Crossbred cow adoption and milk market participation in a multivariate count data framework

Cross-bred cow adoption is an important and potent policy variable precipitating subsistence household entry into emerging milk markets. This paper focuses on the problem of designing policies that encourage and sustain milkmarket expansion among a sample of subsistence households in the Ethiopian highlands. In this context it is desirable to measure households’ ‘proximity’ to market in terms of the level of deficiency of essential inputs. This problem is compounded by four factors. One is the existence of cross-bred cow numbers (count data) as an important, endogenous decision by the household; second is the lack of a multivariate generalization of the Poisson regression model; third is the censored nature of the milk sales data (sales from non-participating households are, essentially, censored at zero); and fourth is an important simultaneity that exists between the decision to adopt a cross-bred cow, the decision about how much milk to produce, the decision about how much milk to consume and the decision to market that milk which is produced but not consumed internally by the household. Routine application of Gibbs sampling and data augmentation overcome these problems in a relatively straightforward manner. We model the count data from two sites close to Addis Ababa in a latent, categorical-variable setting with known bin boundaries. The single-equation model is then extended to a multivariate system that accommodates the covariance between crossbred-cow adoption, milk-output, and milk-sales equations. The latent-variable procedure proves tractable in extension to the multivariate setting and provides important information for policy formation in emerging-market settings

Simulated and observed fluxes of sensible and latent heat and CO2 at the WLEF-TV tower using SiB2.5

Three years of meteorological data collected at the WLEF-TV tower were used to drive a revised version of the Simple Biosphere (SiB 2.5) Model. Physiological properties and vegetation phenology were specified from satellite imagery. Simulated fluxes of heat, moisture, and carbon were compared to eddy covariance measurements taken onsite as a means of evaluating model performance on diurnal, synoptic, seasonal, and interannual time scales. The model was very successful in simulating variations of latent heat flux when compared to observations, slightly less so in the simulation of sensible heat flux. The model overestimated peak values of sensible heat flux on both monthly and diurnal scales. There was evidence that the differences between observed and simulated fluxes might be linked to wetlands near the WLEF tower, which were not present in the SiB simulation. The model overestimated the magnitude of the net ecosystem exchange of CO2 in both summer and winter. Mid-day maximum assimilation was well represented by the model, but late afternoon simulations showed excessive carbon uptake due to misrepresentation of within-canopy shading in the model. Interannual variability was not well simulated because only a single year of satellite imagery was used to parameterize the model.

Simulated variations in atmospheric CO2 over a Wisconsin forest using a coupled ecosystem-atmosphere model

Ecosystem fluxes of energy, water, and CO2 result in spatial and temporal variations in atmospheric properties. In principle, these variations can be used to quantify the fluxes through inverse modelling of atmospheric transport, and can improve the understanding of processes and falsifiability of models. We investigated the influence of ecosystem fluxes on atmospheric CO2 in the vicinity of the WLEF-TV tower in Wisconsin using an ecophysiological model (Simple Biosphere, SiB2) coupled to an atmospheric model (Regional Atmospheric Modelling System). Model parameters were specified from satellite imagery and soil texture data. In a companion paper, simulated fluxes in the immediate tower vicinity have been compared to eddy covariance fluxes measured at the tower, with meteorology specified from tower sensors. Results were encouraging with respect to the ability of the model to capture observed diurnal cycles of fluxes. Here, the effects of fluxes in the tower footprint were also investigated by coupling SiB2 to a high-resolution atmospheric simulation, so that the model physiology could affect the meteorological environment. These experiments were successful in reproducing observed fluxes and concentration gradients during the day and at night, but revealed problems during transitions at sunrise and sunset that appear to be related to the canopy radiation parameterization in SiB2.

A low-order model investigation of the analysis of gravity waves in the ensemble Kalman filter.

