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Modern Applied Statistics With S

The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

Beginning with Emlen (1966) and MacArthur and Pianka (1966) and extending through the last ten years, several authors have sought to predict the foraging behavior of animals by means of mathematical models. These models are very similar,in that they all assume that the fitness of a foraging animal is a function of the efficiency of foraging measured in terms of some "currency" (Schoener, 1971) -usually energy- and that natural selection has resulted in animals that forage so as to maximize this fitness. As a result of these similarities, the models have become known as "optimal foraging models"; and the theory that embodies them, "optimal foraging theory." The situations to which optimal foraging theory has been applied, with the exception of a few recent studies, can be divided into the following four categories: (1) choice by an animal of which food types to eat (i.e., optimal diet); (2) choice of which patch type to feed in (i.e., optimal patch choice); (3) optimal allocation of time to different patches; and (4) optimal patterns and speed of movements. In this review we discuss each of these categories separately, dealing with both the theoretical developments and the data that permit tests of the predictions. The review is selective in the sense that we emphasize studies that either develop testable predictions or that attempt to test predictions in a precise quantitative manner. We also discuss what we see to be some of the future developments in the area of optimal foraging theory and how this theory can be related to other areas of biology. Our general conclusion is that the simple models so far formulated are supported are supported reasonably well by available data and that we are optimistic about the value both now and in the future of optimal foraging theory. We argue, however, that these simple models will requre much modification, espicially to deal with situations that either cannot easily be put into one or another of the above four categories or entail currencies more complicated that just energy.

Citation classic - optimal foraging - a selective review of theory and tests

https://pubag.nal.usda.gov/download/10780/pdf

rosetta: a computer program for estimating soil hydraulic parameters with hierarchical pedotransfer functions

https://core.ac.uk/download/pdf/374223.pdf

A manifesto for the equifinality thesis

We compare the capability of ground penetrating radar (GPR) and time domain reflectometry (TDR) to assess the temporal development of spatial variation of surface volumetric water content. In the case of GPR, we measured surface water content with the ground wave, which is a direct wave between the sender and receiver through the upper centimeters of the soil. Spatial water content variation was measured on 18 d with GPR and TDR during a 30-d monitoring period. To ensure large fluctuations in the spatial water content variation, we created a heterogeneous pattern of water content by irrigation on 2 d. The temporal development of the spatial variation was studied by means of the variogram and interpolated water content maps. To compare GPR and TDR variograms, we estimated confidence intervals of the experimental variograms and the variogram model parameters with a jackknife approach and a first-order approximation of model parameter uncertainty. The results showed that the 95% confidence intervals of the GPR experimental variogram were one to two orders of magnitude smaller than the 95% confidence intervals of the TDR experimental variogram because of the larger number of GPR measurements. Consequently, the uncertainty in the variogram model parameters was also much lower for GPR, which meant that the temporal development of the fitted GPR variogram model parameters was easier to interpret. Furthermore, the larger GPR measurement volume resulted in a low spatial nugget variance of 1 × 10-6 to 1 × 10-9 (m3 m-3)2 because short distance variation was averaged. This meant that GPR accurately measured spatial correlation lengths, even in the case of low water content variation. Interpolated maps showing the increase of water content due to irrigation and the subsequent gradual drying of the soil were more accurate and reproducible for GPR. It was concluded that the noninvasive GPR measurements provide the means to accurately and consistently monitor the development of spatial water content variation in time.

Monitoring Temporal Development of Spatial Soil Water Content Variation: Comparison of Ground Penetrating Radar and Time Domain Reflectometry

Bird flight is strongly influenced by local meteorological conditions. With increasing amounts of high-frequency GPS data of bird movement becoming available, as tags become cheaper and lighter, opportunities are created to obtain large datasets of quantitative meteorological information from observations conducted by bird-borne tags. In this article we propose a method for estimating wind velocity and convective velocity scale from tag-based high-frequency GPS data of soaring birds in flight.The flight patterns of soaring birds are strongly influenced by the interactions between atmospheric boundary layer processes and the morphology of the bird; climb rates depend on vertical air motion, flight altitude depends on boundary layer height, and drift off the bird’s flight path depends on wind speed and direction. We combine aerodynamic theory of soaring bird flight, the bird’s morphological properties, and three-dimensional GPS measurements at 3-s intervals to estimate the convective velocity scale ...

