Stanley G. Benjamin and Kevin J. Brundage
NOAA/ERL Forecast Systems Laboratory
Boulder, Colorado
Lauren L. Morone
National Meteorological Center, Development Division
NWS/NOAA, Washington, D.C.
During the late 1980s and early 1990s, there occurred a large increase in asynoptic meteorological observations over the United States, primarily due to the advent of widespread automated reporting from commercial aircraft and the implementation of a demonstration network of wind profilers. These new observations provided a database on which the time interval between three-dimensional analyses over this region could be reduced, for the first time, to less than 12 hours. A 3-h frequency analysis/forecast data assimilation system known as the Mesoscale Analysis and Prediction System (MAPS) was developed by NOAA/ERL's Forecast Systems Laboratory (FSL) to take advantage of these new data. The first 3-h MAPS assimilation cycle began testing in late 1988 at FSL. Since that time, many significant improvements have been made, including increased resolution, more sophisticated analysis and modeling techniques, and the inclusion of new data types. In 1994, a version of MAPS software is starting official operations at NMC as the Rapid Update Cycle (RUC), the latest of NMC's operational analysis/forecast systems.
References will be made to previous publications concerning specific aspects of MAPS/RUC as appropriate. The reader may find useful general information about MAPS in Benjamin et al. (1991, 1993a, b).
In the rest of this document, more detailed information is presented about the RUC, including its domain, analysis technique, and forecast model.
The Rapid Update Cycle uses a hybrid isentropic-sigma vertical coordinate in which most of the atmosphere is resolved with isentropic (defined as constant virtual potential temperature (thetav) for the RUC) coordinates except for a layer near the ground where terrain-following (sigma) coordinates are used. For most of the domain, then, the RUC possesses the well-known advantages of isentropic (theta) coordinates in providing extra resolution in an adaptive manner near fronts and the tropopause. Some of the other advantages for isentropic coordinates in data assimilation include:
Level Reference Isentropic Value 1 224 K 2 232 K 3 240 K 4 248 K 5 256 K 6 264 K 7 272 K 8 280 K 9 286 K 10 292 K 11 296 K 12 300 K 13 304 K 14 308 K 15 312 K 16 316 K 17 320 K 18 325 K 19 330 K 20 335 K 21 342 K 22 350 K 23 360 K 24 380 K 25 410 K
The vertical resolution of the RUC is much higher than that of the 16-level Nested Grid Model near the surface and in stable layers aloft, as shown in the example below.
For the RUC analysis and forecast model, there is no vertical staggering of the grid, meaning that all variables are defined on the same levels.
The current version of the Rapid Update Cycle covers the lower 48 United States and adjacent areas of Canada, Mexico, and oceanic areas with a 60-km grid.
The terrain field used for the RUC, also depicted in Fig. 4, is an envelope topography field (mean plus standard deviation over grid box) taken from a 5-minute resolution topography data set. The envelope topography field is subjected to one smoothing and one desmoothing pass from the filter developed by Shapiro (1970). The maximum elevation is 3433 m over central Colorado.
The RUC analysis is performed on the same horizontal and hybrid isentropic/sigma vertical grid described in section 2. It is determined by calculating an analysis increment field, a correction that is added to a forecast background field, similar to the procedure for analyses used to initialize most operational forecast models. The analysis increment is calculated by analyzing the observation residuals, the differences between observations and the background field interpolated to the observation points. The RUC analysis, then, is the sum of the background field and the analysis increment (correction) field. The background field for the RUC analysis is the previous 3-h forecast valid at the time of the current analysis. If the RUC assimilation cycle has been interrupted and the previous 3-h RUC forecast is not available, alternative background fields, NGM or older (>= 6 h) RUC forecasts, may be used.
There are six three-dimensional variables analyzed by the RUC on the model-coordinate or native hybrid-b surfaces. These variables are pressure (p), Montgomery stream function (M = CpT + gz), virtual potential temperature (thetav), condensation pressure (Pc, equivalent to the lifting condensation level), and the horizontal wind components relative to the grid (u and v). In the hybrid-b structure, thetav usually will be constant for the top 6-12 hybrid coordinate surfaces, but this varies depending on the season. As described in section 3.4, heights (z) are used in the RUC analysis, but the final output variable is M. Pc is currently used as the analyzed moisture variable because it is a conservative variable in the absence of evaporation or condensation and because it varies more linearly (e.g., from 100 to 1000 mb) than other conserved moisture variables such as specific humidity (e.g., from 20 to 0.01 g/kg with exponential variation). Byers (1938) discusses other advantages of condensation pressure over specific humidity for use on isentropic charts. However, as described in section 4, mixing ratio is used as the water vapor moisture variable within the RUC forecast model.
