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User guide to ECMWF forecast
products
Copyright 2011, 2013 ECMWF
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Date of original issue: October 2011
Author: Anders Persson
Version number Date Changed by Change description
1.1 23/07/2013 Erik Andersson New terminology, ENS
initial perturbations
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1.Introduction..............................................................................................................................1
2. The ECMWF forecasting and assimilation system...............................................................2
2.1. The ECMWF global atmospheric model.......................................................................2
2.1.1. The modelequations.....................................................................................2
2.1.2. The numerical formulation..........................................................................2
2.1.3. The rationale for high resolution.................................................................3
2.1.4. Topographical and climatological fields...................................................... 3
2.1.5. The formulation of physical processes......................................................... 4
2.1.6. The land surface model................................................................................6
2.1.7. The ocean wave model..................................................................................6
2.2. The dynamic ocean model..............................................................................................7
2.3.
Data assimilation.............................................................................................................7
2.3.1. The four-dimensional data assimilation (4D-Var)....................................... 8
2.3.2. The ECMWF early delivery system............................................................. 8
2.4. Retrieving ECMWF forecasts......................................................................................10
2.4.1. Temporal retrieval.....................................................................................10
2.4.2. Spatial retrieval..........................................................................................10
2.4.3. Orography..................................................................................................10
2.4.4. The bi-linear interpolation.........................................................................10
2.4.5. The subsampling procedure.......................................................................12
2.4.6. Interpolating land and seapoints...............................................................13
2.5. The relation between grid point values andobservations........................................... 15
2.6. Some characteristics of NWP output...........................................................................16
2.6.1. Forecast error growth................................................................................16
2.6.2. Downstream spread of influence................................................................16
2.6.3. The relation between scale and predictive skill......................................... 17
2.6.4. Forecast jumpiness.................................................................................20
2.6.5. Flip-flopping forecasts................................................................................21
2.6.6.
Jumpiness and forecastskill.......................................................................22
2.6.7. Forecast trends cannot be extrapolated..................................................... 22
2.6.8. Other state-of-the-art deterministic models.............................................. 22
3. The forecast ensemble...........................................................................................................25
3.1. The rationale behind theensemble...............................................................................25
3.1.1. Qualitative use of the ensemble..................................................................25
3.1.2. Quantitative use of the ENS.......................................................................25
3.1.3. Characteristics of a good ensemble............................................................ 26
3.2.
Generation of the ENS..................................................................................................26
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3.2.1. Different perturbation techniques.............................................................26
3.2.2. Quality of the individual perturbed analyses............................................ 29
3.2.3. Quality of the individual perturbedforecasts............................................ 31
3.3.
The ensemble at different lead times...........................................................................32
3.3.1. The 10-day range........................................................................................32
3.3.2. The day 9 to 10 overlap..............................................................................33
3.3.3. The 10 to 15 day range...............................................................................33
3.3.4. Forecasts from 15 to 32 days......................................................................33
3.3.5. Seasonal forecast........................................................................................33
3.4. Basic forecast products.................................................................................................33
3.4.1. Postage stampmaps................................................................................33
3.4.2. Spaghetti diagrams.................................................................................34
3.4.3.
Plumes.....................................................................................................34
3.4.4. Ensemble mean andmedian.......................................................................35
3.4.5. Ensemblespread.........................................................................................35
3.4.6. Probabilities................................................................................................36
3.4.7. Forecast expressed in terms of intervals.................................................... 36
4. Recommendations on categorical and probabilistic medium-rangeforecasting ............... 37
4.1. Relation between deterministic and probabilistic forecasts....................................... 37
4.2. Differences between short- and medium-range operational useof NWP ................. 37
4.3.
