# Numerical Modelling for Weather Prediction in Hong Kong

Introduction : Hong Kong is located at the southern rim of the East Asian continent, in the land of the Asian monsoon and bordering the South China Sea. Its climate is subjected to the vagaries of both tropical and extratropical weather systems. The presence of hilly terrain and large land-sea contrast also gives rise to complex small-scale atmospheric circulations, which in turn lead to significant variations in weather conditions within Hong Kong. As such, suitable forecasting tools are needed to encompass the full range of vastly different meteorological factors over a broad range of spatial scales, from synoptic systems over the expanse of the continent down to local systems arising from orographic influence.

Atmospheric Numerical Modelling : Weather stems from the constant evolution of the atmosphere governed by physical laws. Using high-speed computers to solve a complex set of mathematical equations that represents the governing laws, numerical weather prediction (NWP) is a technique for simulating the atmospheric evolution in order to delineate the resultant weather changes. The variables involved in the equations include wind, temperature, pressure and moisture content. In principle, given the initial and boundary conditions, the atmospheric variables can be numerically solved as functions of time and form the basis of weather forecast. Commonly used numerical methods include "spectral transform method" and "finite difference method". The corresponding models are often referred to as "spectral models" and "finite difference models" respectively. To reduce the computational demand, approximations and assumptions are made to simplify the governing equations. As such, the numerical simulation will never be a perfect representation of the real atmosphere.

NWP at the Hong Kong Observatory : Over the years, the Hong Kong Observatory has been receiving and making use of NWP data provided by overseas sources (see the section on "Medium-range NWP Products" for more details). For prognosis of large-scale weather systems such as cold surges associated with the winter monsoon, the forecast results are generally satisfactory. However, the relatively coarse resolution of these NWP data often fails to resolve the small-scale systems (e.g. rainstorms) that play a crucial role in the generation of inclement weather conditions. In an attempt to improve local weather forecasts through the development of a higher resolution model, the Operational Regional Spectral Model (ORSM) was adopted and set up for use at the Observatory. The model was put into operation in December 1999 on a vector computer. It was subsequently replaced with a parallel version of the model in November 2008 and put to run on a server cluster.

Choices of Domain and Coordinates : The ORSM is currently configured to run on a smaller but higher resolution (20-km) inner domain covering Hong Kong and its neighbouring areas, nested within a larger but coarser resolution (60-km) outer domain covering East Asia and the western Pacific ( Fig.1). From the current setting of domain size and model resolutions, both the inner and outer domains have 151 x 145 grid points in the horizontal in Mercator map projection and 40 levels in the vertical. A hybrid of pressure and terrain-following vertical co-ordinates is used in which the upper levels tend towards the pressure coordinate and near-surface layers tend towards the terrain-following coordinate (Fig. 2). Transformation of physical variables between grid-point space and spectral space is required.

 Fig.1 Model domains for 60-km ORSM (outer) and 20-km ORSM (inner). Fig.2 Vertical structure of the grid points in the ORSM: upper levels are close to the pressure coordinate while lower levels are terrain-following.

Model Initialization : Observations obtained from overseas sources as well as from local networks are decoded and quality-checked for doubtful or erroneous data. Short-range forecast fields (i.e. 3-hour forecast from 20-km inner model and 6-hour forecast from 60-km outer model) from the previous model run are used as first-guess or background in assimilating the latest observational data. Objective analyses are then carried out and currently a three-dimensional optimal interpolation method is used to prepare the initial fields for the model forecast. Hourly rainfall information, derived from the digital cloud data of geostationary meteorological satellites and from the real-time calibration of radar reflectivity by local raingauge data, is incorporated into the model through a physical initialization process. In this process, the moisture of the initial field between the lifting condensation level and the cloud top at the point where rain is observed is adjusted to allow precipitation process to be switched on. The heating rate of the precipitation process is also adjusted to correspond to the rainfall amount observed.

