Overview on NCEP's Data Assimilation System ------------------------------------------ The climate data assimilation system (CDAS) used for Reanalysis is very similar to the global data assimilation system (GDAS) that is run operationally. They are both run on 6-hour cycles. | | |-------------------->| 6 hour forecast is made | | from 00Z analysis. This 00Z 06Z becomes the first guess analysis forecast | | 03Z obs | 09Z obs data from 6 hour window \ | / (i.e., 03Z-09Z) is used \ | / These are the 'obs'. \ | / Quality control will \ | / reject some of the data. \ | / \ | / \ | / \ | / \ | / Assimilation sys. takes \|/ 1st guess and the obs. | produces a 06Z analysis | Within the 6 hr window, | all obs. are used. | V | | |-------------------->| 6 hour forecast is made | | (cycle is repeated) 06Z 12Z analysis forecast | | 09Z obs | 15Z obs \ | / \ | / \ | / \ | / \ | / \ | / \ | / \ | / \ | / \|/ | | V | | |-------------------->| | | 12Z 18Z analysis forecast To make an analysis, a 6 hour forecast and observations merged together. Such a procedure is necessary because the number of degrees of freedom in the atmosphere is much greater than the number of observations made, and we have an under determined system. The merging consists of finding an atmospheric state (A) that is closest to the first guess and the observations. Symbolically you want to find A that minimizes W1((first_guess - A)^2) + W2((observations - A)^2) where W1 and W2 are weighting functions. The above equation is symbolic, and in matrix notation would be written as T T J = (F - A) W1 (F - A) + (O - L A) W2 (O - L A) where A is the column vector of the atmospheric state F is the column vector of the first guess (6 hour forecast) W1 and W2 are square matrices describing the weights O is a column vector of the observations L is matrix to convert the atmospheric state vector to a synthetic observations vector -------------------------------------------------------------------------- The following is by John Derber. It applies to the operational system. The differences are 1) Reanalysis is run at T62, 2) Reanalysis neither uses interactive retrievals nor SSM/I winds. -------------------------------------------------------------------------- SSI analysis system documentation as of Sep. 8, 1994 Documentation The initial version of the SSI analysis system is presented in Parrish and Derber (1992). Some initial updates are contained in Derber et al. (1991) and a more complete description of the latest version is being prepared by Rizvi and Parrish(1994). Numerical/Computational Properties Horizontal Representation The analysis variables are defined spectrally. For comparison to the observations, the variables are transformed to Gaussian grid and then linearly interpolated to observation location. Horizontal Resolution Same as forecast model. Spectral triangular 126 (T126). The Gaussian grid of 384x192 contains two additional rows over that used in model (north and south pole points). This resolution is essentially equivalent to 1x1 degree latitude/longitude. Vertical Representation and domain Same as forecast model. Sigma coordinate. For a surface pressure of 1000 hPa, twenty eight levels from 995hPa to 2.7hPa Computer/Operating System Currently optimized for Cray computers. It has run on Y/MP, C90, and EL at various resolutions with up to 14 processors. Computational performance On C90 at full resolution, the wall clock time using 14 processors is about 5 minutes. Analysis Components and basic properties Basic Problem The problem being solved is to minimize the weighted fit of the analysis to the guess plus the weighted fit of the analysis to the observations plus the weighted fit of the divergence tendency to the guess divergence tendency. The weights are given by the statistics described below. Analysis variables The analysis variables can be uniquely transformed into the model variables of vorticity, divergence, temperature, ln(surface pressure) and specific humidity. The analysis variables are normalized vorticity, non-balanced divergence, non-balanced temperature, surface streamfunction and specific humidity. Each of these are deviations from the guess, decomposed in the vertical based on the vertical error covariance and are normalized with the standard deviation of the error. The balanced part of the divergence and the temperature are implied using a linear balance equation with empirical friction from the streamfunction. Observation types Currently, the analysis system uses the following data: 1. Rawindsondes -- winds, temperatures, specific humidity, surface pressure 2. Conventional aircraft reports -- winds 3. Acars aircraft reports (above 700mb) -- winds, temperatures 4. Cloud tracked winds from GOES, Japanese and European satellites 5. Surface marine observations -- winds, temperatures, specific humidity, surface pressure 6. Surface land observations -- specific humidity, surface pressure 7. SSM/I wind speeds (with assigned direction) 8. TOVS temperature retrievals in Southern Hemisphere (over land above 100mb only). 9. Interactive temperature retrievals in Northern Hemisphere (over land above 100mb only). 10. Dropwindsondes -- winds, temperatures, specific humidity 11. Australian sea level pressure boguses Observational error statistics The observational error statistics can vary with each observation location. They are currently input from the quality control routines. Background error statistics The background error statistics are used to weight the background (first guess) field. They are defined spectrally and are currently nearly homogeneous around a latitude band. The statistics are calculated by scaling the statistics from a sequence of differences between 24 and 48 hour forecasts valid at the same time. Balance constraint A nonlinear balance constraint is currently being used in the analysis system. The nonlinear balance constraint is linearized around the guess in the analysis system. Vertical advection, surface friction and diabatic heating are not yet incorporated. The analysis system penalizes for differences from the guess divergence tendency. The penalty is defined in spectral space and the weights are defined as for the background error statistics