Some effects of vertical resolution on modelling forced planetary waves with a time‐dependent model

Abstract

Previous studies by Nakamura (1976) and Kirkwood and Derome (1977) have shown that the use of a relatively low vertical resolution in a numerical model of the atmosphere can lead to a poor representation of the forced stationary planetary waves. In the present study the consequences of this result on short‐term numerical forecasts are investigated. This is done by performing forecast experiments using a low resolution linear β‐plane model that is initialized with data extracted from the steady forced solution of the high resolution (reference) version of the model. The deviation of the low resolution forecast from the initial state, which can be interpreted as the forecast error due to insufficient vertical resolution, is examined as a function of time.

It is shown that the short‐range forecast error is dominated by a westward propagating external mode and that in time some of the eastward moving internal modes gain in importance.     

Predictability as a function of scale

Abstract

The forecast skill of the Canadian Meteorological Centre (CMC) operational global forecast/analysis system is assessed as a function of scale for the traditional forecast variable of 500‐hPa geopotential height using results from January 2002. These results are compared to an earlier analysis of forecasts from the European Centre for Medium‐range Weather Forecasts (ECMWF) which indicated unexpectedly enhanced skill at high wavenumbers (small scales) especially in the mean forecast component identified with local topographical structures. The global rms error for the CMC forecasts is dominated by the transient component compared to the mean and continues to grow with time during the six days of the forecast. Geographically the transient error grows most rapidly in middle and high latitude regions of large natural variability. The relative error behaves differently and grows most rapidly initially in tropical regions and is inferred to exhibit both climatological and flow‐dependent error growth.

In terms of spherical harmonic two‐dimensional wavenumber n, low wavenumber (large scale) 500‐hPa geopotential height structures are dominated by the mean component but beyond wavenumber 10 to 15 the transient component dominates and exhibits an approximately n–5 spectral slope consistent with a quasi‐two dimensional turbulence enstrophy cascading subrange. Error grows slowly for the large scales dominated by mean climatological structures but these are not of interest for daily weather forecasting. Transient error grows rapidly at small scales and penetrates toward larger scales with time in keeping with the expected predictability behaviour. An expression of the form f(n, τ) = 1 – e–^τ/^τp(n) is fitted to the growth of relative error as a function of wavenumber and forecast range and gives a scale dependent predictability timescale for the transient component that varies as τ_p ? n^?3/2, although the generality of the relationship is not known.

The mean component at intermediate/high wavenumbers exhibits an apparent region of enhanced skill in the CMC system apparently connected to the topography. The result supports the possibility that some small‐scale mean flow structures, although containing only a minor amount of variance, are maintained in the face of errors in other scales. The results do not support the level of enhanced skill found in an earlier analysis of ECMWF results suggesting them to be an artefact of the analysis/forecast system in use at the time.     

Estimating the error in vertically interpolated forecast‐observation differences: U‐ and v‐wind components

Abstract

Data assimilation in numerical weather forecasting corrects current forecast values by subtracting a portion of interpolated forecast‐minus‐observation differences at the points of a three‐dimensional grid. Deviations used in updating a forecast data field are forecast errors obtained or derived from observations available at update time. When observations are missing at mandatory levels, construction of full vertical soundings by interpolation introduces extraneous errors. The present paper is concerned with determination of the error in vertical extrapolations of surface winds, and of aircraft and satellite cloud‐tracked winds. In addition it examines the effect on accuracy of using location‐specific statistics compared to averaged statistics as the basis for the interpolation weighting scheme and compares errors of one‐ and two‐variable interpolations.

Interpolation accuracy tests demonstrate the influence of the interpolation scheme on the quality of interpolated information used in forecast updating. The results show that the level of accuracy exceeds the benchmark provided by monthly mean forecast error values only with bivariate interpolation of wind components from off‐level data sources.     

