Composite Time Series Research Articles

Forecasting compositional time series

Compositional data sets occur in many disciplines and give rise to some interesting statistical considerations. In recent years, the modelling and forecasting of compositional time series has seen some important developments, although this approach does not seem to be widely known. This paper represents a modest step towards rectifying this. After briefly setting out the basic structure of compositional data sets and outlining the implications for forecasting compositional time series, it illustrates the techniques using three examples: modelling and forecasting expenditure shares in the U.K. economy; forecasting trends in obesity in England; and examining shifts in the proportions of English first class cricketers born during particular quarters of the year.

Species‐sorting may explain an apparent minimal effect of immigration on freshwater bacterial community dynamics

Long distance atmospheric transport of bacterial cells is often implied as a driver of the apparent cosmopolitan distribution of bacterial taxa. Surprisingly, efforts to measure immigration in bacterial communities are rare. An 8-week time series of within-lake bacterial community composition and atmospheric deposition rates and composition were used to estimate the influence of immigration on bacterial community dynamics in two north temperate lakes. Characterization of bacterial community dynamics using automated ribosomal intergenic spacer analysis suggested moderate overlap in composition between the lakes and atmospherically deposited cells. However, taxa that appeared to be delivered by atmospheric deposition had a relatively minor influence on lake bacterial community dynamics. The weak influence of immigrating bacterial taxa suggests that a species-sorting concept best describes aquatic bacterial metacommunity dynamics.

Reconstruction of solar UV irradiance since 1974

Variations of the solar UV irradiance are an important driver of chemical and physical processes in the Earth's upper atmosphere and may also influence global climate. Here we reconstruct solar UV irradiance in the range 115–400 nm over the period 1974–2007 by making use of the recently developed empirical extension of the Spectral And Total Irradiance Reconstruction (SATIRE) models employing Solar Ultraviolet Spectral Irradiance Monitor (SUSIM) data. The evolution of the solar photospheric magnetic flux, which is a central input to the model, is described by the magnetograms and continuum images recorded at the Kitt Peak National Solar Observatory between 1974 and 2003 and by the Michelson Doppler Imager instrument on SOHO since 1996. The reconstruction extends the available observational record by 1.5 solar cycles. The reconstructed Ly‐α irradiance agrees well with the composite time series by Woods et al. (2000). The amplitude of the irradiance variations grows with decreasing wavelength and in the wavelength regions of special interest for studies of the Earth's climate (Ly‐α and oxygen absorption continuum and bands between 130 and 350 nm) is 1–2 orders of magnitude stronger than in the visible or if integrated over all wavelengths (total solar irradiance).

The effect of thresholding on temporal avalanche statistics

We discuss intermittent time series consisting of discrete bursts or avalanches separated bywaiting or silent times. The short time correlations can be understood to follow from theproperties of individual avalanches, while longer time correlations often present in suchsignals reflect correlations between triggerings of different avalanches. As onepossible source of the latter kinds of correlations in experimental time series, weconsider the effect of a finite detection threshold, due to e.g. experimental noise thatneeds to be removed. To this end, we study a simple toy model of an avalanche,a random walk returning to the origin or a Brownian bridge, in the presenceand absence of superimposed delta-correlated noise. We discuss the propertiesafter thresholding of artificial time series obtained by mixing toy avalanches andwaiting times from a Poisson process. Most of the resulting scalings for individualavalanches and the composite time series can be understood via random walktheory, except for the waiting time distributions when strong additional noise isadded. Then, to compare with a more complicated case we study the Mannasandpile model of self-organized criticality, where some further complicationsappear.