The behavior of the ensemble Kalman filter (EnKF) is examined in the context of a model that exhibits a nonlinear chaotic (slow) vortical mode coupled to a linear (fast) gravity wave of a given amplitude and frequency. It is shown that accurate recovery of both modes is enhanced when covariances between fast and slow normal-mode variables (which reflect the slaving relations inherent in balanced dynamics) are modeled correctly. More ensemble members are needed to recover the fast, linear gravity wave than the slow, vortical motion. Although the EnKF tends to diverge in the analysis of the gravity wave, the filter divergence is stable and does not lead to a great loss of accuracy. Consequently, provided the ensemble is large enough and observations are made that reflect both time scales, the EnKF is able to recover both time scales more accurately than optimal interpolation (OI), which uses a static error covariance matrix. For OI it is also found to be problematic to observe the state at a frequency that is a subharmonic of the gravity wave frequency, a problem that is in part overcome by the EnKF.However, error in themodeled gravity wave parameters can be detrimental to the performance of the EnKF and remove its implied advantages, suggesting that a modified algorithm or a method for accounting for model error is needed.

Four-dimensional data assimilation and balanced dynamics

The problem of spurious excitation of gravity waves in the context of four-dimensional data assimilation is investigated using a simple model of balanced dynamics. The model admits a chaotic vortical mode coupled to a comparatively fast gravity wave mode, and can be initialized such that the model evolves on a so-called slow manifold, where the fast motion is suppressed. Identical twin assimilation experiments are performed, comparing the extended and ensemble Kalman filters (EKF and EnKF, respectively). The EKF uses a tangent linear model (TLM) to estimate the evolution of forecast error statistics in time, whereas the EnKF uses the statistics of an ensemble of nonlinear model integrations. Specifically, the case is examined where the true state is balanced, but observation errors project onto all degrees of freedom, including the fast modes. It is shown that the EKF and EnKF will assimilate observations in a balanced way only if certain assumptions hold, and that, outside of ideal cases (i.e., with very frequent observations), dynamical balance can easily be lost in the assimilation. For the EKF, the repeated adjustment of the covariances by the assimilation of observations can easily unbalance the TLM, and destroy the assumptions on which balanced assimilation rests. It is shown that an important factor is the choice of initial forecast error covariance matrix. A balance-constrained EKF is described and compared to the standard EKF, and shown to offer significant improvement for observation frequencies where balance in the standard EKF is lost. The EnKF is advantageous in that balance in the error covariances relies only on a balanced forecast ensemble, and that the analysis step is an ensemble-mean operation. Numerical experiments show that the EnKF may be preferable to the EKF in terms of balance, though its validity is limited by ensemble size. It is also found that overobserving can lead to a more unbalanced forecast ensemble and thus to an unbalanced analysis.

A unified neurofuzzy model for classification

This work proposes a unified neurofuzzy modelling scheme. To begin with, the initial fuzzy base construction method is based on fuzzy clustering utilising a Gaussian mixture model (GMM) combined with the analysis of covariance (ANOVA) decomposition in order to obtain more compact univariate and bivariate membership functions over the subspaces of the input features. The mean and covariance of the Gaussian membership functions are found by the expectation maximisation (EM) algorithm with the merit of revealing the underlying density distribution of system inputs. The resultant set of membership functions forms the basis of the generalised fuzzy model (GFM) inference engine. The model structure and parameters of this neurofuzzy model are identified via the supervised subspace orthogonal least square (OLS) learning. Finally, instead of providing deterministic class label as model output by convention, a logistic regression model is applied to present the classifier’s output, in which the sigmoid type of logistic transfer function scales the outputs of the neurofuzzy model to the class probability. Experimental validation results are presented to demonstrate the effectiveness of the proposed neurofuzzy modelling scheme.

