Fire history and the Global Charcoal Database: a new tool for hypothesis testing and data exploration

Version 1 of the Global Charcoal Database is now available for regional fire history reconstructions, data exploration, hypothesis testing, and evaluation of coupled climate–vegetation–fire model simulations. The charcoal database contains over 400 radiocarbon-dated records that document changes in charcoal abundance during the Late Quaternary. The aim of this public database is to stimulate cross-disciplinary research in fire sciences targeted at an increased understanding of the controls and impacts of natural and anthropogenic fire regimes on centennial-to-orbital timescales. We describe here the data standardization techniques for comparing multiple types of sedimentary charcoal records. Version 1 of the Global Charcoal Database has been used to characterize global and regional patterns in fire activity since the last glacial maximum. Recent studies using the charcoal database have explored the relation between climate and fire during periods of rapid climate change, including evidence of fire activity during the Younger Dryas Chronozone, and during the past two millennia.

Transdifferential and transintegral calculus

The set of transreal numbers is a superset of the real numbers. It totalises real arithmetic by defining division by zero in terms of three def- inite, non-finite numbers: positive infinity, negative infinity and nullity. Elsewhere, in this proceedings, we extended continuity and limits from the real domain to the transreal domain, here we extended the real derivative to the transreal derivative. This continues to demonstrate that transreal analysis contains real analysis and operates at singularities where real analysis fails. Hence computer programs that rely on computing deriva- tives { such as those used in scientific, engineering and financial applica- tions { are extended to operate at singularities where they currently fail. This promises to make software, that computes derivatives, both more competent and more reliable. We also extended the integration of absolutely convergent functions from the real domain to the transreal domain.

Transreal limits expose category errors in IEEE 754 floating-point arithmetic and in mathematics

The IEEE 754 standard for oating-point arithmetic is widely used in computing. It is based on real arithmetic and is made total by adding both a positive and a negative infinity, a negative zero, and many Not-a-Number (NaN) states. The IEEE infinities are said to have the behaviour of limits. Transreal arithmetic is total. It also has a positive and a negative infinity but no negative zero, and it has a single, unordered number, nullity. We elucidate the transreal tangent and extend real limits to transreal limits. Arguing from this firm foundation, we maintain that there are three category errors in the IEEE 754 standard. Firstly the claim that IEEE infinities are limits of real arithmetic confuses limiting processes with arithmetic. Secondly a defence of IEEE negative zero confuses the limit of a function with the value of a function. Thirdly the definition of IEEE NaNs confuses undefined with unordered. Furthermore we prove that the tangent function, with the infinities given by geometrical con- struction, has a period of an entire rotation, not half a rotation as is commonly understood. This illustrates a category error, confusing the limit with the value of a function, in an important area of applied mathe- matics { trigonometry. We brie y consider the wider implications of this category error. Another paper proposes transreal arithmetic as a basis for floating- point arithmetic; here we take the profound step of proposing transreal arithmetic as a replacement for real arithmetic to remove the possibility of certain category errors in mathematics. Thus we propose both theo- retical and practical advantages of transmathematics. In particular we argue that implementing transreal analysis in trans- floating-point arith- metic would extend the coverage, accuracy and reliability of almost all computer programs that exploit real analysis { essentially all programs in science and engineering and many in finance, medicine and other socially beneficial applications.

Effects of past climate variability on fire and vegetation in the cerrãdo savanna of the Huanchaca Mesetta, NE Bolivia

Cerrãdo savannas have the greatest fire activity of all major global land-cover types and play a significant role in the global carbon cycle. During the 21st century, temperatures are projected to increase by ∼ 3 ◦C coupled with a precipitation decrease of ∼ 20 %. Although these conditions could potentially intensify drought stress, it is unknown how that might alter vegetation composition and fire regimes. To assess how Neotropical savannas responded to past climate changes, a 14 500-year, high-resolution, sedimentary record from Huanchaca Mesetta, a palm swamp located in the cerrãdo savanna in northeastern Bolivia, was analyzed with phytoliths, stable isotopes, and charcoal. A nonanalogue, cold-adapted vegetation community dominated the Lateglacial–early Holocene period (14 500–9000 cal yr BP, which included trees and C3 Pooideae and C4 Panicoideae grasses. The Lateglacial vegetation was fire-sensitive and fire activity during this period was low, likely responding to fuel availability and limitation. Although similar vegetation characterized the early Holocene, the warming conditions associated with the onset of the Holocene led to an initial increase in fire activity. Huanchaca Mesetta became increasingly firedependent during the middle Holocene with the expansion of C4 fire-adapted grasses. However, as warm, dry conditions, characterized by increased length and severity of the dry season, continued, fuel availability decreased. The establishment of the modern palm swamp vegetation occurred at 5000 cal yr BP. Edaphic factors are the first-order control on vegetation on the rocky quartzite mesetta. Where soils are sufficiently thick, climate is the second-order control of vegetation on the mesetta. The presence of the modern palm swamp is attributed to two factors: (1) increased precipitation that increased water table levels and (2) decreased frequency and duration of surazos (cold wind incursions from Patagonia) leading to increased temperature minima. Natural (soil, climate, fire) drivers rather than anthropogenic drivers control the vegetation and fire activity at Huanchaca Mesetta. Thus the cerrãdo savanna ecosystem of the Huanchaca Plateau has exhibited ecosystem resilience to major climatic changes in both temperature and precipitation since the Lateglacial period.

Fire, climate and vegetation linkages in the Bolivian Chiquitano Seasonally Dry Tropical Forest

South American seasonally-dry tropical forests (SDTF) are critically endangered, with only a small proportion of their original distribution remaining. This paper presents a 12,000 year reconstruction of climate change, fire and vegetation dynamics in the Bolivian Chiquitano SDTF, based upon pollen and charcoal analysis, to examine the resilience of this ecosystem to drought and fire. Our analysis demonstrates a complex relationship between climate, fire and floristic composition over multi-millennial time scales, and reveals that moisture variability is the dominant control upon community turnover in this ecosystem. Maximum drought during the early Holocene, consistent with regional drought reconstructions, correlates with a period of significant fire activity between 8,000 and 7,000 cal yr BP which resulted in a decrease in SDTF diversity. As fire activity declined, but severe regional droughts persisted through the mid-Holocene, SDTF, including Anadenanthera and Astronium, became firmly established in the Bolivian lowlands. The trend of decreasing fire activity during the last two millennia promotes the idea among forest ecologists that SDTF are threatened by fire. Our analysis shows that the Chiquitano seasonally dry biome has been more resilient to Holocene changes in climate and fire regime than previously assumed, but raises questions over whether this resilience will continue in the future under increased temperatures and drought coupled with a higher frequency anthropogenic fire regime.