Representation of Physical Processes : ORSM includes physical processes such as radiative transfer, phase changes of water substance, re-distribution of energy due to cumulus convection, transport of momentum, energy and moisture by turbulence, and exchanges between the atmosphere and the surface layer. As yet, these physical processes are still too complex to be understood in full and, in practice, have to be represented by different parameterization schemes.

Boundary Conditions : The numerical methods utilized in solving the set of mathematical equations involve calculating the spatial rate of change of variables, which means a priori grid point value (GPV) information along the boundary outside the model domain has to be separately provided to set up time-dependent boundary conditions for computing the governing equations. For the 60-km ORSM, the boundary conditions are prepared from JMA's Global Spectral Model (GSM) outputs, which include surface data as well as upper level data on 16 standard pressure levels all the way up to 10 hPa (about 30 km above ground in altitude). Boundary data for the inner 20-km model are extracted from the outer 60-km model.

Operational Implementation of ORSM : The main objective of ORSM is to provide short-range weather forecasts for the next couple of days. The 20-km ORSM is run eight times a day (at 00, 03, 06, 09, 12, 15, 18 and 21 UTC) to provide 42-hour forecasts. The 60-km ORSM is run four times a day (at 00, 06, 12 and 18 UTC) to provide 72-hour forecasts. Prognostic charts and other post-processed products are made available around 3.5 hours and 4.5 hours after analysis time for 20-km and 60-km models respectively. Web-based two-dimensional and three-dimensional graphical products are generated to facilitate forecasters' interpretation. Model-extracted information is customized and packaged for optimal visualization, e.g. time-series forecast of surface wind, temperature, humidity, cloud cover and cumulative rainfall over Hong Kong ( Fig.3). Other derived products include regional temperature forecasts, rain index, vertical profiles, meteorograms and a selection of specially prepared weather maps. For short-range warning of heavy rain and thunderstorms, ORSM forecasts are integrated with the nowcasting system for a combined display of operation-critical information ( Fig.4).

 Fig.3 Time series of surface wind, temperature, humidity, cloud cover and 3-hourly accumulated rainfall forecast by 60-km ORSM. Fig.4 Combined warning panel for short-range prediction of heavy rain based on forecasts from ORSM and nowcasting system.

Medium-range NWP Products : While ORSM focuses on forecasts in the shorter range, medium range forecasts up to 7 days ahead have to rely on global NWP models run elsewhere. The Observatory has been using GPV model outputs from the European Centre for Medium-Range Weather Forecasts (ECMWF) and the United Kingdom Meteorological Office via the Global Telecommunication System (GTS) of the World Meteorological Organization since 1985. Starting from 1996, JMA's GSM products are routinely downloaded via GTS and the Internet. From 1999 onwards, additional ECMWF higher resolution GPV products in GRIB format are obtained via Beijing and Offenbach. And beginning in 2002, global model products from the US National Center for Environmental Prediction are also retrieved via the Internet. To maximize the usage of NWP guidance available from a multitude of sources, an ensemble approach based on different models has been pursued, from which probability forecasts are being generated for special users in their planning and decision-making processes.

Looking Ahead : While there has been a significant improvement in model resolution over the years all the way down to the current 20 km, it is still not precise enough to depict the highly uneven spatial distribution of rainfall ( Fig.5). With the aim of providing more quantitative and location-specific guidance on inclement weather events such as heavy rain, the Observatory has been experimenting with high-resolution non-hydrostatic models and exploring the feasibility of implementing such models operationally. Model physics will become more sophisticated as model resolutions increase further. New data types at irregular hours from non-conventional sources, particularly from highly tuned remote-sensing platforms, will be studied for potential NWP applications to improve model initial fields. To that end, more involved data assimilation methods, e.g. three-dimensional or four-dimensional variational analysis and Extended Kalman Filtering technique, will be employed.

 Fig.5 Comparison of 20-km ORSM forecast rainfall at grid points near Hong Kong and actual rainfall distribution within the territory. Rainfall unit is in millimetres (mm). The limited grid point spacing would not be able to resolve the localized heavy rain (shown in colours of yellow and red) over the eastern part of Hong Kong Island and Tseung Kwan O.

 2003 Last revision date: <19 Dec 2012>