Kinetic Theory for Electron Dynamics Near a Positive Ion

A theoretical description of time correlation functions for electron properties in the presence of a positive ion of charge number Z is given. The simplest case of an electron gas distorted by a single ion is considered. A semi-classical representation with a regularized electron - ion potential is used to obtain a linear kinetic theory that is asymptotically exact at short times. This Markovian approximation includes all initial (equilibrium) electron - electron and electron - ion correlations through renormalized pair potentials. The kinetic theory is solved in terms of single particle trajectories of the electron - ion potential and a dielectric function for the inhomogeneous electron gas. The results are illustrated by a calculation of the autocorrelation function for the electron field at the ion. The dependence on charge number Z is shown to be dominated by the bound states of the effective electron - ion potential. On this basis, a very simple practical representation of the trajectories is proposed and shown to be accurate over a wide range including strong electron - ion coupling. This simple representation is then used for a brief analysis of the dielectric function for the inhomogeneous electron gas.Comment: 30 pages, 5 figures, submitted to Journal of Statistical Mechanics: Theory and Experimen

Evidence-Based Insurance Development for Nigeria’s Farmers: Briefing paper for Nigerian Federal Ministry of Agriculture and Rural Development (FMARD)-CCAFS Knowledge-Sharing Workshop, London, 27-28 January 2015

Agricultural insurance has been a feature in Nigeria for over two decades. The Federal Government has plans to expand agricultural insurance in the Country as part of several initiatives under the Agricultural Transformation Agenda (ATA). The Government wishes to extend crop insurance to those farmers benefiting from fertilizer subsidies under the Growth Enhancement Support Scheme (GES). The Government also wishes to implement weather index insurance (parametric insurance) in selected parts of the country susceptible droughts and floods. Experiences from index insurance initiatives worldwide provide important lessons for the development of crop index insurance in Nigeria. Experiences from India, Kenya, Rwanda, Ethiopia and Senegal suggest that there is demand for index insurance; that the bundling of insurance with key farm inputs e.g. improved seed and fertilizer, makes the insurance package more attractive to farmers; but that several challenges still to overcome, including data management, basis risk, logistical and client communication. CCAFS could play a role in working with the Federal Government to overcome some of these challenges

Bias correction of daily GCM rainfall for crop simulation studies

General circulation models (GCMs), used to predict rainfall at a seasonal lead-time, tend to simulate too many rainfall events of too low intensity relative to individual stations within a GCM grid cell. Even if bias in total rainfall is corrected relative to a target location, this distortion of frequency and intensity is expected to adversely affect simulations of crop growth and yield. We present a procedure that calibrates both the frequency and the intensity distribution of daily GCM rainfall relative to a target station, and demonstrate its application to maize yield simulation at a location in semi-arid Kenya. If GCM rainfall frequency is greater than observed frequency for a given month, averaged across years, GCM rainfall frequency is corrected by discarding rainfall events below a calibrated threshold. To correct the intensity distribution, each GCM rainfall amount above the calibrated threshold is mapped from the GCM intensity distribution onto the observed distribution. We used a gamma distribution for observed rainfall intensity, and considered both gamma and empirical distributions for GCM rainfall intensity. At the study location, the proposed correction procedure corrected both the mean and variance of monthly and seasonal GCM rainfall total, frequency and mean intensity. The empirical (GCM)-gamma (observed) transformation overestimated mean intensity slightly. A simple multiplicative shift did a better job of correcting monthly and seasonal rainfall totals, but left substantial frequency and intensity bias. All of the bias correction procedures improved maize yield simulations, but resulted in substantial negative mean bias. This bias appears to be associated with a tendency for the GCM rainfall to be more strongly autocorrelated than observed rainfall, resulting in unrealistically long dry spells during the growing season. Nonlinearity of crop response to the variability of water availability across GCM realizations may also contribute. Averaging simulated yields each year across multiple GCM realizations improved yield predictions. The proposed correction procedure provides an option for using the daily output of dynamic climate prediction models for impact studies in a manner that preserves any useful predictive information about the timing of rainfall within the season. However, its practical utility for yield forecasting at a long lead-time may be limited by the ability of GCMs to simulate rainfall with a realistic time structure

