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.     

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.     

Local error propagation in a global spectral shallow water model: Its implication for regional forecast modelling: Research note

Abstract

Inaccuracies in the data at the boundaries of a limited area may be a major source of forecast errors in that area. With a global spectral shallow water model we show that the major part of these local errors propagate from the boundaries at a speed equal to the local wind speed with a maximum speed of propagation along the jet stream. Thus, taking into account the forecast length and the accuracy of the data at the boundaries in limited‐area models, one needs to adjust the extent of the buffer region where errors propagate and contaminate the forecast.     

A study of planetary wave errors in a spectral numerical weather prediction model

Abstract

A series of fifteen 96‐h forecasts made with a spectral numerical weather prediction model is studied with reference to errors in the planetary wavelengths. The major contributor to the short (less than 48‐h) range forecast error is identified as an external mode. The medium range forecast error (96 h) is internal in character and reflects a deficiency in the simulation of the quasi‐stationary components.     

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.     

A comparison of shelf observation platforms for assimilation in an eddy-resolving ocean model

An assessment of the likely benefits of assimilating in situ temperature (T) and salinity (S) observations from repeat glider transects and surface velocity observations from high-frequency radar arrays into an eddy-resolving ocean model is presented. The deployment of new shelf observation platforms around Australia is being undertaken through the Australian Integrated Marine Observing System program. In this study, various options for an observing system along the coast of New South Wales, Australia, are assessed for their benefits to an ocean forecast and reanalysis system. The forecast system considered here uses ensemble optimal interpolation (EnOI) for data assimilation. Using error estimates from the EnOI scheme, estimates of the theoretical analysis errors are calculated for different observing systems that include a range of remotely sensed and in situ observations. The results demonstrate that if HF radar observations are assimilated along with the standard components of the global ocean observing system, the analysis errors are likely to reduce by as much as 80% for velocity and 60% for T, S and sea-level in the vicinity of the observations. Owing to the relatively short along-shore decorrelation length-scales for T and S near the shelf, the glider observations are likely to provide the forecast system with a more modest gain.     

A comparison of shelf observation platforms for assimilation in an eddy-resolving ocean model

An assessment of the likely benefits of assimilating in situ temperature (T) and salinity (S) observations from repeat glider transects and surface velocity observations from high-frequency radar arrays into an eddy-resolving ocean model is presented. The deployment of new shelf observation platforms around Australia is being undertaken through the Australian Integrated Marine Observing System program. In this study, various options for an observing system along the coast of New South Wales, Australia, are assessed for their benefits to an ocean forecast and reanalysis system. The forecast system considered here uses ensemble optimal interpolation (EnOI) for data assimilation. Using error estimates from the EnOI scheme, estimates of the theoretical analysis errors are calculated for different observing systems that include a range of remotely sensed and in situ observations. The results demonstrate that if HF radar observations are assimilated along with the standard components of the global ocean observing system, the analysis errors are likely to reduce by as much as 80% for velocity and 60% for T, S and sea-level in the vicinity of the observations. Owing to the relatively short along-shore decorrelation length-scales for T and S near the shelf, the glider observations are likely to provide the forecast system with a more modest gain.     

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.     

A decision‐analytic study of the joint value of seasonal precipitation and temperature forecasts in a choice‐of‐crop problem

Abstract

A static decision‐analytic method is used to investigate the economic value of bivariate ‐ precipitation and temperature ‐ seasonal forecasts of the form currently issued by the U.S. National Weather Service. This method is applied to a corn versus spring wheat choice‐of‐crop decision‐making problem by considering a transect of four counties across the northwestern margin of the North American corn belt. Numerical results indicate that seasonal forecasts of current quality can be of appreciable value (≥$1/ha) for some locations when the optimal action chosen on the basis of climatological information is only marginally preferred to another action. Increases in forecast value follow from hypothetical increases in the quality of both the precipitation and temperature components of the forecasts in the spring wheat region, whereas forecast value increases primarily as a function of the quality of the precipitation forecasts alone in the corn belt region. The results are very sensitive to absolute and relative crop prices.     

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.     

Verification of Toronto temperature and precipitation forecasts for the period 1960–1979

Abstract

The accuracy of temperature and precipitation forecasts for Toronto was studied for the 20‐year period 1960–1979. Since any archive of official forecasts extends for only a small part of this period, it was necessary to retrieve the forecasts from newspaper records. The possible errors involved in such a data source were examined through a comparison of newspaper reported observations and the official record. On only a few occasions were significant differences observed.

For temperature forecasts, the record indicates a significant loss of skill over the 20‐year periodin the prediction of maximum temperature for the first day. This was observed not only for the Bloor Street observing station for which the entire 20‐year record was analysed, but also for observing stations at Toronto Island, Downsview and Malton. The loss of skill over the years is greatest in winter when temperature is consistently predicted too low at all stations.

For the entire period under study, precipitation forecasts consisted only of words and no quantitative information (such as probability of precipitation forecasts) was issued. Word choice is intended to carry information on the duration and expected spatial coverage of precipitation, but substantial inconsistencies between word choice and subsequent precipitation occurrence were found. Consequently, the verification procedure for these forecasts was very simple and ignored any differences implied in word choice. With this technique precipitation forecasts were shown to have improved over the 20‐year period.     

Verification of the Weather Research and Forecasting Model when Forecasting Daily Surface Conditions in Southern Alberta

The Weather Research and Forecasting (WRF) model was compared with daily surface observations to verify the accuracy of the WRF model in forecasting surface temperature, pressure, precipitation, wind speed, and direction. Daily forecasts for the following two days were produced at nine locations across southern Alberta, Canada. Model output was verified using station observations to determine the differences in forecast accuracy for each season.

