A Field Evaluation of the Time-of-Detection Method to Estimate Population Size and Density for Aural Avian Point Counts

The time-of-detection method for aural avian point counts is a new method of estimating abundance, allowing for uncertain probability of detection. The method has been specifically designed to allow for variation in singing rates of birds. It involves dividing the time interval of the point count into several subintervals and recording the detection history of the subintervals when each bird sings. The method can be viewed as generating data equivalent to closed capture–recapture information. The method is different from the distance and multiple-observer methods in that it is not required that all the birds sing during the point count. As this method is new and there is some concern as to how well individual birds can be followed, we carried out a field test of the method using simulated known populations of singing birds, using a laptop computer to send signals to audio stations distributed around a point. The system mimics actual aural avian point counts, but also allows us to know the size and spatial distribution of the populations we are sampling. Fifty 8-min point counts (broken into four 2-min intervals) using eight species of birds were simulated. Singing rate of an individual bird of a species was simulated following a Markovian process (singing bouts followed by periods of silence), which we felt was more realistic than a truly random process. The main emphasis of our paper is to compare results from species singing at (high and low) homogenous rates per interval with those singing at (high and low) heterogeneous rates. Population size was estimated accurately for the species simulated, with a high homogeneous probability of singing. Populations of simulated species with lower but homogeneous singing probabilities were somewhat underestimated. Populations of species simulated with heterogeneous singing probabilities were substantially underestimated. Underestimation was caused by both the very low detection probabilities of all distant individuals and by individuals with low singing rates also having very low detection probabilities.

Tripleclouds: an efficient method for representing horizontal cloud inhomogeneity in 1D radiation schemes by using three regions at each height

Radiation schemes in general circulation models currently make a number of simplifications when accounting for clouds, one of the most important being the removal of horizontal inhomogeneity. A new scheme is presented that attempts to account for the neglected inhomogeneity by using two regions of cloud in each vertical level of the model as opposed to one. One of these regions is used to represent the optically thinner cloud in the level, and the other represents the optically thicker cloud. So, along with the clear-sky region, the scheme has three regions in each model level and is referred to as “Tripleclouds.” In addition, the scheme has the capability to represent arbitrary vertical overlap between the three regions in pairs of adjacent levels. This scheme is implemented in the Edwards–Slingo radiation code and tested on 250 h of data from 12 different days. The data are derived from cloud retrievals using radar, lidar, and a microwave radiometer at Chilbolton, southern United Kingdom. When the data are grouped into periods equivalent in size to general circulation model grid boxes, the shortwave plane-parallel albedo bias is found to be 8%, while the corresponding bias is found to be less than 1% using Tripleclouds. Similar results are found for the longwave biases. Tripleclouds is then compared to a more conventional method of accounting for inhomogeneity that multiplies optical depths by a constant scaling factor, and Tripleclouds is seen to improve on this method both in terms of top-of-atmosphere radiative flux biases and internal heating rates.

Boundary integral equations on unbounded rough surfaces: Fredholmness and the finite section method

We consider a class of boundary integral equations that arise in the study of strongly elliptic BVPs in unbounded domains of the form $D = \{(x, z)\in \mathbb{R}^{n+1} : x\in \mathbb{R}^n, z > f(x)\}$ where $f : \mathbb{R}^n \to\mathbb{R}$ is a sufficiently smooth bounded and continuous function. A number of specific problems of this type, for example acoustic scattering problems, problems involving elastic waves, and problems in potential theory, have been reformulated as second kind integral equations $u+Ku = v$ in the space $BC$ of bounded, continuous functions. Having recourse to the so-called limit operator method, we address two questions for the operator $A = I + K$ under consideration, with an emphasis on the function space setting $BC$. Firstly, under which conditions is $A$ a Fredholm operator, and, secondly, when is the finite section method applicable to $A$?

Assessment of the effect of time and temperature on the availability of residual phosphate in a glasshouse study of four soils using the Olsen method

The Olsen method is an indicator of plant-available phosphorus (P). The effect of time and temperature on residual phosphate in soils was measured using the Olsen method in a pot experiment. Four soils were investigated: two from Pakistan and one each from England (calcareous) and Colombia (acidic). Two levels of residual phosphate were developed in each soil after addition of phosphate by incubation at either 10degreesC or 45degreesC. The amount of phosphate added was based on the P maximum of each soil, calculated using the Langmuir equation. Rvegrass was used as the test crop. The pooled data for the four soils incubated at 10degreesC showed good correlation between Olsen P and dry matter yield or P uptake (r(2) = 0.85 and 0.77, respectively), whereas at 45 degreesC, each soil had its own relationship and pooled data did not show correlation of Olsen P with dry matter yield or P uptake. When the data at both temperatures were pooled, Olsen P was a good indicator of yield and uptake for the English soil. For the Pakistani soils, Olsen P after 45 degreesC treatment was an underestimate relative to the 10 degreesC data and for the Colombian soil it was an overestimate. The reasons for these differences need to be explored further before high temperature incubation can be used to simulate long-term changes in the field.

