# Impact of horizontal and vertical localization scales on microwave sounder SAPHIR radiance assimilation

05 May 2016-Vol. 9876

Abstract: In the present study, the effect of horizontal and vertical localization scales on the assimilation of direct SAPHIR radiances is studied. An Artificial Neural Network (ANN) has been used as a surrogate for the forward radiative calculations. The training input dataset for ANN consists of vertical layers of atmospheric pressure, temperature, relative humidity and other hydrometeor profiles with 6 channel Brightness Temperatures (BTs) as output. The best neural network architecture has been arrived at, by a neuron independence study. Since vertical localization of radiance data requires weighting functions, a ANN has been trained for this purpose. The radiances were ingested into the NWP using the Ensemble Kalman Filter (EnKF) technique. The horizontal localization has been taken care of, by using a Gaussian localization function centered around the observed coordinates. Similarly, the vertical localization is accomplished by assuming a function which depends on the weighting function of the channel to be assimilated. The effect of both horizontal and vertical localizations has been studied in terms of ensemble spread in the precipitation. Aditionally, improvements in 24 hr forecast from assimilation are also reported.

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Topics: Ensemble Kalman filter (55%), Radiance (52%)

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01 Jan 2020-

Abstract: The Megha-Tropiques mission is operating since 12 October, 2011 and serves research and operational objectives related to the tropical water and energy cycle. The satellite is on a low inclination orbit that enhances the sampling over the intertropical belt. The original payloads were dedicated to the estimation of the radiation budget at the top of the atmosphere, the water vapor profiles and the instantaneous precipitation rate. The original suite of geophysical products that was developed permitted to demonstrate the proof of concept of the mission in the early part of its operation. Following an unfortunately expedited exploitation of the conically scanning multispectral radiometer (16 months), efforts have been geared to mitigate the loss by extending the use of the 183 GHz sounder towards the precipitation objectives. This induced some delays in the setting of the current set of products that are now being used for research investigations. Despites not being an operational meteorological satellite, the real time capability of the mission has shown its usefulness with a large and growing set of Numerical Weather Prediction centers assimilating the Megha-Tropiques data, in clear and total skies. After 7 years in space, the satellite and operating instruments are in excellent shape and sustain their very good initial performances. The mission has acquired a large and unique set of observations of the tropical water and energy cycle which is only at the beginning of its exploitation.

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3 citations

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Abstract: Ingesting microwave sounder radiances from SAPHIR of Megha–Tropiques has been attempted. A local ensemble transform Kalman filter assimilation algorithm is adopted to ingest radiances directly into the ARW–WRF model. The forward radiative transfer calculations were surrogated with an artificial neural network (ANN) based on the fast radiative transfer model. Raining pixels from the observations were removed using a threshold test on the observed brightness temperatures. Following this, corrections of both scan and air mass biases were accomplished using a predictor-based approach. The bias characteristics of each channel were calculated from ab initio clear-sky profiles from European reanalysis Interim reanalysis data. The vertical localization functions required for the radiance observations were chosen to be similar to the weighting function of the respective channel. The overall performance of the SAPHIR radiance assimilation in terms of the average error over the forecast period showed a positive impact on the cyclone track prediction when compared with the control run and the best track data from the Indian Meteorological Department. The effect of assimilation is observed to improve the minimum sea-level pressure values, whereas the improvements in the maximum sustainable wind speed are not significant. An assimilation experiment was set up to ingest channel-wise radiances independently, and it was concluded that the assimilation of channel 5 radiances results in the least error in the track forecast. The effect of using ensembles generated by initial perturbations in (i) temperature and (ii) both temperature and humidity was studied. The ensembles generated from perturbations in both humidity and temperature resulted in a better 72-h track compared with perturbation of only one of them. The overall performance of the assimilation of all the six channels for both 48- and 72-h forecast lead times showed a considerable improvement against the control run without any assimilation. Furthermore, the results show a degradation of the forecast of cyclone track in the first 24 h. The sensitivity toward channel-wise radiances showed a positive impact on the precipitation forecast when compared with global precipitation mission rainfall estimates. Threat and bias scores were used for quantitative assessment of precipitation, which indicated improvements in skill after assimilating all six channel radiances from SAPHIR. Finally, a sequential assimilation experiment was set up, and the improvements in the analysis fields were computed.

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Abstract: A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The unbounded error growth found in the extended Kalman filter, which is caused by an overly simplified closure in the error covariance equation, is completely eliminated. Open boundaries can be handled as long as the ocean model is well posed. Well-known numerical instabilities associated with the error covariance equation are avoided because storage and evolution of the error covariance matrix itself are not needed. The results are also better than what is provided by the extended Kalman filter since there is no closure problem and the quality of the forecast error statistics therefore improves. The method should be feasible also for more sophisticated primitive equation models. The computational load for reasonable accuracy is only a fraction of what is required for the extended Kalman filter and is given by the storage of, say, 100 model states for an ensemble size of 100 and thus CPU requirements of the order of the cost of 100 model integrations. The proposed method can therefore be used with realistic nonlinear ocean models on large domains on existing computers, and it is also well suited for parallel computers and clusters of workstations where each processor integrates a few members of the ensemble.