Medium-range forecasting without theensemble.......................................................38
4.3.1. Assessment based on the latest forecasts................................................... 38
4.3.2. Assessment based on the two latestforecasts............................................. 38
4.3.3. Assessment based on the last three or more forecasts............................... 38
4.3.4. Is it possible to compare manual and computer-generateddeterministic
forecasts?...................................................................................................................39
4.4. Medium-range forecasting based only on theENS..................................................... 40
4.4.1. Use of the ensemble mean (EM).................................................................40
4.4.2. Criticism of the EM....................................................................................40
4.4.3.
A synoptic example of combining EM and probabilities........................... 40
4.4.4. Use of probabilities.....................................................................................42
4.4.5. Probabilities over time intervals................................................................43
4.4.6. Probabilities over areas..............................................................................44
4.4.7. Probabilities of combinedevents................................................................44
4.4.8. Modification of the probabilities................................................................45
4.4.9. Calibration of probabilities........................................................................45
4.4.10. Ensemble jumpiness...............................................................................45
4.5.
Medium-range forecasting with the ENS andHRES................................................. 46
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4.5.1. Weather situations with good agreement between ENS andHRES ......... 46
4.5.2. When the ENS and HRES differ with respect to spread only.................. 47
4.5.3. Weather situations where agreement between the ENS andHRES is poor
48
4.5.4. Forecaster intervention with theENS........................................................ 51
4.6. Forecasting high-impact weather in the medium range.............................................. 52
4.6.1. The forecasters role...................................................................................52
4.6.2. Probabilities or categorical forecasts?....................................................... 52
4.7. Summary: do the opposite to the computer!...............................................................53
5. Derived products based on the ENS.....................................................................................55
5.1.1. Ensemble mean and spread charts............................................................ 55
5.2.EPSgrams.......................................................................................................................55
5.2.1.
Overview.....................................................................................................55
5.2.2. Ten-day EPSgrams.....................................................................................56
5.2.3. Fifteen-day EPSgrams................................................................................57
5.2.4. The weather parameters in EPSgrams...................................................... 57
5.2.5. Interpreting EPSgrams..............................................................................59
5.3. Wave EPSgrams............................................................................................................61
5.4. The Extreme Forecast Index(EFI)...............................................................................63
5.4.1. The EFI reference climate..........................................................................63
5.4.2. The cumulative distribution function........................................................ 63
5.4.3. Calculating the EFI....................................................................................65
5.4.4. The interpretation of the EFI.....................................................................66
5.4.5. EFI maps....................................................................................................67
5.5. Tropical cyclone diagrams...........................................................................................67
5.6. Cyclone track maps.......................................................................................................70
5.7.Clustering.......................................................................................................................71
5.7.1. Weather scenario clustering.......................................................................72
5.7.2. Climatological weather regimes.................................................................73
5.7.3.
Tubing.........................................................................................................74
6. Epilogue: how to increase the publics trust in medium-rangeweather forecasts ............ 75
6.1. How can trust in medium-range forecasts be increased?........................................... 75
6.1.1. Improving the forecast system...................................................................75
6.1.2. Trust in individual forecasts......................................................................75
6.1.3. When the deterministic forecast cannot be trusted................................... 75
6.2. The role of the forecaster in the medium-range.......................................................... 76
6.3. How the forecaster can addvalue.............................................................................76
Appendix A
Some statistical concepts to facilitate the use andinterpretation of deterministicmedium-range forecasts................................................................................................................77
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Introduction................................................................................................................................77
A-1 Forecastvalidation......................................................................................................77
A-1.1 The mean error...........................................................................................77
A-1.2
Forecastvariability.....................................................................................78
A-1.3 False systematic errors...............................................................................79
A-1.4 False model climate drift............................................................................80
A-2 Forecastverification...................................................................................................81
