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- Author or Editor: Frank Schmidt x
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Abstract
Recently, a special group of global spherical coordinate transformations has been introduced in order to focus attention on the interactions of an enlarged spectral band of only one selected area, while de-focusing the rest of the globe and thus keeping the overall cost low.
Applied to spherical harmonic expansions, the filter properties are studied diagnostically and prognostically. In the former case, the low-pass character of the filter is displayed by application to while noise and to locally sounding bell-shaped functions among others. In the latter case, the shallow-water equations are integrated for different kinds of focusing. Also the equations have been perturbed in order to simulate still smaller scale effects and test their implications in the current context.
Locally the variably resolving harmonics behave like untransformed harmonies of the same actual local degree. No fading due to resolution gradients is observed. In order to set up a meaningful simulation only meteorological aspects of the scales supplied have to be observed.
Abstract
Recently, a special group of global spherical coordinate transformations has been introduced in order to focus attention on the interactions of an enlarged spectral band of only one selected area, while de-focusing the rest of the globe and thus keeping the overall cost low.
Applied to spherical harmonic expansions, the filter properties are studied diagnostically and prognostically. In the former case, the low-pass character of the filter is displayed by application to while noise and to locally sounding bell-shaped functions among others. In the latter case, the shallow-water equations are integrated for different kinds of focusing. Also the equations have been perturbed in order to simulate still smaller scale effects and test their implications in the current context.
Locally the variably resolving harmonics behave like untransformed harmonies of the same actual local degree. No fading due to resolution gradients is observed. In order to set up a meaningful simulation only meteorological aspects of the scales supplied have to be observed.
Abstract
Different grid distributions or different equidistantly subdivided coordinate frames, nonlinearly depending on each other, imply different truncation errors, thus different results. This is well known, and (for given coordinates) discussions of truncation errors of difference approximations to differential systems are obligatory. However, it is also customary to use altitude as well as pressure for the vertical coordinate, to use equi-angular polar-coordinate grids in addition to (Kurihara-type) equi-area grids, to use σ-coordinates for avoiding difficulties with a lower topographic boundary, or even to use transformed coordinates in order to parameterize subgrid structures. The reasons of numerical simplicity and stability and of adaptation to special physical structures usually motivate the special choice.
The deviations due to grids of equal degree of resolution but with different types of distributions, and their importance, are studied for some examples of initial-value differential problems, and some inferences are given. For example, the fulfilment of a few conservative properties (as mass and energy) proves to be quite insufficient to overcome the deviations. Instead of grids with special distributions, spectral representation and orthogonal truncation processes are employed in order to achieve the greatest accuracy (like separation from truncation errors due to differencing) and utility.
Abstract
Different grid distributions or different equidistantly subdivided coordinate frames, nonlinearly depending on each other, imply different truncation errors, thus different results. This is well known, and (for given coordinates) discussions of truncation errors of difference approximations to differential systems are obligatory. However, it is also customary to use altitude as well as pressure for the vertical coordinate, to use equi-angular polar-coordinate grids in addition to (Kurihara-type) equi-area grids, to use σ-coordinates for avoiding difficulties with a lower topographic boundary, or even to use transformed coordinates in order to parameterize subgrid structures. The reasons of numerical simplicity and stability and of adaptation to special physical structures usually motivate the special choice.
The deviations due to grids of equal degree of resolution but with different types of distributions, and their importance, are studied for some examples of initial-value differential problems, and some inferences are given. For example, the fulfilment of a few conservative properties (as mass and energy) proves to be quite insufficient to overcome the deviations. Instead of grids with special distributions, spectral representation and orthogonal truncation processes are employed in order to achieve the greatest accuracy (like separation from truncation errors due to differencing) and utility.
Abstract
The representation of tropical precipitation is evaluated across three generations of models participating in phases 3, 5, and 6 of the Coupled Model Intercomparison Project (CMIP). Compared to state-of-the-art observations, improvements in tropical precipitation in the CMIP6 models are identified for some metrics, but we find no general improvement in tropical precipitation on different temporal and spatial scales. Our results indicate overall little changes across the CMIP phases for the summer monsoons, the double-ITCZ bias, and the diurnal cycle of tropical precipitation. We find a reduced amount of drizzle events in CMIP6, but tropical precipitation occurs still too frequently. Continuous improvements across the CMIP phases are identified for the number of consecutive dry days, for the representation of modes of variability, namely, the Madden–Julian oscillation and El Niño–Southern Oscillation, and for the trends in dry months in the twentieth century. The observed positive trend in extreme wet months is, however, not captured by any of the CMIP phases, which simulate negative trends for extremely wet months in the twentieth century. The regional biases are larger than a climate change signal one hopes to use the models to identify. Given the pace of climate change as compared to the pace of model improvements to simulate tropical precipitation, we question the past strategy of the development of the present class of global climate models as the mainstay of the scientific response to climate change. We suggest the exploration of alternative approaches such as high-resolution storm-resolving models that can offer better prospects to inform us about how tropical precipitation might change with anthropogenic warming.
Abstract
The representation of tropical precipitation is evaluated across three generations of models participating in phases 3, 5, and 6 of the Coupled Model Intercomparison Project (CMIP). Compared to state-of-the-art observations, improvements in tropical precipitation in the CMIP6 models are identified for some metrics, but we find no general improvement in tropical precipitation on different temporal and spatial scales. Our results indicate overall little changes across the CMIP phases for the summer monsoons, the double-ITCZ bias, and the diurnal cycle of tropical precipitation. We find a reduced amount of drizzle events in CMIP6, but tropical precipitation occurs still too frequently. Continuous improvements across the CMIP phases are identified for the number of consecutive dry days, for the representation of modes of variability, namely, the Madden–Julian oscillation and El Niño–Southern Oscillation, and for the trends in dry months in the twentieth century. The observed positive trend in extreme wet months is, however, not captured by any of the CMIP phases, which simulate negative trends for extremely wet months in the twentieth century. The regional biases are larger than a climate change signal one hopes to use the models to identify. Given the pace of climate change as compared to the pace of model improvements to simulate tropical precipitation, we question the past strategy of the development of the present class of global climate models as the mainstay of the scientific response to climate change. We suggest the exploration of alternative approaches such as high-resolution storm-resolving models that can offer better prospects to inform us about how tropical precipitation might change with anthropogenic warming.
