scholarly journals Efficient Bootstrap Estimates for Tail Statistics

2016 ◽  
Author(s):  
Øyvind Breivik ◽  
Ole Johan Aarnes

Abstract. Bootstrap resamples can be used to investigate the tail of empirical distributions as well as return value estimates based on the extremal behaviour of the distribution. Specifically, the confidence intervals on return value estimates or bounds on in-sample tail statistics can be estimated using bootstrap techniques. However, bootstrapping from the entire data set is expensive. It is shown here that it suffices to bootstrap from a small subset consisting of the highest entries in the sequence to make estimates that are essentially identical to bootstraps from the entire sequence. Similarly, bootstrap estimates of confidence intervals of threshold return estimates are found to be well approximated by using a subset consisting of the highest entries. This has practical consequences in fields such as meteorology, oceanography and hydrology where return estimates are routinely made from very large gridded model integrations spanning decades at high temporal resolution. In such cases the computational savings are substantial.

2017 ◽  
Vol 17 (3) ◽  
pp. 357-366 ◽  
Author(s):  
Øyvind Breivik ◽  
Ole Johan Aarnes

Abstract. Bootstrap resamples can be used to investigate the tail of empirical distributions as well as return value estimates from the extremal behaviour of the sample. Specifically, the confidence intervals on return value estimates or bounds on in-sample tail statistics can be obtained using bootstrap techniques. However, non-parametric bootstrapping from the entire sample is expensive. It is shown here that it suffices to bootstrap from a small subset consisting of the highest entries in the sequence to make estimates that are essentially identical to bootstraps from the entire sample. Similarly, bootstrap estimates of confidence intervals of threshold return estimates are found to be well approximated by using a subset consisting of the highest entries. This has practical consequences in fields such as meteorology, oceanography and hydrology where return values are calculated from very large gridded model integrations spanning decades at high temporal resolution or from large ensembles of independent and identically distributed model fields. In such cases the computational savings are substantial.


2019 ◽  
Vol 11 (11) ◽  
pp. 1266 ◽  
Author(s):  
Mingzheng Zhang ◽  
Dehai Zhu ◽  
Wei Su ◽  
Jianxi Huang ◽  
Xiaodong Zhang ◽  
...  

Continuous monitoring of crop growth status using time-series remote sensing image is essential for crop management and yield prediction. The growing season of summer corn in the North China Plain with the period of rain and hot, which makes the acquisition of cloud-free satellite imagery very difficult. Therefore, we focused on developing image datasets with both a high temporal resolution and medium spatial resolution by harmonizing the time-series of MOD09GA Normalized Difference Vegetation Index (NDVI) images and 30-m-resolution GF-1 WFV images using the improved Kalman filter model. The harmonized images, GF-1 images, and Landsat 8 images were then combined and used to monitor the summer corn growth from 5th June to 6th October, 2014, in three counties of Hebei Province, China, in conjunction with meteorological data and MODIS Evapotranspiration Data Set. The prediction residuals ( Δ P R K ) in NDVI between the GF-1 observations and the harmonized images was in the range of −0.2 to 0.2 with Gauss distribution. Moreover, the obtained phenological curves manifested distinctive growth features for summer corn at field scales. Changes in NDVI over time were more effectively evaluated and represented corn growth trends, when considered in conjunction with meteorological data and MODIS Evapotranspiration Data Set. We observed that the NDVI of summer corn showed a process of first decreasing and then rising in the early growing stage and discuss how the temperature and moisture of the environment changed with the growth stage. The study demonstrated that the synthesized dataset constructed using this methodology was highly accurate, with high temporal resolution and medium spatial resolution and it was possible to harmonize multi-source remote sensing imagery by the improved Kalman filter for long-term field monitoring.


2015 ◽  
Vol 8 (7) ◽  
pp. 2901-2907 ◽  
Author(s):  
Z. Wang ◽  
D. Liu ◽  
Y. Wang ◽  
Z. Wang ◽  
G. Shi

Abstract. A strong diurnal variation of aerosol has been observed in many heavily polluted regions in China. This variation could affect the direct aerosol radiative forcing (DARF) evaluation if the daily averaged value is used as normal rather than the time-resolved values. To quantify the effect of using the daily averaged DARF, 196 days of high temporal resolution ground-based data collected in SKYNET Hefei site during the period from 2007 to 2013 is used to perform an assessment. We demonstrate that strong diurnal changes of heavy aerosol loading have an impact on the 24-h averaged DARF when daily averaged optical properties are used to retrieve this quantity. The DARF errors varying from −7.6 to 15.6 W m−2 absolutely and from 0.1 to 28.5 % relatively were found between the calculations using daily average aerosol properties, and those using time-resolved aerosol observations. These errors increase with increasing daily aerosol optical depth (AOD) and decreasing daily single-scattering albedo (SSA), indicating that the high temporal resolution DARF data set should be used in the model instead of the normal daily-averaged one, especially under heavy aerosol loading conditions for regional campaign studies. We also found that statistical errors (0.3 W m−2 absolutely and 11.8 % relatively) will be less, which means that the effect of using the daily averaged DARF can be weakened by using a long-term observational data set.