A-2.1 Measures of accuracy.................................................................................81
A-2.2 The effect of mean, analysis and observation errors on theRMSE .......... 81
A-2.3 The decomposition of MSE........................................................................82
A-2.4 Forecast error baseline...............................................................................82
A-2.5 Error saturation level.................................................................................83
A-2.6
Measure of skill - the anomaly correlation coefficient.............................. 83
A-3 Interpretation of verificationstatistics....................................................................84
A-3.1 Interpretation of RMSE and ACC.............................................................84
A-3.2 Effect of flow dependency..........................................................................84
A-3.3 The double penalty effect.......................................................................85
A-3.4 Subjective evaluations................................................................................85
A-4 Graphicalrepresentation...........................................................................................85
A-4.1 Forecast errors...........................................................................................86
A-4.2
Flow dependence........................................................................................87
A-4.3 Damping of forecast anomalies..................................................................88
A-4.4 Forecast error correlation..........................................................................88
A-4.5 Forecast jumpiness and forecast skill........................................................ 89
A-4.6 Combining forecasts...................................................................................89
A-5 The usefulness of statisticalknow-how....................................................................90
A-6 Utilityverification.......................................................................................................91
A-6.1 The contingency table.................................................................................91
A-6.2 The expected expenses............................................................................91
A-7 Practicalexamples......................................................................................................92
A-7.1 A situation with no weather forecast service............................................. 92
A-7.2 The benefit of a local weather service........................................................ 93
A-7.3 The establishment of two new weather services........................................ 93
A-8 An introduction to probabilistic weatherforecasting........................................... 95
A-8.1 Uncertainty - how to turn a disadvantage into an advantage................... 95
A-8.2 Making even more use of uncertainty - probabilities................................ 96
A-8.3 Towards more useful weather forecasts.................................................... 98
A-8.4
Quality of probabilistic forecasts...............................................................98
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A-8.5 When probabilities are not required......................................................... 98
A-8.6 An extension of the contingency table the SEEPS score..................... 99
Appendix B Some statistical concepts to facilitate the use andinterpretation of ensemble
forecasts 101
Introduction..............................................................................................................................101
B-1 The reliabilitydiagram............................................................................................101
B-1.1 Reliability.................................................................................................103
B-1.2 Sharpness..................................................................................................103
B-1.3 Under- and overconfident probability forecasts...................................... 104
B-2 Rank histogram (Talagranddiagram)..................................................................105
B-3 Verificationmeasures...............................................................................................107
B-3.1 The Brier score - the MSE of probability forecasts................................. 107
B-3.2
Decomposition of the Brier score.............................................................107
B-3.3 The Brier score is a proper score......................................................... 109
B-3.4 The Brier skill score.................................................................................109
B-3.5 The rank probability score (RPS)............................................................109
B-4 The relative operating characteristics (ROC)diagram......................................109
B-5 Calibration ofprobabilities.....................................................................................111
B-6 Statistical post-processing model outputstatistics............................................113
B-6.1 The MOS equation...................................................................................113
B-6.2 Simultaneous corrections of mean error and variability........................ 113
B-6.3 Short-range MOS.....................................................................................114
B-6.4 Medium-range MOS................................................................................114
B-6.5 Adaptive MOS methods...........................................................................115
References and furtherliterature.................................................................................................119
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1. Introduction
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1. Introduction
Behind good forecast practices are often hidden goodtheories;
equally, good theories should provide a basis for goodforecastpractices. Professor Tor Bergeron, personal communication1974
The aim of this User Guide is to help meteorologists makeoptimal use of the forecast
products from ECMWF, develop new products and reach new sectorsof society and thereby
satisfy new demands. This is done by presenting the forecastsystem and advising on how best
to use the output, not least how to build up trust in theforecast information. The emphasis is
on the medium-range forecast products, since the way forecastersdeal with medium-range
NWP output differs in many ways from how they deal withshort-range NWP on the one hand
and monthly and seasonal NWP on the other. The main outline:
1. The ECMWF forecasting system, i.e. the dynamical model, thedata assimilation and
the product delivery system, are described in broad andnon-technical terms.
