The Development of a Nonhydrostatic Global Spectral Model

With the development of numerical weather prediction technology,the traditional global hydrostatic models used in many countries of the world for operational weather forecasting and numerical simulations of general circulation have become more and more unfit for high-impact weather prediction.To address this,it is important to invest in the development of global nonhydrostatic models.Few existing nonhydrostatic global models use consistently the grid finite difference scheme for the primitive equations of dynamical cores,which can subsequently degrade the accuracy of the calculations.A new nonhydrostatic global spectral model,which utilizes the Eulerian spectral method,is developed here from NCAR Community Atmosphere Model 3.0(CAM3.0).Using Janjic's hydrostatic/nonhydrostatic method,a global nonhydrostatic spectral method for the primitive equations has been formulated and developed.In order to retain the integrity of the nonhydrostatic equations,the atmospheric curvature correction and eccentricity correction are considered. In this paper,the Held-Suarez idealized test and an idealized baroclinic wave test are first carried out,which shows that the nonhydrostatic global spectral model has similar climate states to the results of many other global models for long-term idealized integration,as well as better simulation ability for short-term idealized integration.Then,a real case experiment is conducted using the new dynamical core with the full physical parameterizations of subgrid-scale physical processes.The 10-day numerical integration indicates a decrease in systematic error and a better simulation of zonal wind,temperature,and 500-hPa height.     

Variation of Radio Refractivity with Respect to Moisture and Temperature and Influence on Radar Ray Path

In this study, the variation of radio refractivity with respect to temperature and moisture is analyzed. Also, the effects of vertical gradients in temperature and moisture on the propagation paths of electromagnetic waves of weather radar are examined for several sites across the United States using several years of sounding data from the National Weather Service. The ray path is important for identifying storm characteristics and for properly using the radar data in initializing numerical weather prediction models. It is found that during the warm season the radio refractivity gradient is more sensitive to moisture gradients than to temperature gradients. Ray paths from the commonly accepted vertical ray path model are compared to a ray path computed from a stepwise ray tracing algorithm using data from actual soundings. For the sample of about 16 000 soundings examined, we find that only a small fraction of the ray paths diverge significantly from those calculated using a ray path model based on the US Standard Atmosphere. While the problem of ray dueting in the presence of a temperature inversion is fairly well known, we identify the presence of a strong vertical moisture gradient as the culprit in the majority of the cases where significant deviations occurred.     

A comparison of the radar ray path equations and approximations for use in radar data assimilation

The radar ray path equations are used to determine the physical location of each radar measurement. These equations are necessary for mapping radar data to computational grids for diagnosis, display and numerical weather prediction (NWP). They are also used to determine the forward operators for assimilation of radar data into forecast models. In this paper, a stepwise ray tracing method is developed. The influence of the atmospheric refractive index on the ray path equations at different locations related to an intense cold front is examined against the ray path derived from the new tracing method. It is shown that the radar ray path is not very sensitive to sharp vertical gradients of refractive index caused by the strong temperature inversion and large moisture gradient in this case. In the paper, the errors caused by using the simplified straight ray path equations are also examined. It is found that there will be significant errors in the physical location of radar measurements if the earth’s curvature is not considered, especially at lower elevation angles. A reduced form of the equation for beam height calculation is derived using Taylor series expansion. It is computationally more efficient and also avoids the need to use double precision variables to mitigate the small difference between two large terms in the original form. The accuracy of this reduced form is found to be sufficient for modeling use.     

Analysis of Wind Power Assessment Based on the WRF Model

Assessing wind energy is a key step in selecting a site for a wind farm. The accuracy of the assessment is essential for the future operation of the wind farm. There are two main methods for assessing wind power： one is based on observational data and the other relies on mesoscale numerical weather prediction（NWP）. In this study, the wind power of the Liaoning coastal wind farm was evaluated using observations from an anemometer tower and simulations by the Weather Research and Forecasting（WRF） model, to see whether the WRF model can produce a valid assessment of the wind power and whether the downscaling process can provide a better evaluation. The paper presents long-term wind data analysis in terms of annual, seasonal, and diurnal variations at the wind farm, which is located on the east coast of Liaoning Province. The results showed that, in spring and summer, the wind speed, wind direction, wind power density, and other main indicators were consistent between the two methods. However, the values of these parameters from the WRF model were significantly higher than the observations from the anemometer tower. Therefore, the causes of the differences between the two methods were further analyzed. There was much more deviation in the original material, National Centers for Environmental Prediction（NCEP） final（FNL） Operational Global Analysis data, in autumn and winter than in spring and summer. As the region is vulnerable to cold-air outbreaks and windy weather in autumn and winter, and the model usually forecasted stronger high or low systems with a longer duration, the predicted wind speed from the WRF model was too large.     

