Numerical investigations of linear least squares methods for derivative estimation

The results of a numerical investigation into the errors for least squares estimates of function gradients are presented. The underlying algorithm is obtained by constructing a least squares problem using a truncated Taylor expansion. An error bound associated with this method contains in its numerator terms related to the Taylor series remainder, while its denominator contains the smallest singular value of the least squares matrix. Perhaps for this reason the error bounds are often found to be pessimistic by several orders of magnitude. The circumstance under which these poor estimates arise is elucidated and an empirical correction of the theoretical error bounds is conjectured and investigated numerically. This is followed by an indication of how the conjecture is supported by a rigorous argument

Habitat conversion and global avian biodiversity loss

The magnitude of the impacts of human activities on global biodiversity has been documented at several organizational levels. However, although there have been numerous studies of the effects of local-scale changes in land use (e.g. logging) on the abundance of groups of organisms, broader continental or global-scale analyses addressing the same basic issues remain largely wanting. None the less, changing patterns of land use, associated with the appropriation of increasing proportions of net primary productivity by the human population, seem likely not simply to have reduced the diversity of life, but also to have reduced the carrying capacity of the environment in terms of the numbers of other organisms that it can sustain. Here, we estimate the size of the existing global breeding bird population, and then make a first approximation as to how much this has been modified as a consequence of land-use changes wrought by human activities. Summing numbers across different land-use classes gives a best current estimate of a global population of less than 100 billion breeding bird individuals. Applying the same methodology to estimates of original land-use distributions suggests that conservatively this may represent a loss of between a fifth and a quarter of pre-agricultural bird numbers. This loss is shared across a range of temperate and tropical land-use types

Drought events and their effects on vegetation productivity in China

Many parts of the world have experienced frequent and severe droughts during the last few decades. Most previous studies examined the effects of specific drought events on vegetation productivity. In this study, we characterized the drought events in China from 1982 to 2012 and assessed their effects on vegetation productivity inferred from satellite data. We first assessed the occurrence, spatial extent, frequency, and severity of drought using the Palmer Drought Severity Index (PDSI). We then examined the impacts of droughts on China\u27s terrestrial ecosystems using the Normalized Difference Vegetation Index (NDVI). During the period 1982–2012, China\u27s land area (%) experiencing drought showed an insignificant trend. However, the drought conditions had been more severe over most regions in northern parts of China since the end of the 1990s, indicating that droughts hit these regions more frequently due to the drier climate. The severe droughts substantially reduced annual and seasonal NDVI. The magnitude and direction of the detrended NDVI under drought stress varied with season and vegetation type. The inconsistency between the regional means of PDSI and detrended NDVI could be attributed to different responses of vegetation to drought and the timing, duration, severity, and lag effects of droughts. The negative effects of droughts on vegetation productivity were partly offset by the enhancement of plant growth resulting from factors such as lower cloudiness, warming climate, and human activities (e.g., afforestation, improved agricultural management practices)

Observation Needs for Climate Services and Research

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Challenges of a Sustained Climate Observing System

Observations of planet Earth and especially all climate system components and forcings are increasingly needed for planning and informed decision making related to climate services in the broadest sense. Although significant progress has been made, much more remains to be done before a fully functional and dependable climate observing system exists. Observations are needed on spatial scales from local to global, and all time scales, especially to understand and document changes in extreme events. Climate change caused by human activities adds a new dimension and a vital imperative: to acquire climate observations of sufficient quality and coverage, and analyze them into products for multiple purposes to inform decisions for mitigation, adaptation, assessing vulnerability and impacts, possible geoengineering, and predicting climate variability and change and their consequences. A major challenge is to adequately deal with the continually changing observing system, especially from satellites and other remote sensing platforms such as in the ocean, in order to provide a continuous climate record. Even with new computational tools, challenges remain to provide adequate analysis, processing, meta-data, archival, access, and management of the resulting data and the data products. As volumes of data continue to grow, so do the challenges of distilling information to allow us to understand what is happening and why, and what the implications are for the future. The case is compelling that prompt coordinated international actions are essential to provide for information-based actions and decisions related to climate variability and change

The Global Landsat Archive: Status, Consolidation, and Direction

New and previously unimaginable Landsat applications have been fostered by a policy change in 2008 that made analysis-ready Landsat data free and open access. Since 1972, Landsat has been collecting images of the Earth, with the early years of the program constrained by onboard satellite and ground systems, as well as limitations across the range of required computing, networking, and storage capabilities. Rather than robust on-satellite storage for transmission via high bandwidth downlink to a centralized storage and distribution facility as with Landsat-8, a network of receiving stations, one operated by the U.S. government, the other operated by a community of International Cooperators (ICs), were utilized. ICs paid a fee for the right to receive and distribute Landsat data and over time, more Landsat data was held outside the archive of the United State Geological Survey (USGS) than was held inside, much of it unique. Recognizing the critical value of these data, the USGS began a Landsat Global Archive Consolidation (LGAC) initiative in 2010 to bring these data into a single, universally accessible, centralized global archive, housed at the Earth Resources Observation and Science (EROS) Center in Sioux Falls, South Dakota. The primary LGAC goals are to inventory the data held by ICs, acquire the data, and ingest and apply standard ground station processing to generate an L1T analysis-ready product. As of January 1, 2015 there were 5,532,454 images in the USGS archive. LGAC has contributed approximately 3.2 million of those images, more than doubling the original USGS archive holdings. Moreover, an additional 2.3 million images have been identified to date through the LGAC initiative and are in the process of being added to the archive. The impact of LGAC is significant and, in terms of images in the collection, analogous to that of having had twoadditional Landsat-5 missions. As a result of LGAC, there are regions of the globe that now have markedly improved Landsat data coverage, resulting in an enhanced capacity for mapping, monitoring change, and capturing historic conditions. Although future missions can be planned and implemented, the past cannot be revisited, underscoring the value and enhanced significance of historical Landsat data and the LGAC initiative. The aim of this paper is to report the current status of the global USGS Landsat archive, document the existing and anticipated contributions of LGAC to the archive, and characterize the current acquisitions of Landsat-7 and Landsat-8. Landsat-8 is adding data to the archive at an unprecedented rate as nearly all terrestrial images are now collected. We also offer key lessons learned so far from the LGAC initiative, plus insights regarding other critical elements of the Landsat program looking forward, such as acquisition, continuity, temporal revisit, and the importance of continuing to operationalize the Landsat program