Comparison of Canadian daily ice charts with surface observations off Newfoundland,winter 1992

Abstract

Forecast ice drift rates and thicknesses displayed on daily ice charts and forecast winds for the Canadian east coast are compared to on‐ice observations made during the second Canadian Atlantic Storm Program (CASP II) of March 1992. Observed and 24‐hour forecasts of daily ice drift rates were weakly correlated even though long‐term means closely matched observations. Daily drift rates have an RMS error of 13 cm s^‐1 relative to a 15 cm s^‐1 mean in addition to an RMS direction error of 50 degrees. Contributions towards daily drift uncertainties were: the estimation of winds, unmodelled physics of ocean and ice cover processes; and the inconsistency in the methods used by the ice forecaster. Correlation coefficients between forecast winds and on‐ice observed winds decreased from 0.8 at 0‐hour to 0.7 for the 30‐hour forecast. Similar results were found between ice drift rates from forecast winds. Histograms of ice thicknesses observed along narrow swaths using a helicopter‐towed electromagnetic sensor compared well with undeformed ice thicknesses representing large areas on ice charts, with differences mainly caused by difference in ice type representation and by co‐registering the two data sets.     

Cross‐equatorial error propagation: Research note

Abstract

Numerical simulation experiments published in 1974 by Daley have been repeated with a much higher resolution, spectral, shallow water model. With a forecast period extending toll d, it is shown that a global model in which only the largest scales are used at initial time in the Southern Hemisphere yields a more accurate forecast for the Northern Hemisphere than a hemispheric model does. Compared with a uniform high‐resolution, global model, the error in the Northern Hemisphere forecast is high in the ultra‐long waves but decreases rather rapidly while the resolution of the initial Southern Hemispheric data is increased.     

An evaluation of extrapolation techniques for the short‐term prediction of rain amounts

Abstract

Twenty‐seven radar cells from the Tropical Atlantic observed during GATE were followed and measurements of their fluxes and areas for initial time increments T₀ were fitted to various extrapolation schemes. The extrapolation procedure that gave the smallest error inforecasting the changes influx and area, was found to be the linear one and the optimum increment T₀ was about 30 min. However, even though these techniques have the advantage of establishing a trend in the behaviour of the flux and area with time, a comparison of the forecast errors from the linear extrapolation scheme with those from the “status quo” (persistence) assumption shows little if any improvement.

A technique including both cell motion and internal changes influx and area of the rain cells was developed to evaluate the accuracy of rain accumulation forecasts. It was found that the errors generated by the “status quo” assumption were of the order of 77% for a 2‐h forecast with little improvement by allowing for the extrapolation of area and flux.     

Atmospheric data assimilation on the equatorial beta plane

Abstract

Kalman filter theory shows great promise when applied to the assimilation of atmospheric observations. Previous work has concentrated on extratropical dynamics, and tropical aspects have not yet been seriously tackled. In this article, a Kalman filter is applied to the linearized shallow water equations on an equatorial beta plane. The system or model error is constructed from the slow eigenmodes of the model and is based on an expansion in parabolic cylinder functions. The resulting second‐moment statistics are discussed in some detail. The Kalman filter is applied to a special observation network that allows the diagonalization of the system. Following Daley and Ménard (1993), it is then possible to obtain the complete space and time solution for the second‐moment forecast and analysis error statistics. The slow (low‐frequency) and fast (high‐frequency) error statistics are examined separately for both the optimal and suboptimal cases.     

Anticipated changes in analysis accuracy with the removal of Ocean Weather Ship P

Abstract

Analysis error patterns have been established for the Pacific Weather Centre Experiment Area, and comparisons made between errors computed for meteorological observing arrays, including Ocean Weather Ship (OWS) P, and errors computed for several alternative arrays which excluded OWS P. These assessments of the impact of replacing the ocean weather ship with alternative observing equipment indicate that, above the 1000‐mb pressure surface, there will be a significant loss of accuracy in the forecast‐minus‐observation analyses regardless of proposed additional report systems. Near the surface, forecast error variances are estimated to decrease slightly with an increase of reports from buoys and ships of opportunity within the region.

The dependence of the assessments on the data selection procedure and on correlation representations for the region suggest that some loss may be compensated by more efficient use of available data. Refinements in the objective analysis scheme are seen to be especially important to analysis accuracy in regions lacking radiosonde coverage.     

