Spatial analysis of the error in a model of soil nitrogen

Models of the dynamics of nitrogen in soil (soil-N) can be used to aid the fertilizer management of a crop. The predictions of soil-N models can be validated by comparison with observed data. Validation generally involves calculating non-spatial statistics of the observations and predictions, such as their means, their mean squared-difference, and their correlation. However, when the model predictions are spatially distributed across a landscape the model requires validation with spatial statistics. There are three reasons for this: (i) the model may be more or less successful at reproducing the variance of the observations at different spatial scales; (ii) the correlation of the predictions with the observations may be different at different spatial scales; (iii) the spatial pattern of model error may be informative. In this study we used a model, parameterized with spatially variable input information about the soil, to predict the mineral-N content of soil in an arable field, and compared the results with observed data. We validated the performance of the N model spatially with a linear mixed model of the observations and model predictions, estimated by residual maximum likelihood. This novel approach allowed us to describe the joint variation of the observations and predictions as: (i) independent random variation that occurred at a fine spatial scale; (ii) correlated random variation that occurred at a coarse spatial scale; (iii) systematic variation associated with a spatial trend. The linear mixed model revealed that, in general, the performance of the N model changed depending on the spatial scale of interest. At the scales associated with random variation, the N model underestimated the variance of the observations, and the predictions were correlated poorly with the observations. At the scale of the trend, the predictions and observations shared a common surface. The spatial pattern of the error of the N model suggested that the observations were affected by the local soil condition, but this was not accounted for by the N model. In summary, the N model would be well-suited to field-scale management of soil nitrogen, but suited poorly to management at finer spatial scales. This information was not apparent with a non-spatial validation. (c),2007 Elsevier B.V. All rights reserved.

Errors associated with the preparation of aseptic products in UK hospital pharmacies: lessons from the national aseptic error reporting scheme

Background Pharmacy aseptic units prepare and supply injectables to minimise risks. The UK National Aseptic Error Reporting Scheme has been collecting data on pharmacy compounding errors, including near-misses, since 2003. Objectives The cumulative reports from January 2004 to December 2007, inclusive, were analysed. Methods The different variables of product types, error types, staff making and detecting errors, stage errors detected, perceived contributory factors, and potential or actual outcomes were presented by cross-tabulation of data. Results A total of 4691 reports were submitted against an estimated 958 532 items made, returning 0.49% as the overall error rate. Most of the errors were detected before reaching patients, with only 24 detected during or after administration. The highest number of reports related to adult cytotoxic preparations (40%) and the most frequently recorded error was a labelling error (34.2%). Errors were mostly detected at first check in assembly area (46.6%). Individual staff error contributed most (78.1%) to overall errors, while errors with paediatric parenteral nutrition appeared to be blamed on low staff levels more than other products were. The majority of errors (68.6%) had no potential patient outcomes attached, while it appeared that paediatric cytotoxic products and paediatric parenteral nutrition were associated with greater levels of perceived patient harm. Conclusions The majority of reports were related to near-misses, and this study highlights scope for examining current arrangements for checking and releasing products, certainly for paediatric cytotoxic and paediatric parenteral nutrition preparations within aseptic units, but in the context of resource and capacity constraints.

A singular vector perspective of 4D-Var: Filtering and interpolation

Four-dimensional variational data assimilation (4D-Var) combines the information from a time sequence of observations with the model dynamics and a background state to produce an analysis. In this paper, a new mathematical insight into the behaviour of 4D-Var is gained from an extension of concepts that are used to assess the qualitative information content of observations in satellite retrievals. It is shown that the 4D-Var analysis increments can be written as a linear combination of the singular vectors of a matrix which is a function of both the observational and the forecast model systems. This formulation is used to consider the filtering and interpolating aspects of 4D-Var using idealized case-studies based on a simple model of baroclinic instability. The results of the 4D-Var case-studies exhibit the reconstruction of the state in unobserved regions as a consequence of the interpolation of observations through time. The results also exhibit the filtering of components with small spatial scales that correspond to noise, and the filtering of structures in unobserved regions. The singular vector perspective gives a very clear view of this filtering and interpolating by the 4D-Var algorithm and shows that the appropriate specification of the a priori statistics is vital to extract the largest possible amount of useful information from the observations. Copyright © 2005 Royal Meteorological Society

Moist singular vectors and the predictability of some high impact European cyclones

