A 3‐dimensional variational data assimilation (3D‐Var) scheme for the High Resolution Limited Area Model (HIRLAM) forecasting system is described. The HIRLAM 3D‐Var is based on the minimization of a cost function that consists of one term Jb, which measures the distance between the resulting analysis and a background field, in general a short‐range forecast, and another term J0, which measures the distance between the analysis and the observations. This paper is concerned with the general formulation of the HIRLAM 3D‐Var and with Jb, while the companion paper by Lindskog and co‐workers is concerned with the handling of observations, including the Jo term, and with validation of the 3D‐Var through extended parallel assimilation and forecast experiments. The 3D‐Var minimization requires a pre‐conditioning that is achieved by a transformation of the minimization control variable. This change of variable is designed as an operator approximating an inverse square root of the forecast error covariance matrix in the model space. The main transformations are the subtraction of the geostrophic wind increment, the bi‐Fourier transform, and the projection on vertical eigenvectors. The spectral bi‐Fourier approach allows one to derive non‐separable structure functions in a limited area model, in the form of vertically dependent horizontal spectra and scale‐dependent vertical correlations. Statistics have been accumulated from differences between + 24 h and +48 h HIRLAM forecasts valid at the same time. Results from single observation impact studies as well as results from assimilation cycles using operational observations are presented. It is shown that the HIRLAM 3D‐Var produces assimilation increments in accordance with the applied analysis structure functions, that the fit of the analysis to the observations is in agreement with the assumed error statistics, and that assimilation increments are well balanced. It is also shown that the particular problems associated with the limited area formulation have been solved. These results, together with the results of the companion paper, indicate that the 3D‐Var scheme performs significantly better than the statistical interpolation scheme.
A 3‐dimensional variational data assimilation (3D‐Var) scheme for the High Resolution Limited Area Model (HIRLAM) forecasting system is described. The HIRLAM 3D‐Var is based on the minimisation of a cost function that consists of one term, Jb, which measures the distance between the resulting analysis and a background field, in general a short‐range forecast, and another term, Jo, which measures the distance between the analysis and the observations. This paper is concerned with Jo and the handling of observations, while the companion paper by Gustafsson et al. (2001) is concerned with the general 3D‐Var formulation and with the Jb term. Individual system components, such as the screening of observations and the observation operators, and other issues, such as the parallelisation strategy for the computer code, are described. The functionality of the observation quality control is investigated and the 3D‐Var system is validated through data assimilation and forecast experiments. Results from assimilation and forecast experiments indicate that the 3D‐Var assimilation system performs significantly better than two currently used HIRLAM systems, which are based on statistical interpolation. The use of all significant level data from multilevel observation reports is shown to be one factor contributing to the superiority of the 3D‐Var system. Other contributing factors are most probably the formulation of the analysis as a single global problem, the use of non‐separable structure functions and the variational quality control, which accounts for non‐Gaussian observation errors.
A meteorological synoptic situation using Global Positioning System (GPS) observations and a numerical weather prediction (NWP) model in the vicinity of the Madrid Sierra, Spain, between 2 and 15 December 1996 has been studied. The experiment was characterized by high precipitable water (PW) values associated to rainfall events. The PW was estimated at the level of 1 mm with five GPS receivers to study the passage of a winter frontal system. The GPS network had baselines ranging from 5 to 50 km. These observations have been used to study the spatial and temporal variations of PW.For this same location and time period, PW calculations were carried out by HIRLAM (High-Resolution Limited Area Modeling), the hydrostatic NWP system operational at the Spanish National Weather Service. HIRLAM has been run in two modes: analysis (HIRLAM/A) and forecast (HIRLAM/F).The comparison of PW values obtained using GPS and high-resolution HIRLAM/A shows a PW bias of Ϫ0.4 mm (GPS-derived PW higher), and a root-mean-square (rms) difference of 2 mm (relative agreement of 85%), which is in agreement with the standard deviation of each method. A similar comparison between GPS and the high-resolution HIRLAM/F results in a bias and rms that increase when extending the forecast range up to a bias of Ϫ1.2 mm and an rms of 3 mm (relative agreement of 78%) for the longest forecast range studied, which is 24 h.Radiosonde profiles from a location near one of the sites of the GPS network have also been used to estimate PW. The PW bias and rms that result from comparing this data to the previous two methods are Ϫ1 and 1.6 mm (relative agreement of 88%) between GPS and radiosondes, and Ϫ1.2 and 1.3 mm (relative agreement of 90%) between radiosonde and HIRLAM/A.The PW estimated from GPS is probed to be an accurate measurement to validate NWP models. The study also shows that GPS measurements can detect small-scale fluctuations and therefore can be used to evaluate NWP models with finer resolution.
Abstract. The influence of targeted observations on shortrange forecasts is tested over two different periods of PRE-VIEW (2008) and MEDEX (2009) data targeting field campaigns for a set of Mediterranean high-impact weather events. As targeted observations we have used not only extra radiosondes, but also enhanced satellite data observed in singular vector (SV)-based sensitive regions. Three parallel observing system experiments, based on the High-Resolution Limited-Area Model (HIRLAM) data assimilation and forecast system, have been conducted. Forecasts of the three experiments have been assessed using both verifying analyses for upper-air fields, and surface observations for several meteorological parameters. Furthermore, quantitative precipitation forecasts (QPF) have been objectively verified using the novel feature oriented Structure-Amplitude-Location (SAL) method.The results obtained show that extra radiosondes have an overall positive impact on the forecasts (average improvement of all upper-air variables and vertical levels studied is 3.6 %). When in addition to extra radiosonde data also enhanced satellite data are assimilated, the overall forecast skill is almost doubled. However, a distinct behaviour is found between the PREVIEW and MEDEX cases. While for MEDEX cases the improvement is slight, for PREVIEW cases the improvement is significant (average improvements of 1.7 % and 8.9 %, respectively, for the experiment with enhanced satellite data). It is suggested that this is due to the location of the target areas and the spatial distribution of the composite observing system and to the different atmospheric predictability in these two periods.
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