Size distribution, mass concentration, chemical and mineralogical composition and derived optical parameters of the boundary layer aerosol at Tinfou, Morocco, during SAMUM 2006

During the SAMUM 2006 field campaign in southern Morocco, physical and chemical properties of desert aerosols were measured. Mass concentrations ranging from 30μgm−3 for PM2.5 under desert background conditions up to 300 000μgm−3 for total suspended particles (TSP) during moderate dust storms were measured. TSP dust concentrations are correlated with the local wind speed, whereasPM10 andPM2.5 concentrations are determined by advection from distant sources. Size distributions were measured for particles with diameter between 20 nm and 500μm (parametrizations are given). Two major regimes of the size spectrum can be distinguished. For particles smaller than 500 nm diameter, the distributions show maxima around 80 nm, widely unaffected of varying meteorological and dust emission conditions. For particles larger than 500 nm, the range of variation may be up to one order of magnitude and up to three orders of magnitude for particles larger than 10μm. The mineralogical composition of aerosol bulk samples was measured by X-ray powder diffraction. Major constituents of the aerosol are quartz, potassium feldspar, plagioclase, calcite, hematite and the clay minerals illite, kaolinite and chlorite. A small temporal variability of the bulk mineralogical composition was encountered. The chemical composition of approximately 74 000 particles was determined by electron microscopic single particle analysis. Three size regimes are identified: for smaller than 500 nm in diameter, the aerosol consists of sulphates and mineral dust. For larger than 500 nm up to 50μm, mineral dust dominates, consisting mainly of silicates, and—to a lesser extent—carbonates and quartz. For diameters larger than 50μm, approximately half of the particles consist of quartz. Time series of the elemental composition show a moderate temporal variability of the major compounds. Calcium-dominated particles are enhanced during advection from a prominent dust source in Northern Africa (Chott El Djerid and surroundings). The particle aspect ratio was measured for all analysed particles. Its size dependence reflects that of the chemical composition. For larger than 500 nm particle diameter, a median aspect ratio of 1.6 is measured. Towards smaller particles, it decreases to about 1.3 (parametrizations are given). From the chemical/mineralogical composition, the aerosol complex refractive index was determined for several wavelengths from ultraviolet to near-infrared. Both real and imaginary parts show lower values for particles smaller than 500 nm in diameter (1.55–2.8 × 10−3i at 530 nm) and slightly higher values for larger particles (1.57–3.7 × 10−3i at 530 nm).

The Large-Scale Circulation Change at the End of the Baiu Season in Japan as Seen in ERA40 Data

The time evolution of the circulation change at the end of the Baiu season is investigated using ERA40 data. An end-day is defined for each of the 23 years based on the 850 hPa θe value at 40˚Nin the 130-140˚E sector exceeding 330 K. Daily time series of variables are composited with respect to this day. These composite time-series exhibit a clearer and more rapid change in the precipitation and the large-scale circulation over the whole East Asia region than those performed using calendar days. The precipitation change includes the abrupt end of the Baiu rain, the northward shift of tropical convection perhaps starting a few days before this, and the start of the heavier rain at higher latitudes. The northward migration of lower tropospheric warm, moist tropical air, a general feature of the seasonal march in the region, is fast over the continent and slow over the ocean. By mid to late July the cooler air over the Sea of Japan is surrounded on 3 sides by the tropical air. It is suggestive that the large-scale stage has been set for a jump to the post-Baiu state, i.e., for the end of the Baiu season. Two likely triggers for the actual change emerge from the analysis. The first is the northward movement of tropical convection into the Philippine region. The second is an equivalent barotropic Rossby wave-train, that over a 10-day period develops downstream across Eurasia. It appears likely that in most years one or both mechanisms can be important in triggering the actual end of the Baiu season.

Seasonal evolution of the isotopic composition of atmospheric water vapour above a tropical lake: Deuterium excess and implication for water recycling