2. The interpretation of the NWP output is complicated by itsoften counter-intuitive,
non-linear behaviour. The high-resolution forecast (HRES) shouldtherefore not be
over-interpreted, in particular not in the medium-range or whenextreme weather is
likely. Then the use of probabilities or other risk assessmentsare needed.
3. A good forecast that is not trusted is a worthless forecast.The ECMWF forecast
ensemble (ENS), which is given extensive coverage, provides abasis for formulating
the most accurate categorical forecasts and the probabilities ofalternative
developments. Methods to combine HRES and ENS are suggested.
4. In the medium-range the use of statistical know-how counts asmuch as synoptic
experience, since daily operational work is to a large extent amatter of assessing,
combining and correcting NWP information. In two appendicesstatistical concepts
for validating and verifying deterministic and probabilisticforecasts and for making
the best use of NWP information are presented.
5. The forecaster is not a computer. Throughout the User Guideforecasters are advised
not to try to imitate NWP, but to perform quite differently,with fewer details, more
uncertainty and no U-turns.
This User Guide is the fruit of several years of discussionswith scientists, forecasters and
meteorologists who are interested in statistics, both fromEurope and elsewhere. The
interaction between these three specialized groups has been themain driving force and
inspiration for this publication.
The User Guide gives only an introduction to the forecastinformation provided by ECMWF.
Users are advised to keep themselves updated about the productsthrough the ECMWF
Newsletter and web site.
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2. The ECMWF forecasting and assimilation system
The ECMWF forecasting system (the IFS) consists of severalcomponents: an atmosphericgeneral circulation model, an ocean wavemodel, a land surface model, an ocean general
circulation model and perturbation models for the dataassimilation (EDA) and forecast (ENS)
ensembles (see Chapter3), producing forecasts from days to weeksand months ahead.
2.1.
The ECMWF global atmospheric model
The atmospheric general circulation model describes thedynamical evolution on the resolved
scale and is augmented by the physical parameterisation,describing the mean effect of sub-
grid processes and the land-surface model. Coupled to this is anocean wave model (Bechtold
et al, 2008).
2.1.1. The model equations
The model formulation is based on a set of basic equations, ofwhich some are diagnostic and
describe the static relationship between pressure, density,temperature and height, and some
are prognostic and describe the time evolution of the horizontalwind components, surface
pressure, temperature and the water vapour contents of an airparcel.
Additional equations describe changes in the hydrometeors (rain,snow, liquid water, cloud
ice content etc). There are options for passive tracers such asozone. The processes of
radiation, gravity wave drag, vertical turbulence, convection,clouds and surface interaction
are, due to their relatively small scales (unresolved by themodels resolution), described in a
statistical way asparametrization processes (arranged inentirely vertical columns).
2.1.2. The numerical formulation
The model equations are discretized in space and time and solvednumerically by a semi-
Lagrangian advection scheme. It ensures stability and accuracy,while using as large time-
steps as possible to progress the computation of the forecastwithin an acceptable time.
For the horizontal representation a dual representation ofspectral components and grid
points is used. All fields are described in grid point space.Due to the convergence of the
meridians, computational time can be saved by applying a reducedGaussian grid. This
keeps the east-west separation between points almost constant bygradually decreasing thenumber of grid points towards the poles atevery latitude in the extra-tropics. For the
convenience of computing horizontal derivatives and tofacilitate the time-stepping scheme, a
spectral representation, based on a series expansion ofspherical harmonics, is used for a
subset of the prognostic variables.
The vertical resolution is finest in geometric height in theplanetary boundary layer and
coarsest near the model top. The -levels follow the earthssurface in the lower-most
troposphere, where the Earths orography displays largevariations. In the upper stratosphere
and lower mesosphere they are surfaces of constant pressure witha smooth transition in
between.