Forecasts of hydrological parameters over the Mackenzie River Basin: Sensitivity to initial conditions,horizontal resolution and forecast range

Abstract

As part of the Global Energy and Water Cycle Experiment, Canadian global spectral forecast model predictions of surface water and energy fluxes over the Mackenzie River basin are examined. Two nine‐member ensemble forecasts of one month duration are produced with the operational model, for a spring and a summer case, at a horizontal resolution of about 100 km (T95). The sensitivity to initial conditions is measured by the degree to which the individual forecasts in the ensembles vary one from another. The evolution in time of this estimated error (ensemble standard deviation) is determined for the surface energy and water accumulations, averaged over the basin. For comparison the calculations are repeated for the Mississippi basin and over North America. The greatest sensitivity is found for the net accumulation of precipitation minus evaporation. The spring ensemble is redone at a coarser horizontal resolution (T47), and the results are similar. The forecast uncertainty (ensemble standard deviation) of the area‐averages over the basin appear to be unaffected by this change, although the ensemble mean values are sensitive to the change in resolution. The ensemble standard deviation makes a significant, abrupt increase toward the end of the second week into the forecasts. This investigation suggests a need for an improved model, if the forecasts’ useful range is to extend to one month. Available upgrades to the land‐surface, precipitation and evaporation schemes will be used in subsequent work, and the forecasts reported here will serve as a baseline for comparison.     

Assimilation of ERS‐2 scatterometer winds using the Canadian 3D‐var

Abstract

The goal of this study is to evaluate the impact of incorporating the marine surface winds retrieved from the ERS‐2 scatterometer in the Canadian three‐dimensional variational analysis system, (3D‐var). The aspects of the 3D‐var most relevant to the assimilation of surface ‐wind observations and a general method for resolving the directional ambiguity of the retrieved scatterometer ‐winds are first described. A comparison ‐with 6‐h forecasted winds is then made to demonstrate that these data are of high quality, but exhibit a speed bias that can be removed by increasing their amplitudes by about 5%. The analysis increment from a single scatterometer wind observation is calculated to illustrate the response of the 3D‐var to surface wind observations. As a consequence of the forecast error covariance model, the assimilation of surface wind observations produces meteorologically consistent increments for both the rotational and divergent wind components and the mass field. The results from a series of cross‐validation experiments using ship‐based wind data demonstrate a positive impact of assimilating scatterometer winds and the effectiveness of a simple method for estimating and removing the speed bias. The impact of assimilating scatterometer data within a short assimilation cycle is also evaluated. Overall, the results show that including scatterometer data in the analysis decreases the 6‐h forecast error of surface wind by 13%. Over the northern extra‐tropics the improvement is only 4% and for the southern extra‐tropics it is 16%. Results from a series of two‐day forecasts produced using the analyses from the assimilation cycles with and without retrieved scatterometer winds included are also presented. Using radiosonde observations at 850 hPa, 500 hPa, 250 hPa and 100 hPafor verification, the impact on the forecasts is nearly neutral in the northern hemisphere and the tropics. Conversely, a significant positive impact is found on both wind and mass fields in the southern hemisphere over the entire two‐day forecast.     

Sensitivity of retrieved atmospheric profiles from infrared radiances to physical and statistical parameters of the data assimilation system

Abstract

The direct assimilation of satellite radiances is now operational in a few forecast centres, providing global temperature (T) and moisture (Q) information. The critical parameters which influence the quality of the resulting analysis are mainly the selection of channels, the respective errors of the background field and radiance observations, and the quality of the radiative transfer model. These various aspects are studied from sensitivity experiments based on 1‐D variational assimilations using the ensemble of 19 infrared channels (HIRS) of the NOAA‐14 satellite.

It is shown that significant improvements in the retrievals would be obtained if the radiance observation error (measurement plus radiative transfer), currently estimated to be about equal to that of the background (in radiance units), were decreased. This could in principle be achieved by improving the forward radiative transfer model (RTM). Two RTMs suitable for radiance assimilation are compared in terms of analyzed increments, Jacobians, brightness temperature and equivalent background error. Important differences are noted for all of these interrelated measures. The existence of air‐mass dependent biases of fast radiative transfer models of the order of 1.5 K is confirmed in several channels from additional comparison with a line‐by‐line model. The importance of correctly specifying surface emissivity and the effective angle for downward calculations is demonstrated.