The development and initial tests of an atmospheric model based on a vertical coordinate with a smooth transition from terrain following to isentropic coordinates

An atmospheric model (η model) is developed by modifying the UW θ－σ hybrid model. In the η model, the vertical coordinate transforms smoothly from terrain following to isentropic coordinates. The model is developed to capitalize on the inherent advantage of numerical modeling in isentropic coordinates and to eliminate the interface between the sigma planetary boundary layer and isentropic free atmosphere present in the UW θ－σ model. This formulation provides the potential for the data assimilation and the application of higher order schemes. This paper describes the structure of the η model and presents results from initial numerical experiments. The first experiment tests the capability of the η model for simulating the baroclinic development process. In the 48-hr numerical weather forecast experiment, the η model produces reasonable precipitation and synoptic fields at all levels which are similar to those from the UW θ-σ model. The second and third experiments test the capability of the η model for conserving 1) the joint distribution of isentropic potential vorticity (IPV) and proxy ozone and 2) equivalent potential temperature under frictionless and isentropic conditions. These experiments show that distributions of IPV and proxy ozone in the pure isentropic domain and the distributions of prognostic and diagnostic equivalent potential temperature in the model domain remain highly correlated to day 10.     

A generalized layered radiative transfer model in the vegetation canopy

In this paper, a generalized layered model for radiation transfer in canopy with high vertical resolution is developed. Differing from the two-stream approximate radiation transfer model commonly used in the land surface models, the generalized model takes into account the effect of complicated canopy morphology and inhomogeneous optical properties of leaves on radiation transfer within the canopy. In the model, the total leaf area index （LAI） of the canopy is divided into many layers. At a given layer, the influences of diffuse radiation angle distributions and leaf angle distributions on radiation transfer within the canopy are considered. The derivation of equations serving the model are described in detail, and these can deal with various diffuse radiation transfers in quite broad categories of canopy with quite inhomogeneons vertical structures and uneven leaves with substantially different optical properties of adaxial and abaxial faces of the leaves. The model is used to simulate the radiation transfer for canopies with horizontal leaves to validate the generalized model. Results from the model are compared with those from the two-stream scheme, and differences between these two models are discussed.     

Synchronization of Radar Observations with Multi-Scale Storm Tracking

The 3-D radar reflectivity data has become increasingly important for use in data assimilation towards convective scale numerical weather prediction as well as next generation precipitation estimation. Typically, reflectivity data from multiple radars are objectively analyzed and mosaiced onto a regional 3-D Cartesian grid prior to being assimilated into the models. One of the scientific issues associated with the mosaic of multi-radar observations is the synchronization of all the observations. Since radar data is usually rapidly updated (～every 5--10 min), it is common in current multi-radar mosaic techniques to combine multiple radar' observations within a time window by assuming that the storms are steady within the window. The assumption holds well for slow evolving precipitation systems, but for fast evolving convective storms, this assumption may be violated and the mosaic of radar observations at different times may result in inaccurate storm structure depictions. This study investigates the impact of synchronization on storm structures in multiple radar data analyses using a multi-scale storm tracking algorithm.     

