scholarly journals A Note on Parabolic Homogenization with a Mismatch between the Spatial Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Liselott Flodén ◽  
Anders Holmbom ◽  
Marianne Olsson Lindberg ◽  
Jens Persson
Keyword(s):  
Spatial Scale ◽  
Parabolic Problem ◽  
Spatial Scales ◽  
Time Derivative ◽  
Local Problem ◽  
Linear Parabolic Problem ◽  
Spatial Oscillations ◽  
Spatial Oscillation

We consider the homogenization of the linear parabolic problem which exhibits a mismatch between the spatial scales in the sense that the coefficient of the elliptic part has one frequency of fast spatial oscillations, whereas the coefficient of the time derivative contains a faster spatial scale. It is shown that the faster spatial microscale does not give rise to any corrector term and that there is only one local problem needed to characterize the homogenized problem. Hence, the problem is not of a reiterated type even though two rapid scales of spatial oscillation appear.

scholarly journals A Strange Term in the Homogenization of Parabolic Equations with Two Spatial and Two Temporal Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
L. Flodén ◽  
A. Holmbom ◽  
M. Olsson Lindberg
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Time Derivative ◽  
Local Problem ◽  
Temporal Scales ◽  
Space And Time ◽  
Temporal Oscillation ◽  
Spatial Oscillations ◽  
Spatial Oscillation

We study the homogenization of a parabolic equation with oscillations in both space and time in the coefficienta(x/ε,t/ε2)in the elliptic part and spatial oscillations in the coefficientρ(x/ε)that is multiplied with the time derivative∂tuε. We obtain a strange term in the local problem. This phenomenon appears as a consequence of the combination of the spatial oscillation inρ(x/ε)and the temporal oscillation ina(x/ε,t/ε2)and disappears if either of these oscillations is removed.

scholarly journals Smoothing properties in multistep backward difference method and time derivative approximation for linear parabolic equations

2005 ◽  
Vol 2005 (4) ◽  
pp. 523-536
Author(s):  
Yubin Yan
Keyword(s):  
Difference Method ◽  
Parabolic Equations ◽  
Parabolic Problem ◽  
Approximation Scheme ◽  
Time Derivative ◽  
Nonsmooth Data ◽  
Smoothing Property ◽  
Linear Parabolic Equations ◽  
Linear Parabolic Problem ◽  
Data Error

A smoothing property in multistep backward difference method for a linear parabolic problem in Hilbert space has been proved, where the operator is selfadjoint, positive definite with compact inverse. By using the solutions computed by a multistep backward difference method for the parabolic problem, we introduce an approximation scheme for time derivative. The nonsmooth data error estimate for the approximation of time derivative has been obtained.

scholarly journals 8-Day and Daily Maximum and Minimum Air Temperature Estimation via Machine Learning Method on a Climate Zone to Global Scale

2021 ◽  
Vol 13 (12) ◽  
pp. 2355
Author(s):  
Linglin Zeng ◽  
Yuchao Hu ◽  
Rui Wang ◽  
Xiang Zhang ◽  
Guozhang Peng ◽  
...  
Keyword(s):  
Spatial Scale ◽  
Air Temperature ◽  
Spatial Scales ◽  
Model Performance ◽  
Global Scale ◽  
Scale Model ◽  
Validation Dataset ◽  
Daily Maximum ◽  
Climate Zone ◽  
Temporal And Spatial

Air temperature (Ta) is a required input in a wide range of applications, e.g., agriculture. Land Surface Temperature (LST) products from Moderate Resolution Imaging Spectroradiometer (MODIS) are widely used to estimate Ta. Previous studies of these products in Ta estimation, however, were generally applied in small areas and with a small number of meteorological stations. This study designed both temporal and spatial experiments to estimate 8-day and daily maximum and minimum Ta (Tmax and Tmin) on three spatial scales: climate zone, continental and global scales from 2009 to 2018, using the Random Forest (RF) method based on MODIS LST products and other auxiliary data. Factors contributing to the relation between LST and Ta were determined based on physical models and equations. Temporal and spatial experiments were defined by the rules of dividing the training and validation datasets for the RF method, in which the stations selected in the training dataset were all included or not in the validation dataset. The RF model was first trained and validated on each spatial scale, respectively. On a global scale, model accuracy with a determination coefficient (R2) > 0.96 and root mean square error (RMSE) < 1.96 °C and R2 > 0.95 and RMSE < 2.55 °C was achieved for 8-day and daily Ta estimations, respectively, in both temporal and spatial experiments. Then the model was trained and cross-validated on each spatial scale. The results showed that the data size and station distribution of the study area were the main factors influencing the model performance at different spatial scales. Finally, the spatial patterns of the model performance and variable importance were analyzed. Both daytime and nighttime LST had a significant contribution in the 8-day Tmax estimation on all the three spatial scales; while their contribution in daily Tmax estimation varied over different continents or climate zones. This study was expected to improve our understanding of Ta estimation in terms of accuracy variations and influencing variables on different spatial and temporal scales. The future work mainly includes identifying underlying mechanisms of estimation errors and the uncertainty sources of Ta estimation from a local to a global scale.