The paper also evaluates, in some detail, the impact of uncertainties on the background error covariance matrix. The uncertainty on the skin temperature (TJ error affects mostly the retrieval of that parameter; it has a modest impact on the T and Q profiles in the low troposphere. The uncertainty on the Q‐Q elements has more impact than that on the T‐T elements. Off‐diagonal elements of the background error covariance matrix are very important as they impose smoothness and level‐to‐level consistency, especially for Q retrievals. Finally, T_s‐T correlations, often ignored, could result in significant improvements in the retrieval of temperature at low levels. Research issues are discussed in the conclusion.     

Currents along the pacific coast of Canada

Abstract

A powerful storm passed over the coastal waters of eastern Canada on the 21 and 22 January 2000 causing significant damage to coastal infrastructure. The storm generated a large (>1.4 m) storm surge in the southern Gulf of St. Lawrence that unfortunately coincided with a high spring tide. This resulted in record high water levels in the southern Gulf of St. Lawrence (e.g., the highest level at Charlottetown since records began in 1911) and severe flooding around Prince Edward Island and along the eastern shore of New Brunswick.

During January 2000, a recently developed storm surge forecast system was running in pre‐operational mode at Dalhousie University. The core of the forecast system is a depth‐averaged, non‐linear, barotropic ocean model driven by forecast winds and air pressures produced by the Canadian Meteorological Centre's regional atmospheric forecast model. In this study we assess the forecast skill of the surge model for the 21 January storm by comparing its 24‐hour forecasts with two independent hourly dataseis: (i) sea levels recorded by 12 tide gauges located in eastern Canada and the north‐eastern United States, and (ii) depth‐mean currents recorded by an acoustic Doppler current profiler deployed on the outer Scotian Shelf. Overall, the forecasts of coastal sea level and depth‐mean currents are reasonable and have forecast errors below about 0.1 m and 0.1 m s^?1 respectively.     

Seasonal predictions based on two dynamical models

Abstract

Two dynamical models are used to perform a series of seasonal predictions. One model, referred to as GCM2, was designed as a general circulation model for climate studies, while the second one, SEF, was designed for numerical weather prediction. The seasonal predictions cover the 26‐year period 1969–1994. For each of the four seasons, ensembles of six forecasts are produced with each model, the six runs starting from initial conditions six hours apart. The sea surface temperature (SST) anomaly for the month prior to the start of the forecast is persisted through the three‐month prediction period, and added to a monthly‐varying climatological SST field.

The ensemble‐mean predictions for each of the models are verified independently, and the two ensembles are blended together in two different ways: as a simple average of the two models, denoted GCMSEF, and with weights statistically determined to minimize the mean‐square error (the Best Linear Unbiased Estimate (BLUE) method).

The GCMSEF winter and spring predictions show a Pacific/North American (PNA) response to a warm tropical SST anomaly. The temporal anomaly correlation between the zero‐lead GCMSEF mean‐seasonal predictions and observations of the 500‐hPa height field (Z₅₀₀) shows statistically significant forecast skill over parts of the PNA area for all seasons, but there is a notable seasonal variability in the distribution of the skill. The GCMSEF predictions are more skilful than those of either model in winter, and about as skilful as the better of the two models in the other seasons.

The zero‐lead surface air temperature GCMSEF forecasts over Canada are found to be skilful (a) over the west coast in all seasons except fall, (b) over most of Canada in summer, and (c) over Manitoba, Ontario and Quebec in the fall. In winter the skill of the BLUE forecasts is substantially better than that of the GCMSEF predictions, while for the other seasons the difference in skill is not statistically significant.

When the Z₅₀₀ forecasts are averaged over months two and three of the seasons (one‐month lead predictions), they show skill in winter over the north‐eastern Pacific, western Canada and eastern North America, a skill that comes from those years with strong SST anomalies of the El Niño/La Niña type. For the other seasons, predictions averaged over months two and three show little skill in Z₅₀₀ in the mid‐latitudes. In the tropics, predictive skill is found in Z₅₀₀ in all seasons when a strong SST anomaly of the El Niño/La Niña type is observed. In the absence of SST anomalies of this type, tropical forecast skill is still found over much of the tropics in months two and three of the northern hemisphere spring and summer, but not in winter and fall.     