The ECMWF full-physics and dry singular vector (SV) packages, using a dry energy norm and a 1-day optimization time, are applied to four high impact European cyclones of recent years that were almost universally badly forecast in the short range. It is shown that these full-physics SVs are much more relevant to severe cyclonic development than those based on dry dynamics plus boundary layer alone. The crucial extra ingredient is the representation of large-scale latent heat release. The severe winter storms all have a long, nearly straight region of high baroclinicity stretching across the Atlantic towards Europe, with a tongue of very high moisture content on its equatorward flank. In each case some of the final-time top SV structures pick out the region of the actual storm. The initial structures were generally located in the mid- to low troposphere. Forecasts based on initial conditions perturbed by moist SVs with opposite signs and various amplitudes show the range of possible 1-day outcomes for reasonable magnitudes of forecast error. In each case one of the perturbation structures gave a forecast very much closer to the actual storm than the control forecast. Deductions are made about the predictability of high-impact extratropical cyclone events. Implications are drawn for the short-range forecast problem and suggestions made for one practicable way to approach short-range ensemble forecasting. Copyright © 2005 Royal Meteorological Society.

Adjoint goal-based error norms for adaptive mesh ocean modelling

Flow in the world's oceans occurs at a wide range of spatial scales, from a fraction of a metre up to many thousands of kilometers. In particular, regions of intense flow are often highly localised, for example, western boundary currents, equatorial jets, overflows and convective plumes. Conventional numerical ocean models generally use static meshes. The use of dynamically-adaptive meshes has many potential advantages but needs to be guided by an error measure reflecting the underlying physics. A method of defining an error measure to guide an adaptive meshing algorithm for unstructured tetrahedral finite elements, utilizing an adjoint or goal-based method, is described here. This method is based upon a functional, encompassing important features of the flow structure. The sensitivity of this functional, with respect to the solution variables, is used as the basis from which an error measure is derived. This error measure acts to predict those areas of the domain where resolution should be changed. A barotropic wind driven gyre problem is used to demonstrate the capabilities of the method. The overall objective of this work is to develop robust error measures for use in an oceanographic context which will ensure areas of fine mesh resolution are used only where and when they are required. (c) 2006 Elsevier Ltd. All rights reserved.

An event-based approach to validating solar wind speed predictions: high-speed enhancements in the Wang-Sheeley-Arge model

One of the primary goals of the Center for Integrated Space Weather Modeling (CISM) effort is to assess and improve prediction of the solar wind conditions in near‐Earth space, arising from both quasi‐steady and transient structures. We compare 8 years of L1 in situ observations to predictions of the solar wind speed made by the Wang‐Sheeley‐Arge (WSA) empirical model. The mean‐square error (MSE) between the observed and model predictions is used to reach a number of useful conclusions: there is no systematic lag in the WSA predictions, the MSE is found to be highest at solar minimum and lowest during the rise to solar maximum, and the optimal lead time for 1 AU solar wind speed predictions is found to be 3 days. However, MSE is shown to frequently be an inadequate “figure of merit” for assessing solar wind speed predictions. A complementary, event‐based analysis technique is developed in which high‐speed enhancements (HSEs) are systematically selected and associated from observed and model time series. WSA model is validated using comparisons of the number of hit, missed, and false HSEs, along with the timing and speed magnitude errors between the forecasted and observed events. Morphological differences between the different HSE populations are investigated to aid interpretation of the results and improvements to the model. Finally, by defining discrete events in the time series, model predictions from above and below the ecliptic plane can be used to estimate an uncertainty in the predicted HSE arrival times.

Characterising the background errors for the boundary-layer capping inversion

The one-dimensional variational assimilation of vertical temperature information in the presence of a boundary-layer capping inversion is studied. For an optimal analysis of the vertical temperature profile, an accurate representation of the background error covariances is essential. The background error covariances are highly flow-dependent due to the variability in the presence, structure and height of the boundary-layer capping inversion. Flow-dependent estimates of the background error covariances are shown by studying the spread in an ensemble of forecasts. A forecast of the temperature profile (used as a background state) may have a significant error in the position of the capping inversion with respect to observations. It is shown that the assimilation of observations may weaken the inversion structure in the analysis if only magnitude errors are accounted for as is the case for traditional data assimilation methods used for operational weather prediction. The positional error is treated explicitly here in a new data assimilation scheme to reduce positional error, in addition to the traditional framework to reduce magnitude error. The distribution of the positional error of the background inversion is estimated for use with the new scheme.