Although there were seasonal differences in the WRF model, the summer season forecasts generally had the greatest accuracy, determined by the lowest root mean square errors, whereas the winter season forecasts were the least accurate. The WRF model generally produced skillful forecasts throughout the year although with a smaller diurnal temperature range than observed. The WRF model forecast the prevailing wind direction more accurately than other directions, but it tended to slightly overestimate precipitation amounts. A sensitivity analysis consisting of three microphysics schemes showed relatively minor differences between simulated precipitation as well as 2?m surface temperatures.     

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.     

Sensitivity experiments for polar low forecasting with the CMC mesoscale finite‐element model

Abstract

High‐resolution versions of the Canadian operational regional finite‐element model (RFE) have been developed to assess their potential in simulating mesoscale, difficult‐to‐forecast and potentially dangerous weather systems commonly referred to as polar lows. The operational (1989) 100‐km version and a 50‐km version of the model have been run for two different polar low cases: one over Hudson Bay and one over Davis Strait. More integrations have also been performed on the Hudson Bay event both at 50 and 25 km to assess the model sensitivity to ice cover. As expected, the reduction in spatial truncation errors provided by the increase in resolution results in a better simulation of the systems. Moreover, when run at higher resolutions the model shows a significant sensitivity to ice cover. The results of the ice‐cover experiments also put into perspective the interaction between the heat and moisture fluxes at the surface, the low‐level wind structure, and the relation of these to the development of the polar low. This study suggests that the improved forecast accuracy obtained from increased resolution is limited by the correctness of the analysis of the ice cover, which acts as a stationary forcing for the entire forecast period.     

On the average errors of an ensemble of forecasts 1

Abstract

The average error fields of an ensemble of 10‐day forecasts made with a global model at the European Centre for Medium Range Weather Forecasts, and first presented by Hollingsworth et al. (1980), are examined. The time evolution of the error fields is presented together with horizontal and vertical cross‐sections through the fields at fixed times to reveal some features of their three‐dimensional structure. The most striking deficiency of the model is seen to be its inability to maintain the amplitude of the quasi‐stationary zonal wavenumber 2 in the middle and upper troposphere.     

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.     

Improving Multi-Model Ensemble Forecasts of Tropical Cyclone Intensity Using Bayesian Model Averaging

This paper proposes a method for multi-model ensemble forecasting based on Bayesian model averaging (BMA), aiming to improve the accuracy of tropical cyclone (TC) intensity forecasts, especially forecasts of minimum surface pressure at the cyclone center (P_min). The multi-model ensemble comprises three operational forecast models: the Global Forecast System (GFS) of NCEP, the Hurricane Weather Research and Forecasting (HWRF) models of NCEP, and the Integrated Forecasting System (IFS) of ECMWF. The mean of a predictive distribution is taken as the BMA forecast. In this investigation, bias correction of the minimum surface pressure was applied at each forecast lead time, and the distribution (or probability density function, PDF) of P_min was used and transformed. Based on summer season forecasts for three years, we found that the intensity errors in TC forecast from the three models varied significantly. The HWRF had a much smaller intensity error for short lead-time forecasts. To demonstrate the proposed methodology, cross validation was implemented to ensure more efficient use of the sample data and more reliable testing. Comparative analysis shows that BMA for this three-model ensemble, after bias correction and distribution transformation, provided more accurate forecasts than did the best of the ensemble members (HWRF), with a 5%–7% decrease in root-mean-square error on average. BMA also outperformed the multi-model ensemble, and it produced “predictive variance” that represented the forecast uncertainty of the member models. In a word, the BMA method used in the multi-model ensemble forecasting was successful in TC intensity forecasts, and it has the potential to be applied to routine operational forecasting.     

Skill assessment of seasonal hindcasts from the Canadian historical forecast project

Abstract

The performance of seasonal hindcasts produced with four global atmospheric models in the second phase of the Canadian Historical Forecasting Project is evaluated. Deterministic and probabilistic forecast skill assessments are carried out using common verification measures. Several methods of combining multi‐model output to produce deterministic and probabilistic forecasts of near‐surface air temperature, 500 hPa geopotential height, and 700 hPa temperature for zero‐month and one‐month leads are considered. A variance‐based weighting modestly improves the skill of deterministic and probabilistic hindcasts in some cases. A parametric Gaussian probability estimator is superior to a non‐parametric count‐method estimator for producing multi‐model probability forecasts. Statistical adjustment is beneficial for deterministic and probabilistic hindcasts of near‐surface temperature over the ocean but not always over land. Skill improves with the number of different models used for a given total ensemble size. The four‐model ensemble is shown to be a reasonable multi‐model configuration.     

Inferring salinity from temperature or depth for dynamic height computations in the north pacific

Abstract

A computational method is developed where salinities inferred from mean salinity profiles (computed from all available data) are used to calculate 0/500 db dynamic height from temperature profiles. Using data from Ocean Weather Station P (50°N, 145°W), the method yielded a much smaller uncertainty in inferred 0/500 db dynamic height (～3 dyn cm) than that found using a mean temperature‐salinity relationship (～10 dyn cm). Applied to historical hydrographic data averaged over 5° squares in the North Pacific (north of 30°N), the method led to inferred dynamic‐height uncertainties typically less than 4 dyn cm in the region north of the Subarctic Front (～40°N). In this same region, dynamic heights inferred from mean temperature‐salinity curves had large uncertainties. South of the Subarctic Front, the dynamic‐height uncertainties associated with the temperature‐salinity curves were smaller than those computed with the mean salinity profiles. A combination of these two methods was used to compute inferred dynamic height from a climatology of temperature structure in the region from 30–50°N, 130°W‐150°E.     

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.