Tropical Atlantic variability modes (1979–2002). Part I: Time-evolving SST modes related to West African rainfall

This work presents a description of the 1979–2002 tropical Atlantic (TA) SST variability modes coupled to the anomalous West African (WA) rainfall during the monsoon season. The time-evolving SST patterns, with an impact on WA rainfall variability, are analyzed using a new methodology based on maximum covariance analysis. The enhanced Climate Prediction Center (CPC) Merged Analysis of Precipitation (CMAP) dataset, which includes measures over the ocean, gives a complete picture of the interannual WA rainfall patterns for the Sahel dry period. The leading TA SST pattern, related to the Atlantic El Niño, is coupled to anomalous precipitation over the coast of the Gulf of Guinea, which corresponds to the second WA rainfall principal component. The thermodynamics and dynamics involved in the generation, development, and damping of this mode are studied and compared with previous works. The SST mode starts at the Angola/Benguela region and is caused by alongshore wind anomalies. It then propagates westward via Rossby waves and damps because of latent heat flux anomalies and Kelvin wave eastward propagation from an off-equatorial forcing. The second SST mode includes the Mediterranean and the Atlantic Ocean, showing how the Mediterranean SST anomalies are those that are directly associated with the Sahelian rainfall. The global signature of the TA SST patterns is analyzed, adding new insights about the Pacific– Atlantic link in relation to WA rainfall during this period. Also, this global picture suggests that the Mediterranean SST anomalies are a fingerprint of large-scale forcing. This work updates the results given by other authors, whose studies are based on different datasets dating back to the 1950s, including both the wet and the dry Sahel periods.

Data assimilation with correlated observation errors: experiments with a 1-D shallow water model

Remote sensing observations often have correlated errors, but the correlations are typically ignored in data assimilation for numerical weather prediction. The assumption of zero correlations is often used with data thinning methods, resulting in a loss of information. As operational centres move towards higher-resolution forecasting, there is a requirement to retain data providing detail on appropriate scales. Thus an alternative approach to dealing with observation error correlations is needed. In this article, we consider several approaches to approximating observation error correlation matrices: diagonal approximations, eigendecomposition approximations and Markov matrices. These approximations are applied in incremental variational assimilation experiments with a 1-D shallow water model using synthetic observations. Our experiments quantify analysis accuracy in comparison with a reference or ‘truth’ trajectory, as well as with analyses using the ‘true’ observation error covariance matrix. We show that it is often better to include an approximate correlation structure in the observation error covariance matrix than to incorrectly assume error independence. Furthermore, by choosing a suitable matrix approximation, it is feasible and computationally cheap to include error correlation structure in a variational data assimilation algorithm.

The simulation of the opposing fluxes of latent heat and CO2 over various land-use types: coupling a gas exchange model to a mesoscale atmospheric model

A mesoscale meteorological model (FOOT3DK) is coupled with a gas exchange model to simulate surface fluxes of CO2 and H2O under field conditions. The gas exchange model consists of a C3 single leaf photosynthesis sub-model and an extended big leaf (sun/shade) sub-model that divides the canopy into sunlit and shaded fractions. Simulated CO2 fluxes of the stand-alone version of the gas exchange model correspond well to eddy-covariance measurements at a test site in a rural area in the west of Germany. The coupled FOOT3DK/gas exchange model is validated for the diurnal cycle at singular grid points, and delivers realistic fluxes with respect to their order of magnitude and to the general daily course. Compared to the Jarvis-based big leaf scheme, simulations of latent heat fluxes with a photosynthesis-based scheme for stomatal conductance are more realistic. As expected, flux averages are strongly influenced by the underlying land cover. While the simulated net ecosystem exchange is highly correlated with leaf area index, this correlation is much weaker for the latent heat flux. Photosynthetic CO2 uptake is associated with transpirational water loss via the stomata, and the resulting opposing surface fluxes of CO2 and H2O are reproduced with the model approach. Over vegetated surfaces it is shown that the coupling of a photosynthesis-based gas exchange model with the land-surface scheme of a mesoscale model results in more realistic simulated latent heat fluxes.