Enhancing the utility of daily GCM rainfall for crop yield prediction

Global climate models (GCMs) are promising for crop yield predictions because of their ability to simulate seasonal climate in advance of the growing season. However, their utility is limited by unrealistic time structure of daily rainfall and biases in rainfall frequency and intensity distributions. Crop growth is very sensitive to daily variations of rainfall; thus any mismatch in daily rainfall statistics could impact crop yield simulations. Here, we present an improved methodology to correct GCM rainfall biases and time structure mismatches for maize yield prediction in Katumani, Kenya. This includes GCM bias correction (BC), to correct over- or under-predictions of rainfall frequency and intensity, and nesting corrected GCM information with a stochastic weather generator, to generate daily rainfall realizations conditioned on a given monthly target. Bias-corrected daily GCM rainfall and generated rainfall realizations were used to evaluate crop response. Results showed that corrections of GCM rainfall frequency and intensity could improve crop yield prediction but yields remain under-predicted. This is strongly attributed to the time structure mismatch in daily GCM rainfall leading to excessively long dry spells. To address this, we tested several ways of improving daily structure of GCM rainfall. First, we tested calibrating thresholds in BC but were found not very effective for improving dry spell lengths. Second, we tested BC-stochastic disaggregation (BC-DisAg) and appeared to simulate more realistic dry spell lengths using bias-corrected GCM rainfall information (e.g., frequency, totals) as monthly targets. Using rainfall frequency alone to condition the weather generator removed biases in dry spell lengths, improved predicted yields, but under-predicted yield variability. Combining rainfall frequency and totals, however, not only produced more realistic yield variability but also corrected under-prediction of yields. We envisaged that the presented method would enhance the utility of daily GCM rainfall in crop yield prediction

Enhancing the utility of daily GCM rainfall for crop yield prediction

Global climate models (GCMs) are promising for crop yield predictions because of their ability to simulate seasonal climate in advance of the growing season. However, their utility is limited by unrealistic time structure of daily rainfall and biases in rainfall frequency and intensity distributions. Crop growth is very sensitive to daily variations of rainfall; thus any mismatch in daily rainfall statistics could impact crop yield simulations. Here, we present an improved methodology to correct GCM rainfall biases and time structure mismatches for maize yield prediction in Katumani, Kenya. This includes GCM bias correction (BC), to correct over- or under-predictions of rainfall frequency and intensity, and nesting corrected GCM information with a stochastic weather generator, to generate daily rainfall realizations conditioned on a given monthly target. Bias-corrected daily GCM rainfall and generated rainfall realizations were used to evaluate crop response. Results showed that corrections of GCM rainfall frequency and intensity could improve crop yield prediction but yields remain under-predicted. This is strongly attributed to the time structure mismatch in daily GCM rainfall leading to excessively long dry spells. To address this, we tested several ways of improving daily structure of GCM rainfall. First, we tested calibrating thresholds in BC but were found not very effective for improving dry spell lengths. Second, we tested BC-stochastic disaggregation (BC-DisAg) and appeared to simulate more realistic dry spell lengths using bias-corrected GCM rainfall information (e.g., frequency, totals) as monthly targets. Using rainfall frequency alone to condition the weather generator removed biases in dry spell lengths, improved predicted yields, but under-predicted yield variability. Combining rainfall frequency and totals, however, not only produced more realistic yield variability but also corrected under-prediction of yields. We envisaged that the presented method would enhance the utility of daily GCM rainfall in crop yield prediction

Development of Monsoonal Asia Climate Risk Analysis Maprooms

The Asian monsoon plays a major role in the variability of seasonal temperature and precipitation and the sub-seasonal statistics of these and other climate variables.  Due to its considerable impact on the quality and quantity of agricultural output, there is an essential need for greater understanding of the historical risk associated with the Asian monsoon, with the ultimate goal being better climate risk analysis to support agricultural decision-making in South and South East Asia. In response to partner demand expressed by the CCAFS South Asia Regional Program, CCAFS worked with the International Research Institute for Climate and Society (IRI) to develop a suite of online “Maproom” tools for analyzing agriculturally important aspects of climate variability, based on gridded historical daily precipitation and temperature data. This report documents the rationale, development of, and use of the Monsoon Asia Historical Precipitation and Temperature Monitoring Maprooms. These tools aim to provide enough flexibility to support a demanding range of analysis and decision support needs. The weather factors that impact agriculture, and the analyses that are needed to support agricultural decision-making, vary considerably by location, production system and time of year. These Maprooms serve as the precursors to the later developed of the Daily Climate Analysis Maprooms