VERIFICATION OF TROPICAL CYCLONE RAINFALL PREDICTIONS FROM CMA AND JMA GLOBAL MODELS

The number of tropical cyclone (TC) genesis over the South China Sea and the Northwest Pacific Ocean in 2009 is significantly less than the average (27.4). However, the number of landfall TC over mainland China and its associated rainfall is more than the average. This paper focuses on the performance of numerical weather prediction (NWP) of landfall TC precipitation over China in 2009. The China Meteorological Administration (CMA) and Japan Meteorological Agency (JMA) models are compared. Although the schemes of physical processes, the data assimilation system and the dynamic frame are entirely different for the two models, the results of forecast verification are similar to each other for TC rainfall and track except for TC Goni. In this paper, a day with daily rainfall amount greater than 50 mm was selected as a storm rain day when there was a TC affecting the mainland. There are 32 storm rain days related to the landing of typhoons and tropical depressions. The rainfall forecast verification methods of National Meteorological Centre (NMC) of CMA are selected to verify the models’ rainfall forecast. Observational precipitation analyses related to TCs in 2009 indicate a U-shape spatial distribution in China. It is found that the rain belt forecasted by the two models within 60 hours shows good agreement with observations, both in the location and the maximum rainfall center. Beyond 3 days, the forecasted rainfall belt shifts northward on average, and the rainfall amount of the model forecasts becomes under-predicted. The rainfall intensity of CMA model forecast is more reasonable than that of JMA model. For heavy rain, the JMA model made more missing forecasts. The TC rainfall is verified in Guangdong, Guangxi, Fujian and Hainan where rainfall amount related to TCs is relatively larger than in other regions. The results indicate that the model forecast for Guangdong and Guangxi is more skillful than that for Hainan. The rainfall forecast for Hainan remains difficult for the models because of insufficient observation data and special tropical ocean climate.     

AN INTEGRATION METHOD WITH FITTING CUBIC SPLINE FUNCTIONS TO A NUMERICAL MODEL OF 2ND-ORDER SPACE-TIME DIFFERENTIAL REMAINDER——FOR AN IDEAL GLOBAL SIMULATION CASE WITH PRIMITIVE ATMOSPHERIC EQUATIONS

In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.     

Kinetic Energy Budget Equations of Rotational and Divergent Flow in Terrain-following Coordinates

In this study, kinetic energy budget equations of rotational and divergent flow in pressure coordinates are derived on terrain-following coordinates. The new formulation explicitly shows the terrain effects and can be applied directly to model-simulated dynamic and thermodynamic fields on the model’s original vertical grid. Such application eliminates interpolation error and avoids errors in virtual weather systems in mountainous areas. These advantages and their significance are demonstrated by a numerical study in terrain-following coordinates of a developing vortex after it moves over the Tibetan Plateau in China.     

An improved dynamic core for a non-hydrostatic model system on the Yin-Yang grid

A 3D dynamic core of the non-hydrostatic model GRAPES(Global/Regional Assimilation and Prediction System) is developed on the Yin-Yang grid to address the polar problem and to enhance the computational efficiency. Three-dimensional Coriolis forcing is introduced to the new core, and full representation of the Coriolis forcing makes it straightforward to share code between the Yin and Yang subdomains. Similar to that in the original GRAPES model, a semi-implicit semi-Lagrangian scheme is adopted for temporal integration and advection with additional arrangement for cross-boundary transport. Under a non-centered second-order temporal and spatial discretization, the dry nonhydrostatic frame is summarized as the solution of an elliptical problem. The resulting Helmholtz equation is solved with the Generalized Conjugate Residual solver in cooperation with the classic Schwarz method. Even though the coefficients of the equation are quite different from those in the original model, the computational procedure of the new core is just the same. The bi-cubic Lagrangian interpolation serves to provide Dirichlet-type boundary conditions with data transfer between the subdomains. The dry core is evaluated with several benchmark test cases, and all the tests display reasonable numerical stability and computing performance. Persistency of the balanced flow and development of both the mountain-induced Rossby wave and Rossby–Haurwitz wave confirms the appropriate installation of the 3D Coriolis terms in the semi-implicit semi-Lagrangian dynamic core on the Yin-Yang grid.     

HIGH-RESOLUTION NUMERICAL SIMULATION OF TYPHOON LONGWANG (2005) WITH THE SPECTRUM NUDGING TECHNIQUE

With the Weather Research and Forecasting model (WRFV3.2.1), the application of spectrum nudging techniques in numerical simulation of the genesis and development of typhoon Longwang (2005) is evaluated in this work via four numerical experiments with different nudging techniques. It is found that, due to the ability to capture the large-scale fields and to keep the meso-to small-scale features derived from the model dynamics, the experiment with spectrum nudging technique can simulate the formation, intensification and motion of Longwang properly. The improvement on the numerical simulation of Longwang induced by the spectrum nudging depends on the nudging coefficients. A weak spectrum nudging does not make significant improvement on the simulation of Longwang. Although the experiment with four-dimensional data assimilation, i.e., FDDA, also derives the genesis and movement of Longwang appropriately, it fails to simulate the intensifying process of Longwang properly. The reason is that, as the large-scale features derived from the model are nudged to the observational data, the meso- to small-processes produced by the model dynamics important to the intensification of typhoon are nearly smoothed by FDDA.     