scholarly journals Characteristics of Climate Change and Extreme Weather from 1951 to 2011 in China

2018 ◽  
Vol 15 (11) ◽  
pp. 2540 ◽  
Author(s):  
Chunli Zhao ◽  
Jianguo Chen ◽  
Peng Du ◽  
Hongyong Yuan
Keyword(s):  
Climate Change ◽  
Spatial Scale ◽  
Spatial Scales ◽  
Seasonal Fluctuation ◽  
Extreme Weather ◽  
Temperature And Precipitation ◽  
Weather Variation ◽  
Variation Characteristics ◽  
Established Fact ◽  
Temporal And Spatial

It has been demonstrated that climate change is an established fact. A good comprehension of climate and extreme weather variation characteristics on a temporal and a spatial scale is important for adaptation and response. In this work, the characteristics of temperature, precipitation, and extreme weather distribution and variation is summarized for a period of 60 years and the seasonal fluctuation of temperature and precipitation is also analyzed. The results illustrate the reduction in daily and annual temperature divergence on both temporal and spatial scales. However, the gaps remain relatively significant. Furthermore, the disparity in daily and annual precipitation are found to be increasing on both temporal and spatial scales. The findings indicate that climate change, to a certain extent, narrowed the temperature gap while widening the precipitation gap on temporal and spatial scales in China.

Scale-dependent relationships between benthic habitat characteristics and abundances of blacklip abalone, Haliotis rubra (Leach)

2010 ◽  
Vol 61 (11) ◽  
pp. 1227 ◽  
Author(s):  
Elisabeth M. A. Strain ◽  
Craig R. Johnson
Keyword(s):  
Spatial Scale ◽  
Red Algae ◽  
Positive Relationship ◽  
Spatial Scales ◽  
Habitat Characteristics ◽  
Benthic Habitat ◽  
Sessile Invertebrates ◽  
Haliotis Rubra ◽  
The Relationship ◽  
Biotic Characteristics

Habitat characteristics can influence marine herbivore densities at a range of spatial scales. We examined the relationship between benthic habitat characteristics and adult blacklip abalone (Haliotis rubra) densities across local scales (0.0625–16 m2), at 2 depths, 4 sites and 2 locations, in Tasmania, Australia. Biotic characteristics that were highly correlated with abalone densities included cover of non-calcareous encrusting red algae (NERA), non-geniculate coralline algae (NCA), a matrix of filamentous algae and sediment, sessile invertebrates, and foliose red algae. The precision of relationships varied with spatial scale. At smaller scales (0.0625–0.25 m2), there was a positive relationship between NERA and ERA, and negative relationships between sediment matrix, sessile invertebrates and abalone densities. At the largest scale (16 m2), there was a positive relationship between NERA and abalone densities. Thus, for some biotic characteristics, the relationship between NERA and abalone densities may be scalable. There was very little variability between depths and sites; however, the optimal spatial scale differed between locations. Our results suggest a dynamic interplay between the behavioural responses of H. rubra to microhabitat and/or to abalone maintaining NERA free of algae, sediment, and sessile invertebrates. This approach could be used to describe the relationship between habitat characteristics and species densities at the optimal spatial scales.

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.

Synchrony of frond dynamics among patches of the clonal seaweed Mazzaella parksii (Rhodophyta) at local spatial scale

2004 ◽  
Vol 84 (5) ◽  
pp. 883-886 ◽  
Author(s):  
Ricardo Scrosati
Keyword(s):  
Spatial Scale ◽  
Seasonal Changes ◽  
Pacific Coast ◽  
Spatial Scales ◽  
Sampling Effort ◽  
Confidence Limits ◽  
Seasonal Trends ◽  
Intertidal Seaweed ◽  
The Mean

This study investigated the synchrony of frond dynamics among patches of the intertidal seaweed Mazzaella parksii (=M. cornucopiae; Rhodophyta: Gigartinales) at local spatial scale. At Prasiola Point (Pacific coast of Canada), the mean synchrony of the seasonal changes in frond density among seven permanent, 100-cm2 quadrats was significant (mean Pearson's r=0·73, with 0·65–0·81 as 95% confidence limits) between 1993 and 1995. This indicates that predicting seasonal trends for non-monitored patches at local spatial scale can be done relatively well based on observations on a limited number of quadrats. The identification of the spatial scales at which seaweed populations covary synchronously will permit minimizing sampling effort while retaining the ability to make valid predictions for non-monitored sites.

scholarly journals Evaluation of Asian summer precipitation in different configurations of a high-resolution general circulation model in a range of decision-relevant spatial scales

