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Lanzhou Zhongchuan International Airport [International Civil Aviation Organization (ICAO) code ZLLL] is located in a wind shear prone area in China, where most low-level wind shear events occur in dry weather conditions. We analyzed temporal distribution and synoptic circulation background for 18 dry wind shear events reported by pilots at ZLLL by using the NCEP final (FNL) operational global analysis data, and then proposed a lidar-based regio-nal divergence algorithm (RDA) to determine wind shear intensity and location. Low-level wind shear at ZLLL usually occurs in the afternoon and evening in dry conditions. Most wind shear events occur in an unstable atmosphere over ZLLL, with changes in wind speed or direction generally found at 700 hPa and 10-m height. Based on synoptic circulations at 700 hPa, wind shear events could be classified as strong northerly, convergence, southerly, and weak wind types. The proposed RDA successfully identified low-level wind shear except one southerly case, achieving 94% alerting rate compared with 82% for the operational system at ZLLL and 88% for the ramp detection algorithm (widely used in some operational alert systems) based on the same dataset. The RDA-unidentified southerly case occurred in a near neutral atmosphere, and wind speed change could not be captured by the Doppler lidar.

Low-level wind shear could occur not only in rainy weather conditions but also in non-rainy weather conditions, which is dangerous to aircraft safety for its rapid changes in wind direction or velocity. Recently, dry wind shear occurred in non-rainy condition has drawn more and more attention. Rain-detecting Doppler radar has no capabilities in detecting dry wind shear occurred in non-rainy condition, while Doppler Lidar observations with higher spatial and temporal resolution provide valuable information for dry wind shear. For this, considering dry wind shear cases reported by pilots at Lanzhou Zhongchuan International Airport as study object, lidar observations (radial velocities) were assimilated along with surface data to improve the prediction skill of dry wind shear events.All experiments were conducted with Weather Research and Forecasting (WRF) model and its three-dimensional variational (3D-VAR) system. Three-nested domains were employed with 1-km horizontal resolution in the innermost domain. The model was derived by the NCEP FNL data. Lidar data was processed and only assimilated in the innermost domain. Experimental results show that the low-level wind shear can not be found in the experimental results without lidar data assimilation, while lidar data assimilation experiment successfully represented wind shear small-scale characteristics and simulated radial wind pattern was close to lidar observation. In addition, assimilation cycles with short time intervals effectively improved simulation accuracy of wind shear events.

Cloud analysis module (GCAS) in GRAPES model can combine radar reflectivity data, satellite data and surface observations to provide there-dimensional cloud information. To show application effect of GCAS on 3-km resolution forecasts in arid and semi-arid areas of Northwest China, three sets of forecast experiments were conducted with GRAPES_Meso model, which includes control experiment (Con_exp), gcas experiment (Gcas_exp) and hot-start experiment (Hot_exp). The impact of cloud analysis on the prediction effect was investigated using 13 heavy rainfall cases and one month continuous experiments.These experimental results show the use of cloud analysis can significantly improve forecasting skills of precipitation. Compared with hourly precipitation observations, Gcas_exp performed better than Con_exp and Hot_exp, which gets a higher threat scores of precipitation both for 13 cases and for one-month continuous experiments. Hot_exp presented an positive effect only in the first few hours. Oftentimes, Hot_exp got a worse forecast than Con_exp after the first several hours. In addition, gcas_exp has a positive effect on the prediction of 2m temperature, 10m wind and other variables, but forecasted composite reflectivity was stronger than its observations. Hot_exp can reduce this strength bias to some extent.

The relationship between the radar reflectivity factor (Z) and the rainfall rate (R) is recalculated based on radar observations from 10 Doppler radars and hourly rainfall measurements at 6529 automatic weather stations over the Yangtze–Huaihe River basin. The data were collected by the National 973 Project from June to July 2013 for severe convective weather events. The Z–R relationship is combined with an empirical qr–R relationship to obtain a new Z–qr relationship, which is then used to correct the observational operator for radar reflectivity in the three-dimensional variational (3DVar) data assimilation system of the Weather Research and Forecasting (WRF) model to improve the analysis and prediction of severe convective weather over the Yangtze–Huaihe River basin. The performance of the corrected reflectivity operator used in the WRF 3DVar data assimilation system is tested with a heavy rain event that occurred over Jiangsu and Anhui provinces and the surrounding regions on 23 June 2013. It is noted that the observations for this event are not included in the calculation of the Z–R relationship. Three experiments are conducted with the WRF model and its 3DVar system, including a control run without the assimilation of reflectivity data and two assimilation experiments with the original and corrected reflectivity operators. The experimental results show that the assimilation of radar reflectivity data has a positive impact on the rainfall forecast within a few hours with either the original or corrected reflectivity operators, but the corrected reflectivity operator achieves a better performance on the rainfall forecast than the original operator. The corrected reflectivity operator extends the effective time of radar data assimilation for the prediction of strong reflectivity. The physical variables analyzed with the corrected reflectivity operator present more reasonable mesoscale structures than those obtained with the original reflectivity operator. This suggests that the new statistical Z–R relationship is more suitable for predicting severe convective weather over the Yangtze–Huaihe River basin than the Z–R relationships currently in use.