Statistics of the Z–R Relationship for Strong Convective Weather over the Yangtze–Huaihe River Basin and Its Application to Radar Reflectivity Data Assimilation for a Heavy Rain Event

The relationship between the radar reflectivity factor(Z) and the rainfall rate(R) is recalculated based on radar observations from 10 Doppler radars and hourly rainfall measurements at 6529 automatic weather stations over the Yangtze–Huaihe River basin. The data were collected by the National 973 Project from June to July 2013 for severe convective weather events. The Z–R relationship is combined with an empirical qr–R relationship to obtain a new Z–qr relationship, which is then used to correct the observational operator for radar reflectivity in the three-dimensional variational(3 DVar) data assimilation system of the Weather Research and Forecasting(WRF) model to improve the analysis and prediction of severe convective weather over the Yangtze–Huaihe River basin. The performance of the corrected reflectivity operator used in the WRF 3 DVar data assimilation system is tested with a heavy rain event that occurred over Jiangsu and Anhui provinces and the surrounding regions on 23 June 2013. It is noted that the observations for this event are not included in the calculation of the Z–R relationship. Three experiments are conducted with the WRF model and its 3 DVar system, including a control run without the assimilation of reflectivity data and two assimilation experiments with the original and corrected reflectivity operators. The experimental results show that the assimilation of radar reflectivity data has a positive impact on the rainfall forecast within a few hours with either the original or corrected reflectivity operators, but the corrected reflectivity operator achieves a better performance on the rainfall forecast than the original operator. The corrected reflectivity operator extends the effective time of radar data assimilation for the prediction of strong reflectivity. The physical variables analyzed with the corrected reflectivity operator present more reasonable mesoscale structures than those obtained with the original reflectivity operator. This suggests that the new statistical Z–R relationship is more suitable for predicting severe convective weather over the Yangtze–Huaihe River basin than the Z–R relationships currently in use.     

THE EFFECTIVENESS OF GENETIC ALGORITHM IN CAPTURING CONDITIONAL NONLINEAR OPTIMAL PERTURBATION WITH PARAMETERIZATION “ON-OFF” SWITCHES INCLUDED BY A MODEL

In the typhoon adaptive observation based on conditional nonlinear optimal perturbation (CNOP), the ‘on-off’ switch caused by moist physical parameterization in prediction models prevents the conventional adjoint method from providing correct gradient during the optimization process. To address this problem, the capture of CNOP, when the “on-off” switches are included in models, is treated as non-smooth optimization in this study, and the genetic algorithm (GA) is introduced. After detailed algorithm procedures are formulated using an idealized model with parameterization “on-off” switches in the forcing term, the impacts of “on-off” switches on the capture of CNOP are analyzed, and three numerical experiments are conducted to check the effectiveness of GA in capturing CNOP and to analyze the impacts of different initial populations on the optimization result. The result shows that GA is competent for the capture of CNOP in the context of the idealized model with parameterization ‘on-off’ switches in this study. Finally, the advantages and disadvantages of GA in capturing CNOP are analyzed in detail.     

Using Statistical Downscaling to Quantify the GCM-Related Uncertainty in Regional Climate Change Scenarios： A Case Study of Swedish Precipitation

There are a number of sources of uncertainty in regional climate change scenarios. When statistical downscaling is used to obtain regional climate change scenarios, the uncertainty may originate from the uncertainties in the global climate models used, the skill of the statistical model, and the forcing scenarios applied to the global climate model. The uncertainty associated with global climate models can be evaluated by examining the differences in the predictors and in the downscaled climate change scenarios based on a set of different global climate models. When standardized global climate model simulations such as the second phase of the Coupled Model Intercomparison Project （CMIP2） are used, the difference in the downscaled variables mainly reflects differences in the climate models and the natural variability in the simulated climates. It is proposed that the spread of the estimates can be taken as a measure of the uncertainty associated with global climate models. The proposed method is applied to the estimation of global-climate-model-related uncertainty in regional precipitation change scenarios in Sweden. Results from statistical downscaling based on 17 global climate models show that there is an overall increase in annual precipitation all over Sweden although a considerable spread of the changes in the precipitation exists. The general increase can be attributed to the increased large-scale precipitation and the enhanced westerly wind. The estimated uncertainty is nearly independent of region. However, there is a seasonal dependence. The estimates for winter show the highest level of confidence, while the estimates for summer show the least.     