The Role of Climate Perceptions, Expectations, and Forecasts in Farmer Decision Making: The Argentine Pampas and South Florida: Final Report of an IRI Seed Grant Project

This project sought to extend previous research efforts with both a “front end” – mental models that influence climatic expectations and forecast applications – and a “back end” – the decision processes in response to climate expectations derived from farmers’ mental models and externally-provided information. Research in this report was motivated by three lines of social science inquiry: (a) the importance of subjective perception of risk, (b) differences in the impact of small-probability events when information about them is learned by personal experience over time as opposed to being provided as a statistical summary, and (c) the role of both material and nonmaterial (including cognitive and affective) goals and processes in risky decision making. This study provided multiple insights into determinants of use of climate information related to perception and communication, and some evidence that improved presentation may overcome some of the barriers and enhance utility. We see several avenues for extending results and addressing limitations of the project’s scope and study design

A framework for the simulation of regional decadal variability for agricultural and other applications

Climate prediction on decadal time scales is currently an active area of research, and reliable model-based forecasts of regional "near-term" climate change have yet to be demonstrated. In the absence of such forecasts, synthetic data sequences that capture the statistical properties of observed near-term climate variability have potential value. Incorporation of a climate change component in such sequences can help define risk estimates for a range of climatic stresses, including those lying beyond what has been experienced in the past. Properly conditioned simulations can be used to drive agricultural, hydrological or other application models, enabling resilience testing of adaptation or decision systems. The use of statistically-based methods enables the efficient generation of large ensembles of synthetic sequences and consequently, the creation of well-defined probabilistic risk estimates. In this report we examine some procedures for the generation of synthetic climate sequences that incorporate both the statistics of observed variability and expectations regarding future regional climate change. Model fitting and simulation are considered in the framework of classical time series analysis, with methodology conditioned by requirements particular to the decadal climate problem. A method of downscaling annualized simulations to the daily time step, while preserving subannual statistical properties, is presented and other possible methods discussed. Deployment in the applications setting, the details of which may vary considerably, depending on regional climate characteristics, available data and the design of follow-on models, is considered and elements of a case study presented

A dynamical theory of homogeneous nucleation for colloids and macromolecules

Homogeneous nucleation is formulated within the context of fluctuating hydrodynamics. It is shown that for a colloidal or macromolecular system in the strong damping limit the most likely path for nucleation can be determined by gradient descent in density space governed by a nontrivial metric fixed by the dynamics. The theory provides a justification and extension of more heuristic equilibrium approaches based solely on the free energy. It is illustrated by application to liquid-vapor nucleation where it is shown that, in contrast to most free energy-based studies, the smallest clusters correspond to long wavelength, small amplitude perturbations.Comment: final version; 4 pages, 2 figure

Density Functional Theory of Inhomogeneous Liquids: II. A Fundamental Measure Approach

Previously, it has been shown that the direct correlation function for a Lennard-Jones fluid could be modeled by a sum of that for hard-spheres, a mean-field tail and a simple linear correction in the core region constructed so as to reproduce the (known) bulk equation of state of the fluid(Lutsko, JCP 127, 054701 (2007)). Here, this model is combined with ideas from Fundamental Measure Theory to construct a density functional theory for the free energy. The theory is shown to accurately describe a range of inhomogeneous conditions including the liquid-vapor interface, the fluid in contact with a hard wall and a fluid confined in a slit pore. The theory gives quantitatively accurate predictions for the surface tension, including its dependence on the potential cutoff. It also obeys two important exact conditions: that relating the direct correlation function to the functional derivative of the free energy with respect to density, and the wall theorem.Comment: to appear in J. Chem. Phy