Five years of carbon dioxide fluxes measurements in a highly vegetated suburban area

Suburban areas continue to grow rapidly and are potentially an important land-use category for anthropogenic carbon-dioxide (CO2) emissions. Here eddy covariance techniques are used to obtain ecosystem-scale measurements of CO2 fluxes (FC) from a suburban area of Baltimore, Maryland, USA (2002–2006). These are among the first multi-year measurements of FC in a suburban area. The study area is characterized by low population density (1500 inhabitants km−2) and abundant vegetation (67.4% vegetation land-cover). FC is correlated with photosynthetic active radiation (PAR), soil temperature, and wind direction. Missing hourly FC is gap-filled using empirical relations between FC, PAR, and soil temperature. Diurnal patterns show net CO2 emissions to the atmosphere during winter and net CO2 uptake by the surface during summer daytime hours (summer daily total is −1.25 g C m−2 d−1). Despite the large amount of vegetation the suburban area is a net CO2 source of 361 g C m−2 y−1 on average.

Ensemble transform Kalman-Bucy filters

Two recent works have adapted the Kalman–Bucy filter into an ensemble setting. In the first formulation, the ensemble of perturbations is updated by the solution of an ordinary differential equation (ODE) in pseudo-time, while the mean is updated as in the standard Kalman filter. In the second formulation, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-time. Neither requires matrix inversions except for the frequently diagonal observation error covariance. We analyse the behaviour of the ODEs involved in these formulations. We demonstrate that they stiffen for large magnitudes of the ratio of background error to observational error variance, and that using the integration scheme proposed in both formulations can lead to failure. A numerical integration scheme that is both stable and is not computationally expensive is proposed. We develop transform-based alternatives for these Bucy-type approaches so that the integrations are computed in ensemble space where the variables are weights (of dimension equal to the ensemble size) rather than model variables. Finally, the performance of our ensemble transform Kalman–Bucy implementations is evaluated using three models: the 3-variable Lorenz 1963 model, the 40-variable Lorenz 1996 model, and a medium complexity atmospheric general circulation model known as SPEEDY. The results from all three models are encouraging and warrant further exploration of these assimilation techniques.

Estimating interchannel observation-error correlations for IASI radiance data in the Met Office system

The optimal utilisation of hyper-spectral satellite observations in numerical weather prediction is often inhibited by incorrectly assuming independent interchannel observation errors. However, in order to represent these observation-error covariance structures, an accurate knowledge of the true variances and correlations is needed. This structure is likely to vary with observation type and assimilation system. The work in this article presents the initial results for the estimation of IASI interchannel observation-error correlations when the data are processed in the Met Office one-dimensional (1D-Var) and four-dimensional (4D-Var) variational assimilation systems. The method used to calculate the observation errors is a post-analysis diagnostic which utilises the background and analysis departures from the two systems. The results show significant differences in the source and structure of the observation errors when processed in the two different assimilation systems, but also highlight some common features. When the observations are processed in 1D-Var, the diagnosed error variances are approximately half the size of the error variances used in the current operational system and are very close in size to the instrument noise, suggesting that this is the main source of error. The errors contain no consistent correlations, with the exception of a handful of spectrally close channels. When the observations are processed in 4D-Var, we again find that the observation errors are being overestimated operationally, but the overestimation is significantly larger for many channels. In contrast to 1D-Var, the diagnosed error variances are often larger than the instrument noise in 4D-Var. It is postulated that horizontal errors of representation, not seen in 1D-Var, are a significant contributor to the overall error here. Finally, observation errors diagnosed from 4D-Var are found to contain strong, consistent correlation structures for channels sensitive to water vapour and surface properties.

Representativity error for temperature and humidity using the Met Office high-resolution model

The observation-error covariance matrix used in data assimilation contains contributions from instrument errors, representativity errors and errors introduced by the approximated observation operator. Forward model errors arise when the observation operator does not correctly model the observations or when observations can resolve spatial scales that the model cannot. Previous work to estimate the observation-error covariance matrix for particular observing instruments has shown that it contains signifcant correlations. In particular, correlations for humidity data are more significant than those for temperature. However it is not known what proportion of these correlations can be attributed to the representativity errors. In this article we apply an existing method for calculating representativity error, previously applied to an idealised system, to NWP data. We calculate horizontal errors of representativity for temperature and humidity using data from the Met Office high-resolution UK variable resolution model. Our results show that errors of representativity are correlated and more significant for specific humidity than temperature. We also find that representativity error varies with height. This suggests that the assimilation scheme may be improved if these errors are explicitly included in a data assimilation scheme. This article is published with the permission of the Controller of HMSO and the Queen's Printer for Scotland.

