June 19, 2007June 19, 2007

GRIDDED MOSGRIDDED MOS

• STARTS WITH POINT (STATION) MOSSTARTS WITH POINT (STATION) MOS

– Essentially the same MOS that is in text Essentially the same MOS that is in text bulletinsbulletins

– Number and type of stations differ for Number and type of stations differ for different weather elementsdifferent weather elements

June 19, 2007June 19, 2007

Elements

MOS Stations available to analysisMETAR

•Probability of Precipitation

•QPF

June 19, 2007June 19, 2007

•Sky Cover

•Wind Gusts

MOS Stations available to analysisMETAR, Marine

Elements

June 19, 2007June 19, 2007

•Wind Direction

•Wind Speed

•2-m Temperature

•2-m Dew Point

•Relative Humidity

MOS Stations available to analysisMETAR, Marine, Mesonet

Elements

June 19, 2007June 19, 2007

MOS Stations available to analysisMETAR, Marine, Mesonet, COOP, RFC

•Daytime Maximum Temperature

•Nighttime Minimum Temperature

Elements

June 19, 2007June 19, 2007

TWO METHODS OF TWO METHODS OF PROVIDING GRIDDED MOSPROVIDING GRIDDED MOS

• Develop in such a way that forecasts can Develop in such a way that forecasts can be produced directly at gridpointsbe produced directly at gridpoints

– Regional Operator Equations (RO)Regional Operator Equations (RO)– Generalized Operator Equations (GO) - (One big region)Generalized Operator Equations (GO) - (One big region)– RO and GO forecasts not as accurate as single stationRO and GO forecasts not as accurate as single station– RO equations applied to a fine scale grid produce RO equations applied to a fine scale grid produce

discontinuities between regionsdiscontinuities between regions• Develop for and apply at stations, and grid Develop for and apply at stations, and grid

themthem

– Successive Correction analysis (e.g., Cressman, Barnes)Successive Correction analysis (e.g., Cressman, Barnes)– Relatively simple and fastRelatively simple and fast– Details of application vary with weather elementDetails of application vary with weather element– One or more passes over data, correcting the “current” One or more passes over data, correcting the “current”

grid by an amount determined by the difference between grid by an amount determined by the difference between the analysis and the forecastthe analysis and the forecast

June 19, 2007June 19, 2007

SUCCESSIVE CORRECTION SUCCESSIVE CORRECTION

• Start with first guessStart with first guess

– Can be a constant (generally doesn’t matter what Can be a constant (generally doesn’t matter what constant, except for error checking (e.g., a specified constant, except for error checking (e.g., a specified constant or the average of all values to be analyzed), or constant or the average of all values to be analyzed), or can be, for instance, a similar model fieldcan be, for instance, a similar model field

– Current analysis value at a station determined by Current analysis value at a station determined by interpolation (bilinear)interpolation (bilinear)

– Difference between current analysis and forecast, with Difference between current analysis and forecast, with possibly an elevation correction, determines correction possibly an elevation correction, determines correction at nearby gridpoints within a radius of influence R at nearby gridpoints within a radius of influence R according to one of three algorithmsaccording to one of three algorithms

– R varies by passR varies by pass

• Approximately 35 to 40 on first pass and 15 to 20 on Approximately 35 to 40 on first pass and 15 to 20 on last passlast pass

June 19, 2007June 19, 2007

CORRECTION METHODS CORRECTION METHODS

•3 Possible types of correction for 3 Possible types of correction for each gridpointeach gridpoint

– 1) Average contribution from all stations 1) Average contribution from all stations – 2 Weight contributions from all stations 2 Weight contributions from all stations

by distance between station and by distance between station and gridpointgridpoint

– 3) Same as 2), except divide sum by 3) Same as 2), except divide sum by sum of weightssum of weights

• No. 3 used almost exclusivelyNo. 3 used almost exclusively

June 19, 2007June 19, 2007

SMOOTHING ALGORITHMSMOOTHING ALGORITHM• Basic methodBasic method

– Average the point to be smoothed with average of the Average the point to be smoothed with average of the surrounding 4 (or 8) points, weighting the average by a surrounding 4 (or 8) points, weighting the average by a specified factorspecified factor

• Terrain-FollowingTerrain-Following– Smoothing is not done across significant valleys and Smoothing is not done across significant valleys and

ridges (> 100 m elevation difference across the ridges (> 100 m elevation difference across the valley or ridgevalley or ridge

– Smoothing across an island or spit of land is not doneSmoothing across an island or spit of land is not done– Only land points involved in smoothing of land gridpointsOnly land points involved in smoothing of land gridpoints– Only water points involved in smoothing of water Only water points involved in smoothing of water

gridpointsgridpoints– High and low values for the forecasts can be smoothed High and low values for the forecasts can be smoothed

or not with either 5- or 9-point smoother, depending on or not with either 5- or 9-point smoother, depending on weather element and terrain differences.weather element and terrain differences.

