{"Bibliographic":{"Title":"The LFM-II model -- 1980","Authors":"","Publication date":"1981","Publisher":""},"Administrative":{"Date created":"08-20-2023","Language":"English","Rights":"CC 0","Size":"0000037679"},"Pages":["H\nQQ\n851\nU6N5\nno.66\nOF\nCOMMUNITY\nNOAA Technical Memorandum NWS NMC 66\n*\n*\nwith\nSTATES\nOF\nTHE LFM-II MODEL -- 1980\nWashington, D.C.\nSeptember 1981\nU.S. DEPARTMENT OF\nNational Oceanic and\nNational Weather\nCOMMERCE\nAtmospheric Administration\nService","National Meteorological Center\nNational Weather Service, National Meterological Center Series\nThe National Meteorological Center (NMC) of the National Weather Service (NWS) produces weather anal-\nyses and forecasts for the Northern Hemisphere. Areal coverage is being expanded to include the entire\nglobe. The Center conducts research and development to improve the accuracy of forecasts, to provide\ninformation in the most useful form, and to present data as automatically as practicable.\nNOAA Technical Memorandums in the NWS NMC series facilitate rapid dissemination of material of general\ninterest which may be preliminary in nature and which may be published formally elsewhere at a later\ndate. Publications 34 through 37 are in the former series, Weather Bureau Technical Notes (TN), Na-\ntional Meterological Center Technical Memoranda; publications 38 through 48 are in the former series\nESSA Technical Memoranda, Weather Bureau Technical Memoranda (WBTM). Beginning with 49, publications\nare now part of the series, NOAA Technical Memorandums NWS.\nPublications listed below are available from the National Technical Information Service (NTIS), U.S.\nDepartment of Commerce, Sills Bldg., 5285 Port Royal Road, Springfield, VA 22161. Prices vary for\npaper copies; $3.50 microfiche. Order by accession number, when given, in parentheses.\nWeather Bureau Technical Notes\nTN\n22\nNMC 34 Tropospheric Heating and Cooling for Selected Days and Locations over the United States\nDuring Winter 1960 and Spring 1962. Philip F. Clapp and Francis J. Winninghoff, 1965,\n18 pp. (PB-170-584)\nTN\n30\nNMC 35 Saturation Thickness Tables for the Dry Adiabatic, Pseudo-adiabatic, and Standard Atmo-\nspheres. Jerrold A. LaRue and Russell J. Younkin, January 1966, 18 pp. (PB-169-382)\nTN 37 NMC 36\nSummary of Verification of Numerical Operational Tropical Cyclone Forecast Tracks for\n1965. March 1966, 6 pp. (PB-170-410)\nTN 40 NMC\n37 Catalog of 5-Day Mean 700-mb. Height Anomaly Centers 1947-1963 and Suggested Applica-\ntions. J. F. O'Connor, April 1966, 63 pp. (PB-170-376)\nESSA Technical Memoranda\nWBTM NMC 38 A Summary of the First-Guess Fields Used for Operational Analyses. J. E. McDonell, Feb-\nruary 1967, 17 pp. (AD-810-279)\nWBTM\nNMC 39 Objective Numerical Prediction Out to Six Days Using the Primitive Equation Model-A Test\nCase. A. J. Wagner, May 1967, 19 pp. (PB-174-920)\nWBTM NMC 40 A Snow Index. R. J. Younkin, June 1967, 7 pp. (PB-175-641)\nWBTM NMC 41 Detailed Sounding Analysis and Computer Forecasts of the Lifted Index. John D. Stackpole,\nAugust 1967, 8 pp. (PB-175-928)\nWBTM\nNMC 42 On Analysis and Initialization for the Primitive Forecast Equations. Takashi Nitta and\nJohn B. Hovermale, October 1967, 24 pp. (PB-176-510)\nWBTM\nNMC 43 The Air Pollution Potential Forecast Program. John D. Stackpole, November 1967, 8 pp.\n(PB-176-949)\nWBTM NMC 44 Northern Hemisphere Cloud Cover for Selected Late Fall Seasons Using TIROS Nephanalyses.\nPhilip F. Clapp, December 1968, 11 pp. (PB-186-392)\nWBTM\nNMC\n45\nOn a Certain Type of Integration Error in Numerical Weather Prediction Models. Hans\nOkland, September 1969, 23 pp. (PB-187-795)\nWBTM NMC 46 Noise Analysis of a Limited-Area Fine-Mesh Prediction Model. Joseph P. Gerrity, Jr., and\nRonald D. McPherson, February 1970, 81 pp. (PB-191-188)\nWBTM NMC 47 The National Air Pollution Potential Forecast Program. Edward Gross, May 1970, 28 pp.\n(PB-192-324)\nWBTM\nNMC 48 Recent Studies of Computational Stability. Joseph P. Gerrity, Jr., and Ronald D. McPher-\nson, May 1970, 24 pp. (PB-192-979)\n(Continued on inside back cover)","QC\n851\nU6N5\n66\nno.\nNOAA Technical Memorandum NWS NMC 66\nTHE LFM-II - MODEL -- 1980\nJohn E. Newell and\nDennis G. Deaven\nWashington, D.C.\nSeptember 1981\nCENTRAL\nLIBRARY\nNOV 4\n1981\nN.O.A.A.\nU. s Dept of Company's\nATMOSPHERIC\nAND\nSECURITY\nNOAA\nUNITED STATES\nNational Oceanic and\nNational Weather\nAMOUNT\nDEPARTMENT OF COMMERCE\nAtmospheric Administration\nService\nMalcolm Baldrige, Secretary\nJohn V. Byrne, Administrator\nRichard E. Hallgren, Director\nUS\n81 3417\nOF","CONTENTS\nPage\nAbstract\n1\n1.\nIntroduction\n1\n2.\nThe Grids Used by the Model\n1\n3.