The Fourier finite-element method (FFEM) on the sphere, which performs with an operation count of O(N 2 log 2 N) for 2N 3 N grids in spherical coordinates, was developed using linear basis functions. Dependent field variables are expanded with the Fourier series in the longitude, and the Fourier coefficients are represented with a series of first-order finite elements. Different types of pole conditions were incorporated into the Fourier coefficients of the scalar and vector variables in order to avoid discontinuity at the poles. For the Laplacian operator, the linear element was defined as a function of the sine of latitude instead of the latitude. The FFEM was applied to the derivatives of the first-and second-order elliptic equations and the transport equations. The scale-selective high-order Laplacian-type filter was implemented as a hyperviscosity. For the first-order derivative the fourth-order convergence rate of the accuracy, as is expected from the theoretical analysis, was achieved. Elliptic equations were found to be solved accurately without pole discontinuity, and the convergence rate turned out to be second order. The cosine bell advection, time-differenced with a thirdorder Runge-Kutta method, showed that the squared-norm error convergence rate was slightly above second order. Both the Gaussian bell advection and the deformational flow produced the theoretical convergence rate of fourth order. The high-order filter was found to be effective in maintaining a quasi-uniform resolution over the sphere, and thus allowed a large time step size. Sensitivity experiments of cosine bell advection over the poles revealed that the CFL number, as defined with the maximum grid size on the global domain, can be taken to be as large as unity.

<p>Since the dynamical core of Korean Integrated Model (KIM) was developed in the 1st phase (2011~2019) of KIAPS, we have been aiming to develop a variable resolution prediction system covering short to medium range in the 2nd phase (2020.9~2026). As a first step towards moving to km-scale resolution, we have increased the model resolution from 12 km to 8 km horizontally and 91 to 137 layers vertically. For increasing the resolution horizontally, dynamics core configurations and terrain elevation data were newly set up. For vertically, vertical coordinates of 137 layers followed that of the European Center for Intermediate Forecasting (ECMWF) Integrated Forecasting System (IFS), which has been increased vertical resolution throughout the troposphere and stratosphere comparing to 91 layers.<br>This study discusses the forecast impact of high-resolution KIM in terms of objective verification scores against observations and analyses. The overall conclusion for horizontal high-resolution is that it shows slightly positive in southern hemisphere and mainly neutral for northern hemisphere, but also some negative in tropics. One of distinguished results is increasing horizontal resolution leads to cooling in the temperature in the lower and upper troposphere. The cooling in the lower tropospheric over the tropics seems to come from smaller time step that has to be for smaller dx, which results in enlarged low cloud formation and thus more radiative cooling. In case of the upper troposphere, the cooling results from outgoing long-wave radiative cooling by decreasing hydrometeors in physical response to smaller grid spacing. The increase of vertical resolution had an effect of neutral to slight positive in northern hemisphere but showed significant degradation in tropics. To achieve the consistency and improvement for high-resolution model, it is necessary to understand the physical processes related to time step and horizontal and vertical grid spacing.</p><p> </p><p><strong>Acknowledgement</strong><br>One of the authors, S-J Choi, wishes to acknowledge this study was supported by 2023 New Professor Support Program of Natural Science Research Institute in Gangneung-Wonju National University).</p>

<p>Multi-model ensemble using statistical post-processing is one of the methods to provide the impact of uncertainties of the Numerical Weather Prediction (NWP) models, with low cost and better accuracy for extreme weather forecasts. Extreme weather events such as heat/cold waves, windstorms, and heavy rainfall result in severe damage in human life and properties. However, the performance of the NWP models, particularly, heavy rain forecast is still low due to the intermittent and non-Gaussian properties. The light rain tends to be overestimated and the strong rain tends to be underestimated averagely on the NWP models. Thus the multi-model ensemble using statistical post-processing is activated to correct the discrepancies between the observation and the model intensity of precipitation.<br>The aim of this study is to provide the improvement of precipitation forecasts in probabilistic and deterministic aspects using a multi-model ensemble method with more weights on the less error and without any bias correction. Six types of models, namely, Local Data assimilation and Prediction System (LDPS), Local ENsemble System (LENS), Global Data assimilation and Prediction System (GDPS), Ensemble Prediction System-Global (EPSG) of Korea Meteorological Administration (KMA), the single and ensemble models of European Centre for Medium-Range Weather Forecasts (ECMWF), are used to blend. The preliminary results of the multi-model ensemble show similar results to the ECMWF ensemble mean in deterministic for 3-hourly accumulated precipitation over the East Asia and the middle of the performance among individual models in probabilistic over the South Korea. More details of the methodology, results, and improvements will be discussed in the presentation.</p>