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2.1.3. The rationale for high resolution
The higher the numerical resolution, the more accurate thecalculations become. A high
spatial resolution also enables a better representation oftopographical fields, such as
mountains and coastlines, and the effect they have on thelarge-scale flow. It also produces amore accurate description ofhorizontal and vertical structures, which facilitates the
assimilation of observations.
The smallest atmospheric features which can be resolved byhigh-resolution forecasts have
wave lengths four or five times the numerical resolution.Although these atmospheric systems
have a predictability of only some hours, which is about thetime it takes to disseminate the
forecasts, their representation is nevertheless important forenergetic exchanges between
different atmospheric scales.
Increasing the resolution not only benefits the analyses andforecasts of the small-scale
systems associated with severe weather but also those oflarge-scale systems. The abilityaccurately to forecast theformation of large-scale blocking omega anticyclones and cut-
off lows depends crucially on increasing the resolution tokilometres (Miller et al, 2010).
The interpolation technique used when forecasts are retrieved ispresented in section2.4.
2.1.4. Topographical and climatological fields
The model orography is derived from a data set with a resolutionof about 1 km which
contains values of the mean elevation above the mean sea level,the fraction of land and the
fractional cover of different vegetation types. This detaileddata is aggregated (upscaled) to
the coarser model resolution.
The resulting mean orographycontains the values of the meanelevation above the mean sea
level. In mountainous areas it is supplemented by sub-gridorographic fields, to enable the
parametrization of the effects of gravity waves and provideflow-dependent blocking of the
air flow. For example, cold air drainage in valleys makes thecold air effectively lift the
orography.
The land-sea mask is a geographical field that contains thepercentage of land and water
between 0 (100% sea) and 1 (100% land) for every grid point. Agrid point is defined as a
land point if its value indicates that more than 50% of the areawithin the grid-box is covered
by land, see section2.4.6.
The albedo is determined by a combination of background monthlyclimate fields and
forecast surface fields (e.g. from snow depth). Continental,maritime, urban and desert
aerosols are provided as monthly means from data bases derivedfrom transport models
covering both the troposphere and the stratosphere.
Soil temperatures and moisture in the groundare prognosticvariables. There is a lack of
observational data, so observed 2m temperature and relativehumidity act as very efficient
proxy data for the analysis.
The snow coveragedepthis analysed every six hours fromsnow-depth observations, satellite
snow extent and a snow-depth background field. The snowtemperature is also analysed from
satellite observations. They are forecast variables.
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Sea surface temperature (SST) and ice concentrationare based onanalyses received daily
from the Met Office (OSTIA, 5 km). It is updated during themodel integration, according to
the tendency obtained from climatology.
The temperature at the ice surface is variable and calculatedaccording to a simple energy
balance/heat budget scheme, where the SST of the underlyingocean is assumed to be -1.7C.
The sea-ice cover, which is kept constant in the 10-day forecastintegration, is relaxed
towards climatology between days 10 and 30, with a linearregression. Beyond day 30 the
sea-ice concentration is based on climatological values only(from the ERA 1979-2001 data).
2.1.5. The formulation of physical processes
The effect of sub-scale physical processes on weather systems isexpressed in terms of
resolved model variables in a technique called parametrization.It involves both statistical
methods and simplified mathematical-physical models, such asadjustment processes. So, forexample, the air closest to the earthssurface exchanges heat with the surface through
turbulent diffusion or convection, which adjusts unstable airtowards neutral stability (Jung et
al, 2010).
The convection scheme does not predict individual convectiveclouds, only their physical
effect on the surrounding atmosphere, in terms of latent heatrelease, precipitation and the
associated transport of moisture and momentum. The schemedifferentiates between deep,
shallow and mid-level convection. Only one type of convectioncan occur at any given grid
point at one time (seeFigure 1).