2018 ◽  
Vol 15 (7) ◽  
pp. 2021-2032 ◽  
Author(s):  
Maria Provenzale ◽  
Anne Ojala ◽  
Jouni Heiskanen ◽  
Kukka-Maaria Erkkilä ◽  
Ivan Mammarella ◽  
...  

Abstract. Lakes are important actors in biogeochemical cycles and a powerful natural source of CO2. However, they are not yet fully integrated in carbon global budgets, and the carbon cycle in the water is still poorly understood. In freshwater ecosystems, productivity studies have usually been carried out with traditional methods (bottle incubations, 14C technique), which are imprecise and have a poor temporal resolution. Consequently, our ability to quantify and predict the net ecosystem productivity (NEP) is limited: the estimates are prone to errors and the NEP cannot be parameterised from environmental variables. Here we expand the testing of a free-water method based on the direct measurement of the CO2 concentration in the water. The approach was first proposed in 2008, but was tested on a very short data set (3 days) under specific conditions (autumn turnover); despite showing promising results, this method has been neglected by the scientific community. We tested the method under different conditions (summer stratification, typical summer conditions for boreal dark-water lakes) and on a much longer data set (40 days), and quantitatively validated it comparing our data and productivity models. We were able to evaluate the NEP with a high temporal resolution (minutes) and found a very good agreement (R2≥0.71) with the models. We also estimated the parameters of the productivity–irradiance (PI) curves that allow the calculation of the NEP from irradiance and water temperature. Overall, our work shows that the approach is suitable for productivity studies under a wider range of conditions, and is an important step towards developing this method so that it becomes more widely used.


Polar Record ◽  
2002 ◽  
Vol 38 (205) ◽  
pp. 115-120 ◽  
Author(s):  
Yongwei Sheng ◽  
Laurence C. Smith ◽  
Karen E. Frey ◽  
Douglas E. Alsdorf

AbstractRadar backscatter in Arctic and sub-Arctic regions is temporally dynamic and reflects changes in sea ice, glacier facies, soil thaw state, vegetation cover, and moisture content. Wind scatterometers on the ERS-1 and ERS-2 satellites have amassed a global archive of C-band radar backscatter data since 1991. This paper derives three high temporal resolution data products from this archive that are designed to facilitate scatterometer research in high-latitude environments. Radar backscatter data have a grid spacing of 25 km and are mapped northwards from 60°N latitude over intervals of one, three, and seven days for the period 1991–2000. Data are corrected to a normalized incident angle of 40°. Animations and full-resolution data products are freely available for scientific use at http://merced.gis.ucla.edu/scatterometer/index.htm.


2017 ◽  
Author(s):  
Maria Provenzale ◽  
Anne Ojala ◽  
Jouni Heiskanen ◽  
Kukka-Maaria Erkkilä ◽  
Ivan Mammarella ◽  
...  

Abstract. Lakes are important actors in biogeochemical cycles and a powerful natural source of CO2. However, they are not yet fully integrated in carbon budgets, and the carbon cycle in the water is still poorly understood. In freshwater ecosystems, productivity studies have usually been carried out with traditional methods (bottle incubations, 14C technique), which are imprecise and have a poor temporal resolution. Consequently, our ability to quantify and predict the net ecosystem productivity (NEP) is limited: the estimates are prone to errors and the NEP cannot be parameterized from environmental variables. Here we expand the testing of a free-water method based on the direct measurement of the CO2 concentration in the water. The approach was proposed already in 2008, but was tested on a very short data set (3 days) under specific conditions (autumn turnover); despite showing promising results, it has not been used ever since. We tested the method under different conditions (summer stratification, typical summer conditions for boreal dark-water lakes) and on a much longer data set (40 days), and quantitatively validated it comparing our data and productivity models. We were able to evaluate the NEP with a high temporal resolution (minutes) and found an excellent agreement with the models. We also estimated the parameters of the productivity-irradiance (PI) curves that allow the calculation of the NEP from irradiance and water temperature. Overall, our work shows that the approach is suitable for productivity studies under a wider range of conditions, and is an important step towards developing it so that it becomes even more general.