\nThe Pressure Gradient Averaging Technique\n2\n4.\nThe Vertical Structure of the LFM-II\n3\n5.\nCalculation of Convective Precipitation\n4\n6.\nLateral Boundary Conditions\n6\n7.1\nPost-Processing the Forecast\n9\n7.2 The Vertical Interpolation from Sigma to Pressure\n9\n7.3\nThe Deslosh Procedure\n11\n7.4 The Filtering of the Forecast\n12\n8.1 Evaluation of the Circulation Forecasts\n12\n8.2 Evaluation of the Precipitation Forecasts\n18\nReferences\n20\nii","THE LFM-II MODEL -- 1980\nJohn E. Newell and Dennis G. Deaven\nNOAA, NWS, National Meteorological Center\nWashington, DC 20233\nABSTRACT. The changes incorporated in the LFM model\nsince the end of 1976 are documented. Emphasis is\nplaced on the computational grids used by the model\nand on its vertical structure. The calculation of\nconvective precipitation and the vertical interpola-\ntion from the model's coordinate to isobaric surfaces\nfor display purposes are treated in detail. The cir-\nculation and precipitation forecasts of the LFM are\nevaluated by presenting monthly values of S1 scores\nand of threat scores for the years 1976 through 1979.\n1. INTRODUCTION\nThe purpose of this NOAA Technical Memorandum is to bring up to\ndate the information contained in the previous documentation of the LFM\nmodel by Gerrity (1977). The description in that work was current as\nof\nthe end of 1976. Since then, some important changes have been made in\nthe procedures used in the limited area forecast system.\nThe previous documentation was quite detailed and the bulk of it is\nstill valid. There is, therefore, no need to repeat it here. Instead,\nwe will focus either on features of the model which were not described\nby Gerrity (1977) or on those aspects of the June 1980 version of the\nLFM which differ from the model as it was at the end of 1976.\n2.\nTHE GRIDS USED BY THE MODEL\nThe LFM forecast is computed on a polar stereographic map projection\ntrue at 60 degrees north latitude. Two distinct grids, covering exactly\nthe same geographical area of the globe, are used by the model. The\nfirst of these is the LFM-I grid, an array consisting of 53 columns\nalong the I-axis and 45 rows along the J-axis for a total of 2385 grid-\npoints. The second grid is the LFM-II grid in which I ranges from 1 to\n79 and J from 1 to 67, a total of 5293 points.\nThe grid spacing of the LFM-I grid is 190.5 km at 60 degrees north\nlatitude, while that of the LFM-II is exactly two thirds of this value,\nor 127.0 km. Essentially, each two grid intervals of LFM-I are replaced\nby three of LFM-II. The coordinates of the two grids are related by the\nformulas\n3\nI2 (I1 - 1) + 1\n(2.1)\n1","U2 = 2 (J1 - 1) + 1\n(2.2)\nThe analyses prepared for the LFM model are contained on the LFM-I\ngrid. When they are read into the computer by the model initialization\ncode, they are immediately interpolated biquadratically to the LFM-II\ngrid so that the initialization process itself is carried out on the\nfiner mesh grid, as is the complete forecast calculation. The post-\nprocessing section of the LFM model, which prepares the calculation for\ndisplay at six-hour intervals, is performed on the LFM-II grid. As a\nfinal step, those fields selected for display are interpolated to the\nLFM-I grid for processing by graphics and other output programs.\nThe rationale for having the analyses and the display on the LFM-I\ngrid is flexibility and economy of programming. The motivation for\ncomputing the initialization and the forecast on the LFM-II grid is to\ngain the greatest possible accuracy within the limits imposed by the\navailable resources.\n3.\nTHE PRESSURE GRADIENT AVERAGING TECHNIQUE\nWhen the LFM-I was converted to LFM-II, it was not necessary to\nreduce the time step despite the reduction in mesh length. This is so\nbecause of the introduction of an economical time integration scheme\nwhich has been discussed by Shuman (1971) and by Brown and Campana (1978).\nThe essential feature of this method is that the pressure gradient\nterm is not evaluated at a single time level, but rather is represented\nby a time-averaged value. If we let denote the pressure gradient\nterm in the tendency equation for the u-component of the wind, then\nX\nis evaluated as\n+\n(3.1)\nwith a similar expression for Here I denotes the time level at\nwhich the quantity is to be evaluated and a is a real number.\nUse of pressure gradient averaging allows for a timestep increment\nup to twice as large as that used in the conventional leapfrog time-\ndifferencing scheme. However, in order to control computational modes\nwhich amplify as powers of the time, the model employs time-smoothing\nof the predicted quantities. The use of the time damping results in a\nreduction of the maximum allowable time increment to a value somewhat\nless than twice that of the usual leapfrog scheme.