/pdf/using-high-resolution-gps-tracking-data-of-bird-flight-for-2xhn7vqf9d.pdf

Using high resolution GPS tracking data of bird flight for meteorological observations

[1] Travel time analysis algorithms are used to extract dielectric permittivity (and thereby water content) from time domain reflectometry (TDR) waveforms. A limitation of travel time analysis is the need to define subjective analysis parameters for reproducible measurements. The aim of this paper is to compare three methods to remove subjectivity from the analysis of TDR waveforms: (1) travel time analysis with optimized analysis parameters, (2) fitting a simulated waveform based on a model with frequency-dependent permittivity, and (3) fitting a waveform based on a model with an apparent dielectric permittivity. We performed an outflow experiment on a sandy soil sample and simultaneously collected soil water content measurements (determined from outflow) and duplicate TDR measurements. After optimizing the travel time analysis parameters by minimizing the difference between duplicate measurements, we found little difference in accuracy and reproducibility between the three methods. However, we showed that small deviations from the optimal travel time analysis parameters have a significant influence on both the accuracy and the reproducibility of travel time analysis. A comparison of the two inverse modeling approaches showed that the inclusion of frequency-dependent permittivity did not greatly improve the fit between measured and modeled waveforms and that a frequency-independent (apparent) permittivity adequately describes the TDR measurements made in this sandy soil. We conclude that the removal of subjectivity resulted in similar accuracy and reproducibility for all three methods. Nevertheless, we consider inverse modeling an interesting alternative to travel time analysis because it is a fully automated analysis with high accuracy and reproducibility.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2001WR000259

Comparison of travel time analysis and inverse modeling for soil water content determination with time domain reflectometry

Oxygen concentrations within forest floor litter were studied at various water contents and oxygen consumption rates. A micromanipulator moved micro-electrodes (dia 7.5 μm) downward at a velocity of 2 μm s−1. In oxygen profiles, particles and pores could be identified. The sizes of these particles agreed with particle sizes derived from a thin section of the same forest floor material. In oxygen profiles, no gradients in concentration occurred in litter macropores at water contents of 2–3.9 g g−1 dry weight, which represented the average range in field water contents. By contrast, steep oxygen gradients occurred inside organic particles. Larger organic particles in general had lower intraparticle oxygen concentrations, compared to smaller organic particles and in some particles oxygen was absent (>250 μm dia). These anoxic sites occurred at all water contents (2–3.9 g g−1 dry weight) and oxygen consumption rates (0.4–3.2 μmol g−1 h−1). The anoxic organic matter fraction of the forest floor did not significantly increase with water content nor with a stimulated oxygen consumption rate due to addition of glucose. The recognition that permanent anoxic sites exist in litter helps us understand how anaerobic processes, such as denitrification, may contribute to forest floor N2O production.

Anoxic microsites in Douglas fir litter

Rooting depths in a forested stand (0.11 ha) were estimated indirectly by inverse modeling maps of soil water contents from time domain reflectometry (TDR) measurements at 150 points. These maps were described with a calibrated one-dimensional soil water flow model, with specific values for the rooting depth, van Genuchten's [1980] α parameter, and throughfall fraction at each point. At about one third of the 150 points, modeled rooting depths did not fall within the a priori likely range of rooting depths; these values were discarded when kriging the point estimates to a map of rooting depths. The resulting rooting depths range from 0.8 m to 3.5 m within the stand in good agreement with root observations (R2 = 0.85). Several factors contributed positively to this good match, such as the fairly uniform soil hydraulic properties and the high sensitivity of soil water dynamics to root water uptake. Overall, the results demonstrate the suitability of soil water content maps based on TDR measurements to quantify spatial variability in soil water dynamics.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1999WR900173

Willem Bouten

Papers

Monitoring Temporal Development of Spatial Soil Water Content Variation: Comparison of Ground Penetrating Radar and Time Domain Reflectometry

Using high resolution GPS tracking data of bird flight for meteorological observations

Comparison of travel time analysis and inverse modeling for soil water content determination with time domain reflectometry

Anoxic microsites in Douglas fir litter

Assessing rooting depths of an austrian pine stand by inverse modeling soil water content maps