Four types of observations are currently used in the Rapid Update Cycle, those provided by rawinsondes, commercial aircraft, wind profilers, and surface stations. The data cut-off for the current 3-h RUC is one hour and 25 minutes after the analysis time.
Rawinsonde data are usually available from 75-80 stations within the RUC domain twice daily, at 0000 and 1200 UTC. Asynoptic rawinsonde reports are used in the RUC, when available. Rawinsonde data are converted to the RUC analysis variables shown in section 3.1. The full profile with mandatory- and significant-level data for all variables is then interpolated vertically to the levels (defined by pressure) of the hybrid-b background forecast. The background, in turn, is interpolated horizontally to the location of the station. For stations where the surface pressure is greater than the RUC background surface pressure (defined by the RUC terrain), this means that the lowest part of the sounding may be truncated and not used in the RUC analysis. This happens regularly at some stations in the western United States such as Grand Junction, Colorado (GJT) and Denver, Colorado (DEN). Only the interpolated data (up to 25 levels) are used in the RUC analysis. Heights are interpolated to these levels, as well as thetav, Pc, u, and v.
The only aircraft data used in the RUC are those with automated digital reporting through ACARS (ARINC [Aeronautical Radio, Inc.] Communications, Addressing, and Reporting System). As of April 1994, about 12,000 to 13,000 ACARS reports per day are used in the RUC. The diurnal distribution of this aircraft data is dependent on the commercial route structure, and, therefore, has a strong diurnal variation (Fig. 6).
Data from 27-30 wind profilers, mostly from the Wind Profiler Demonstration Network in the central United States, are available to the RUC as of April 1994. These profiles are interpolated to the pressure levels of the background forecast field at the observation point, as done for rawinsonde profiles. The mapping from height (where raw wind profiler observations are defined) to pressure is performed using (p,z) data from the RUC background forecast. Only wind observations are currently available from profilers. Profiler quality control flags are examined at each raw data level, and only data that have passed a time-height single-station consistency check are passed to the RUC. More information on the accuracy and quality control of profiler winds is available in Weber et al. (1990), Martner et al. (1993), and Miller et al. (1994).
Observations from surface stations over land and buoys are used in the RUC. The data cut-off for surface data assimilated into the RUC is earlier, 35 minutes after analysis time, than that used for the upper-air observations. The surface observations used in the RUC are initially processed in an hourly surface analysis cycle. Surface observations of z, Pc, u, and v are used. If the actual station pressure (calculated from the altimeter setting and station elevation) is more than 30 mb greater than the RUC surface pressure defined at the horizontal location of the station, the surface observation is not used in the RUC analysis because of inaccuracies in extrapolating the observations vertically. If this pressure difference is less than 30 mb, a height observation valid at the background surface pressure is determined using a standard lapse rate and the observed surface pressure (e.g., a variation of Eq. (1) in Benjamin and Miller 1990). A value for thetav to be applied at the model surface pressure is also extrapolated via the standard lapse rate, and Pc is set so that the relative humidity is the same as in the original observation. The observed surface horizontal wind components are used directly.
Considerable attention has been given to observation quality control for the RUC. An outline of the RUC quality control procedures is given below, but more detail may be found in Miller and Benjamin (1991). Three levels of observation quality control are used in the RUC:
A series of gross error checks is then conducted. The most important of these are lapse rate checks and hydrostatic checks (the latter similar to that of Gandin 1988) for rawinsonde profiles, and wind shear checks for profiles from both rawinsondes and profilers. For each of these checks, corrections to the profiles can be made in the event of inconsistencies.
A horizontal consistency or "buddy" check is then performed for the single-level observations and profile observations interpolated to hybrid-b levels. First, the background field interpolated to observation locations is subtracted from all observations to produce observation residuals. Then, surrounding observation residuals are interpolated to the location of each observation via univariate optimal interpolation. This "analyzed" residual, based on neighboring observations, is compared to the observed residual in question. If the difference exceeds a threshold based on expected random observation errors and a calculated analysis error, the observation is flagged as incorrect and not used in subsequent QC checks or in the RUC analysis. The buddy check for surface observations uses only other surface observations; the background for the surface QC is the previous hourly surface analysis from an hourly surface analysis cycle. More detail about the RUC buddy check and associated decision-making algorithms is given by Miller and Benjamin (1991).
The RUC performs a multivariate height/wind analysis and subsequent univariate analyses of thetav and Pc, all using optimal interpolation. The multivariate analysis allows height observations to influence the wind analysis and wind observations to influence the height analysis. More detailed information on an earlier, pure isentropic analysis similar to the current RUC hybrid-b analysis is provided in Benjamin (1989).
In the following discussion, differences from the background, whether for observations (observation residuals) or for analyzed fields (analysis increments), are designed with the symbol '.