\nThe time smoothing of a forecast variable, u for example, can be\nwritten as\n+ +\n(3.2)\n2","where the asterisk subscript refers to an intermediate value and the\nabsence of it refers to the time-smoothed value. The quantity b is a\ndamping coefficient. As shown by Brown and Campana (1978), , for a given\nchoice of b, there is a value of a in equation (3.1), which affords the\nmaximum stable time step. This optimum value of a, namely aMAX, is\nrelated to the time filter coefficient by\n/4\n(3.3)\nIn the current LFM-II, b is given a value of 0.075 and a is computed\nfrom equation (3.3).\n4.\nTHE VERTICAL STRUCTURE OF THE LFM\nThe model is divided into three distinct domains in the vertical.\nThese are the boundary layer, the tropospheric and the stratospheric\ndomains. The vertical coordinate used in the model is a modification\nof the sigma system of Phillips (1957). Sigma is a dimensionless number\ndefined as the ratio of two pressures.\nIn the boundary layer domain, sigma is given by\np - (PG - PB)\n(4.1)\nwhere P is the pressure at some level in the boundary layer, PG is the\npressure at the ground and PB is a constant (50 mb) representing the\nfixed depth of the boundary layer.\nIn the tropospheric domain, sigma is written as\n(4.2)\nwhere P is an arbitrary pressure level in the troposphere and PT is the\ntropopause pressure.\nIn the stratospheric domain, sigma is defined by\n(4.3)\nwhere P is an arbitrary pressure level in the stratosphere and P50\nrepresents the constant value of the 50 mb isobaric surface, which is\ntaken as the top of the model.\n3","Note that in each domain O varies from a value of 0 at the top\n(lower pressure) to a value of 1 at the bottom (higher pressure). The\nstratosphere is divided into three layers, each of pressure thickness\nequal to (PT - P50)/3. The troposphere is also divided into three\nlayers, each of pressure thickness (PG - PB - PT)/3. With the addition\nof the boundary layer, the model is appropriately termed the 7-layer\nLFM. Wind and temperature are predicted in each of the layers, while\nprecipitable water is forecast in the three lowest layers.\nThe ground surface, the tropopause and the 50 mb level are considered\nto be material surfaces, with the result that the vertical velocity, &,\nvanishes at those levels. Elsewhere, & is computed diagnostically at the\ninterface between each of the model layers.\nThe vertical structure of the model is indicated in Figure 1. The\nsolid lines are called sigma levels or sigma surfaces and mark the upper\nand lower boundaries of the layers. The dashed lines represent the mid-\npoint of the layers. The predicted values of wind component, u and V,\npotential temperature, 0, and moisture, RH, are considered to be carried\nin the middle of the layers. The height, Z, and vertical velocity, 8,\nare computed diagnostically and are located at the sigma levels.\n5.\nCALCULATION OF CONVECTIVE PRECIPITATION\nBecause moisture is carried in only three layers of the present\nversion of the LFM model, the scheme for the parameterization of con-\nvection can only crudely approximate atmospheric convective processes.\nThe algorithm is applied layer by layer, starting in the boundary layer\nand working upward at each column of grid points. Convective precipita-\ntion is computed once an hour (every ninth timestep) in order to conserve\ncomputer resources.\nThe algorithm is presented in the flow chart following this section,\nin which the index k refers to the model layer under consideration. As\nshown in the flow diagram, there are four tests applied to the layer to\ndetermine the occurrence of convection. These are:\n1. The mean relative humidity in the layer must be at least 75\npercent.\n2. There must be convergence of precipitable water, W, into the layer\nas measured by a positive tendency in W.\n3. The pressure of the lifting condensation level of a parcel origin-\nating at the midpoint of layer k must be greater than the pressure at the\nmidpoint of layer (k + 1).\n4. When lifted to the midpoint of layer (k + 1), the parcel must\nbe warmer than its environment.\n4","78, 08\np = P50\nu7, V7, 07\nZ7, 87\nu6, V6, 06\n26, 86\nu5, V5, 05\nZ5, 85\np = PT\n04\nu4,\nV4,\nZ4, 84\nu3, V3, O3, RH3\nZ3, 83\nV2, O2, RH2\nU2,\n22, 82\np = PG - PB\nu1, V1, 01, RH1\n21, 81\np = PG\nFigure 1. Vertical Structure of the LFM-II Model.