Figure 1: The ECMWF total convective rainfall forecast from 28November 2010 12 UTC + 30h. The
convection scheme has difficulty in advecting wintery showersinland over Scotland and northernEngland from the relatively warmNorth Sea. The convection scheme is diagnostic and works on a
model column, so cannot produce large amounts of precipitationover the relatively dry and cold
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(stable) wintery land areas. In nature these showers succeed inpenetrating inland through a
convectively induced upper-level warm anomaly leading tolarge-scale lifting and saturation.
Clouds, both convective and non-convective, are handled byexplicit equations for cloud
water, ice and cloud cover. Liquid and frozen precipitation arestrongly coupled to other
parametrized processes, in particular the convective scheme andthe radiation. The scheme
also takes into account important cloud processes, such ascloud-top entrainment and the
evaporation of water. Fog is represented in the scheme as cloudsthat form in the lowest
model level.
The radiation spectrum is divided into a long-wave part(thermal) and a short-wave part
(solar radiation). Since it has to take the cloud-radiationinteraction into account in
considerable detail, it makes use of a cloud-overlap algorithm,which calculates the relative
placement of clouds across levels. For the sake of computationalefficiency, the radiation
scheme is called less frequently than the model time step on areduced grid. Nevertheless, it
accounts for a considerable fraction of the total computationaltime.
For the precipitation and hydrological cycles both convectiveand stratiform precipitation
are included in the ECMWF model. Evaporation of theprecipitation, before it reaches the
ground, is assumed not to take place within the cloud, only inthe cloud-free, non-saturated air
beside or below the model clouds. The melting of falling snowoccurs in a thin layer of a few
hundred metres below the freezing level. It is assumed that snowcan melt in each layer,
whenever the temperature exceeds 0C. The cloud-overlap algorithmis also important for the
life history of falling precipitation: from level-with-cloud tolevel-with-clear-sky and vice
versa.
The near-surface wind forecastdisplays severe weaknesses in somemountain areas, due to
the difficulty in parametrizing the interaction between the airflow and the highly varying sub-
grid orography (seeFigure 2). As with many other sub-grid-scalephysical processes that need
to be treated in simplified ways, this problem will ultimatelybe reduced when the air-surface
interaction can be described explicitly, thanks to a higher andappropriate resolution. The
system also produces wind-gust forecasts as part ofpost-processing (Balsamo et al, 2011).
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Figure 2: MSLP and 10 m wind forecast from 2 March 2011 12 UTC +12 h. The 10 m winds are
unrealistically weak over the rugged Norwegian mountains. Valuesof 10 m/s might be realistic in
sheltered valleys, but not on exposed mountain ranges.
2.1.6. The land surface model
In the H-TESSEL scheme (Hydrology-Tiled ECMWF Scheme for SurfaceExchange overLand) the main types of natural surfaces found overland are represented by a "mosaic"
approach. In other words, each atmospheric model grid-box is incontact and exchanges
energy and water with up to 6 different types of parcel or"tile" on the ground. These are: bare
soil, low and high vegetation, water intercepted by leaves, andshaded and exposed snow.
Each land-surface tile has its own properties, describing theheat, water and momentum
exchanges with the atmosphere; particular attention is paid toevaporation, as near-surface
temperature and humidity are very closely related to thisprocess.
The soil (with its four layers) and the snow-pack (with onelayer) have dedicated physical
parametrizations, since they represent the main land reservoirsthat can store water and energy
and release them into the atmosphere in lagged mode.
Finally, the vegetation seasonality is described by the leafarea index (LAI) from
climatalogical data. The LAI describes the growing, mature,senescent and dormant phases of
several vegetation types in H-TESSEL (four types of forests andten types of low vegetation).
2.1.7. The ocean wave model
The wave model at ECMWF is called the WAM. It describes the rateof change of the 2-
dimensional wave spectrum, in any water depth, caused byadvection, wind input, dissipation
due to white capping and bottom friction and non-linear waveinteractions. It is set up so as
to allow the two-way interaction of wind and waves with theatmospheric model. It is also
incorporated in the medium-range, monthly and seasonalensembles.