An Approach to Quantify the Heat Wave Strength and Price a Heat Derivative for Risk Hedging

Mitigating the heat stress via a derivative policy is a vital financial option for agricultural producers and other business sectors to strategically adapt to the climate change scenario. This study has provided an approach to identifying heat stress events and pricing the heat stress weather derivative due to persistent days of high surface air temperature (SAT). Cooling degree days (CDD) are used as the weather index for trade. In this study, a call-option model was used as an example for calculating the price of the index. Two heat stress indices were developed to describe the severity and physical impact of heat waves. The daily Global Historical Climatology Network (GHCN-D) SAT data from 1901 to 2007 from the southern California, USA, were used. A major California heat wave that occurred 20-25 October 1965 was studied. The derivative price was calculated based on the call-option model for both long-term station data and the interpolated grid point data at a regular 0.1 ×0.1 latitude-longitude grid. The resulting comparison indicates that (a) the interpolated data can be used as reliable proxy to price the CDD and (b) a normal distribution model cannot always be used to reliably calculate the CDD price. In conclusion, the data, models, and procedures described in this study have potential application in hedging agricultural and other risks.     

Atmosphere-Ocean Coupling Schemes in a One-Dimensional Climate Model

In this paper, the coupling schemes of atmosphere-ocean climate models are discussed with one-dimensional advection equations. The convergence and stability for synchronous and asynchronous schemes are demonstrated and compared.Conclusions inferred from the analysis are given below. The synchronous scheme as well as the asynchronous-implicit scheme in this model are stable for arbitrary integrating time intervals. The asynchronous explicit scheme is unstable under certain conditions, which depend upon advection velocities and heat exchange parameters in the atmosphere and oceans. With both synchronous and asynchronous stable schemes the discrete solutions converge to their unique exact ones. Advections in the atmosphere and ocean accelerate the rate of convergence of the asynchronous-implicit scheme. It is suggusted that the asynchronous-implicit coupling scheme is a stable and efficient method for most climatic simulations.     

VARIATION IN WIND VELOCITY OVER WATER

Starting from the equations of motion and continuity, a theoretical model is deduced in this paper for the variation in wind velocity over water caused by abrupt changes in surface roughness and temperature when air flows from land to water, based on the consideration that the turbulent exchange coefficient varies with height and distance from the upwind edge. According to the computation of this model, the variation in wind velocity over water, as the drift of air is from land to water, occurs mainly in the first few kilometers from the upwind edge. The wind velocity over water increases to a maximum when the air over land is stable, it tends to moderate when neutral condition is reached, and least variation is shown in unstable condition. And when the air over land is unstable the wind velocity is less over water than over land in strong winds, but somewhat greater in light winds.     

Surface Weather Parameters Forecasting Using Analog Ensemble Method over the Main Airports of Morocco

Surface weather parameters detain high socioeconomic impact and strategic insights for all users, in all domains(aviation, marine traffic, agriculture, etc.). However, those parameters were mainly predicted by using deterministic numerical weather prediction(NWP) models that include a wealth of uncertainties. The purpose of this study is to contribute in improving low-cost computationally ensemble forecasting of those parameters using analog ensemble method(AnEn) and comparing it to the operatio...     

PHYSICAL DISSIPATIVE TECHNIQUE AND ITS APPLICATION TO THE MM4

Under the traditional framework of fluid dynamics,the problem of the numerical weatherprediction is often expressed as the deterministic initial value problem of the classical Newtonianmechanics.The atmosphere is.however,a many-body system,the methodology by which thesystem with two bodies could be precisely solved would cause bigger errors and problems whenhandling the many-body system by it.A kind of technique to incorporate “the irreversiblethermodynamic operators” into the numerical weather prediction models is.therefore,suggestingin this paper,to control the evolutionary direction of the many-body system according to theconstraining way of the second law of thermodynamics,and thus the forecasting accuracy of thenumerical weather prediction has been noticeably improved.For example,in the MM4 theaveraged relative root mean square error of the fields of the temperature,humidity,height andwhole wind velocity has decreased by about 13%,among which the averaged error of the 48 hforecasts has decreased by more than 20%.Since the technique to introduce the irreversablethermodynamic operator suggested in this paper is based on the physical law that describes thedissipativity and does not come from the computational consideration only.it is thus named as thephysical dissipative technique.In view of the universality of the principle incorporating theirreversible thermodynamics operators suggested in this paper for the fluid dynamics andatmospheric numerical models,the applications and generalization of this incorporating techniquewould produce a great impact on the field of geophysical fluid dynamics.