\n5","When all the conditions for convection are satisfied, an amount of\nprecipitation attributed to convection is computed from the formula\nCNRAIN = AO Cp D p k+1\nk+1\n(5.1)\ngL\nwhere DO is the difference between the temperature of the parcel lifted,\nfirst dry and then moist adiabatically, to the midpoint of layer (k + 1)\nand the temperature of the environment at that level, cp is the specific\nheat of dry air at constant pressure, AP k+1 is the pressure thickness of\nlayer (k + 1), , II k+1 is the value of the Exner function at the midpoint\nof layer (k + 1), g is the acceleration of gravity and L is the latent\nheat of vaporization or condensation. The precipitable water in layer\nk\nis reduced by an amount equal to CNRAIN. In addition, the potential\ntemperature of layer (k + 1) is increased by an amount so. This aspect\nof the scheme was designed to simulate convective pumping of heat aloft\nin cumulus clouds. Also, it should be noted in the flow chart that the\ntemperature of layer k is increased by 2 degrees Kelvin prior to computing\nthe pressure of the LCL. This is done to simulate large scale lifting by\nenhancing the buoyancy.\n6.\nLATERAL BOUNDARY CONDITIONS\nThe five outermost grid rows surrounding the LFM forecast area form\nthe lateral boundary region. Values for the specification of the time-\ndependent lateral boundaries of the LFM are obtained from a large-scale\n(hemispheric or global) forecast made twelve hours earlier. The large-\nscale prediction from 12 to 60 hours, at six-hour intervals, is used to\ndetermine large-scale tendencies at the boundary zone grid points.\nThe first step in this procedure is the horizontal interpolation of\nforecast isobaric fields of wind, height, temperature, and tropopause\npressure from the grid points of the large-scale model to those of the LFM\nboundary region. A vertical interpolation is then done at the LFM points\nfrom the isobaric values to the sigma system of the 7-1ayer LFM. The\nvertical interpolation uses the same techniques employed in the initializa-\ntion section of the model and yields values of wind and potential temperature\nin each of the layers, and of the pressure thickness of the troposphere and\nstratosphere. Next, the sigma layer values are time-differenced to form\nsix-hour tendencies, which are then scaled to the timestep used by the LFM.\nFinally, large-scale values of wind, temperature, and pressure thickness at\npoints of the boundary region are obtained at each timestep by adding the\nscaled tendency to the LFM model's initial values.\nAt the outermost row of grid points, these large-scale values are used\nat each timestep without modification. At the next four inner rows (rows\n2 through 5) a diffusive \"nudge\" in the form of:\nT\nTHE T+1 T-1 + 2 At at LFM\n+ K 2 T-1\n(6.1)\n6","Convective Precipitation Flow Chart\nStart\nk = 0\nA\nk = k + 1\nIs k > 3?\nend\nyes\nno\nIs the relative humidity of layer k All 75 per cent?\nno\nyes\nIs WW/at > 0?\nno\nyes\nAdd 2 degrees Kelvin to the temperature of layer k and\ncalculate the pressure, PCL, and the temperature, TCL,\nat the lifting condensation level, LCL.\nIs PCL > the pressure at the midpoint of layer (k + 1)?\nno\nyes\n7","Calculate the saturation vapor pressure at the temperature TCL\nCalculate the pseudo-equivalent potential temperature EE\nof a parcel in layer k lifted to the LCL dry adiabatically.\nCalculate the potential temperature 1 corresponding\nto OF at the midpoint pressure of layer (k+1).\nAO = 1 - 0k+1\nIs so > 0.1?\nno\nyes\nCalculate convective rain, CNRAIN, as shown by equation (5.1).\nAdd CNRAIN to total precipitation.\nkk1 = 0 k+1 + AO\nWk = Wk - CNRAIN\ngo to A\n8","is used to modify the LFM grid point values. Here 0 represents a prognostic\nvariable, the superscript I denotes the timestep index, the subscript LFM\ndenotes a value obtained from the model equations and the subscript LS\nrefers to the large-scale value.\nThe finite form of the Laplacian operator is defined by:\nV2QI,J + 1,J+1 + I,J-1 401,J\n(6.2)\nand the value of the diffusion coefficient, K, is fixed at 0.04 in the\nboundary region. Note that all space and time scales have been absorbed\nin the value of K and the finite form of the Laplacian. This procedure is\napplied during each timestep of the model's integration to all prognostic\nvariables except precipitable water which is kept constant on the boundary.\nIf a large-scale forecast is not available, then LFM grid points on the\noutermost row are kept fixed at their initial values during the integration\nand the contribution of the large-scale model to the Laplacian in Equation\n(6.1) is set equal to zero. This procedure produces a constant boundary\ncondition with increased diffusion in the boundary zone.