We present an analysis of the rainfall–evaporation–atmospheric moisture cycle in a semi-arid tropical zone (southwestern Madagascar) to quantify the recycling and mixing processes that occur above an endorheic lake system (Lake Ihotry) during an annual cycle. The study combines an isotope mass balance with a detailed field investigation of the lake system and a previously established daily time-step lake water balance model. The mass balance and Craig-Gordon equations are used to calculate the isotopic composition of the evaporative flux from the lake surface ( δ E) and to derive a daily time series of the ambient atmospheric water vapour composition above the lake ( δ AL) during a 8-month dry season. Calculated δ AL results from a mixing between regional moisture ( δ AR) and locally evaporated water ( δ E), the latter representing 50% of δ AL at the end of the dry season. The contribution of recycled moisture to on-lake precipitation during the wet season is estimated to ⩾16%. We show that, as expected, the deuterium excess is high in recycled precipitation and low in evaporated precipitation, but also that the recycled moisture in an endorheic system may have a low deuterium excess resulting from the low deuterium excess in regional precipitation. In case of a long evaporative season, the atmospheric moisture is not in isotopic equilibrium with the annual composition of precipitation because of the contribution of the recycled vapour to the local atmospheric pool. Our approach demonstrates the importance of water recycling on the atmospheric moisture cycle and precipitation in a tropical semi-arid system, and can be applied to other natural systems, enlarging the potential range of investigation of the atmospheric vapour cycle and rainfall sources in tropical lands. It may also represent a valuable complement to direct water vapour sampling, in yielding the long-term evolution of the atmospheric vapour composition with spatially averaged values and smoothed temporal variations.

How Rossby wave breaking over the Pacific forces the North Atlantic Oscillation

Anticyclonic Rossby wave breaking (RWB) over a well‐defined, limited‐area region of the east Pacific leads to the positive polarity of the North Atlantic Oscillation (NAO) by locally piling up wave activity where it may be advected downstream, resulting in increased wave activity flux and anticyclonic RWB over the subtropical Atlantic. A composite time series shows that Pacific RWB occurs several days prior to the Atlantic RWB and the peak of the NAO index. Following Pacific RWB, a channel of increased pseudomomentum flux extends from the Pacific wave breaking region, northeastward toward midlatitudes of eastern North America where pseudomomentum density accumulates for several days prior to moving eastward and leading to anticyclonic RWB over the Atlantic.

A Hybrid Remote Sensing Approach to Quantifying Crop Residue Burning in the United States

Crop residue burning is an important land use activity in the United States. Currently, satellite-based burned area methodologies specifically calibrated for crop residue burning are limited. This article describes a satellite observations-based hybrid approach to estimate the amount of burned crop residues that combines Moderate Resolution Imaging Spectroradiometer (MODIS) 8-day differencing of Normalized Burn Ratio (dNBR) burned area mapping with MODIS active fire counts calibrated into area. The dNBR approach utilizes the spectral response of the 2.1-µm shortwave infrared MODIS band to detect burned pixels. A time series of 8-day MODIS composites produces burned area estimates during harvest on a near-weekly scale. This approach was tested on the study area of MODIS tile h10v05, which encompasses much of the Mississippi River Delta and the southern Great Plains, for the years 2003 through 2006. Within this area, an average of 12,700 and 10,835 km2 burned in the spring and fall harvests, respectively. Results from the hybrid approach are validated through comparison with high-resolution Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) data and field data. Validation of the hybrid approach shows strong correspondence with both the ASTER (mean R2 = 0.92) and in-situ data (mean accuracy 85.5%). At the state level, the estimated burn rates from this analysis compare well with reported Arkansas burn rates. Results suggest potential for using the approach to monitor and quantify fire activity in cropland areas of the United States.

Regionalization and reconstruction of snow water equivalent in the upper Colorado River basin

Summary This study focuses on regionalization and reconstruction of April 1 snow water equivalent (SWE) of snow courses stations located in the Upper Colorado River basin (UCRB) and evaluates regional drought scenarios for the last 480 years. Rotated principal component analysis (PCA) and cluster analysis were used to regionalize the snow course stations in the UCRB. Both methods of regionalization identified four regions of snow course stations, which were spatially distributed in the regions (east, west, north and south). Then, partial least squares regression (PLSR) was used to reconstruct three regional SWE time series in the UCRB based on residual tree-ring chronologies. Tree-ring chronologies that were positively and negatively correlated with higher than 95% confidence levels (based on the absolute value of correlation with the regional composite April 1 SWE) were screened and retained as a pool of predictors. The PLSR reconstruction model was developed using all the ranked chronologies available in the pool of predictors, and then sequentially the least correlated predictor was removed and PLSR was rerun. This process was continued until an optimal performance was obtained. In addition to the regional composite April 1 SWE reconstruction, individual April 1 SWE stations with the highest loading from each principal component were also reconstructed in order to compare the performance. The regional reconstruction of SWE had better statistical performance as compared to the individual station’s reconstruction. The spatial and temporal variability of drought was evaluated based on the duration as identified by the 3-year, 5-year and 10-year moving average of three reconstructed regional composite time series of April 1 SWE. Finally, the drought duration from SWE was compared with the drought duration based on three reconstructed water year streamflow each from the identified regions. The results indicate the average drought duration in the basin was 3–14 years depending upon the variables (April 1 SWE and water year streamflow) and the moving average considered.