In model-based sensitivity studies, the growth of model error over long-term integrations may lead to serious deviations between the simulated and actual states. To reduce these errors, we have developed a new modeling approach with application of the Newtonian relaxation technique, or nudging. In this approach, an identical artificial Newtonian relaxation term that reflects the difference between the model reference state and its analysis (available in many sensitivity studies) is added to the prognostic equations of the two simulated states, the reference state and the perturbed state (for which observations are nonexistent). We have conducted idealized sensitivity experiments with a shallow-water model to evaluate the benefits and viability of this approach and to test its sensitivity to changes in the nudging period and error in the analysis data. The experimental results confirm that this approach lead to more credible atmospheric responses to modified external forcing if the data error is within a reasonable range. The results also indicate that a 12-hour period is more favorable for nudging than a 24-hour period.

In model-based climate sensitivity studies, model errors may grow during continuous long-term integrations in both the “reference” and “perturbed” states and hence the climate sensitivity (defined as the difference between the two states). To reduce the errors, we propose a piecewise modeling approach that splits the continuous long-term simulation into subintervals of sequential short-term simulations, and updates the modeled states through re-initialization at the end of each subinterval. In the re-initialization processes, this approach updates the reference state with analysis data and updates the perturbed states with the sum of analysis data and the difference between the perturbed and the reference states, thereby improving the credibility of the modeled climate sensitivity. We conducted a series of experiments with a shallow-water model to evaluate the advantages of the piecewise approach over the conventional continuous modeling approach. We then investigated the impacts of analysis data error and subinterval length used in the piecewise approach on the simulations of the reference and perturbed states as well as the resulting climate sensitivity. The experiments show that the piecewise approach reduces the errors produced by the conventional continuous modeling approach, more effectively when the analysis data error becomes smaller and the subinterval length is shorter. In addition, we employed a nudging assimilation technique to solve possible spin-up problems caused by re-initializations by using analysis data that contain inconsistent errors between mass and velocity. The nudging technique can effectively diminish the spin-up problem, resulting in a higher modeling skill.

An observation localization scheme is introduced into an ensemble-based three-dimensional variational (3DVar) assimilation method based on the singular value decomposition technique (SVD-En3DVar) to improve assimilation skill. A point-by-point analysis technique is adopted in which the weight of each observation decreases with increasing distance between the analysis point and the observation point. A set of numerical experiments, in which simulated Doppler radar data are assimilated into the Weather Research and Forecasting (WRF) model, is designed to test the scheme. The results are compared with those obtained using the original global and local patch schemes in SVD-En3DVar, neither of which includes this type of observation localization. The observation localization scheme not only eliminates spurious analysis increments in areas of missing data, but also avoids the discontinuous analysis fields that arise from the local patch scheme. The new scheme provides better analysis fields and a more reasonable short-range rainfall forecast than the original schemes. Additional forecast experiments that assimilate real data from 10 radars indicate that the short-term precipitation forecast skill can be improved by assimilating radar data and the observation localization scheme provides a better forecast than the other two schemes.

A variational method based on previous numerical forecasts is developed to estimate and correct non-systematic component of numerical weather forecast error. In the method, it is assumed that the error is linearly dependent on some combination of the forecast fields, and three types of forecast combination are applied to identifying the forecasting error: 1) the forecasts at the ending time, 2) thecombination of initial fields and the forecasts at the ending time, and 3) the combination of the forecasts at the ending time and the tendency of the forecast. The Single Value Decomposition (SVD) of the covariance matrix between the forecast and forecasting error is used to obtain the inverse mapping from flow space to the error space during the training period. The background covariance matrix is hereby reduced to a simple diagonal matrix. The method is tested with a shallow-water equation model by introducing two different model errors. The results of error correction for 6, 24 and 48 h forecasts show that the method is effective for improving the quality of the forecast when the forecasting error obviously exceeds the analysis error and it is optimal when the third type of forecast combinations is applied.

A new data assimilation method called the explicit four-dimensional variational (4DVAR) method is proposed. In this method, the singular value decomposition (SVD) is used to construct the orthogonal basis vectors from a forecast ensemble in a 4D space. The basis vectors represent not only the spatial structure of the analysis variables but also the temporal evolution. After the analysis variables are ex-pressed by a truncated expansion of the basis vectors in the 4D space, the control variables in the cost function appear explicitly, so that the adjoint model, which is used to derive the gradient of cost function with respect to the control variables, is no longer needed. The new technique significantly simplifies the data assimilation process. The advantage of the proposed method is demonstrated by several experiments using a shallow water numerical model and the results are compared with those of the conventional 4DVAR. It is shown that when the observation points are very dense, the conventional 4DVAR is better than the proposed method. However, when the observation points are sparse, the proposed method performs better. The sensitivity of the proposed method with respect to errors in the observations and the numerical model is lower than that of the conventional method.