\n7.1 Post-Processing the Forecast\nAt six-hour intervals after initial time the forecast calculations\nare interpolated vertically from the sigma-coordinate system to standard\nisobaric levels and then are filtered horizontally for display and\ntransmission to users. This procedure is known as post-processing and\nits principal steps will be described in the next three sections.\n7.2 The Vertical Interpolation from Sigma to Pressure\nThe pressure at each of the sigma levels shown in Figure 1 is obtained\nby using the forecast values of pressure thickness in the stratospheric\nand tropospheric domains and integrating downward from the top of the model\nat 50 mb to the earth's surface. Values of the Exner function and of the\nlogarithm of pressure are computed from the pressure at the sigma levels.\nA value of the Exner function in the middle of each layer is calculated\nfrom the values on the sigma levels, and from this a value of the logarithm\nof pressure in the middle of the layer is determined.\nThe absolute temperature, T, at sigma levels other than the tropopause\nis defined by modeling T linear in logarithm of pressure. The height, z,\nof each sigma surface is computed by integrating upward from the ground,\nusing the forecast pressure-temperature profile in the vertical.\nTemperature, T, at the tropopause is obtained as a weighted mean of\na value, TA, extrapolated from above the tropopause, and a value, TB,\nextrapolated from below. The extrapolation is done by modeling T linear\nin pressure. Using the vertical indexing scheme shown in Figure 1, TA and\nTB can be written as:\n9","TA=15 T5-0.5T6 =\n(7.1)\nTB= 15T4-0.5T3\nIt is convenient to define some additional quantities.\na = (PT - P50) /3\n(7.2)\nB=26\nThe value of tropopause temperature, T*, is computed as\nT*(aTB+BTA)/2\n(7.3)\nThe wind components (u*, v*) at the tropopause level are computed using\nthe same procedure employed for temperature.\nTemperature, wind, and relative humidity at standard isobaric levels\nare computed using the values in the sigma layers. It is assumed that\neach of these quantities varies linearly in the log of pressure.\nFor isobaric levels located above ground, the height is computed\nhydrostatically from the values of height on the sigma surfaces and the\nknown vertical distribution of temperature. T is modeled linear in log\nof pressure.\nAt gridpoints where a desired isobaric level lies below the ground,\nthe height of that level is computed using a technique designed to simulate,\nat least in part, the method employed at observing stations to reduce\nthe measured station pressure to a value of sea-level pressure. Using\nthe symbols of Figure 1 we define\n0.5 (Z2 + Z3)\n(7.4)\n-\nTSLT+0.0065 21\nIf TSL is less than or equal to 290.66K, the height of the isobaric\nlevel is given as\n(7.5)\n=\n10","where R is the gas constant for pure dry air, g the gravitational accelera-\ntion, Z1 the height of the model's terrain, PG the pressure at the surface\nof the earth, and p the value of the isobaric level. Basically, T2 has\nbeen extrapolated downward at a lapse rate of 0.0065K per meter to define\nT*, the ground temperature, and TSL, the temperature at sea-level. If\nTSL exceeds 290.66K and if T* is less than or equal to 290.66, then\nTSL is set equal to 290.66 in equation (7.5). If T* exceeds 290.66,\nthen TSL is redefined as\nTsp = 290.66 - 0.005 - (Tx - 290.66)\n(7.6)\nfor use in (7.5).\n7.3 The Deslosh Procedure\nThe isobaric height fields are subjected to a procedure known as\n\"desloshing\". The relative vorticity at 500 mb is computed from the\nwind components at that level, with m denoting the map factor.\n(7.7)\nA stream function, 4, is then obtained from the known values of vorticity\nby applying a relaxation procedure to the equation\n2 4 = 5\n(7.8)\nThe stream function field is used in the inverse form of the balance\nequation to obtain Z500, where the superscript D indicates that the\nheight field has been desloshed. The original hydrostatic height field,\nZ500, is subtracted from Z500 to obtain the value of the deslosh\nat each point.\n(7.9)\nThe deslosh field is then added to each isobaric hydrostatic height to\nobtain the desloshed height field for that level\nZD==HH+D\n(7.10)\nIn equation (7.7) the relative vorticity, 5, is computed only for\ninterior points. On the boundary it is set to zero. A scaled value of\nZ500 is used as the boundary condition on 4 in (7.8), and in the inverse\nform of the balance equation Z500 is used as the boundary condition in\nD\nobtaining Z500. Essentially, the deslosh procedure preserves the value\nof on the boundary at all levels. It adjusts interior values of\nZ500 to fit the boundary values and the forecast 500 mb vorticity at\ninterior points. Finally, it preserves the original thickness between\nthe 500 mb level and all other isobaric levels.