热带气旋路径预报“真实”误差分析

目前,热带气旋预报性能的检验和分析多采用各中心每年台汛后整编的最佳路径数据集(即"年鉴")资料作为真值。然而,由于年鉴资料通常在次年才能发布,所以在业务上,常以实时定位、定强资料作为"真值"进行预报性能的检验,因而不同机构(口径)给出的预报性能往往不尽相同,造成了混乱。此外,实际业务预报中,因没有实时的年鉴资料,各预报方法的起报位置只能采用实时业务定位,显然不可避免地导致了误差。为分析使用实时定位和年鉴作为"真值"进行预报性能检验的差异、评估定位误差对预报性能造成的可能影响,本文首先考察最佳路径和实时/初始定位之间的差异(即定位误差)及其分布特征,然后分析采用实时/初始定位和最佳路径作为"真值"计算预报误差时的差异,最后基于最基础的气候可持续性(Climatology and Persistence,CLIPER)预报方法初步评估了预报性能对定位误差的敏感性。结果表明:以中国气象局整编的年鉴(CMA-STI的最佳路径数据集)资料为"真值",2013—2019年间国内外各主要预报机构及全球模式的定位误差平均为24.3 km;若以东京台风中心(RSMC-Tokyo)的年鉴资料为"真值",则定位误差平均为26.2 km。分析发现,定位误差与强度密切相关,热带风暴阶段的定位误差高达35.7~41.1 km,而超强台风阶段的定位误差仅为7.5~8.3 km;在96 h预报时效内,以最佳路径为"真值"计算得到的平均预报误差均略小于以实时/初始定位为"真值"的误差,但强度越强差异越小;定位误差对短时效内的预报性能有较显著的影响。     

A study of arctic sea ice and sea‐level pressure using POP and neural network methods

Abstract

We examine Arctic sea‐ice concentration (SIC) and sea‐level pressure (SLP) data using principal oscillation pattern (POP) and neural network methods. The POP method extracts oscillating patterns from multivariate time series, each pattern being characterized by an oscillation period and a decay time. Predictions can be made for patterns whose decay time is comparable with the period. For both the SIC and SLP, however, the decay times are much shorter than the oscillation periods, and therefore the forcast skill is poor. A neural network is a model of the learning behaviour of a living neural system. Presented with training data, a neural network can learn the linear or non‐linear rules embedded in the data. We trained neural networks with sea‐ice and sea‐level pressure data, and estimated the forecast skill using a cross‐validation technique. The neural networks did not exhibit forecast skill significantly better than that of persistence. We contrast the Arctic situation with previous studies in which POP and neural networks were successfully used to forecast El Niño at lead times up to 6 months. Reasons for the lack of skill in both methods are discussed.     

中央气象台台风强度综合预报误差分析

本文从总误差、逐年趋势、误差分布等方面对2001—2012年中央气象台（Central Meteorological Observatory, CMO）的台风（TC）强度综合预报水平进行分析,初步分析了强度迅速变化台风预报偏差大的原因。结果表明,强度预报水平没有明显改善,预报误差呈现逐年波动状态,强度稳定TC的预报误差最小,迅速加强TC的预报误差最大。24、96~120 h预报偏强的概率较大,而48~72 h预报偏弱的概率大。南海东北部等海域的预报误差较大,应在业务预报中特别予以关注。随着TC强度的逐渐增强,强度预报在120 h内预报偏强的可能性变大,而强度预报偏弱的可能性减小。根据误差分析结果,提出了一个强度概率预报方案,检验结果表明可在业务中参考使用。     

Estimates of the accuracy of vertically extrapolated forecast errors: Isobaric height and temperature

Abstract

Study of vertical extrapolations of the errors in forecast values of pressure‐level heights and temperatures indicates that they do not provide accurate off‐level information. Indeed it appears that, above 850 mb, forecast errors interpolated from observed 1000‐mb values are less accurate than level‐specific monthly mean differences. These results suggest that the de facto function of vertically interpolated single‐level forecast errors, in numerical forecast model updating, is the provision of vertical consistency rather than the injection of time‐specific information – except at the level of observation.     