Total Solar Irradiance Measurement and Modelling during Cycle 23

During solar cycle 23, which is now close to its end, variations of the total solar irradiance were measured by six different instruments, providing four independent time series of the irradiance variation over the complete solar cycle. A new composite time series constructed using five of these six instruments provides unprecedented instrument stability for the study of the open question of solar irradiance variations between minima. An independent analysis of the different composite time series is performed through an empirical proxy model fit. The new composite is fitted with 0.96 correlation (R2=93%) and RMS error of 0.15 W m−2, thus reaching the limit of the individual instrument stabilities. Both the measurements and the model indicate that for the current cycle the minimum irradiance level has not yet been reached. Therefore we use the model to extrapolate measurements up to 2008 when the minimum irradiance level is expected. If we assume that there will be no changes in the solar irradiance from 2006 to 2008 that are not captured by the regression model, it can be predicted that there will be no variation of the solar minimum irradiance level during cycle 23 with an uncertainty of ±0.14 W m−2.

A VARI-based relative greenness from MODIS data for computing the Fire Potential Index

The Fire Potential Index (FPI) relies on relative greenness (RG) estimates from remote sensing data. The Normalized Difference Vegetation Index (NDVI), derived from NOAA Advanced Very High Resolution Radiometer (AVHRR) imagery is currently used to calculate RG operationally. Here we evaluated an alternate measure of RG using the Visible Atmospheric Resistant Index (VARI) derived from Moderate Resolution Imaging Spectrometer (MODIS) data. VARI was chosen because it has previously been shown to have the strongest relationship with Live Fuel Moisture (LFM) out of a wide selection of MODIS-derived indices in southern California shrublands. To compare MODIS-based NDVI-FPI and VARI-FPI, RG was calculated from a 6-year time series of MODIS composites and validated against in-situ observations of LFM as a surrogate for vegetation greenness. RG from both indices was then compared in terms of its performance for computing the FPI using historical wildfire data. Computed RG values were regressed against ground-sampled LFM at 14 sites within Los Angeles County. The results indicate that VARI-based RG consistently shows a stronger relationship with observed LFM than NDVI-based RG. With an average R 2 of 0.727 compared to a value of only 0.622 for NDVI-RG, VARI-RG showed stronger relationships at 13 out of 14 sites. Based on these results, daily FPI maps were computed for the years 2001 through 2005 using both NDVI-RG and VARI-RG. These were then validated against 12,490 fire detections from the MODIS active fire product using logistic regression. Deviance of the logistic regression model was 408.8 for NDVI-FPI and 176.2 for VARI-FPI. The c-index was found to be 0.69 and 0.78, respectively. The results show that VARI-FPI outperforms NDVI-FPI in distinguishing between fire and no-fire events for historical wildfire data in southern California for the given time period.

Multi‐sensor analysis of water storage variations of the Caspian Sea

We perform a multi‐sensor analysis of water storage and surface height variations of the Caspian Sea, from mid‐2002 through 2006. Data from three satellite missions (GRACE, Jason‐1, and Aqua) are used to examine the relationship between changes in spatially averaged sea surface height (SSH) and water storage in and around the Caspian Sea. Two composite time series are constructed to represent the mass change signal, the first by removing a model of nearby hydrological signals from the GRACE time series, and the second by subtracting a MODIS SST‐based estimate of thermal expansion from the Jason‐1 time series. The composite time series agree well (rms difference = 5.2 cm), and a positive trend is seen in both the GRACE (4.5 ± 0.7 cm/yr) and Jason (3.2 ± 0.3 cm/yr) composite time series. This analysis provides an indirect means of validating these data at regional spatial and monthly temporal scales.