\n11","7.4 The Filtering of the Forecast\nAfter completion of the vertical interpolation from sigma to pressure\nand after the desloshing of the heights, all forecast fields are filtered\non the LFM-II grid. A bilinear interpolation is then used to obtain\nvalues on the LFM-I grid. After interpolation to the LFM-I grid, most\nfields are again filtered. The only output quantities which are not filtered\non the LFM-I grid are: precipitation amount, surface pressure, precipitable\nwater, boundary layer potential temperature and wind components, tropo-\npause temperature and wind components, and the vertical speed shear at\nthe tropopause. It is the values on the LFM-I grid which are used as\nthe official forecast.\n8.1 Evaluation of the Circulation Forecasts\nTables 8.1.1 through 8.1.8 present monthly S1 scores for 500 mb\nheight and sea-level-pressure forecasts from the LFM model for the period\n1976 to 1979. The S1 scores were computed using a forty-nine point\nlatitude-longitude grid centered over the United States. The gridpoint\nspacing is five degrees latitude by ten degrees longitude. The verifying\nanalysis is the LFM analysis. All LFM forecasts were used in computing\nthe results in the tables.\nOn 31 August 1977 LFM-II replaced LFM-I as the operational limited-\narea model. It is interesting to examine the tables of S1 scores to see\nwhether the change of model is reflected there. It is our view that the\nS1 scores for the 500 mb height forecasts do not offer convincing evidence\nof change in the quality of the predictions at that level. However, the\nfigures for the sea level pressure forecasts indicate an improved skill\n(lower S1 score) during the last two years. We believe that some of this\nchange is due to the finer resolution of LFM-II. The improvement is\nevident at sea level but not at 500 mb because of the difference in\nscale of the circulation features at the two levels.\nTable 8.1.9 contains S1 scores for the LFM 500 mb forecast heights\nfor 1979 for separate western and eastern grids. The superiority of\nthe eastern predictions over the western is clear. The western area\nforecasts are degraded more quickly because of the nearness of the up-\nstream boundaries and the upstream sparse data area.\n12","Table 8.1.1\nS1 SCORES FOR 12-HOUR 500 MB FORECAST FROM\nTHE LFM MODEL\n1976\n1977\n1978\n1979\nJan\n16\n17\n18\n17\n16\n17\n19\n17\nFeb\n16\n18\n17\n19\nMar\nApr\n21\n18\n20\n18\n20\n20\n25\n21\nMay\n22\n23\n22\n20\nJun\n22\n24\nJul\n23\n21\n22\n20\n21\n22\nAug\n21\n21\n20\nSep\n21\n18\n19\n18\n20\nOct\n16\n18\n17\n18\nNov\nDec\n15\n18\n16\n18\n19\n20\n20\nAverage\n19\nTable 8.1.2\nS1 SCORES FOR 24-HOUR 500 MB FORECASTS FROM\nTHE LFM MODEL\n1976\n1977\n1978\n1979\n23\n24\n24\n24\nJan\n21\n24\n25\n22\nFeb\n22\n24\n23\n24\nMar\n28\n23\n26\n24\nApr\n27\n26\n26\n27\nMay\n25\n28\n28\n27\nJun\n26\n28\nJul\n28\n26\n28\n24\n25\n26\nAug\n25\n26\n26\n25\nSep\n24\n25\n22\n25\nOct\n22\n23\n23\n24\nNov\n20\n24\n22\n24\nDec\n25\n25\n25\n25\nAverage\n13","Table 8.1.3\nS1 SCORES FOR 36-HOUR 500 MB FORECASTS FROM\nTHE LFM MODEL\n1976\n1977\n1978\n1979\nJan\n31\n32\n32\n31\n28\nFeb\n31\n32\n28\n29\n30\n30\nMar\n31\n36\n29\n33\n31\nApr\nMay\n35\n33\n35\n34\n-\nJun\n36\n35\n32\n31\nJul\n35\n32\n32\n34\n35\n31\n31\n32\nAug\nSep\n33\n33\n33\n31\nOct\n31\n31\n28\n31\nNov\n29\n30\n29\n30\nDec\n27\n31\n29\n31\nAverage\n32\n32\n31\n31\nTable 8.1.4\nS1 SCORES FOR 48-HOUR 500 MB FORECASTS FROM\nTHE LFM MODEL\n1976\n1977\n1978\n1979\nJan\n38\n39\n38\n36\n37\n38\n34\nFeb\n34\n37\nMar\n36\n39\nApr\n46\n35\n42\n37\nMay\n42\n41\n41\n40\nJun\n43\n42\n38\n37\nJul\n42\n36\n37\n39\n42\n36\n37\nAug\n37\nSep\n39\n39\n40\n36\n38\n36\n33\n37\nOct\nNov\n36\n38\n35\n36\n33\n39\n34\n37\nDec\nAverage\n39\n38\n38\n37\n14","Table 8.1.5\nS1 SCORES FOR 12-HOUR SEA LEVEL PRESSURE FORECASTS\nFROM THE LFM MODEL\n1976\n1977\n1978\n1979\n36\n38\n38\n35\nJan\n40\n36\n35\n34\nFeb\n38\n35\n34\n34\nMar\n39\n37\n33\n37\nApr\n37\n39\n39\n35\nMay\n40\n38\n35\n36\nJun\n41\n39\n36\n36\nJul\n41\n40\n35\n38\nAug\n34\n42\n39\n35\nSep\n37\n37\n33\n35\nOct\n35\n35\n38\n40\nNov\n36\n34\n38\n38\nDec\n39\n38\n35\n35\nAverage\nTable 8.1.6\nS1 SCORES FOR 24-HOUR SEA LEVEL PRESSURE FORECASTS\nFROM THE LFM MODEL\n1979\n1976\n1977\n1978\n44\n45\n46\n42\nJan\n44\n42\n47\n45\nFeb\n41\n41\n45\n42\nMar\n45\n44\n39\n44\nApr\n43\n45\n45\n42\nMay\n42\n47\n46\n41\nJun\n42\n42\n47\n44\nJul\n42\n43\n47\n45\nAug\n40\n47\n45\n43\nSep\n41\n42\n40\n39\nOct\n43\n42\n44\n46\nNov\n43\n41\n44\n46\nDec\n42\n42\n45\n45\nAverage\n15","Table 8.1.7\nS1 SCORES FOR 36-HOUR SEA LEVEL PRESSURE FORECASTS\nFROM THE LFM