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.     

On the variable‐lag and variable‐velocity cell‐to‐cell routing schemes for climate models

Abstract

The cell‐to‐cell channel routing schemes used in General Circulation Models (GCMs) and Regional Climate Models (RCMs) are revisited. A simpler parsimonious routing scheme based on Askew's formula (1970) for computing time‐evolving channel lags is implemented and tested against observations and compared with the variable‐velocity scheme of Arora and Boer (1999). The variable‐lag routing scheme agrees very well with the variable‐velocity scheme. The variable‐lag scheme has the advantage of using fewer parameters, which is a major advantage at fine resolution over a large domain, where the uncertainty associated with parameters can be quite large.

The spatial resolutions of RCMs are much finer than those of GCMs and hence there is a need for channel routing at fine spatial resolutions. The task of extending the cell‐to‐cell routing schemes developed for large‐scale routing, as in GCMs, to finer spatial scales, as in RCMs, is addressed. The sensitivity of the variable‐lag scheme to the routing time interval is studied. The choice of the routing time interval is very critical and varies with the spatial resolution as in any hydrological model. A simple method for determining the appropriate range of routing intervals at different spatial resolutions for the variable‐lag scheme is presented.     

Some experiments with multivariate objective analysis scheme of heights and winds using optimum interpolation

A two-dimensional, multitvariate objective analysis scheme for simultaneous analysis of geopotential height and wind fields has been developed over Indian and adjoining region for use in numerical weather prediction. The height-height correlations calculated using daily data of four July months (1976-1979), are used to derive the other autocorrelations and cross-correlations assuming geostropic relationship. A Gaussian function is used to model the autocorrelation function. Since the scheme is multivariate the regression coefficients (weights) are matrix.Near the equator, the geostrophic approximation relating mass and wind is decoupled in a way similar to Bergman (1979). The objective analyses were made over Indian and adjoining region for 850, 700, 500, 300 and 200 hPa levels for the period from 4 July to 8 July 1979, 12 GMT. The analyses obtained using multivariate optimum in-terpolation scheme depict the synoptic situations satisfactorily. The analyses were also compared with the FGGE ana-lyses (from ECMWF) and also with the station observations by computing the root mean square (RMS) errors and the RMS errors are comparable with those obtained in other similar studies.     

Spatial correlation of marine wind‐speed observations

Abstract

The spatial characteristics of the wind speeds from ships, drilling platforms, and satellites (SASS and SMMR) were investigated through autocorrelation analysis. Values of the spatial correlation coefficient in minimum separation classes revealed that SASS winds contained the least noise, followed by drilling‐platform and SMMR winds, measured ship winds and estimated ship winds. The variances explained by wind‐speed observations within a 100‐km radius of each other were found to be 86, 72, 62, 48 and 41%, respectively. Ship wind‐speed estimates made during hours of darkness showed significantly higher noise than daytime reports.     

An explicit approach to microphysics in MC2

Abstract

An explicit microphysics scheme, including warm rain and ice‐phase processes, has been incorporated into the Canadian Mesoscale Compressible Community Model (MC2). Three equations for cloud water mixing ratio, rain water mixing ratio, and ice or snow mixing ratio are solved explicitly. The hydrometeor mass loading term is also included. For the single ice category, a generalized gamma size distribution is assumed and a new formulation by Meyers et al. (1992) is used to predict the ice concentration.

A numerical simulation of the ERICA IOP2 cyclone shows that the scheme is efficient. Despite running at a relatively large time step, the scheme succeeded in capturing the deepening rates and the mesoscale features of the cyclone. The distribution of cloud and precipitation is in good agreement with satellite observations. Comparison with other implicit schemes available in MC2 show comparable performance in terms of deepening rate and precipitation rate. However, the explicit scheme generates mesoscale features in better agreement with observations.     

Oceanic tides over the Newfoundland and Scotian Shelves from TOPEX/POSEIDON altimetry

Abstract

A modified response analysis in the form of an orthotide parametrization is used to derive major semi‐diurnal and diurnal tidal constituents over the Newfoundland and Scotian Shelves from TOPEX/POSEIDON altimeter data. The orthotide formulation simultaneously solves for eight major semi‐diurnal and diurnal constituents, and has an accuracy of better than ～1.5 cm for each constituent. Tidal elevations are derived from the altimeter data on the ascending and descending satellite ground tracks, and interpolated using the method of statistical interpolation. The semi‐diurnal constituents (M₂, S₂ and N₂) compare favourably with available in‐situ observations and a numerical model. The diurnals (K₁ and O₁) are not as accurate as the semi‐diurnals, especially in the nearshore environment. The paper demonstrates the ability of TOPEX/POSEIDON altimetry to provide accurate tidal data over a continental shelf.     

