CONDITIONAL NONLINEAR OPTIMAL PERTURBATIONS: APPLICATION IN TROPICAL CYCLONE FORECASTS

Considering the feature of tropical cyclones (TCs) that strong positive vorticity exists in the lower layers of troposphere, this study proposed to use vorticity at 850 hPa as cost function to find the conditional nonlinear optimal perturbation (CNOP), which was largely different from those previous studies using total energy of perturbed forecast variables. The CNOP was obtained by an ensemble-based approach. All of the sensitive areas determined by CNOP with vorticity at 850 hPa as cost function for the three cases were located over the TC core region and its vicinity. The impact of the CNOP-based adaptive observations on TC forecasts was evaluated with three cases via observational system simulation experiments (OSSEs). Results showed obvious improvements in TC intensity or track forecasts due to the CNOP-based adaptive observations, which were related to the main error source of the verification area, i.e., intensity error or location error.     

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.     

Sensitivity to Tendency Perturbations of Tropical Cyclone Short-range Intensity Forecasts Generated by WRF

The present study uses the nonlinear singular vector(NFSV)approach to identify the optimally-growing tendency perturbations of the Weather Research and Forecasting(WRF)model for tropical cyclone(TC)intensity forecasts.For nine selected TC cases,the NFSV-tendency perturbations of the WRF model,including components of potential temperature and/or moisture,are calculated when TC intensities are forecasted with a 24-hour lead time,and their respective potential temperature components are demonstrated to have more impact on the TC intensity forecasts.The perturbations coherently show barotropic structure around the central location of the TCs at the 24-hour lead time,and their dominant energies concentrate in the middle layers of the atmosphere.Moreover,such structures do not depend on TC intensities and subsequent development of the TC.The NFSV-tendency perturbations may indicate that the model uncertainty that is represented by tendency perturbations but associated with the inner-core of TCs,makes larger contributions to the TC intensity forecast uncertainty.Further analysis shows that the TC intensity forecast skill could be greatly improved as preferentially superimposing an appropriate tendency perturbation associated with the sensitivity of NFSVs to correct the model,even if using a WRF with coarse resolution.     

The Sensitive Regions Identified by CNOPs of Three Typhoon Events

In this paper, several sets of observing system simulation experiments (OSSEs) were designed for three typhoon cases to determine whether or not the additional observation data in the sensitive regions identified by conditional nonlinear optimal perturbations (CNOPs) could improve the short-range forecast of typhoons. The results show that the CNOPs capture the sensitive regions for typhoon forecasts, which implies that conducting additional observation in these specific regions and eliminating initial errors could reduce forecast errors. It is inferred from the results that dropping sondes in the CNOP sensitive regions could lead to improvements in typhoon forecasts.     

Ensemble Forecasts of Tropical Cyclone Track with Orthogonal Conditional Nonlinear Optimal Perturbations

This paper preliminarily investigates the application of the orthogonal conditional nonlinear optimal perturbations(CNOPs)–based ensemble forecast technique in MM5(Fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model). The results show that the ensemble forecast members generated by the orthogonal CNOPs present large spreads but tend to be located on the two sides of real tropical cyclone(TC) tracks and have good agreements between ensemble spreads and ensemble-mean forecast errors for TC tracks. Subsequently, these members reflect more reasonable forecast uncertainties and enhance the orthogonal CNOPs–based ensemble-mean forecasts to obtain higher skill for TC tracks than the orthogonal SVs(singular vectors)–, BVs(bred vectors)– and RPs(random perturbations)–based ones. The results indicate that orthogonal CNOPs of smaller magnitudes should be adopted to construct the initial ensemble perturbations for short lead–time forecasts, but those of larger magnitudes should be used for longer lead–time forecasts due to the effects of nonlinearities. The performance of the orthogonal CNOPs–based ensemble-mean forecasts is case-dependent,which encourages evaluating statistically the forecast skill with more TC cases. Finally, the results show that the ensemble forecasts with only initial perturbations in this work do not increase the forecast skill of TC intensity, which may be related with both the coarse model horizontal resolution and the model error.     