Modelling habitat selection and distribution of the critically endangered Jerdon's courser Rhinoptilus bitorquatus in scrub jungle: an application of a new tracking method

1. Jerdon's courser Rhinoptilus bitorquatus is a nocturnally active cursorial bird that is only known to occur in a small area of scrub jungle in Andhra Pradesh, India, and is listed as critically endangered by the IUCN. Information on its habitat requirements is needed urgently to underpin conservation measures. We quantified the habitat features that correlated with the use of different areas of scrub jungle by Jerdon's coursers, and developed a model to map potentially suitable habitat over large areas from satellite imagery and facilitate the design of surveys of Jerdon's courser distribution. 2. We used 11 arrays of 5-m long tracking strips consisting of smoothed fine soil to detect the footprints of Jerdon's coursers, and measured tracking rates (tracking events per strip night). We counted the number of bushes and trees, and described other attributes of vegetation and substrate in a 10-m square plot centred on each strip. We obtained reflectance data from Landsat 7 satellite imagery for the pixel within which each strip lay. 3. We used logistic regression models to describe the relationship between tracking rate by Jerdon's coursers and characteristics of the habitat around the strips, using ground-based survey data and satellite imagery. 4. Jerdon's coursers were most likely to occur where the density of large (>2 m tall) bushes was in the range 300-700 ha(-1) and where the density of smaller bushes was less than 1000 ha(-1). This habitat was detectable using satellite imagery. 5. Synthesis and applications. The occurrence of Jerdon's courser is strongly correlated with the density of bushes and trees, and is in turn affected by grazing with domestic livestock, woodcutting and mechanical clearance of bushes to create pasture, orchards and farmland. It is likely that there is an optimal level of grazing and woodcutting that would maintain or create suitable conditions for the species. Knowledge of the species' distribution is incomplete and there is considerable pressure from human use of apparently suitable habitats. Hence, distribution mapping is a high conservation priority. A two-step procedure is proposed, involving the use of ground surveys of bush density to calibrate satellite image-based mapping of potential habitat. These maps could then be used to select priority areas for Jerdon's courser surveys. The use of tracking strips to study habitat selection and distribution has potential in studies of other scarce and secretive species.

Comparing sampling needs for variograms of soil properties computed by the method of moments and residual maximum likelihood

It has been generally accepted that the method of moments (MoM) variogram, which has been widely applied in soil science, requires about 100 sites at an appropriate interval apart to describe the variation adequately. This sample size is often larger than can be afforded for soil surveys of agricultural fields or contaminated sites. Furthermore, it might be a much larger sample size than is needed where the scale of variation is large. A possible alternative in such situations is the residual maximum likelihood (REML) variogram because fewer data appear to be required. The REML method is parametric and is considered reliable where there is trend in the data because it is based on generalized increments that filter trend out and only the covariance parameters are estimated. Previous research has suggested that fewer data are needed to compute a reliable variogram using a maximum likelihood approach such as REML, however, the results can vary according to the nature of the spatial variation. There remain issues to examine: how many fewer data can be used, how should the sampling sites be distributed over the site of interest, and how do different degrees of spatial variation affect the data requirements? The soil of four field sites of different size, physiography, parent material and soil type was sampled intensively, and MoM and REML variograms were calculated for clay content. The data were then sub-sampled to give different sample sizes and distributions of sites and the variograms were computed again. The model parameters for the sets of variograms for each site were used for cross-validation. Predictions based on REML variograms were generally more accurate than those from MoM variograms with fewer than 100 sampling sites. A sample size of around 50 sites at an appropriate distance apart, possibly determined from variograms of ancillary data, appears adequate to compute REML variograms for kriging soil properties for precision agriculture and contaminated sites. (C) 2007 Elsevier B.V. All rights reserved.