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4,357 citations

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01 Jun 2005-

Abstract: : The development of the Weather Research and Forecasting (WRF) modeling system is a multiagency effort intended to provide a next-generation mesoscale forecast model and data assimilation system that will advance both the understanding and prediction of mesoscale weather and accelerate the transfer of research advances into operations. The model is being developed as a collaborative effort ort among the NCAR Mesoscale and Microscale Meteorology (MMM) Division, the National Oceanic and Atmospheric Administration's (NOAA) National Centers for Environmental Prediction (NCEP) and Forecast System Laboratory (FSL), the Department of Defense's Air Force Weather Agency (AFWA) and Naval Research Laboratory (NRL), the Center for Analysis and Prediction of Storms (CAPS) at the University of Oklahoma, and the Federal Aviation Administration (FAA), along with the participation of a number of university scientists. The WRF model is designed to be a flexible, state-of-the-art, portable code that is an efficient in a massively parallel computing environment. A modular single-source code is maintained that can be configured for both research and operations. It offers numerous physics options, thus tapping into the experience of the broad modeling community. Advanced data assimilation systems are being developed and tested in tandem with the model. WRF is maintained and supported as a community model to facilitate wide use, particularly for research and teaching, in the university community. It is suitable for use in a broad spectrum of applications across scales ranging from meters to thousands of kilometers. Such applications include research and operational numerical weather prediction (NWP), data assimilation and parameterized-physics research, downscaling climate simulations, driving air quality models, atmosphere-ocean coupling, and idealized simulations (e.g boundary-layer eddies, convection, baroclinic waves).

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2,485 citations

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Abstract: This paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter. It is shown that the observations must be treated as random variables at the analysis steps. That is, one should add random perturbations with the correct statistics to the observations and generate an ensemble of observations that then is used in updating the ensemble of model states. Traditionally, this has not been done in previous applications of the ensemble Kalman filter and, as will be shown, this has resulted in an updated ensemble with a variance that is too low. This simple modification of the analysis scheme results in a completely consistent approach if the covariance of the ensemble of model states is interpreted as the prediction error covariance, and there are no further requirements on the ensemble Kalman filter method, except for the use of an ensemble of sufficient size. Thus, there is a unique correspondence between the error statistics from the ensemble Kalman filter and the standard Kalman filter approach.

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1,713 citations

### Additional excerpts

...The three steps which RK3 solves for the prognostic variables are Φ∗ = Φ + ∆t 3 R(Φ) (2)...

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Abstract: The possibility of performing data assimilation using the flow-dependent statistics calculated from an ensemble of short-range forecasts (a technique referred to as ensemble Kalman filtering) is examined in an idealized environment. Using a three-level, quasigeostrophic, T21 model and simulated observations, experiments are performed in a perfect-model context. By using forward interpolation operators from the model state to the observations, the ensemble Kalman filter is able to utilize nonconventional observations. In order to maintain a representative spread between the ensemble members and avoid a problem of inbreeding, a pair of ensemble Kalman filters is configured so that the assimilation of data using one ensemble of shortrange forecasts as background fields employs the weights calculated from the other ensemble of short-range forecasts. This configuration is found to work well: the spread between the ensemble members resembles the difference between the ensemble mean and the true state, except in the case of the smallest ensembles. A series of 30-day data assimilation cycles is performed using ensembles of different sizes. The results indicate that (i) as the size of the ensembles increases, correlations are estimated more accurately and the root-meansquare analysis error decreases, as expected, and (ii) ensembles having on the order of 100 members are sufficient to accurately describe local anisotropic, baroclinic correlation structures. Due to the difficulty of accurately estimating the small correlations associated with remote observations, a cutoff radius beyond which observations are not used, is implemented. It is found that (a) for a given ensemble size there is an optimal value of this cutoff radius, and (b) the optimal cutoff radius increases as the ensemble size increases.

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1,701 citations

### Additional excerpts

...Φ∗∗ = Φ + ∆t 2 R(Φ∗) (3) Φ = Φ +∆tR(Φ∗∗) (4) Where Φ refers to the prognostic variables at time t and R(Φ) refers to the model....

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Abstract: This article focuses on the construction, directly in physical space, of simply parametrized covariance functions for data-assimilation applications. A self-contained, rigorous mathematical summary of relevant topics from correlation theory is provided as a foundation for this construction. Covariance and correlation functions are defined, and common notions of homogeneity and isotropy are clarified. Classical results are stated, and proven where instructive. Included are smoothness properties relevant to multivariate statistical-analysis algorithms where wind/wind and wind/mass correlation models are obtained by differentiating the correlation model of a mass variable. the Convolution Theorem is introduced as the primary tool used to construct classes of covariance and cross-covariance functions on three-dimensional Euclidean space R3. Among these are classes of compactly supported functions that restrict to covariance and cross-covariance functions on the unit sphere S2, and that vanish identically on subsets of positive measure on S2. It is shown that these covariance and cross-covariance functions on S2, referred to as being space-limited, cannot be obtained using truncated spectral expansions. Compactly supported and space-limited covariance functions determine sparse covariance matrices when evaluated on a grid, thereby easing computational burdens in atmospheric data-analysis algorithms.
Convolution integrals leading to practical examples of compactly supported covariance and cross-covariance functions on R3 are reduced and evaluated. More specifically, suppose that gi and gj are radially symmetric functions defined on R3 such that gi(x) = 0 for |x| > di and gj(x) = 0 for |xv > dj, O di + dj and |x - y| > 2di, respectively, Additional covariance functions on R3 are constructed using convolutions over the real numbers R, rather than R3. Families of compactly supported approximants to standard second- and third-order autoregressive functions are constructed as illustrative examples. Compactly supported covariance functions of the form C(x,y) := Co(|x - y|), x,y ∈ R3, where the functions Co(r) for r ∈ R are 5th-order piecewise rational functions, are also constructed. These functions are used to develop space-limited product covariance functions B(x, y) C(x, y), x, y ∈ S2, approximating given covariance functions B(x, y) supported on all of S2 × S2.

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1,555 citations

### Additional excerpts

...The above equation can be modified by taking D′ = (D −HA) as A = A+A′(HA′)T (HA′(HA′)T + Υ (Υ ) )−1D′ (14) In the above equation, computing the inverse costs a lot of computational time....

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