June 19, 2007June 19, 2007

ELEVATION ADJUSTMENT ELEVATION ADJUSTMENT • Based on average lapse rate at pairs of Based on average lapse rate at pairs of

stationsstations

– Each station has a list of 60 to 100 neighboring stations Each station has a list of 60 to 100 neighboring stations that are close in horizontal distance but far apart in that are close in horizontal distance but far apart in elevationelevation

– Neighboring stations determined by preprocessing the Neighboring stations determined by preprocessing the metadata and remain the same for all analysesmetadata and remain the same for all analyses

– When analyzing, many of these neighbors may be When analyzing, many of these neighbors may be missing, so lapse rate may not be calculated if too few missing, so lapse rate may not be calculated if too few neighborsneighbors

– Lapse rate for each station is the sum of all forecast Lapse rate for each station is the sum of all forecast differences divided by the sum of elevation differencesdifferences divided by the sum of elevation differences

• Pair always > 130 m separation in the verticalPair always > 130 m separation in the vertical• Pair may be up to 337.5 km away Pair may be up to 337.5 km away

June 19, 2007June 19, 2007

ELEVATION ADJUSTMENT ELEVATION ADJUSTMENT

• Strength of elevation adjustment Strength of elevation adjustment varies by passvaries by pass– Generally full adjustment on Pass 1, with Generally full adjustment on Pass 1, with

lesser on following passeslesser on following passes– Last pass may have no adjustmentLast pass may have no adjustment– Adjustment can be both up and down, or Adjustment can be both up and down, or

only one wayonly one way

• Elevation adjustment may not be used Elevation adjustment may not be used for some weather elements (e.g., U for some weather elements (e.g., U and V wind—used only for direction)and V wind—used only for direction)

June 19, 2007June 19, 2007

ELEVATION ADJUSTMENT ELEVATION ADJUSTMENT

•““Unusual” lapse rates are limitedUnusual” lapse rates are limited– By strength of adjustmentBy strength of adjustment– By distanceBy distance

• Temperature change with elevation Temperature change with elevation usually negative, but may be positive usually negative, but may be positive along the west coastalong the west coast

• ““Unusual” defined for each weather Unusual” defined for each weather elementelement

June 19, 2007June 19, 2007

Unusual Lapse Rates

June 19, 2007June 19, 2007

WATER VERSUS LAND WATER VERSUS LAND

• Gridpoints are designated as either (1) Gridpoints are designated as either (1) Ocean, (2) Inland Water, or (3) LandOcean, (2) Inland Water, or (3) Land

• Stations are designated as either Stations are designated as either (1) Ocean, (2) Inland Water, (3) Land, or (1) Ocean, (2) Inland Water, (3) Land, or (4) Both land and inland water(4) Both land and inland water

• Each type of station affects a Each type of station affects a corresponding type of gridpointcorresponding type of gridpoint– Essentially three analyses in oneEssentially three analyses in one– Interpolation recognizes differenceInterpolation recognizes difference

June 19, 2007June 19, 2007

ERROR CHECKING ERROR CHECKING

• Threshold defined for each weather Threshold defined for each weather element for each analysis passelement for each analysis pass– Difference between the current analysis and Difference between the current analysis and

the forecast must be < the threshold for the the forecast must be < the threshold for the forecast to be used on that passforecast to be used on that pass

– But--Before discarding when threshold is not But--Before discarding when threshold is not met, two nearest neighbors are checked, both met, two nearest neighbors are checked, both with and without terrain adjustmentwith and without terrain adjustment

– If one of the neighbors supports the If one of the neighbors supports the questionable forecast, both are acceptedquestionable forecast, both are accepted

– Nearest neighbor checking is expensive, but is Nearest neighbor checking is expensive, but is used rarely and is highly effectiveused rarely and is highly effective

June 19, 2007June 19, 2007

CATEGORICAL VARIABLESCATEGORICAL VARIABLES

•Analysis is designed for Analysis is designed for continuous fields continuous fields – Many MOS forecasts are developed as Many MOS forecasts are developed as

probabilities of categories of the weather probabilities of categories of the weather variable (e.g., snow amount, precipitation variable (e.g., snow amount, precipitation amount, sky cover), then a “best category” amount, sky cover), then a “best category” determined based on reasonable bias and determined based on reasonable bias and some skill or accuracy scoresome skill or accuracy score

– Necessary because of highly non-normal Necessary because of highly non-normal distribution and the heavy tail is the important distribution and the heavy tail is the important part of the distributionpart of the distribution

– Best category forecasts used with the Best category forecasts used with the probabilities of those forecasts to calculate a probabilities of those forecasts to calculate a near continuous set of values to analyzenear continuous set of values to analyze

June 19, 2007June 19, 2007

CATEGORICAL VARIABLESCATEGORICAL VARIABLES• Categorical values are scaled Categorical values are scaled

between the two extremes of the between the two extremes of the category based on the maximum and category based on the maximum and minimum values of the probabilities minimum values of the probabilities over the grid for that category. over the grid for that category.