VERIFICATION OF TYPHOON FORECASTS BY THE GRAPES MODEL

Four landfalling typhoon cases in 2005 were selected for a numerical simulation study with the Global/Regional Assimilation and Prediction System (GRAPES) model. The preliminary assessment results of the performance of the model, including the predictions of typhoon track, landfall time, location and intensity, etc., are presented and the sources of errors are analyzed. The 24-hour distance forecast error of the typhoon center by the model is shown to be about 131 km, while the 48-hour error is 252 km. The model was relatively more skilful at forecasts of landfall time and locations than those of intensity at landfall. On average, the 24-hour forecasts were slightly better than the 48-hour ones. An analysis of data impacts indicates that the assimilation of unconventional observation data is essential for the improvement of the model simulation. The model could also be improved by increasing model resolution to simulate the mesoscale and fine scale systems and by improving methods of terrain refinement processing.     

Uncertainty in Tropical Cyclone Intensity Predictions due to Uncertainty in Initial Conditions

Focusing on the role of initial condition uncertainty,we use WRF initial perturbation ensemble forecasts to investigate the uncertainty in intensity forecasts of Tropical Cyclone(TC)Rammasun(1409),which is the strongest TC to have made landfall in China during the past 50 years.Forecast results indicate that initial condition uncertainty leads to TC forecast uncertainty,particularly for TC intensity.This uncertainty increases with forecast time,with a more rapid and significant increase after 24 h.The predicted TC develops slowly before 24 h,and at this stage the TC in the member forecasting the strongest final TC is not the strongest among all members.However,after 24 h,the TC in this member strengthens much more than that the TC in other members.The variations in convective instability,precipitation,surface upward heat flux,and surface upward water vapor flux show similar characteristics to the variation in TC intensity,and there is a strong correlation between TC intensity and both the surface upward heat flux and the surface upward water vapor flux.The initial condition differences that result in the maximum intensity difference are smaller than the errors in the analysis system.Differences in initial humidity,and to a lesser extent initial temperature differences,at the surface and at lower heights are the key factors leading to differences in the forecasted TC intensity.These differences in initial humidity and temperature relate to both the overall values and distribution of these parameters.     

The Impact of Horizontal Resolution on the CNOP and on Its Identified Sensitive Areas for Tropical Cyclone Predictions

In this study,the impacts of horizontal resolution on the conditional nonlinear optimal perturbation (CNOP) and on its identified sensitive areas were investigated for tropical cyclone predictions.Three resolutions,30 km,60 km,and 120 km,were studied for three tropical cyclones,TC Mindulle (2004),TC Meari (2004),and TC Matsa (2005).Results show that CNOP may present different structures with different resolutions,and the major parts of CNOP become increasingly localized with increased horizontal resolution.CNOP produces spiral and baroclinic structures,which partially account for its rapid amplification.The differences in CNOP structures result in different sensitive areas,but there are common areas for the CNOP-identified sensitive areas at various resolutions,and the size of the common areas is different from case to case.Generally,the forecasts benefit more from the reduction of the initial errors in the sensitive areas identified using higher resolutions than those using lower resolutions.However,the largest improvement of the forecast can be obtained at the resolution that is not the highest for some cases.In addition,the sensitive areas identified at lower resolutions are also helpful for improving the forecast with a finer resolution,but the sensitive areas identified at the same resolution as the forecast would be the most beneficial.     

A Fast Algorithm for Solving CNOP and Associated Target Observation Tests

Conditional Nonlinear Optimal Perturbation （CNOP） is a new method proposed by Mu et al. in 2003, which generalizes the linear singular vector （LSV） to include nonlinearity. It has become a powerful tool for studying predictability and sensitivity among other issues in nonlinear systems. This is because the CNOP is able to represent, while the LSV is unable to deal with, the fastest developing perturbation in a nonlinear system. The wide application of this new method, however, has been limited due to its large computational cost related to the use of an adjoint technique. In order to greatly reduce the computational cost, we hereby propose a fast algorithm for solving the CNOP based on the empirical orthogonal function （EOF）. The algorithm is tested in target observation experiments of Typhoon Matsa using the Global/Regional Assimilation and PrEdiction System （GRAPES）, an operational regional forecast model of China. The effectivity and feasibility of the algorithm to determine the sensitivity （target） area is evaluated through two observing system simulation experiments （OSSEs）. The results, as expected, show that the energy of the CNOP solved by the new algorithm develops quickly and nonlinearly. The sensitivity area is effectively identified with the CNOP from the new algorithm, using 24 h as the prediction time window. The 24-h accumulated rainfall prediction errors （ARPEs） in the verification region are reduced significantly compared with the ＂true state,＂ when the initial conditions （ICs） in the sensitivity area are replaced with the ＂observations.＂ The decrease of the ARPEs can be achieved for even longer prediction times （e.g., 72 h）. Further analyses reveal that the decrease of the 24-h ARPEs in the verification region is attributable to improved simulations of the typhoon＇s initial warm-core, upper level relative vorticity, water vapor conditions, etc., as a result of the updated ICs in the sensitivity area.     