A robust new method for analyzing community change and an example using 83 years of avian response to forest succession

The composition of animal communities changes over time in response to natural processes (disease dynamics, plant community succession) and anthropogenic disturbances (habitat fragmentation, climate change). Detection and analysis of community change is important for regional and site-specific management and for conservation planning. However, formal time series of animal community composition are rare. We describe a distribution-free method for compiling time series from separate studies to test for changes in community composition. The method, based on rank-permutation, is robust to many problems associated with data from separate studies, including unequal sampling effort, variable-length intervals between sampling, and different sampling protocols. We apply the technique to a time series constructed from five surveys of land bird community composition spanning 83 years of forest succession in northern lower Michigan, USA. We found increases in neotropical migrants, area-sensitive birds, and woodland birds. Despite high species turnover, the overall taxonomic composition of the land bird community did not show significant changes. Although more powerful tests can be applied when data are collected under consistent protocols, our approach is a useful alternative when such data are lacking. In the example provided, our method produced coherent results that are consistent with other published studies from the region.

Defining the climatic signal in stream salinity trends using the Interdecadal Pacific Oscillation and its rate of change

Abstract. The impact of landuse on stream salinity is currently difficult to separate from the effect of climate, as the decadal scale climatic cycles in groundwater and stream hydrology have similar wavelengths to the landuse pattern. These hydrological cycles determine the stream salinity through accumulation or release of salt in the landscape. Widespread patterns apparent in stream salinity are discussed, and a link is demonstrated between stream salinity, groundwater levels and global climatic indicators. The Interdecadal Pacific Oscillation (IPO) has previously been investigated as a contributory climatic indicator for hydrological and related time series in the Southern Hemisphere. This study presents an approach which explores the rate of change in the IPO, in addition to its value, to define an indicator for the climate component of ambient shallow groundwater levels and corresponding stream salinity. Composite time series of groundwater level and stream salinity are compiled using an extensive but irregular database covering a wide geographical area. These are modelled with respect to the IPO and its rate of change to derive control time series. A example is given of how a stream salinity trend changes when the decadal climatic influence is removed.

A review of sea level observations and low frequency sea-level variability in South Atlantic

Sea-level data from South Atlantic stations were quality-controlled and analysed. Eleven time series, longer than 20 years, were selected to study long-term variability. The main features of South Atlantic sea level were described by computing linear trends, mean seasonal cycles and power spectra for the selected time series. The data sparseness made it difficult to achieve a comprehensive description of the basin. The connection between sea-level variability and ENSO was studied using the composite time series obtained by merging data for Buenos Aires and Palermo, on the Argentinian side of Rio de la Plata. It was possible to recognize that sea-level variability is strongly connected with that of river discharge into Rio de la Plata, which in turn exhibits a lagged teleconnection with ENSO. The time lag between ENSO and sea-level anomalies is about 5 months.

800-yr-long records of annual air temperature and precipitation over southern Siberia inferred from Teletskoye Lake sediments

A unique 800-yr-long record of annual temperatures and precipitation over the south of western Siberia has been reconstructed from the bottom sediments of Teletskoye Lake, Altai Mountains using an X-ray fluorescence scanner (XRF) providing 0.1-mm resolution timeseries of elemental composition and X-ray density (XRD). Br content appears to be broadly correlative with mean annual temperature variations because of changes in catchment vegetation productivity. Sr/Rb ratio reflects the proportion of the unweathered terrestrial fraction. XRD appears to reflect water yield regime and sediment flux. Sedimentation is rather continuous because annual clastic supply and deposited mass are the same. The artificial neural networks method was applied to convert annual sedimentary time-series of XRD, Br content, and Sr/Rb ratio to annual records of temperature and precipitation using a transfer function. Comparison of these reconstructed Siberian records with the annual record of air temperature for the Northern Hemisphere shows similar trends in climatic variability over the past 800 yr. Estimated harmonic oscillations of temperature and precipitation values for both historical and reconstructed periods reveal subdecadal cyclicity.