MODEL\n1976\n1977\n1978\n1979\nJan\n54\n53\n50\n51\nFeb\n55\n54\n51\n49\n52\n50\n51\n47\nMar\n52\n52\n47\n53\nApr\n52\n54\n50\n51\nMay\n49\nJun\n55\n55\n49\nJul\n54\n53\n50\n51\n54\n49\n52\nAug\n52\nSep\n53\n51\n54\n48\n49\n46\n46\n49\nOct\nNov\n51\n54\n49\n49\nDec\n52\n55\n50\n49\n53\n52\n50\n50\nAverage\nTable 8.1.8\nS1 SCORES FOR 48-HOUR SEA LEVEL PRESSURE FORECASTS\nFROM THE\nLFM MODEL\n1976\n1977\n1978\n1979\nJan\n62\n58\n57\n63\n62\nFeb\n58\n55\n57\n57\n57\nMar\n54\n60\n58\n53\nApr\n60\n59\n62\nMay\n58\n58\n60\n61\nJun\n55\n57\nJul\n58\n58\n54\n56\n60\n57\n54\nAug\n58\nSep\n61\n58\n60\n53\n57\n50\nOct\n50\n55\nNov\n58\n61\n56\n56\nDec\n59\n62\n56\n56\nAverage\n59\n59\n56\n56\n16","Table 8.1.9\nS1 SCORES FOR THE LFM-II 500 MB FORECASTS FOR THE YEAR 1979\nOVER THE WESTERN (W) AND EASTERN (E) GRIDS. WEST IS THE AREA\nBETWEEN 105W AND 145W, 25N AND 55N. EAST IS THE AREA BETWEEN\n65W AND 105W, 25N AND 55N.\n12-HR\n24-HR\n36-HR\n48-HR\nW\nE\nW\nE\nW\nE\nW\nE\n44\nJan\n23\n16\n29\n20\n37\n27\n32\nFeb\n19\n15\n26\n17\n32\n23\n38\n27\nMar\n22\n16\n28\n20\n37\n27\n44\n34\n27\n40\n34\nApr\n22\n16\n28\n21\n34\nMay\n23\n19\n30\n23\n37\n30\n43\n36\nJun\n25\n19\n29\n23\n35\n29\n40\n35\nJul\n26\n22\n32\n26\n38\n32\n43\n37\n28\n19\n32\n22\n37\n28\n42\n32\nAug\n31\nSep\n25\n17\n20\n37\n26\n43\n31\n24\n17\n30\n21\n35\n26\n41\n32\nOct\nNov\n23\n15\n29\n19\n35\n25\n41\n32\n22\n15\n29\n20\n36\n26\n42\n33\nDec\nAverage\n24\n17\n30\n21\n36\n27\n42\n33\n17","8.2 Evaluation of the Precipitation Forecasts\nTables 8.2.1 and 8.2.2 present monthly results from the verification\nof the LFM precipitation forecasts. The figures are based on the occur-\nrence of 0.01 inch of liquid precipitation in a twelve-hour period at\nmembers of a sixty station network located over the United States and\nsouthern Canada.\nIf the model predicts 0.01 inch or more in a given twelve-hour\nperiod and if 0.01 inch or more is observed at the reporting station,\nthen this forecast is counted as correct. The threat score, TS, is\ncomputed as\n100 C\n(8.2.1)\nTS FF+R- = C\nwhere C is the number of stations correct, F is the number forecast\nto have 0.01 inch or more and R is the number reporting at least that\namount. The bias, B, is computed as\nF\nB = R\n(8.2.2)\nand is a convenient measure of the tendency of the model to forecast\ntoo small or too large an area of significant precipitation.\nBoth tables 8.2.1 and 8.2.2 show a trend of improvement (higher\nthreat scores) over the four-year period. As with the S1 scores for the\nsea-level pressure forecasts, we attribute some of this change to the\nintroduction of LFM-II on the last day of August 1977. It is considered\ntoo early to judge the impact of the convective precipitation scheme\nintroduced in June 1979.\n18","Table 8.2.1\n12-24 HOUR LFM PRECIPITATION FORECAST\nBIAS (B) AND THREAT SCORE (TS)\n1976\n1977\n1978\n1979\nB\nTS\nB\nTS\nB\nTS\nB\nTS\nJan\n0.92\n39\n1.02\n43\n0.86\n48\n0.88\n49\n41\n36\n0.83\n38\n0.99\n46\nFeb\n1.02\n1.06\n41\n47\n0.89\n42\n1.07\n45\nMar\n0.93\n1.32\n0.92\n37\n1.07\n43\n1.06\n43\n1.07\n43\nApr\n0.83\n38\n1.09\n29\n0.98\n45\n0.95\n42\nMay\n32\nJun\n0.89\n27\n0.80\n26\n1.01\n1.15\n34\nJul\n0.90\n25\n1.10\n27\n1.19\n29\n1.16\n31\n28\n1.24\n33\n0.88\n28\nAug\n1.04\n25\n1.14\nSep\n1.23\n34\n1.14\n35\n1.22\n37\n1.18\n43\nOct\n1.04\n46\n1.12\n40\n0.84\n29\n1.05\n41\nNov\n0.95\n35\n1.15\n43\n0.94\n44\n1.12\n50\nDec\n0.82\n37\n1.04\n42\n1.03\n42\n1.14\n48\n0.96\n35\n37\n1.01\n39\n1.05\n42\nAverage\n1.09\nTable 8.2.2\n24-36 HOUR LFM PRECIPITATION FORECAST\nBIAS (B) AND THREAT SCORE (TS)\n1976\n1977\n1978\n1979\nB\nTS\nB\nTS\nB\nTS\nB\nTS\n0.96\n43\n0.91\n43\n0.99\n30\n1.16\n36\nJan\n34\n1.24\n32\n0.86\n34\n1.10\n40\nFeb\n1.16\n39\n1.03\n38\n1.12\n42\n1.04\n38\n1.41\nMar\n32\n1.16\n38\n1.16\n39\n1.15\n40\nApr\n1.10\n39\n1.00\n35\n0.96\n32\n1.24\n28\n1.02\nMay\n27\n1.03\n32\n1.05\n22\n0.85\n26\n0.91\nJun\n1.00\n28\n1.02\n29\nJul\n1.15\n21\n1.16\n26\n24\n1.17\n28\n1.09\n26\n0.76\n29\n1.29\nAug\n1.09\n1.28\n31\n33\n1.12\n34\n1.04\n40\nSep\n1.00\n34\n1.05\n39\n1.14\n35\n0.79\n26\nOct\n42\n1.13\n45\n1.09\n28\n1.26\n39\n1.04\nNov\n41\n1.16\n39\n1.01\n31\n1.15\n39\n1.12\nDec\n1.17\n33\n1.01\n35\n1.04\n37\n1.10\n30\nAverage\n19","REFERENCES\nBrown, J. A. and K. A. Campana, 1978: An Economical Time-Differencing\nSystem for Numerical Weather Prediction. Monthly Weather Review,\n106, 1125-1136.\nGerrity, J. P. , 1977: The LFM Model--1976: A Documentation. NOAA\nTechnical Memorandum NWS NMC 60.\nPhillips, N. A., , 1957: A Coordinate System Having Some Special Advantages\nfor Numerical Forecasting. Journal of Meteorology, 14, 184-185.\nShuman, F. G. 1971: Resuscitation of an Integration Procedure.\nNMC Office Note 54, 55 pp.