STUDY OF THE MODIFICATION OF MULTI-MODEL ENSEMBLE SCHEMES FOR TROPICAL CYCLONE FORECASTS

This study investigates multi-model ensemble forecasts of track and intensity of tropical cyclones over the western Pacific, based on forecast outputs from the China Meteorological Administration, European Centre for Medium-Range Weather Forecasts, Japan Meteorological Agency and National Centers for Environmental Prediction in the THORPEX Interactive Grand Global Ensemble (TIGGE) datasets. The multi-model ensemble schemes, namely the bias-removed ensemble mean (BREM) and superensemble (SUP), are compared with the ensemble mean (EMN) and single-model forecasts. Moreover, a new model bias estimation scheme is investigated and applied to the BREM and SUP schemes. The results showed that, compared with single-model forecasts and EMN, the multi-model ensembles of the BREM and SUP schemes can have smaller errors in most cases. However, there were also circumstances where BREM was less skillful than EMN, indicating that using a time-averaged error as model bias is not optimal. A new model bias estimation scheme of the biweight mean is introduced. Through minimizing the negative influence of singular errors, this scheme can obtain a more accurate model bias estimation and improve the BREM forecast skill. The application of the biweight mean in the bias calculation of SUP also resulted in improved skill. The results indicate that the modification of multi-model ensemble schemes through this bias estimation method is feasible.     

Observation System Experiments for Typhoon Nida (2004) Using the CNOP Method and DOTSTAR Data

This study investigated the influence of dropwindsonde observations on typhoon forecasts. The study also evaluated the feasibility of the conditional nonlinear optimal perturbation (CNOP) method as a basis for sensitivity analysis of such forecasts. This sensitivity analysis could furnish guidance in the selection of targeted observations. The study was performed by conducting observation system experiments (OSEs). This research used the fifth-generation Mesoscale Model (MM5), the Weather Research and Forecasting (WRF) model, and dropsonde observations of Typhoon Nida at 1200 UTC 17 May 2004. The dropsondes were collected under the operational Dropsonde Observations for Typhoon Surveillance near the Taiwan Region (DOTSTAR) program. In this research, five kinds of experiments were designed and conducted:(1) no observations were assimilated; (2) all observations were assimilated;(3) observations in the sensitive area revealed by the CNOP method were assimilated;(4) the same as in (3), but for the region revealed by the first singular vector (FSV) method;and (5) observations within a randomly selected area were assimilated. The OSEs showed that (1) the DOTSTAR data had a positive impact on the forecast of Nida’s track;(2) dropsondes in the sensitive areas identified by the MM5 CNOP and FSV remained effective for improving the track forecast for Nida on the WRF platform;and (3) the greatest improvement in the track forecast resulted from the CNOP-based (third) simulation, which indicated that the CNOP method would be useful in decision making about dropsonde deployments.     

Forecasting Quasi-stationary Front Rainstorm in Southeast China Using Synthetically Multilevel Analog Forecast Technology

The authors use numerical model integral products in a third level forecast of synthetically multi-level analog forecast technology.This is one of the strongest points of this study,which also includes the re-ducing mean vacant-forecast rate method,which pos-sesses many advantages with regard to filtering the analog term.Moreover,the similitude degree between samples is assessed using a combination of meteorological elements,which works better than that described using a single element in earlier analog forecast studies.Based on these techniques,the authors apply the model output,air sounding,surface observation and weather map data from 1990 to 2002 to perform an analog experiment of the quasi-stationary front rainstorm.The most important re-sults are as follows:(1) The forecast successful index is 0.36,and was improved after the forecast model was re-vised.(2) The forecast precise rate (0.59) and the lost-forecast rate (0.33) are also better than those of other methods.(3) Based on the model output data,the syn-thetically multilevel analog forecast technology can pro-duce more accurate forecasts of a quasi-stationary front rainstorm.(4) Optimal analog elements reveal that trig-gering mechanisms are located in the lower troposphere while upper level systems are more important in main-taining the phase of the rainstorm.These variables should be first taken into account in operational forecasts of the quasi-stationary front rainstorm.(5) In addition,experi-ments reveal that the position of the key zone is mainly decided by the position of the system causing the heavy rainfall.     

