Comment on ``Piecewise potential vorticity inversion: Elementary tests''

Egger (2008) constructs some idealised experiments to test the usefulness of piecewise potential vorticity inversion (PPVI) in the diagnosis of Rossby wave dynamics and baroclinic development. He concludes that, ``PPVI does not help us to understand the dynamics of linear Rossby waves. It provides local tendencies of the streamfunction which are unrelated to the true ones. The same way, the motion of baroclinic waves in shear flow cannot be understood by using PPVI. Moreover, the effect of boundary temperatures as determined by PPVI is unrelated to the flow evolution.'' He goes further in arguing that we should not consider velocities as ``induced'' by PV anomalies defined by carving up the global domain. However, these conclusions partly reflect the limitations of his idealised experiments and the manner in which the PV components were partitioned from one another.

A high-order arbitrarily unstructured finite-volume model of the global atmosphere: tests solving the shallow-water equations

Simulations of the global atmosphere for weather and climate forecasting require fast and accurate solutions and so operational models use high-order finite differences on regular structured grids. This precludes the use of local refinement; techniques allowing local refinement are either expensive (eg. high-order finite element techniques) or have reduced accuracy at changes in resolution (eg. unstructured finite-volume with linear differencing). We present solutions of the shallow-water equations for westerly flow over a mid-latitude mountain from a finite-volume model written using OpenFOAM. A second/third-order accurate differencing scheme is applied on arbitrarily unstructured meshes made up of various shapes and refinement patterns. The results are as accurate as equivalent resolution spectral methods. Using lower order differencing reduces accuracy at a refinement pattern which allows errors from refinement of the mountain to accumulate and reduces the global accuracy over a 15 day simulation. We have therefore introduced a scheme which fits a 2D cubic polynomial approximately on a stencil around each cell. Using this scheme means that refinement of the mountain improves the accuracy after a 15 day simulation. This is a more severe test of local mesh refinement for global simulations than has been presented but a realistic test if these techniques are to be used operationally. These efficient, high-order schemes may make it possible for local mesh refinement to be used by weather and climate forecast models.

Crop yield reduction in the tropics under climate change: Processes and uncertainties

Many modelling studies examine the impacts of climate change on crop yield, but few explore either the underlying bio-physical processes, or the uncertainty inherent in the parameterisation of crop growth and development. We used a perturbed-parameter crop modelling method together with a regional climate model (PRECIS) driven by the 2071-2100 SRES A2 emissions scenario in order to examine processes and uncertainties in yield simulation. Crop simulations used the groundnut (i.e. peanut; Arachis hypogaea L.) version of the General Large-Area Model for annual crops (GLAM). Two sets of GLAM simulations were carried out: control simulations and fixed-duration simulations, where the impact of mean temperature on crop development rate was removed. Model results were compared to sensitivity tests using two other crop models of differing levels of complexity: CROPGRO, and the groundnut model of Hammer et al. [Hammer, G.L., Sinclair, T.R., Boote, K.J., Wright, G.C., Meinke, H., and Bell, M.J., 1995, A peanut simulation model: I. Model development and testing. Agron. J. 87, 1085-1093]. GLAM simulations were particularly sensitive to two processes. First, elevated vapour pressure deficit (VPD) consistently reduced yield. The same result was seen in some simulations using both other crop models. Second, GLAM crop duration was longer, and yield greater, when the optimal temperature for the rate of development was exceeded. Yield increases were also seen in one other crop model. Overall, the models differed in their response to super-optimal temperatures, and that difference increased with mean temperature; percentage changes in yield between current and future climates were as diverse as -50% and over +30% for the same input data. The first process has been observed in many crop experiments, whilst the second has not. Thus, we conclude that there is a need for: (i) more process-based modelling studies of the impact of VPD on assimilation, and (ii) more experimental studies at super-optimal temperatures. Using the GLAM results, central values and uncertainty ranges were projected for mean 2071-2100 crop yields in India. In the fixed-duration simulations, ensemble mean yields mostly rose by 10-30%. The full ensemble range was greater than this mean change (20-60% over most of India). In the control simulations, yield stimulation by elevated CO2 was more than offset by other processes-principally accelerated crop development rates at elevated, but sub-optimal, mean temperatures. Hence, the quantification of uncertainty can facilitate relatively robust indications of the likely sign of crop yield changes in future climates. (C) 2007 Elsevier B.V. All rights reserved.

Decadal predictability of the Atlantic Ocean in a coupled GCM: forecast skill and optimal perturbations using Linear Inverse Modelling

The decadal predictability of three-dimensional Atlantic Ocean anomalies is examined in a coupled global climate model (HadCM3) using a Linear Inverse Modelling (LIM) approach. It is found that the evolution of temperature and salinity in the Atlantic, and the strength of the meridional overturning circulation (MOC), can be effectively described by a linear dynamical system forced by white noise. The forecasts produced using this linear model are more skillful than other reference forecasts for several decades. Furthermore, significant non-normal amplification is found under several different norms. The regions from which this growth occurs are found to be fairly shallow and located in the far North Atlantic. Initially, anomalies in the Nordic Seas impact the MOC, and the anomalies then grow to fill the entire Atlantic basin, especially at depth, over one to three decades. It is found that the structure of the optimal initial condition for amplification is sensitive to the norm employed, but the initial growth seems to be dominated by MOC-related basin scale changes, irrespective of the choice of norm. The consistent identification of the far North Atlantic as the most sensitive region for small perturbations suggests that additional observations in this region would be optimal for constraining decadal climate predictions.