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Radar altimeter wave-height data are assimilated fromsatellites. Buoy wave data are not
assimilated; instead, they serve as an independent check on thequality of modelled wave
parameters. The propagation of swell in the wave model ishandled by a simple scheme that
gives rise to a smoothing of the wave field. At present theeffects of surface currents on the
sea state are not taken into account. In particular areas, suchas the Gulf Stream or Agulhas
current, the current effect may give rise to localised changesof up to one metre in the wave
height.
The representation of the sea-ice fields is not as accurate aswould be needed to handle waves
near the ice edge. Due to the present model resolution, waveproducts near the coasts and, to a
lesser extent, in small enclosed basins (e.g. the Baltic Sea)may be of lower quality than the
open-ocean products.
2.2. The dynamic ocean model
The three-dimensional general circulation ocean model canreproduce the general features ofthe circulation and the thermalstructure of the upper layers of the ocean and its seasonal and
inter-annual variations. It has, however, systematic errors,some of which are caused by the
coarse vertical and horizontal resolution: the model thermoclineis too diffuse; the Gulf
Stream does not separate at the right location.
The ocean analysis is performed every 10 days, down to a depthof 2000 m. Observational
input comes from all around the globe, but mostly from thetropical Pacific, the tropical
Atlantic and, to an increasing degree, from the Indian Ocean. Inplaces where the ocean floor
is below 2000 m the information from above 2000 m is propagateddownwards by
statistical vertical influence functions, similar to those inthe atmospheric data assimilation.The ocean-atmosphere couplingisachieved by a two-way interaction: the atmosphere affects
the ocean through its wind, heat and net precipitation(precipitation-evaporation), whilst the
ocean affects the atmosphere through its SST.
For the seasonal forecasts the interaction is once a day, whilefor the ENS it is every hour.
This high-frequency coupling may have some positive impact onthe development of some
synoptic-scale systems, such as tropical cyclones.
2.3. Data assimilation
The observations used for the analysis of the atmosphere can bedivided roughly into
conventional, in-situ observations and non-conventional,remote-sensing observations.
The conventional observations consist of direct observationsfrom surface weather stations,
ships, buoys, radiosonde stations and aircraft, both at synopticand, increasingly, at asynoptic
hours. All surface and mean sea-level-pressure observations areused, with the exception of
cloud cover, 2 m temperature and wind speed (over land). 2 mtemperature and dew point
observations are used in the analysis of soil moisture. Observedwinds are used from ships
and buoys but not from land stations, not even from islands orcoastal stations.
The non-conventional observationsare achieved in two differentways: passive technologies
sense natural radiation emitted by the earth and atmosphere orsolar radiation reflected by the
earth and atmosphere; active technologies transmit radiation andthen sense how much is
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reflected or scattered back. In this way surface-wind vectorinformation is, for example,
derived from the influence of the ocean capillary waves on theback-scattered radar signal of
scatterometer instruments (Hersbach and Janssen, 2007).
2.3.1. The four-dimensional data assimilation (4D-Var)
The increasing availability of asynoptic data andnon-conventional observations has
necessitated the use of advanced analysis procedures, such asfour-dimensional variational
data assimilation (4D-Var), where the concept of a continuousfeedback between observations
and model data is put on a firm mathematical foundation(Andersson and Thpaut, 2008).
The 4D-Var analysis uses the model dynamics and physics tocreate, over a time window,
(currently 12 hours), a sequence of model states that fits asclosely as possible with the
available observations and background, i.e. a short-rangeforecast that serves to bring the
information forward from the previous cycle. These states areconsistent with the dynamics
and physics of the atmosphere, as expressed by the equations ofthe model. The correction of
one model variable generates physically and dynamicallyconsistent corrections of other
variables. For instance, a sequence of observations of humidityfrom a satellite infrared
instrument that shows a displacement of atmospheric structureswill entail a correction not
only of the moisture field but also of the wind and temperaturefields.