Use of adjoint sensitivity analysis to diagnose the CMC global analysis performance: A case study

Abstract

The sensitivity of forecast errors to initial conditions obtained from the adjoint of a numerical weather prediction model provides new insights into the analysis errors responsible for poor short‐range to mediumrange forecasts. In recent years, we have developed a sensitivity analysis system based on the tangent linear and adjoint of the Global Environmental Multiscale model, in which an iterative procedure minimizing the shortrange forecast errors leads to the so‐called key analysis errors. These errors are dominated by a small number of atmospheric structures, those growing the most rapidly. The algorithm has proven very useful in understanding improvements to the three‐dimensional variational data assimilation (3D‐Var) system implemented in the Canadian Meteorological Centre operational suite in December 2001. The main difference between the old and the new 3D‐Var systems is the assimilation of temperature and surface pressure from surface and upper air stations as opposed to geopotential heights, additional Tiros Operational Vertical Sounder channels, new sources of observations such as temperature observations from aircraft, and wind and temperature from dropsondes.

In this paper, we examine key analysis errors of the old 3D‐Var analysis, which led to a very poor 3‐day forecast of a severe winter storm that struck eastern Canada on 10 February 2001. In this case, the same 3‐day forecast from the new 3D‐Var analysis is much better. We compare the difference between the two 3D‐Var analyses and the key analysis errors. We find that the main key analysis errors, in terms of potential vorticity, is located along the west shore of southern California and is characterized by a strong baroclinic structure that has its maximum amplitude in the upper part of the troposphere. The difference between the two analyses is three times more energetic than the key analysis errors and its structure is much more barotropic in the troposphere. However, we show that the large improvement in the new 3D‐Var analysis stems mainly from the reduction of the analysis errors that project onto the key analysis structures.     

RMAPS_Chem V1.0系统SO2排放清单优化效果评估

RMAPS_Chem V1.0系统是基于WRF_Chem模式建立的服务于华北区域雾霾等污染预报业务的模式系统,该研究着重针对系统中污染排放清单不确定性带来的SO₂浓度预报偏差较大问题,采用EnKF源反演和误差统计订正相结合的方法对排放清单进行了改进,形成了一套优化后的华北区域SO₂排放清单。通过输入初始清单和优化清单对2017年10月进行模拟,并与华北地区616个地面环境监测站观测值进行对比,结果表明:EnKF源反演结合误差统计订正的排放清单优化方法适用于SO₂排放清单的改进,有效降低了清单系统性偏差,针对主要区域及重点城市的检验显示模拟结果接近观测值;排放清单优化后模拟误差显著降低,如河北南部、山东西部至北京一带模式预报均方根误差与归一化平均绝对误差明显下降,区域内站点模拟误差呈正态分布特征,误差分布范围、最大概率出现范围均明显变窄,且最大误差概率明显上升。     

Ensemble forecasting of tropical cyclone motion: comparisonbetween regional bred modes and random perturbations

Summary Random perturbations (RPs) and a modified version for breeding of growing modes are used with a regional baroclinic mesoscale model to perform ensemble forecasting of tropical cyclone motion. Based on a sample of six cases, similar conclusions are found as in previous barotropic modeling studies. Even after introducing a larger spatial correlation into the RPs using a multi-quadric analysis scheme, the skill of this ensemble mean track prediction is almost always lower than that of the control forecast in the cases considered. The track prediction performance of the ensemble using regional bred modes (RBMs) as perturbations has a higher average skill. At nearly all forecast intervals except less than 24 h when the initial position error still dominates, the ensemble mean tracks in all six cases are improved over the control forecast. In the 6 h–24 h range, the success rate (ratio of the cases with a forecast improvement to the total number of cases) has a value of 10/24. In the 30 h–48 h range, the success rate increases to 20/24, but drops to 18/24 in the 54 h–72 h range. A relative skill score (RSS) is used to compare the skills of the two perturbation methodologies. It is found that the average RSSs of using RBMs are significantly higher than the corresponding ones of RPs at the 99% confidence level in all three 24-h periods. Note that the above conclusion is only based on ensemble mean forecasts. All of the possibilities from an ensemble-based probabilistic track distribution are not explored in this paper. The ensemble spreads in these RBM ensembles are large enough to include the verifying tracks in all the cases considered. It is also found that the ensemble spread is well correlated with the average error in an ensemble when using RBMs, but not with the ensemble mean forecast error in both methodologies. Received February 7, 2001/Revised April 18, 2001