Evapotranspiration in Northern Eurasia : impact of forcing uncertainties on terrestrial ecosystem model estimates

The ecosystems in Northern Eurasia (NE) play an important role in the global water cycle and the climate system. While evapotranspiration (ET) is a critical variable to understand this role, ET over this region remains largely unstudied. Using an improved version of the Terrestrial Ecosystem Model with five widely used forcing data sets, we examine the impact that uncertainties in climate forcing data have on the magnitude, variability, and dominant climatic drivers of ET for the period 1979-2008. Estimates of regional average ET vary in the range of 241.4-335.7mmyr(-1) depending on the choice of forcing data. This range corresponds to as much as 32% of the mean ET. Meanwhile, the spatial patterns of long-term average ET across NE are generally consistent for all forcing data sets. Our ET estimates in NE are largely affected by uncertainties in precipitation (P), air temperature (T), incoming shortwave radiation (R), and vapor pressure deficit (VPD). During the growing season, the correlations between ET and each forcing variable indicate that T is the dominant factor in the north and P in the south. Unsurprisingly, the uncertainties in climate forcing data propagate as well to estimates of the volume of water available for runoff (here defined as P-ET). While the Climate Research Unit data set is overall the best choice of forcing data in NE according to our assessment, the quality of these forcing data sets remains a major challenge to accurately quantify the regional water balance in NE

On the use of marker data to determine the kinetics of the digestive behaviour of feeds

A model of the transport process that follows the progress of digesta successively through the small intestine of a monogastric is investigated. The process is multi-phase and multi-constituent, as described in detail by Bastianelli et al. [J. Anim. Sci., 74:1873–1887, 1996]. The model describes the movement of marker substances that are used to obtain data on the interactions between the intestinal sections and digesta with differing levels of soluble fibre. A multi-stage process is modelled by a set of coupled first order linear differential equations. Solutions of steady and initial value problems provide information on the transfer rates of the processes. Properties of the solutions as functions of system parameters are examined. References M. Renton, J. Hanan and K. Burrage, Using the canonical modelling approach to simplify the simulation of function in functional-structural plant models. New Phytologist, 166:845–857, 2005. doi:10.1111/j.1469-8137.2005.01330.x D. Bastianelli, D. Sauvant and A. Rerat, Mathematical modeling of digestion and nutrient absorption in pigs. J. Animal Science, 74:1873–1887, 1996. http://www.journalofanimalscience.org/content/74/8/1873.abstract R. G. Lentle and P. W. M. Janssen, Manipulating Digestion with Foods designed to Change the Physical Characteristics of digesta. Critical Reviews in Food Science and Nutrition, 50:130–145, 2010. doi:10.1080/10408390802248726 J. France, J. H. M. Thornley, M. S. Dhanoa and R. C. Siddons, On the mathematics of digesta flow kinetics. Journal of Theoretical Biology, 113:743–758, 1985. doi:10.1016/S0022-5193(85)80191-0 A. Mazanov and J. V. Nolan, Simulation of the dynamics of nitrogen metabolism in sheep. British Journal of Nutrition, 35:149–174, 1976. doi:10.1079/BJN19760017 A. Mazanov, Stability of Multi-pool Models with Lags. Journal of Theoretical Biology, 59:429–442, 1976. doi:10.1016/0022-5193(76)90181-

Land Surface Temperature from Ka-band (37 GHZ) Passive Microwave Observations

An alternative to thermal infrared satellite sensors for measuring land surface temperature (T<inf>s</inf>) is presented. The 37 GHz vertical polarized brightness temperature is used to derive T<inf>s</inf> because it is considered the most appropriate microwave frequency for temperature retrieval. This channel balances a reduced sensitivity to soil surface characteristics with a relatively high atmospheric transmissivity. It is shown that with a simple linear relationship, accurate values for T<inf>s</inf> can be obtained from this frequency, with a theoretical bias of within 1 K for 70% of vegetated land areas of the globe. Barren, sparsely vegetated, and open shrublands cannot be accurately described with this single channel approach because variable surface conditions become important. The precision of the retrieved land surface temperature is expected to be better than 2.5 K for forests and 3.5 K for low vegetation. This method can be used to complement existing infrared derived temperature products, especially during clouded conditions. With several microwave radiometers currently in orbit, this method can be used to observe the diurnal temperature cycles with surprising accuracy. © 2009 by the American Geophysical Union