A numerical study of the probe method

The goal of this work is the numerical realization of the probe method suggested by Ikehata for the detection of an obstacle D in inverse scattering. The main idea of the method is to use probes in the form of point source (., z) with source point z to define an indicator function (I) over cap (z) which can be reconstructed from Cauchy data or far. eld data. The indicator function boolean AND (I) over cap (z) can be shown to blow off when the source point z tends to the boundary aD, and this behavior can be used to find D. To study the feasibility of the probe method we will use two equivalent formulations of the indicator function. We will carry out the numerical realization of the functional and show reconstructions of a sound-soft obstacle.

The point source method for inverse scattering in the time domain

Many recent inverse scattering techniques have been designed for single frequency scattered fields in the frequency domain. In practice, however, the data is collected in the time domain. Frequency domain inverse scattering algorithms obviously apply to time-harmonic scattering, or nearly time-harmonic scattering, through application of the Fourier transform. Fourier transform techniques can also be applied to non-time-harmonic scattering from pulses. Our goal here is twofold: first, to establish conditions on the time-dependent waves that provide a correspondence between time domain and frequency domain inverse scattering via Fourier transforms without recourse to the conventional limiting amplitude principle; secondly, we apply the analysis in the first part of this work toward the extension of a particular scattering technique, namely the point source method, to scattering from the requisite pulses. Numerical examples illustrate the method and suggest that reconstructions from admissible pulses deliver superior reconstructions compared to straight averaging of multi-frequency data. Copyright (C) 2006 John Wiley & Sons, Ltd.

The point-source method for 3D reconstructions for the Helmholtz and Maxwell equations

We use the point-source method (PSM) to reconstruct a scattered field from its associated far field pattern. The reconstruction scheme is described and numerical results are presented for three-dimensional acoustic and electromagnetic scattering problems. We give new proofs of the algorithms, based on the Green and Stratton-Chu formulae, which are more general than with the former use of the reciprocity relation. This allows us to handle the case of limited aperture data and arbitrary incident fields. Both for 3D acoustics and electromagnetics, numerical reconstructions of the field for different settings and with noisy data are shown. For shape reconstruction in acoustics, we develop an appropriate strategy to identify areas with good reconstruction quality and combine different such regions into one joint function. Then, we show how shapes of unknown sound-soft scatterers are found as level curves of the total reconstructed field.

The ASSET intercomparison of ozone analyses: method and first results

This paper aims to summarise the current performance of ozone data assimilation (DA) systems, to show where they can be improved, and to quantify their errors. It examines 11 sets of ozone analyses from 7 different DA systems. Two are numerical weather prediction (NWP) systems based on general circulation models (GCMs); the other five use chemistry transport models (CTMs). The systems examined contain either linearised or detailed ozone chemistry, or no chemistry at all. In most analyses, MIPAS (Michelson Interferometer for Passive Atmospheric Sounding) ozone data are assimilated; two assimilate SCIAMACHY (Scanning Imaging Absorption Spectrometer for Atmospheric Chartography) observations instead. Analyses are compared to independent ozone observations covering the troposphere, stratosphere and lower mesosphere during the period July to November 2003. Biases and standard deviations are largest, and show the largest divergence between systems, in the troposphere, in the upper-troposphere/lower-stratosphere, in the upper-stratosphere and mesosphere, and the Antarctic ozone hole region. However, in any particular area, apart from the troposphere, at least one system can be found that agrees well with independent data. In general, none of the differences can be linked to the assimilation technique (Kalman filter, three or four dimensional variational methods, direct inversion) or the system (CTM or NWP system). Where results diverge, a main explanation is the way ozone is modelled. It is important to correctly model transport at the tropical tropopause, to avoid positive biases and excessive structure in the ozone field. In the southern hemisphere ozone hole, only the analyses which correctly model heterogeneous ozone depletion are able to reproduce the near-complete ozone destruction over the pole. In the upper-stratosphere and mesosphere (above 5 hPa), some ozone photochemistry schemes caused large but easily remedied biases. The diurnal cycle of ozone in the mesosphere is not captured, except by the one system that includes a detailed treatment of mesospheric chemistry. These results indicate that when good observations are available for assimilation, the first priority for improving ozone DA systems is to improve the models. The analyses benefit strongly from the good quality of the MIPAS ozone observations. Using the analyses as a transfer standard, it is seen that MIPAS is similar to 5% higher than HALOE (Halogen Occultation Experiment) in the mid and upper stratosphere and mesosphere (above 30 hPa), and of order 10% higher than ozonesonde and HALOE in the lower stratosphere (100 hPa to 30 hPa). Analyses based on SCIAMACHY total column are almost as good as the MIPAS analyses; analyses based on SCIAMACHY limb profiles are worse in some areas, due to problems in the SCIAMACHY retrievals.