As with the quality control, observation residuals are determined by subtracting the background field from all observations. First, the analysis increment is calculated for heights and winds in a z'/v'/u' multivariate analysis. The geostrophic coupling in the RUC analysis is relaxed by a factor of 0.5 at levels above the surface and further to 0.3 near the surface (Benjamin 1989). This relatively small geostrophic coupling factor means that the RUC analysis increment is allowed to be fairly ageostrophic, especially near the ground, an appropriate procedure for a meso-alpha-scale analysis. Hydrostatic virtual temperature increments are calculated from z' to modify the thetav field before a univariate thetav analysis is performed. Thus, height observations are used in the RUC analysis multivariately, but their real effect is to help improve the temperature field. Both the z' and thetav analyses contribute to the final thetav field. The output Montgomery stream function or geopotential height from the RUC analysis is determined by hydrostatically integrating the analyzed thetav values in each column.
The condensation pressure (Pc) is also analyzed univariately. Horizontal distances, on which analysis weights are dependent, are modified dependent on wind flow and speed for the Pc analysis only, similar to the procedures of Benjamin and Seaman (1985) and DiMego (1988).
At this point, the fields no longer correspond exactly to isentropic surfaces, because the thetav field itself has been changed. Therefore, an adjustment back to the hybrid-b surfaces is performed as a last step. This adjustment is very similar to that performed at each time step in the RUC hybrid-b forecast model (section 4.2). Note that before this final adjustment, the RUC analysis procedure is applicable to any vertical coordinate; the same techniques would be appropriate for a sigma-coordinate or isobaric analysis.
Single-level observations are allowed to influence multiple levels, and the vertical correlation of forecast error is prescribed as a function of potential temperature separation. This prescription is different from that of most other operational analyses, which typically use log-pressure separation. It results in a sharper cut-off of the influence of single-level observations near stable layers such as the tropopause. In the event of a rawinsonde "blow-off" (when the balloon is carried quickly downstream and the elevation angle becomes too small for accurate wind determination), the influence of the highest wind observation in the ascent is extended upward as if it were a single-level observation.
"Superobservations" are created in the RUC analysis by combining observations from similar platforms (e.g., aircraft) if they occur within 50 km of each other and are found in the same analysis layer. The purpose of this procedure is to use as much data as possible in the analysis and to eliminate the potential for nonpositive definite matrices in the optimal interpolation analysis solution. When observations are too close together in an optimal interpolation analysis, the result can be a poor analysis or even a program crash. The chief effect of creating superobservations in the RUC is to combine aircraft reports. If a pair of observations of different types is closer than the distance threshold, the observation type is used to select one or the other in the following order: rawinsonde, surface, profiler, and aircraft.
Observations are selected for 4x4 groups of grid points at each of the 25 levels. The observation selection algorithm locates the nearest observations in each of eight directional sectors, as shown by Benjamin (1989). In each of these sectors, the search algorithm attempts to find a profile observation (rawinsonde or profiler). If single-level observations are found closer to the grid points to be analyzed than the profile observation, they too are included in the analysis. Up to one single-level observation in the same analysis layer and one off-level single-level observation may be used. In total, there may be up to one profile observation (z, u, v) and one additional on-level and one off-level single-level observation (usually aircraft observations, each with u and v) for each of the eight sectors, giving a total of 56 observed values that may be used in a single multivariate analysis for a 4x4 group of horizontal grid points at a single level. The same algorithm is used for selecting observations for the univariate thetav and Pc analyses.
Horizontal correlation of 3-h forecast errors is specified from a study of MAPS forecast errors by Carrière (1991). Forecast error standard deviations are also taken from Carrière, and observation error standard deviations are given by Benjamin (1989).
The Rapid Update Cycle forecast model is the generalized vertical coordinate model described by Bleck and Benjamin (1993). Modifications to a 20-line section of code in the model are sufficient to modify it from the hybrid-b coordinate described in section 2.1 to either a pure sigma or pure isentropic model. More detailed information on the use of generalized vertical coordinates in geophysical models is given by Bleck (1978).
The primary prognostic variables in the current RUC model are pressure thickness between model levels, virtual potential temperature, water vapor mixing ratio, and horizontal wind components. Mixing ratio is converted to Pc for output at the current time.
The Arakawa C grid, in which u and v values are located on their own set of points offset from mass points to improve numerical accuracy, is used for the horizontal grid structure in the RUC model. There is no vertical staggering. The time step is 90 seconds at the current resolution. Positive definite advection schemes, which are very accurate and eliminate the possibility of negative values, are used for advection of pressure thickness (continuity equation) and for horizontal advection of thetav and q (Smolarkiewicz (1983) with modifications described in Bleck and Benjamin (1993)). Adams-Bashforth time differencing is used in the momentum equation with a forward-backward scheme for the Coriolis term.