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.     

Spatial analysis of monthly precipitation in Turkey

Summary  The principal objectives of this paper are to develop and validate an optimum interpolation method for the spatial analysis of monthly precipitation in Turkey. A two-dimensional optimum interpolation objective analysis scheme has been developed for the spatial analysis of precipitation. The model is developed for generating statistically optimum interpolation based on the irregular distribution of meteorological stations. One question that affects the optimum interpolation method and, indeed, all such techniques, is how many observations should be allowed to influence a given grid point? The method developed in this paper addresses this question. For the implementation of the method, 52 stations are considered for Turkey, with 30 years of monthly data at each point. It is observed that each monthly average spatial correlation function shows a monotonically decreasing pattern based on 15 km interval averages. The method provides high estimation accuracy in dense station locations such as in northwestern Turkey. Precipitation contour maps obtained by the optimum interpolation method indicate two spatial trends over Turkey which have not been identified in any previous study. Received June 24, 1999/Revised April 26, 2000     

在四维变分同化中运用集合协方差的试验

利用浅水方程模式和模式模拟资料进行数值试验比较3种不同的背景误差协方差矩阵处理方法对四维变分(4DVAR)资料同化的影响.3种背景误差协方差矩阵分别是:(1)对单一变量将背景误差协方差矩阵简化为对角矩阵;(2)将背景误差协方差矩阵的作用简化为高斯过滤;(3)由预报集合生成背景误差协方差矩阵并利用奇异值分解技术解决矩阵的求逆.通过一系列数值试验,比较不同观测密度、不同观测误差下3种背景误差协方差处理方法对4DVAR同化效果的影响.结果表明,背景误差协方差的结构对4DVAR有重大影响.当观测资料的空间密度不够高时,采用对角矩阵得不到满意的结果.高斯过滤方案可以明显改善同化结果,但是对背景误差特征长度比较敏感.第3种方法采用的背景误差协方差矩阵是流型依赖的,而且并不以显式的方式出现在目标函数中.避免了对它求逆的复杂运算.由于做了降维处理,在观测点的密度较低和观测误差较大时可望取得较好的同化结果,同化效果较为稳定.     

Airborne measurements of the ocean's Ku‐band radar cross‐section at low incidence angles

Abstract

Ocean backscatter data obtained with a K_u‐band airborne radar are presented along with coincident altimeter and directional wave spectral estimates. These data were collected using one sensor, NASA's radar ocean wave spectrometer (ROWS). The measurements are compared with an electromagnetic scattering model for perfectly conducting Gaussian random surfaces. The normalized radar cross‐section (NRCS) data cover those incidence angles (0–20°) where both quasi‐specular and Bragg scattering mechanisms are expected. Under certain conditions, identification and separation of these two mechanisms is possible. The scanning radar allows observations of the azimuthal variations in NRCS that are at times indicative of short‐scale wave generation in the wind direction.     

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.     

Potential and limitations of using satellite data to evaluate the spatial detail in climatological air temperature maps

Abstract

Detailed patterns of spatial variability in surface temperature can be observed with the use of thermal infrared data from satellites. A method is developed to use clear‐sky thermal infrared satellite data to evaluate traditional monthly average maximum air temperature maps interpolated from observations at surface stations using a statistical thin plate smoothing spline method. Results of comparisons over Alberta, Manitoba and Saskatchewan from June to October, for the years 2001 to 2005, are presented. The satellite data allow identification of some limitations in the interpolation technique at high altitudes in mountain ranges and in data‐sparse areas due to low station density. In the data‐sparse areas, the highest discrepancies could be linked to the unrepresentativeness of the stations because of different land cover or the presence of water bodies. Conversely, the interpolated air temperature maps allow the identification of problems with using thermal infrared data to estimate near‐surface air temperatures in areas of significant moisture deficit and at the locations of water bodies.     