Flux comparison of Eulerian and Lagrangian estimates of Agulhas leakage: A case study using a numerical model

Estimating the magnitude of Agulhas leakage, the volume flux of water from the Indian to the Atlantic Ocean, is difficult because of the presence of other circulation systems in the Agulhas region. Indian Ocean water in the Atlantic Ocean is vigorously mixed and diluted in the Cape Basin. Eulerian integration methods, where the velocity field perpendicular to a section is integrated to yield a flux, have to be calibrated so that only the flux by Agulhas leakage is sampled. Two Eulerian methods for estimating the magnitude of Agulhas leakage are tested within a high-resolution two-way nested model with the goal to devise a mooring-based measurement strategy. At the GoodHope line, a section halfway through the Cape Basin, the integrated velocity perpendicular to that line is compared to the magnitude of Agulhas leakage as determined from the transport carried by numerical Lagrangian floats. In the first method, integration is limited to the flux of water warmer and more saline than specific threshold values. These threshold values are determined by maximizing the correlation with the float-determined time series. By using the threshold values, approximately half of the leakage can directly be measured. The total amount of Agulhas leakage can be estimated using a linear regression, within a 90% confidence band of 12 Sv. In the second method, a subregion of the GoodHope line is sought so that integration over that subregion yields an Eulerian flux as close to the float-determined leakage as possible. It appears that when integration is limited within the model to the upper 300 m of the water column within 900 km of the African coast the time series have the smallest root-mean-square difference. This method yields a root-mean-square error of only 5.2 Sv but the 90% confidence band of the estimate is 20 Sv. It is concluded that the optimum thermohaline threshold method leads to more accurate estimates even though the directly measured transport is a factor of two lower than the actual magnitude of Agulhas leakage in this model.

Can 4D-Var use dynamical information from targeted observations of a baroclinic structure?

Targeted observations are generally taken in regions of high baroclinicity, but often show little impact. One plausible explanation is that important dynamical information, such as upshear tilt, is not extracted from the targeted observations by the data assimilation scheme and used to correct initial condition error. This is investigated by generating pseudo targeted observations which contain a singular vector (SV) structure that is not present in the background field or routine observations, i.e. assuming that the background has an initial condition error with tilted growing structure. Experiments were performed for a single case-study with varying numbers of pseudo targeted observations. These were assimilated by the Met Office four-dimensional variational (4D-Var) data assimilation scheme, which uses a 6 h window for observations and background-error covariances calculated using the National Meteorological Centre (NMC) method. The forecasts were run using the operational Met Office Unified Model on a 24 km grid. The results presented clearly demonstrate that a 6 h window 4D-Var system is capable of extracting baroclinic information from a limited set of observations and using it to correct initial condition error. To capture the SV structure well (projection of 0.72 in total energy), 50 sondes over an area of 1×106 km2 were required. When the SV was represented by only eight sondes along an example targeting flight track covering a smaller area, the projection onto the SV structure was lower; the resulting forecast perturbations showed an SV structure with increased tilt and reduced initial energy. The total energy contained in the perturbations decreased as the SV structure was less well described by the set of observations (i.e. as fewer pseudo observations were assimilated). The assimilated perturbation had lower energy than the SV unless the pseudo observations were assimilated with the dropsonde observation errors halved from operational values. Copyright © 2010 Royal Meteorological Society

Quantifying mesoscale variability in ocean transient tracer fields

A powerful way to test the realism of ocean general circulation models is to systematically compare observations of passive tracer concentration with model predictions. The general circulation models used in this way cannot resolve a full range of vigorous mesoscale activity (on length scales between 10–100 km). In the real ocean, however, this activity causes important variability in tracer fields. Thus, in order to rationally compare tracer observations with model predictions these unresolved fluctuations (the model variability error) must be estimated. We have analyzed this variability using an eddy‐resolving reduced‐gravity model in a simple midlatitude double‐gyre configuration. We find that the wave number spectrum of tracer variance is only weakly sensitive to the distribution of (large scale slowly varying) tracer sources and sinks. This suggests that a universal passive tracer spectrum may exist in the ocean. We estimate the spectral shape using high‐resolution measurements of potential temperature on an isopycnal in the upper northeast Atlantic Ocean, finding a slope near k −1.7 between 10 and 500 km. The typical magnitude of the variance is estimated by comparing tracer simulations using different resolutions. For CFC‐ and tritium‐type transient tracers the peak magnitude of the model variability saturation error may reach 0.20 for scales shorter than 100 km. This is of the same order as the time mean saturation itself and well over an order of magnitude greater than the instrumental uncertainty.