\n20","(Continued from inside front cover)\nNOAA Technical Memorandums\nA Study of Non-Linear Computational Instability for a Two-Dimensional Model. Paul D.\nNWS NMC 49\nPolger, February 1971, 22 pp. (COM-71-00246)\nRecent Research in Numerical Methods at the National Meteorological Center. Ronald D.\nNWS NMC 50\nMcPherson, April 1971, 35 pp. (COM-71-00595)\nUpdating Asynoptic Data for Use in Objective Analysis. Armand J. Desmarais, December\nNWS NMC 51\n1972, 19 pp. (COM-73-10078)\nFinger\nNWS NMC 52\nToward Developing a Quality Control System for Rawinsonde Reports. Frederick\nG.\nand Arthur R. Thomas, February 1973, 28 pp. (COM-73-10673)\nA Semi-Implicit Version of the Shuman-Hovermale Model. Joseph P. Gerrity, Jr., Ronald D.\nNWS NMC 53\nMcPherson, and Stephen Scolnik, July 1973, 44 pp. (COM-73-11323)\nNWS NMC 54\nStatus Report on a Semi-Implicit Version of the Shuman-Hovermale Model. Kenneth Campana,\nMarch 1974, 22 pp. (COM-74-11096/AS)\nAn Evaluation of the National Meteorological Center's Experimental Boundary Layer model.\nNWS NMC 55\nPaul D. Polger, December 1974, 16 pp. (COM-75-10267/AS)\nTheoretical and Experimental Comparison of Selected Time Integration Methods Applied to\nNWS NMC 56\nFour-Dimensional Data Assimilation. Ronald D. McPherson and Robert E. Kistler, April\n1975, 62 pp. (COM-75-10882/AS)\nA Test of the Impact of NOAA-2 VTPR Soundings on Operational Analyses and Forecasts.\nNWS NMC 57\nWilliam D. Bonner, Paul L. Lemar, Robert J. Van Haaren, Armand J. Desmarais, and Hugh M.\nO'Neil, February 1976, 43 pp. (PB-256-075)\nOperational-Type Analyses Derived Without Radiosonde Data from NIMBUS 5 and NOAA 2 Temp-\nNWS NMC 58\nerature Soundings. William D. Bonner, Robert van Haaren, and Christopher M. Hayden, March\n1976, 17 pp. (PB-256-099)\nDecomposition of a Wind Field on the Sphere. Clifford H. Dey and John A. Brown, Jr.\nNWS NMC 59\nApril 1976, 13 pp. (PB-265-422)\nThe LFM Model 1976: A Documentation. Joseph P. Gerrity, Jr., December 1977, 68 pp. (PB-\nNWS NMC 60\n279-419)\nSemi-Implicit Higher Order Version of the Shuman-Hovermale Model. Kenneth A. Campana,\nNWS NMC 61\nApril 1978, 55 pp. (PB-286-012)\nAddition of Orography to the Semi-Implicit Version of the Shuman-Hovermale Model. Kenneth\nNWS NMC 62\nA. Campana, April 1978, 17 pp. (PB-286-009)\nDay-Night Differences in Radiosonde Observations in the Stratosphere and Troposphere.\nNWS NMC 63\nRaymond M. McInturff, Frederick G. Finger, Keith W. Johnson, and James D. Laver, September\n1979, 54 pp. (PB80 117989)\nThe Use of Drifting Buoy Data at NMC. David Wright, June 1980, 23 pp. (PB80 220791)\nNWS NMC 64\nEvaluation of TIROS-N Data, January-June 1979. David Wright, June 1980, 21 pp. (PB80\nNWS NMC 65\n220494)","NOAA CENTRAL LIBRARY\nCIRC QC851.U6 N5 no.66\nNewell, John The LFM-II model - 1980\n3 8398 0003 5866 7\nNOAA SCIENTIFIC AND TECHNICAL PUBLICATIONS\nThe National Oceanic and Atmospheric Administration was established as part of the Department of\nCommerce on October 3, 1970. The mission responsibilities of NOAA are to assess the socioeconomic impact\nof natural and technological changes in the environment and to monitor and predict the state of the solid Earth,\nthe oceans and their living resources, the atmosphere, and the space environment of the Earth.\nThe major components of NOAA regularly produce various types of scientific and technical informa-\ntion in the following kinds of publications:\nPROFESSIONAL PAPERS - Important definitive\nTECHNICAL SERVICE PUBLICATIONS - Re-\nresearch results, major techniques, and special inves-\nports containing data, observations, instructions, etc.\ntigations.\nA partial listing includes data serials; prediction and\noutlook periodicals; technical manuals, training pa-\nCONTRACT AND GRANT REPORTS - Reports\npers, planning reports, and information serials; and\nprepared by contractors or grantees under NOAA\nmiscellaneous technical publications.\nsponsorship.\nTECHNICAL REPORTS - Journal quality with\nextensive details, mathematical developments, or data\nATLAS - Presentation of analyzed data generally\nlistings.\nin the form of maps showing distribution of rainfall,\nchemical and physical conditions of oceans and at-\nTECHNICAL MEMORANDUMS - Reports of\nmosphere, distribution of fishes and marine mam-\npreliminary, partial, or negative research or technol-\nmals, ionospheric conditions, etc.\nogy results, interim instructions, and the like.\nAND\nNOAA\nOF\nInformation on availability of NOAA publications can be obtained from:\nENVIRONMENTAL SCIENCE INFORMATION CENTER (D822)\nENVIRONMENTAL DATA AND INFORMATION SERVICE\nNATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION\nU.S. DEPARTMENT OF COMMERCE\n6009 Executive Boulevard\nRockville, MD 20852\nNOAA--S/T 81-121"]}