A two-step variational method is developed to retrieve the three-dimension wind field from single-Doppler radar observation for operational applications. The first step produces a proxy background wind field, and the second step retrieves the detailed wind structures in data dense areas on a high-resolution grid. The background field is called proxy because it is obtained in the first step by a spectral analysis of the same radial-wind observations that will be used in the second step and thus the background is not independent of the observations. In the second step, the wind retrieval is constrained by the proxy background and the advection equation of liquid water content in the cost function. Tested with a dataset collected during Meiyu front heavy rainfall on 22 July 2002 in China, the two-step approach is shown to yield the best performance in comparison with a single-step approach that uses either only the proxy background field or the retrieval without the proxy background.

The detailed kinematic structure of a heavy rain event that occurred in the middle reaches of the Yangtze River was investigated using dual-Doppler radar observation. A variational analysis method was developed to obtain the three-dimensional wind fields. Before the analysis, a data preprocessing procedure was carried out, in which the temporal variation with the scanning time interval and the effect of the earth curvature on the data position were taken into account. The analysis shows that a shear line in the lower and middle levels played an important role in the rainfall event. The precipitation fell mainly on the south end of the shear line where southerly flow prevailed and convergence and updraft were obvious. With the movement and decay of the shear line, the precipitation moved and decayed correspondingly.

[1] Doppler radar observations with high spatial and temporal resolution can effectively improve the description of small-scale structures in the initial condition and enhance the mesoscale and microscale model skills of numerical weather prediction (NWP). In this paper, Doppler radar radial velocity and reflectivity are simultaneously assimilated into a weather research and forecasting (WRF) model by a proper orthogonal-decomposition-based ensemble, three-dimensional variational assimilation method (referred to as PODEn3DVar), which therefore forms the PODEn3DVar-based radar assimilation system (referred to as WRF-PODEn3DVar). The main advantages of WRF-PODEn3DVar over the standard WRF-3DVar are that (1) the PODEn3DVar provides flow-dependent covariances through the evolving ensemble of short-range forecasts, and (2) the PODEn3DVar analysis can be obtained directly without an iterative process, which significantly simplifies the assimilation. Results from real data assimilation experiments with the WRF model show that WRF-PODEn3DVar simulation yields better rainfall forecasting than radar retrieval, and radar retrieval is better than the standard WRF-3DVar assimilation, probably because of the flow-dependence character embedded in the WRF-PODEn3DVar.

Weather Doppler radar can provide high spatial and temporal resolution observations, but most observations are discarded during data assimilation. Only the radar data observed at assimilation time are used in operational prediction. In this paper, the radial velocity observation that not only at the assimilation time but also at some earlier and later time are all assimilated with Ensemble Square Root Kalman Filter (EnSRF) based on WRF model. Result shows that the new scheme produces better analysis than the traditional scheme which only uses radar observations at the assimilation time. The improvement is especially clear in the first several assimilation cycles and then decreases with following assimilation cycles generally.

The comparison of two methods of assimilating Doppler radar wind data with Ensemble Kalman Filter (EnKF) based WRF model is presented. One is to assimilate simulated radar radial velocity observations directly. The other is to assimilate the horizontal winds retrieved from Doppler radar Data. Result shows that the second method which assimilated retrieved winds with small retrieval error gives better analysis than the first method does.

A local scheme is introduced into the Ensemble-based 3DVar approach with SVD and is used to assimilate simulated radar observation with WRF model. Local and global schemes are compared and the sensitivities to the localization parameters are investigated. The experiments show that localization can improve the skill of analysis and forecast by avoiding spurious analysis increment in the vacant area of observation. The behave of assimilation is dependent on the localization scale.

The solution of 4DVar may not be unique if observation information is not enough. In order to get the expected solution we can introduce a smooth operator to carry out transformation on the control variable. The numerical experiments with shallow-water-equation model and model data show that through the transformation the analysis increment is restricted in a smooth subspace and the analysis field is more close to the truth. The study explained the significance of background error covariance matrix in 4DVar from another side.

[1] An ensemble-based four-dimensional variational data assimilation (4DVar) method is proposed to fit the model field to 4-D observations in an increment form in the analysis step of data assimilation. The fitting is similar to that in the 4DVar but the analysis increment is expressed by a linear combination of the leading singular vectors extracted from an ensemble of 4-D perturbation solutions, so the fitting is computationally very efficient and does not require any adjoint integration. In the cost function used for the fitting, the background error covariance matrix is constructed implicitly by the perturbation solutions (through their representative singular vectors) similarly to that in the ensemble Kalman filter, but the perturbation solutions are not updated by the analysis into the next assimilation cycle, so the analysis is simpler and more efficient than that in the ensemble Kalman filter. The potential merits of the method are demonstrated by three sets of observing system simulation experiments performed with a shallow-water equation model. The method is shown to be robust even when the model is imperfect and the observations are incomplete.