation ◽  
Object Locations ◽  
Age Related

The current study investigated a systematic bias in spatial memory in which people, following a perspective shift from encoding to recall, indicated the location of an object further to the direction of the shit. In Experiment 1, we documented this bias by asking participants to encode the position of an object in a virtual room and then indicate it from memory following a perspective shift induced by camera translation and rotation. In Experiment 2, we decoupled the influence of camera translations and camera rotations and examined also whether adding more information in the scene would reduce the bias. We also investigated the presence of age-related differences in the precision of object location estimates and the tendency to display the bias related to perspective shift. Overall, our results showed that camera translations led to greater systematic bias than camera rotations. Furthermore, the use of additional spatial information improved the precision with which object locations were estimated and reduced the bias associated with camera translation. Finally, we found that although older adults were as precise as younger participants when estimating object locations, they benefited less from additional spatial information and their responses were more biased in the direction of camera translations. We propose that accurate representation of camera translations requires more demanding mental computations than camera rotations, leading to greater uncertainty about the position of an object in memory. This uncertainty causes people to rely on an egocentric anchor thereby giving rise to the systematic bias in the direction of camera translation.

Landscape Heterogeneity and Dynamics

2019 ◽  
pp. 42-126
Author(s):  
Kimberly A. With
Keyword(s):  
Landscape Ecology ◽  
Spatial Heterogeneity ◽  
Landscape Structure ◽  
Landscape Heterogeneity ◽  
Spatial Scales ◽  
Anthropogenic Disturbances ◽  
Ecological Processes ◽  
Disturbance Dynamics ◽  
Wide Range ◽  
Over Time

Heterogeneity is a defining characteristic of landscapes and therefore central to the study of landscape ecology. Landscape ecology investigates what factors give rise to heterogeneity, how that heterogeneity is maintained or altered by natural and anthropogenic disturbances, and how heterogeneity ultimately influences ecological processes and flows across the landscape. Because heterogeneity is expressed across a wide range of spatial scales, the landscape perspective can be applied to address these sorts of questions at any level of ecological organization, and in aquatic and marine systems as well as terrestrial ones. Disturbances—both natural and anthropogenic—are a ubiquitous feature of any landscape, contributing to its structure and dynamics. Although the focus in landscape ecology is typically on spatial heterogeneity, disturbance dynamics produce changes in landscape structure over time as well as in space. Heterogeneity and disturbance dynamics are thus inextricably linked and are therefore covered together in this chapter.

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