2021 ◽  
Vol 25 (12) ◽  
pp. 6381-6405
Author(s):  
Mark R. Muetzelfeldt ◽  
Reinhard Schiemann ◽  
Andrew G. Turner ◽  
Nicholas P. Klingaman ◽  
Pier Luigi Vidale ◽  
...  
Keyword(s):  
High Resolution ◽  
Spatial Scale ◽  
Diurnal Cycle ◽  
General Circulation ◽  
Spatial Scales ◽  
Summer Precipitation ◽  
Physical Geography ◽  
Simulated Precipitation ◽  
The Mean ◽  
Precipitation Bias

Abstract. High-resolution general circulation models (GCMs) can provide new insights into the simulated distribution of global precipitation. We evaluate how summer precipitation is represented over Asia in global simulations with a grid length of 14 km. Three simulations were performed: one with a convection parametrization, one with convection represented explicitly by the model's dynamics, and a hybrid simulation with only shallow and mid-level convection parametrized. We evaluate the mean simulated precipitation and the diurnal cycle of the amount, frequency, and intensity of the precipitation against satellite observations of precipitation from the Climate Prediction Center morphing method (CMORPH). We also compare the high-resolution simulations with coarser simulations that use parametrized convection. The simulated and observed precipitation is averaged over spatial scales defined by the hydrological catchment basins; these provide a natural spatial scale for performing decision-relevant analysis that is tied to the underlying regional physical geography. By selecting basins of different sizes, we evaluate the simulations as a function of the spatial scale. A new BAsin-Scale Model Assessment ToolkIt (BASMATI) is described, which facilitates this analysis. We find that there are strong wet biases (locally up to 72 mm d−1 at small spatial scales) in the mean precipitation over mountainous regions such as the Himalayas. The explicit convection simulation worsens existing wet and dry biases compared to the parametrized convection simulation. When the analysis is performed at different basin scales, the precipitation bias decreases as the spatial scales increase for all the simulations; the lowest-resolution simulation has the smallest root mean squared error compared to CMORPH. In the simulations, a positive mean precipitation bias over China is primarily found to be due to too frequent precipitation for the parametrized convection simulation and too intense precipitation for the explicit convection simulation. The simulated diurnal cycle of precipitation is strongly affected by the representation of convection: parametrized convection produces a peak in precipitation too close to midday over land, whereas explicit convection produces a peak that is closer to the late afternoon peak seen in observations. At increasing spatial scale, the representation of the diurnal cycle in the explicit and hybrid convection simulations improves when compared to CMORPH; this is not true for any of the parametrized simulations. Some of the strengths and weaknesses of simulated precipitation in a high-resolution GCM are found: the diurnal cycle is improved at all spatial scales with convection parametrization disabled, the interaction of the flow with orography exacerbates existing biases for mean precipitation in the high-resolution simulations, and parametrized simulations produce similar diurnal cycles regardless of their resolution. The need for tuning the high-resolution simulations is made clear. Our approach for evaluating simulated precipitation across a range of scales is widely applicable to other GCMs.

scholarly journals Forest birds respond to the spatial pattern of exurban development in the Mid-Atlantic region, USA

PeerJ ◽  
2016 ◽  
Vol 4 ◽  
pp. e2039 ◽  
Author(s):  
Marcela Suarez-Rubio ◽  
Todd R. Lookingbill
Keyword(s):  
Spatial Pattern ◽  
Spatial Scale ◽  
Forest Fragmentation ◽  
Spatial Scales ◽  
The United States ◽  
Forest Edge ◽  
Forest Birds ◽  
Bird Diversity ◽  
Forest Loss ◽  
Exurban Development

Housing development beyond the urban fringe (i.e., exurban development) is one of the fastest growing forms of land-use change in the United States. Exurban development’s attraction to natural and recreational amenities has raised concerns for conservation and represents a potential threat to wildlife. Although forest-dependent species have been found particularly sensitive to low housing densities, it is unclear how the spatial distribution of houses affects forest birds. The aim of this study was to assess forest bird responses to changes in the spatial pattern of exurban development and also to examine species responses when forest loss and forest fragmentation were considered. We evaluated landscape composition around North American Breeding Bird Survey stops between 1986 and 2009 by developing a compactness index to assess changes in the spatial pattern of exurban development over time. Compactness was defined as a measure of how clustered exurban development was in the area surrounding each survey stop at each time period considered. We used Threshold Indicator Taxa Analysis to detect the response of forest and forest-edge species in terms of occurrence and relative abundance along the compactness gradient at two spatial scales (400-m and 1-km radius buffer). Our results showed that most forest birds and some forest-edge species were positively associated with high levels of compactness at the larger spatial scale; the proportion of forest in the surrounding landscape also had a significant effect when forest loss and forest fragmentation were accounted for. In contrast, the spatial configuration of exurban development was an important predictor of occurrence and abundance for only a few species at the smaller spatial scale. The positive response of forest birds to compactness at the larger scale could represent a systematic trajectory of decline and could be highly detrimental to bird diversity if exurban growth continues and creates more compacted development.

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