The objective analysis of daily rainfall by distance weighting schemes on a Mesoscale grid

Abstract

The authors studied the error of spatial interpolation in the context of a climatic data gridding project (Cli‐Grid). Four objective analysis (QA) techniques were implemented: the empirical techniques of Barnes, Cressman and Shepard, and a Gandin‐based statistical technique. These were applied to the interpolation of irregularly distributed daily rainfall data. Spatial resolution of the interpolated arrays was 0.05 degree of latitude by 0.05 degree of longitude.

In this experiment, radar rainfall patterns served as reference data for evaluations of O A techniques. Each reference pattern was sampled at the irregularly spaced locations of a climatic rain‐gauge network. The sampled data were then input to one of the four OA techniques. The resulting analysis was subtracted from the corresponding reference pattern. Absolute values of the differences were recorded. This sampling‐to‐difference cycle was repeated with 63 reference patterns. Every map of absolute differences was summed. The resulting map of total errors was normalized by the sum of the reference patterns. Average bias, average RMS error and averages of the ratios of the standard deviations were also computed.

All four OA techniques were evaluated separately. The authors recognized that totally unbiased intercomparisons were not possible because of the range in execution parameters for each OA technique. Reasonable efforts were made to minimize subjectivity in the setting of parameters. For application to the specific project grid, the statistical optimal interpolation technique displayed the lowest RMS errors. This technique and Shepard OA, were found more suitable than the other two techniques studied. Statistical and Barnes OA displayed zero average bias and would be useful for areal average computations. The Cressman OA was judged least suitable for interpolation of daily rainfall.

An application of the two‐dimensional error maps to network analysis was demonstrated by plotting the relationship between interpolation errors and distance (D) from the closest station. Error increased as D^1/2. It was also verified that error and station density were inversely related.     

新一代天气雷达网资料的三维格点化及拼图方法研究

文中研究了几种把球坐标系下的雷达网反射率体扫资料插值到统一的笛卡尔坐标系下的经纬度网格上以及用多个雷达的反射率网格资料进行三维拼图的方法,并对多个雷达同步观测的反射率因子的空间一致性、系统误差以及雷达等距离线上回波的水平和垂直结构进行了分析。结果发现:在雷达资料格点化过程中,径向和方位上的最近邻居法和垂直方向的线性内插法的结合(NVI方法)是一种有效的雷达资料分析方法,它既能得到空间比较连续的反射率分析场,同时也较好地保留了体扫资料中原有的反射率结构特征;广州雷达和梅州雷达同步观测的空间一致性比较好;在多个雷达资料合成拼图的过程中,距离指数权重平均法能提供空间连续的三维反射率拼图数据,拼图也减轻了由雷达波束几何学引起的各种问题。     

基于西南地区台站降雨资料空间插值方法的比较

以西南地区1996～2000年93个气象台站观测的月均降雨量为基础,对各月降雨量进行空间自相关性,变异特征等空间分析后,采用反距离加权法(IDW)和以不同变异函数模型(指数模型、球面模型、高斯模型)为基础的普通克里金(O-Kriging)两种方法进行空间插值,通过交叉验证结果对两种方法进行分析比对。结果表明:(1)西南地区月均降雨量存在明显的空间集聚现象,并具有显著的空间自相关性和变异特征,可对该研究区域降雨量进行空间插值研究。(2)在O-Kriging插值时,变异函数选用指数模型的效果最好,球面模型次之,高斯模型最差。(3)两种方法对月均降雨量及其极大值和极小值插值时,O-Kriging的插值误差均小于IDW,插值误差整体上与降雨量呈正相关关系。在剔除各月降雨量极大值较为集中的两个站点后进行插值,插值结果的误差均明显降低。(4)对研究区域整体来说,O-Kriging的插值效果优于IDW,但就单个站点来看,结果并非如此。在降雨量的空间插值中,由于研究区域和时间尺度的不同,并不存在绝对的最优方法,应根据实际应用效果选择最适方法。     

Improvement of radar quantitative precipitation estimation based on real-time adjustments to <Emphasis Type="Italic">Z-R</Emphasis> relationships and inverse distance weighting correction schemes