Using simulated historical time series to prioritize fuel treatments on landscapes across the United States: The LANDFIRE prototype project

Canopy and surface fuels in many fire-prone forests of the United States have increased over the last 70 years as a result of modern fire exclusion policies, grazing, and other land management activities. The Healthy Forest Restoration Act and National Fire Plan establish a national commitment to reduce fire hazard and restore fire-adapted ecosystems across the USA. The primary index used to prioritize treatment areas across the nation is Fire Regime Condition Class (FRCC) computed as departures of current conditions from the historical fire and landscape conditions. This paper describes a process that uses an extensive set of ecological models to map FRCC from a departure statistic computed from simulated time series of historical landscape composition. This mapping process uses a data-driven, biophysical approach where georeferenced field data, biogeochemical simulation models, and spatial data libraries are integrated using spatial statistical modeling to map environmental gradients that are then used to predict vegetation and fuels characteristics over space. These characteristics are then fed into a landscape fire and succession simulation model to simulate a time series of historical landscape compositions that are then compared to the composition of current landscapes to compute departure, and the FRCC values. Intermediate products from this process are then used to create ancillary vegetation, fuels, and fire regime layers that are useful in the eventual planning and implementation of fuel and restoration treatments at local scales. The complex integration of varied ecological models at different scales is described and problems encountered during the implementation of this process in the LANDFIRE prototype project are addressed.

A late-winter to early-spring temperature reconstruction for southeastern Norway from 1758 to 2006

AbstractSystematic temperature observations were not undertaken in Norway until the early 19th century, and even then only sporadically. Climate-proxy data may be used to reconstruct temperatures before this period, but until now there have not been any climate proxies available for late winter. This situation has recently changed, as a diary containing historical ice break-up data from a farm near lake Randsfjord in southeastern Norway has been discovered. These data, together with observations from lake Mjøsa in the same region, make it possible to reconstruct temperature back to 1758. The reconstructed series, combined with instrumental series from the area near the lake, were merged into one composite time series covering the period 1758–2006. The lowest temperatures are seen during the Dalton sunspot minimum in the early 19th century. The 20th century was 1.3˚C warmer than the 19th century, whereas the 19th century was 0.4˚C warmer than the last 43 years of the 18th century. During the period 1758–1850, the mean temperature was 1.4˚C lower than the mean value of the 20th century. The warmth observed in the 1990s and at the start of the 21st century is unprecedented during the whole series.

Using USDA Crop Progress Data for the Evaluation of Greenup Onset Date Calculated from MODIS 250-Meter Data

Identification of the onset of vegetation greenup is a key factor in characterizing and monitoring vegetation dynamics over large areas. However, the relationship between greenup onset dates estimated from satellite imagery and the actual growth stage of vegetation is often unclear. Herein, we present an approach for comparing pixel-level onset dates to regional planting and emergence information for agricultural crops, with the goal of drawing reliable conclusions regarding the physical growth stage of the vegetation of interest at the time of greenup onset. To accomplish this, we calculated onset of greenup using MODIS 250 m, 16-day composite NDVI time series data for Kansas for 2001 and a recently proposed methodology for greenup detection. We then evaluated the estimated greenup dates using the locations of 1,417 large field sites that were planted to corn, soybeans, or sorghum in 2001, in conjunction with United States Department of Agriculture (USDA) weekly crop progress reports containing crop planting and emergence percentage estimates. Average greenup onset dates calculated for the three summer crops showed that the dates were consistent with the relative planting order of corn, sorghum, and soybeans across the state. However, the influence of pre-crop vegetation (weeds and “volunteer” crops) introduced an early bias for the greenup onset dates calculated for many field sites. This pre-crop vegetation signal was most pronounced for the later planted summer crops (soybeans and sorghum) and in areas of Kansas that receive higher annual precipitation. The most reliable results were obtained for corn in semi-arid western Kansas, where pre-crop vegetation had considerably less influence on the greenup onset date calculations. The greenup onset date calculated for corn in western Kansas was found to occur 23 days after 50 percent of the crop had emerged. Corn’s greenup onset was detected, on average, at the agronomic stage where plants are 15 to 45 cm (6 to 18 inches) tall and the crop begins its rapid growth.