The 20-line section of code that is unique to the hybrid-b coordinate occurs after the continuity (pressure thickness) equation is solved. At this point, the pressure at the reference thetav levels (Table 1) is determined, and if it is less than the prescribed maximum pressure based on the surface pressure and minimum pressure thicknesses, the point remains on the isentropic surface. Otherwise, it is forced to be on a terrain-following surface, as shown in Fig. 2, and its thetav will not be equal to the reference thetav value for that level.
Otherwise, the RUC hybrid-b model appears similar to a sigma-coordinate model. However, in the RUC model, vertical advection only takes place near the ground and in the isentropic part of the domain when there are diabatic processes such as latent heat release. Most of the three-dimensional motion as air ascends and descends is handled two-dimensionally in the RUC model.
The hybrid-b RUC model contains the following physical parameterizations:
At this writing, lateral boundary conditions to the RUC are specified from the Nested Grid Model at the current time. NGM data at 6-h intervals with mandatory-level resolution and 80-km spacing are interpolated to the RUC hybrid-b vertical and horizontal grid. RUC forecasts are nudged each time step toward NGM values linearly interpolated in time according to the Davies (1976) scheme. The most recent NGM forecast available is used for RUC lateral boundary conditions. RUC forecasts initialized at 0000 and 1200 UTC use 12-h old boundary conditions, since the new NGM forecast is not completed at the time the RUC is run. Thus, a RUC 12-h forecast initialized at 0000 or 1200 UTC is nudged toward a 24-h NGM forecast valid at the same time on the boundaries. It is planned that the RUC will be changed to use boundary conditions from the Aviation model at a future time.
Surface characteristics such as albedo, soil moisture, and roughness length are allowed to vary horizontally and are specified as a function of climatology. There are 13 surface land-use types, and a value of each characteristic is specified for each one (Pan et al. 1994, Anthes et al. 1987).
The ground or sea-surface temperature in the RUC is currently set equal to the air temperature at the lowest level in the initial conditions. Until this deficiency is corrected (in the near future), the absence of accurate water temperatures means that RUC grids will typically be too dry in situations such as return southerly flow from the Gulf of Mexico.
There are no special procedures currently used for the upper boundary condition in the RUC.
Before each RUC forecast begins, a forward/backward initialization procedure is applied within the model. The model is run adiabatically for 60 minutes in both the forward and backward directions. The values of mass and wind variables at each time step are averaged with weights specified from a digital filter to produce a more balanced initial state (Lynch and Huang 1992). It has been found that application of this digital filter initialization considerably reduces gravity wave noise in the first few hours of RUC forecasts.
The hybrid-b grid structure and original variables used in the RUC are at least slightly unconventional. Therefore, output is converted to more familiar variables and vertical coordinates for users. In addition, the RUC delivers a number of useful two-dimensional fields not previously discussed. For each 3-h cycle, these fields are output for the analysis, initialized fields, and hourly forecast (1-12 h) times.
The RUC three-dimensional fields are interpolated to isobaric levels between 1000 and 100 mb with 25-mb resolution. The variables output on these surfaces include temperature (rather than virtual temperature), heights, relative humidity, and horizontal (u and v) grid-relative wind components.
Data are also interpolated from the native hybrid-b grids to the isentropic levels in Table 1 between 272 K and 410 K. This interpolation extends to the ground, and an extrapolation is made below the ground for a smooth presentation. Sigma-level data are also provided at 0, 30, 60, 90, 120, and 150 mb above the surface. The variables provided at these levels are the same as those for the hybrid-b levels: p, M, thetav, Pc, u, and v. A non-virtual (standard) temperature field at the surface is also available.
The following grids are produced at both analysis and forecast times by the RUC:
The following fields are produced only at RUC forecast times:
The Rapid Update Cycle is a mesoscale analysis/forecast system that operates on a 3-h cycle to provide high-frequency updates of tropospheric conditions and short-range forecasts over the lower 48 United States and adjacent areas. It covers this area with a 60-km grid and has 25 isentropic-sigma levels on the native grid. The Rapid Update Cycle is based on automated aircraft, profiler, and surface data at asynoptic times.
The authors thank Barry Schwartz, John M. Brown, Tom Schlatter, and Nita Fullerton for their helpful reviews.
The development of MAPS at NOAA/ERL/FSL has been a multi-year project with important contributions from the following scientists: Tracy Smith, Patty Miller, Georg Grell, John M. Brown, Rainer Bleck, Tom Schlatter, Dongsoo Kim, Zaitao Pan, Tanya Smirnova, Dezso Dévényi, Jean-Marie Carrière, Brian Jewett, Keith Brewster, Renate Brümmer, Ruth Lieberman, Gary Rasmussen, and Andres Moreira.
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