Author(s):  
Jing Wang ◽  
Bo Huang

As Moderate Resolution Imaging Spectroradiometer (MODIS) and Enhanced Thematic Mapper Plus (ETM+) has a tradeoff between the high temporal resolution and high spatial resolution, this paper proposed a spatial and temporal model with auto-regression error correction (AREC) method to blend the two types of images in order to obtain the composed image with both high spatial and temporal resolution. Experiments and validation were conducted on a data set located in Shenzhen, China and compared with Spatial and Temporal Adaptive Reflectance Fusion Model (STARFM) in several objective indexes and visual analysis. It was found that AREC could effectively predict the land cover changes and the fusion results had better performances versus the ones of STARFM.


Author(s):  
Jing Wang ◽  
Bo Huang

As Moderate Resolution Imaging Spectroradiometer (MODIS) and Enhanced Thematic Mapper Plus (ETM+) has a tradeoff between the high temporal resolution and high spatial resolution, this paper proposed a spatial and temporal model with auto-regression error correction (AREC) method to blend the two types of images in order to obtain the composed image with both high spatial and temporal resolution. Experiments and validation were conducted on a data set located in Shenzhen, China and compared with Spatial and Temporal Adaptive Reflectance Fusion Model (STARFM) in several objective indexes and visual analysis. It was found that AREC could effectively predict the land cover changes and the fusion results had better performances versus the ones of STARFM.


2015 ◽  
Vol 15 (22) ◽  
pp. 13241-13267 ◽  
Author(s):  
G. Roberts ◽  
M. J. Wooster ◽  
W. Xu ◽  
P. H. Freeborn ◽  
J.-J. Morcrette ◽  
...  

Abstract. Characterising the dynamics of landscape-scale wildfires at very high temporal resolutions is best achieved using observations from Earth Observation (EO) sensors mounted onboard geostationary satellites. As a result, a number of operational active fire products have been developed from the data of such sensors. An example of which are the Fire Radiative Power (FRP) products, the FRP-PIXEL and FRP-GRID products, generated by the Land Surface Analysis Satellite Applications Facility (LSA SAF) from imagery collected by the Spinning Enhanced Visible and Infrared Imager (SEVIRI) onboard the Meteosat Second Generation (MSG) series of geostationary EO satellites. The processing chain developed to deliver these FRP products detects SEVIRI pixels containing actively burning fires and characterises their FRP output across four geographic regions covering Europe, part of South America and Northern and Southern Africa. The FRP-PIXEL product contains the highest spatial and temporal resolution FRP data set, whilst the FRP-GRID product contains a spatio-temporal summary that includes bias adjustments for cloud cover and the non-detection of low FRP fire pixels. Here we evaluate these two products against active fire data collected by the Moderate Resolution Imaging Spectroradiometer (MODIS) and compare the results to those for three alternative active fire products derived from SEVIRI imagery. The FRP-PIXEL product is shown to detect a substantially greater number of active fire pixels than do alternative SEVIRI-based products, and comparison to MODIS on a per-fire basis indicates a strong agreement and low bias in terms of FRP values. However, low FRP fire pixels remain undetected by SEVIRI, with errors of active fire pixel detection commission and omission compared to MODIS ranging between 9–13 % and 65–77 % respectively in Africa. Higher errors of omission result in greater underestimation of regional FRP totals relative to those derived from simultaneously collected MODIS data, ranging from 35 % over the Northern Africa region to 89 % over the European region. High errors of active fire omission and FRP underestimation are found over Europe and South America and result from SEVIRI's larger pixel area over these regions. An advantage of using FRP for characterising wildfire emissions is the ability to do so very frequently and in near-real time (NRT). To illustrate the potential of this approach, wildfire fuel consumption rates derived from the SEVIRI FRP-PIXEL product are used to characterise smoke emissions of the 2007 "mega-fire" event focused on Peloponnese (Greece) and used within the European Centre for Medium-Range Weather Forecasting (ECMWF) Integrated Forecasting System (IFS) as a demonstration of what can be achieved when using geostationary active fire data within the Copernicus Atmosphere Monitoring Service (CAMS). Qualitative comparison of the modelled smoke plumes with MODIS optical imagery illustrates that the model captures the temporal and spatial dynamics of the plume very well, and that high temporal resolution emissions estimates such as those available from a geostationary orbit are important for capturing the sub-daily variability in smoke plume parameters such as aerosol optical depth (AOD), which are increasingly less well resolved using daily or coarser temporal resolution emissions data sets. Quantitative comparison of modelled AOD with coincident MODIS and AERONET (Aerosol Robotic Network) AOD indicates that the former is overestimated by ~ 20–30 %, but captures the observed AOD dynamics with a high degree of fidelity. The case study highlights the potential of using geostationary FRP data to drive fire emissions estimates for use within atmospheric transport models such as those implemented in the Monitoring Atmospheric Composition and Climate (MACC) series of projects for the CAMS.


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