AbstractA new incremental four-dimensional variational (4D-Var) data assimilation algorithm is introduced. The algorithm does not require the computationally expensive integrations with the nonlinear model in the outer loops. Nonlinearity is accounted for by modifying the linearization trajectory of the observation operator based on integrations with the tangent linear (TL) model. This allows us to update the linearization trajectory of the observation operator in the inner loops at negligible computational cost. As a result the distinction between inner and outer loops is no longer necessary.The key idea on which the proposed 4D-Var method is based is that by using Gaussian quadrature it is possible to get an exact correspondence between the nonlinear time evolution of perturbations and the time evolution in the TL model. It is shown that J-point Gaussian quadrature can be used to derive the exact adjoint-based observation impact equations and furthermore that it is straightforward to account for the effect of multiple outer loops in these equations if the proposed 4D-Var method is used. The method is illustrated using a three-level quasi-geostrophic model and the Lorenz (1996) model.

We examine differential equations where nonlinearity is a result of the advection part of the total derivative or the use of quadratic algebraic constraints between state variables (such as the ideal gas law). We show that these types of nonlinearity can be accounted for in the tangent linear model by a suitable choice of the linearization trajectory. Using this optimal linearization trajectory, we show that the tangent linear model can be used to reproduce the exact nonlinear error growth of perturbations for more than 200 days in a quasi-geostrophic model and more than (the equivalent of) 150 days in the Lorenz 96 model. We introduce an iterative method, purely based on tangent linear integrations, that converges to this optimal linearization trajectory. The main conclusion from this article is that this iterative method can be used to account for nonlinearity in estimation problems without using the nonlinear model. We demonstrate this by performing forecast sensitivity experiments in the Lorenz 96 model and show that we are able to estimate analysis increments that improve the two-day forecast using only four backward integrations with the tangent linear model. Copyright (C) 2011 Royal Meteorological Society

We study the feasibility of using the singular vector technique to create initial condition perturbations for shortrange ensemble prediction systems (SREPS) focussing on predictability of severe local storms and in particular deep convection. For this a newfinal time semi-norm based on the convective available potential energy (CAPE) is introduced. We compare singular vectors using the CAPE-norm with SVs using the more common total energy (TE) norm for a 2-week summer period in 2007, which includes a case of mesoscale extreme rainfall in the south west of Finland. The CAPE singular vectors perturb the CAPE field by increasing the specific humidity and temperature of the parcel and increase the lapse rate above the parcel in the lower troposphere consistent with physical considerations. The CAPE-SVs are situated in the lower troposphere. This in contrast to TE-SVs with short optimization times which predominantly remain in the high troposphere. By examining the time evolution of the CAPE singular values we observe that the convective event in the south west of Finland is clearly associated with high CAPE singular values.

2 Background Weather forecasting has to deal with many uncertainties, wh ich may stem from various sources. For example, the parameter settings in physics packages, which are not tr uly known, or the uncertainty in the analysis itself. Here we shall focus on the latter: the uncertainty in the init ial condition of the model. We will use adjoint techniques to determine sensitive geographical areas of th e analysis, where uncertainties in the analysis may have the largest impact on the Hirlam forecast. As such, the c omputations of these fast-growing perturbations or Hirlam singular vectors is a natural component of the Hirlam -Aladin initiative GLAMEPS (see this Newsletter) to define a limited-area model ensemble for Europe. For an ext ensive discussion of the use of singular vectors in ensemble forecasting we refer to [4].

1. Silvoarable agroforestry (SAF) is the cultivation of trees and arable crops on the same parcel of land. SAF may contribute to modern diversified land use objectives in Europe, such as enhanced biodiversity and productivity, reduced leaching of nitrogen, protection against flooding and erosion, and attractiveness of the landscape. Long-term yield predictions are needed to assess long-term economic profitability of SAF.2. A model for growth, resource sharing and productivity in agroforestry systems was developed to act as a tool in forecasts of yield, economic optimization of farming enterprises and exploration of policy options for land use in Europe. The model is called Yield-SAFE; from "YIeld Estimator for Long term Design of Silvoarable AgroForestry in Europe". The model was developed with as few equations and parameters as possible to allow model parameterization under constrained availability of data from long-term experiments.3. The model consists of seven state equations expressing the temporal dynamics of: (1) tree biomass; (2) tree leaf area, (3) number of shoots per tree; (4) crop biomass; (5) crop leaf area index; (6) heat sum; and (7) soil water content. The main outputs of the model are the growth dynamics and final yields of trees and crops. Daily inputs are temperature, radiation and precipitation. Planting densities, initial biomasses of tree and crop species, and soil parameters must be specified.4. A parameterization of Yield-SAFE is generated, using published yield tables for tree growth and output from the comprehensive crop simulation model STICS. Analysis of tree and crop growth data from two poplar agroforestry stands in the United Kingdom demonstrates the validity of the modelling concept and calibration philosophy of Yield-SAFE. A sensitivity analysis is presented to elucidate which biological parameters most influence short and long-term productivity and land equivalent ratio.5. The conceptual model, elaborated in Yield-SAFE, in combination with the outlined procedure for model calibration, offers a valid tool for exploratory land use studies. (c) 2006 Elsevier B.V. All rights reserved.

In this paper a support vector machine (SVM) approach for characterizing the feasible parameter set (FPS) in non-linear set-membership estimation problems is presented. It iteratively solves a regression problem from which an approximation of the boundary of the FPS can be determined. To guarantee convergence to the boundary the procedure includes a no-derivative line search and for an appropriate coverage of points on the FPS boundary it is suggested to start with a sequential box pavement procedure. The SVM approach is illustrated on a simple sine and exponential model with two parameters and an agro-forestry simulation model.