INFLUENCE OF DIFFERENT-SCALE ERRORS INTERACTIONS ON ANALYSIS AND FORECAST OF REGIONAL NWP MODEL

In the previous study, the influences of introducing larger- and smaller-scale errors on the background error covariances estimated at the given scales were investigated, respectively. This study used the covariances obtained in the previous study in the data assimilation and model forecast system based on three-dimensional variational method and the Weather Research and Forecasting model. In this study, analyses and forecasts from this system with different covariances for a period of one month were compared, and the causes for differing results were presented. The variations of analysis increments with different-scale errors are consistent with those of variances and correlations of background errors that were reported in the previous paper. In particular, the introduction of smaller-scale errors leads to greater amplitudes in analysis increments for medium-scale wind at the heights of both high- and low-level jets. Temperature and humidity analysis increments are greater at the corresponding scales at the middle- and upper-levels. These analysis increments could improve the intensity of the jet-convection system that includes jets at different levels and the coupling between them that is associated with latent heat release. These changes in analyses will contribute to more accurate wind and temperature forecasts in the corresponding areas. When smaller-scale errors are included, humidity analysis increments are significantly enhanced at large scales and lower levels, to moisten southern analyses. Thus, dry bias can be corrected, which will improve humidity forecasts. Moreover, the inclusion of larger- (smaller-) scale errors will be beneficial for the accuracy of forecasts of heavy (light) precipitation at large (small) scales because of the amplification (diminution) of the intensity and area in precipitation forecasts.     

The Time and Regime Dependencies of Sensitive Areas for Tropical Cyclone Prediction Using the CNOP Method

This study examines the time and regime dependencies of sensitive areas identified by the conditional nonlinear optimal perturbation(CNOP) method for forecasts of two typhoons.Typhoon Meari(2004) was weakly nonlinear and is herein referred to as the linear case,while Typhoon Matsa(2005) was strongly nonlinear and is herein referred to as the nonlinear case.In the linear case,the sensitive areas identified for special forecast times when the initial time was fixed resembled those identified for other forecast times.Targeted observations deployed to improve a special time forecast would thus also benefit forecasts at other times.In the nonlinear case,the similarities among the sensitive areas identified for different forecast times were more limited.The deployment of targeted observations in the nonlinear case would therefore need to be adapted to achieve large improvements for different targeted forecasts.For both cases,the closer the forecast time,the higher the similarities of the sensitive areas.When the forecast time was fixed,the sensitive areas in the linear case diverged continuously from the verification area as the forecast period lengthened,while those in the nonlinear case were always located around the initial cyclones.The deployment of targeted observations to improve a special forecast depends strongly on the time of deployment.An examination of the efficiency gained by reducing initial errors within the identified sensitive areas confirmed these results.In general,the greatest improvement in a special time forecast was obtained by identifying the sensitive areas for the corresponding forecast time period.     

THE IMPACTS OF INTERACTION OF A TYPHOON WITH THE MIDLATITUDE TROUGH ON ITS TRACK AFTER THE RECURVATURE

Three typhoon cases are selected to conduct a series of simulations that are initialized from sequential analyses. The results show that the forecast error in crucial area where a tropical cyclone (TC) interactes with the upstream trough is highly correlated to the track forecast error after the TC recurvature. Furthermore, sensitivity experiments confirm that the developments of the midlatitude downstream circulations and then the TC track after its recurvature are highly sensitive to the TC intensity and its location relative to the upstream trough, which can give an example or one way of sensitivity of the TC track to the TC-trough interaction. If the TC interacts with the upstream trough more strongly (e.g., the TC being intensified or getting closer to the upstream trough), the downstream circulations will be more meridional, thus the TC track will be more northerly and westerly; otherwise, the downstream circulations will be more zonal, and the TC track will be more southerly and easterly.     