Improved evaporative flux partitioning and carbon flux in the land surface model JULES: impact on the simulation of land surface processes in temperate Europe

The primary role of land surface models embedded in climate models is to partition surface available energy into upwards, radiative, sensible and latent heat fluxes. Partitioning of evapotranspiration, ET, is of fundamental importance: as a major component of the total surface latent heat flux, ET affects the simulated surface water balance, and related energy balance, and consequently the feedbacks with the atmosphere. In this context it is also crucial to credibly represent the CO2 exchange between ecosystems and their environment. In this study, JULES, the land surface model used in UK weather and climate models, has been evaluated for temperate Europe. Compared to eddy covariance flux measurements, the CO2 uptake by the ecosystem is underestimated and the ET overestimated. In addition, the contribution to ET from soil and intercepted water evaporation far outweighs the contribution of plant transpiration. To alleviate these biases, adaptations have been implemented in JULES, based on key literature references. These adaptations have improved the simulation of the spatio-temporal variability of the fluxes and the accuracy of the simulated GPP and ET, including its partitioning. This resulted in a shift of the seasonal soil moisture cycle. These adaptations are expected to increase the fidelity of climate simulations over Europe. Finally, the extreme summer of 2003 was used as evaluation benchmark for the use of the model in climate change studies. The improved model captures the impact of the 2003 drought on the carbon assimilation and the water use efficiency of the plants. It, however, underestimates the 2003 GPP anomalies. The simulations showed that a reduction of evaporation from the interception and soil reservoirs, albeit not of transpiration, largely explained the good correlation between the carbon and the water fluxes anomalies that was observed during 2003. This demonstrates the importance of being able to discriminate the response of individual component of the ET flux to environmental forcing.

The role of sky conditions on gross primary production in a mixed deciduous forest

The role of different sky conditions on diffuse PAR fraction (ϕ), air temperature (Ta), vapor pressure deficit (vpd) and GPP in a deciduous forest is investigated using eddy covariance observations of CO2 fluxes and radiometer and ceilometer observations of sky and PAR conditions on hourly and growing season timescales. Maximum GPP response occurred under moderate to high PAR and ϕ and low vpd. Light response models using a rectangular hyperbola showed a positive linear relation between ϕ and effective quantum efficiency (α = 0.023ϕ + 0.012, r2 = 0.994). Since PAR and ϕ are negatively correlated, there is a tradeoff between the greater use efficiency of diffuse light and lower vpd and the associated decrease in total PAR available for photosynthesis. To a lesser extent, light response was also modified by vpd and Ta. The net effect of these and their relation with sky conditions helped enhance light response under sky conditions that produced higher ϕ. Six sky conditions were classified from cloud frequency and ϕ data: optically thick clouds, optically thin clouds, mixed sky (partial clouds within hour), high, medium and low optical aerosol. The frequency and light responses of each sky condition for the growing season were used to predict the role of changing sky conditions on annual GPP. The net effect of increasing frequency of thick clouds is to decrease GPP, changing low aerosol conditions has negligible effect. Increases in the other sky conditions all lead to gains in GPP. Sky conditions that enhance intermediate levels of ϕ, such as thin or scattered clouds or higher aerosol concentrations from volcanic eruptions or anthropogenic emissions, will have a positive outcome on annual GPP, while an increase in cloud cover will have a negative impact. Due to the ϕ/PAR tradeoff and since GPP response to changes in individual sky conditions differ in sign and magnitude, the net response of ecosystem GPP to future sky conditions is non-linear and tends toward moderation of change.