• Extreme value has to be assumed for Extreme value has to be assumed for the end categorythe end category– Highest category of 6-h QPF is one inch Highest category of 6-h QPF is one inch

and aboveand above– 2 inches chosen as the high value2 inches chosen as the high value

• Elevation correction can adjust Elevation correction can adjust amounts outside category, even at amounts outside category, even at high end.high end.

June 19, 2007June 19, 2007

CONSISTENCY IN SPACE AND CONSISTENCY IN SPACE AND TIMETIME

• Looped graphics of grids produced from Looped graphics of grids produced from MOS forecasts for different cycles “pulse” MOS forecasts for different cycles “pulse” – Equations developed at different times with Equations developed at different times with

different samplesdifferent samples– Equations have different predictorsEquations have different predictors– Basic model may exhibit cycle differencesBasic model may exhibit cycle differences– Different set of stations for different cyclesDifferent set of stations for different cycles

• Analyses are based on average values Analyses are based on average values from two cycles, 12 hours apart.from two cycles, 12 hours apart.– Essentially an ensemble of twoEssentially an ensemble of two– Verification against observations shows no Verification against observations shows no

deterioration with this processdeterioration with this process– Much improved time and space continuityMuch improved time and space continuity

June 19, 2007June 19, 2007

FIT TO DATA 2-M FIT TO DATA 2-M TEMPERATURE MAE DEG FTEMPERATURE MAE DEG F

• Over United States without elevation With Over United States without elevation With elevelev– AnalyzedAnalyzed 1.921.92 1.431.43– WithheldWithheld 2.552.55 1.941.94

• Over West (approx. west of 105 deg. W)Over West (approx. west of 105 deg. W)– AnalyzedAnalyzed 2.912.91 2.042.04– WithheldWithheld 4.434.43 2.722.72

June 19, 2007June 19, 2007

CONSISTENCY AMONG WEATHER ELEMENTS-

POSTPROCESSING•Consistency not dealt with in the Consistency not dealt with in the

analysis procedure analysis procedure •Postprocessing of gridsPostprocessing of grids

– Temperature and dew pointTemperature and dew point– 12-h QPF calculated from two 6-h 12-h QPF calculated from two 6-h

amountsamounts– Wind “gust” grid a combination of Wind “gust” grid a combination of

wind speed and gustswind speed and gusts– Wind direction calculated from U Wind direction calculated from U

and Vand V

June 19, 2007June 19, 2007

Precipitation Amount ModificationPrecipitation Amount Modification

Current Method New Method

• Changed from an expected value to a computed amount based on an Changed from an expected value to a computed amount based on an adjustment of the categorical forecast. This will increase the amounts.adjustment of the categorical forecast. This will increase the amounts.

June 19, 2007June 19, 2007

Current Method New Method• Changed from an expected value to a computed amount based on an Changed from an expected value to a computed amount based on an

adjustment of the categorical forecast. This will increase the amounts.adjustment of the categorical forecast. This will increase the amounts.

Precipitation Amount ModificationPrecipitation Amount Modification

June 19, 2007June 19, 2007

Future UpgradesFuture Upgrades

• Alaska guidance on 3-km gridAlaska guidance on 3-km grid

– Initial release: temperatures, winds, probability of precipitation (PoP)Initial release: temperatures, winds, probability of precipitation (PoP)

– Later releases: QPF, snow, sky cover, wind gusts, thunderstorms, Later releases: QPF, snow, sky cover, wind gusts, thunderstorms, weather, precipitation type, 6-h snowweather, precipitation type, 6-h snow

• Hawaii, Puerto Rico guidance on 2.5 km gridHawaii, Puerto Rico guidance on 2.5 km grid

– Initial release: temperatures, winds, PoPInitial release: temperatures, winds, PoP

– Later releases: QPF, sky cover, wind gustsLater releases: QPF, sky cover, wind gusts

• CONUS guidance on 2.5 km gridCONUS guidance on 2.5 km grid

– Initial release: temperatures, winds, PoPInitial release: temperatures, winds, PoP

– Later releases: QPF, snow, sky cover, wind gusts, weather grids, Later releases: QPF, snow, sky cover, wind gusts, weather grids, precipitation type, 6-h snowprecipitation type, 6-h snow

• Guam guidanceGuam guidance

– Still in planning stagesStill in planning stages