Impact of the Assimilation Frequency of Radar Data with the ARPS 3DVar and Cloud Analysis System on Forecasts of a Squall Line in Southern China

Assimilation configurations have significant impacts on analysis results and subsequent forecasts. A squall line system that occurred on 23 April 2007 over southern China was used to investigate the impacts of the data assimilation frequency of radar data on analyses and forecasts. A three-dimensional variational system was used to assimilate radial velocity data,and a cloud analysis system was used for reflectivity assimilation with a 2-h assimilation window covering the initial stage of the squall line. Two operators of radar reflectivity for cloud analyses corresponding to single-and double-moment schemes were used. In this study, we examined the sensitivity of assimilation frequency using 10-, 20-, 30-, and 60-min assimilation intervals. The results showed that analysis fields were not consistent with model dynamics and microphysics in general;thus, model states, including dynamic and microphysical variables, required approximately 20 min to reach a new balance after data assimilation in all experiments. Moreover, a 20-min data assimilation interval generally produced better forecasts for both single-and double-moment schemes in terms of equitable threat and bias scores. We conclude that a higher data assimilation frequency can produce a more intense cold pool and rear inflow jets but does not necessarily lead to a better forecast.     

Ensemble Forecast： A New Approach to Uncertainty and Predictability

Ensemble techniques have been used to generate daily numerical weather forecasts since the 1990s in numerical centers around the world due to the increase in computation ability. One of the main purposes of numerical ensemble forecasts is to try to assimilate the initial uncertainty （initial error） and the forecast uncertainty （forecast error） by applying either the initial perturbation method or the multi-model/multiphysics method. In fact, the mean of an ensemble forecast offers a better forecast than a deterministic （or control） forecast after a short lead time （3-5 days） for global modelling applications. There is about a 1-2-day improvement in the forecast skill when using an ensemble mean instead of a single forecast for longer lead-time. The skillful forecast （65% and above of an anomaly correlation） could be extended to 8 days （or longer） by present-day ensemble forecast systems. Furthermore, ensemble forecasts can deliver a probabilistic forecast to the users, which is based on the probability density function （PDF） instead of a single-value forecast from a traditional deterministic system. It has long been recognized that the ensemble forecast not only improves our weather forecast predictability but also offers a remarkable forecast for the future uncertainty, such as the relative measure of predictability （RMOP） and probabilistic quantitative precipitation forecast （PQPF）. Not surprisingly, the success of the ensemble forecast and its wide application greatly increase the confidence of model developers and research communities.     

Ensemble Based Diagnosis of the Track Errors of Super Typhoon Mangkhut(2018)

Super Typhoon Mangkhut(2018)was the most high-impact typhoon in 2018 because of its long lifespan and significant intensity.The operational track forecasts in the short-to-medium range(deterministic and probabilistic forecast)showed a great uncertainty and the forecast landing points varied with different lead times.This study applied ensembles of high-resolution ECMWF forecasts to investigate the major factors and mechanisms of the bias production of the Mangkhut forecast track.The ensembles with the largest track bias were analyzed to examine the possible bias associated factors.The results suggested that environmental steering flows were the main cause for the erroneous southward track error with a variance contribution of 72%.The tropical cyclone(TC)size difference and the interaction of the TC with the subtropical high(SH)were other two key factors that contributed to the track error.Particularly,larger TCs may have led to a stronger erosion of the southern part of the SH,and thus induced significant changes in the large-scale environment and eventually resulted in an additional northward movement of TC.     

Analyses and forecasts of a tornadic supercell outbreak using a 3DVAR system ensemble

As part of NOAA’s "Warn-On-Forecast" initiative, a convective-scale data assimilation and prediction system was developed using the WRF-ARW model and ARPS 3DVAR data assimilation technique. The system was then evaluated using retrospective short-range ensemble analyses and probabilistic forecasts of the tornadic supercell outbreak event that occurred on 24 May 2011 in Oklahoma, USA. A 36-member multi-physics ensemble system provided the initial and boundary conditions for a 3-km convective-scale ensemble system. Radial velocity and reflectivity observations from four WSR-88 Ds were assimilated into the ensemble using the ARPS 3DVAR technique. Five data assimilation and forecast experiments were conducted to evaluate the sensitivity of the system to data assimilation frequencies, in-cloud temperature adjustment schemes, and fixed- and mixed-microphysics ensembles. The results indicated that the experiment with 5-min assimilation frequency quickly built up the storm and produced a more accurate analysis compared with the 10-min assimilation frequency experiment. The predicted vertical vorticity from the moist-adiabatic in-cloud temperature adjustment scheme was larger in magnitude than that from the latent heat scheme. Cycled data assimilation yielded good forecasts, where the ensemble probability of high vertical vorticity matched reasonably well with the observed tornado damage path. Overall, the results of the study suggest that the 3DVAR analysis and forecast system can provide reasonable forecasts of tornadic supercell storms.