The errors in radar quantitative precipitation estimations consist not only of systematic biases caused by random noises but also spatially nonuniform biases in radar rainfall at individual rain-gauge stations.In this study,a real-time adjustment to the radar reflectivity-rainfall rates(Z-R) relationship scheme and the gauge-corrected,radar-based,estimation scheme with inverse distance weighting interpolation was developed.Based on the characteristics of the two schemes,the two-step correction technique of radar quantitative precipitation estimation is proposed.To minimize the errors between radar quantitative precipitation estimations and rain gauge observations,a real-time adjustment to the Z-R relationship scheme is used to remove systematic bias on the time-domain.The gauge-corrected,radar-based,estimation scheme is then used to eliminate non-uniform errors in space.Based on radar data and rain gauge observations near the Huaihe River,the two-step correction technique was evaluated using two heavy-precipitation events.The results show that the proposed scheme improved not only in the underestimation of rainfall but also reduced the root-mean-square error and the mean relative error of radar-rain gauge pairs.     

A complementary depiction of the interannual variation of atmospheric circulation associated with ENSO events: Research note

Abstract

A simple diagnostic scheme, which combines a low‐pass temporal filter (with an 18‐month cutoff time) with a regular empirical orthogonal function (EOF) analysis, is used to delineate the synchronous evolution of El Nino‐Southern Oscillation‐related (ENSO‐related) modes in various variables of the ocean‐atmosphere system. Based on the causal relation chain of diabatic heating, divergent circulation and rotational flow, the diagnostic scheme extracts ENSO modes from the following data sources: the Pacific sea surface temperature (SST), the past 14‐years (1979–1992) of data generated by the Global Data Assimilation System of the National Meteorological Center, and a 10‐year (1979–1988) general circulation model climate simulation made at the Goddard Laboratory for Atmospheres. The analysis reveals the following: (a) the eigencoefficient time series of the first eigenmodes of selected filtered variables, which explain about 40–50% of their total variance, synchronize with the filtered SST averaged over Area NINO‐3; (b) the spatial structures of the first eigenmodes resemble the ensemble departures associated with ENSO events of these variables from their long term means; and (c) the results show that the proposed scheme can be easily applied to isolate and illustrate the time evolution of ENSO modes which exist in the long term observational database as well as in climate simulations.     

A new adiabatic kernel for the MC2 model

Abstract

Traditional semi‐implicit formulations of nonhydrostatic compressible models may not be stable in the presence of steep terrain when pressure gradient terms are split and lagged in time. If all pressure gradient terms and the divergence are treated implicitly, the resulting wave equation for the pressure contains off‐diagonal cross‐derivative terms leading to a highly nonsymmetric linear system of equations. In this paper we present a more implicit formulation of the Mesoscale Compressible Community (MC2) model employing a Generalized Minimal Residual (GMRES) Krylov iterative solver and a more efficient semi‐Lagrangian advection scheme. Open boundaries now permit exact upwind interpolation and the ability to reproduce simulations to machine precision is illustrated for one‐way nesting at equivalent resolution. Numerical simulations of hydrostatic and nonhydrostatic mountain waves demonstrate the stability and accuracy of the new adiabatic kernel. The computational efficiency of the model is reported for 1D Jacobi and 3D Alternating Direction Implicit (ADI) line relaxation preconditioned implemented with a parallel data transposition strategy.     

Development of the new CCC/GCM longwave radiation model for extension into the middle atmosphere

Abstract

A new infrared (IR) radiation scheme for extending the CCC/GCM (Canadian Climate Center General Circulation Model) into the middle atmosphere is proposed. It combines the previous CCC/GCM radiation scheme including the effects of H₂O, CO₂, O₃, CH₄, N₂O, CFC11 and CFC12, clouds and aerosols, with a new computationally efficient matrix parameterization for the cooling rate in the middle atmosphere for both LTE (local thermodynamic equilibrium) and non‐LTE layers. The matrix parameterization includes the effects of both the 15 μm CO₂ and the 9.6 μm O₃ bands and provides a proper lower boundary condition for the non‐LTE recurrence formula. The new scheme shows satisfactory agreement with line‐by‐line calculations. The absolute error does not exceed 0.8 ? day^‐1 for vastly different atmospheric conditions. Introducing the new radiation module into the CCC/GCM results in deviations of the simulated temperature from the CIRA‐1986 model of not more than 10 ? throughout most of the altitude‐latitude domain.