The impact of the observations is determined by the assumedaccuracy of the observations
and the model short-range forecasts. While the former can beregarded as more or less static,
the latter are flow-dependent; the uncertainty may be larger ina developing baroclinic low
than in a subtropical high-pressure system. The background-erroraccuracy is also dependent
on the local observation density. To estimate the flow-dependentuncertainty, a set of 3-hourforecasts, valid at the start of the4D-Var time window, is computed from ten perturbed,
equally likely analyses. They differ because of small variationsimposed on the observations,
the sea surface temperature and model error parameterization.These variations reflect the
uncertainties in the observations, the SST and the forecastevolution. The perturbations
produced using this ensemble of data assimilations (EDA) arealso used for the construction
of the perturbations in the forecast ensemble (see chapter3,inparticular Section 3.2.1.For
further detail on the EDA see Isaksen et al, 2010).
The 4D-Var system handles all observational data similarly,including radiances from
satellites. It compares the actual observations with what wouldbe expected, given the model
fields. For satellite radiances the variational scheme modifiesthe model fields of temperature,
wind, moisture and ozone in such a way that the simulatedobservations are brought closer to
the observed values.
2.3.2. The ECMWF early delivery system
The 4D-Var analysis uses observations from a 12-hour timewindow, either 21 - 09 UTC (for
the 00 and 06 UTC analyses) or 09 - 21 UTC (for the 12 and 18UTC analyses). To provide
the best initial condition for the next analysis a fullresolution 3-hour forecast is run, based on
the previous 4D-Var analysis (seeFigure 3).
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Figure 3: The 00 UTC cycle of the delayed cut-off 4D-Varanalysis covering 21 09 UTC starts with a
15-hour forecast from the previous 18 UTC 4D-Var delayed cut-offanalysis (the 09 - 21UTC
assimilation). Waiting for most of the available observations toarrive, the delayed cut-off analysis
starts at 14:00 UTC using the 3-hour forecast as initialcondition. The rest of the 15-hour forecast isused as background(first guess) for the 12-hour delayed cut-off 4D-Var analysis (andsimilarly for
the next 12 UTC analysis cycle).
To ensure the most comprehensive global data coverage, includingsouthern hemisphere
surface data and global satellite-sounding data, the 4D-Varanalysis waits about 5 hours to
ensure that almost all available observations have arrived.
Figure 4: The 12 UTC cycle of the early delivery analysis alsostarts from a 3-hour forecast, now from
06 UTC, which is used as the background (first guess) for a6-hour early delivery 4D-Var analysis
covering the time interval 09 - 15 UTC. The operational ten-dayforecast then starts from the 12 UTC
analysis at about 16:30 UTC. The early delivery cut-off 12 UTCanalysis starts at 16:00 UTC.
Although waiting for later data benefits the quality of theanalysis and its subsequent forecast,
it adversely affects product timeliness. To overcome thisproblem, ECMWF has introduced its
early delivery system,which allows the 00 and 12 UTC operationalanalyses to be produced
significantly earlier, without compromising the operationalquality of the forecast products
(seeFigure 4).
To achieve this, an early cut-off analysis is made, relying onobservations arriving during the
first four hours, which accounts for about 85% of the availableglobal observations. Since 80 -
85% of the value of each 4D-Var analysis stems from thebackground (first guess)
information and only 15-20% from the latest observations, notmaking use of the remaining
15% of the observations reduces the predictive skill by a fewhours. Since this enables
ECMWF to disseminate its forecasts 10 hours earlier, there is anoperational gain of 4 - 6
hours in effective predictability. It is important to note thatthe background information
always comes from the 12-hour 4D-Var where, thanks to the latecut-off, almost all available
observations have been used.
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2.4. Retrieving ECMWF forecasts
The exact value of the forecast parameters can be affected bythe way the data is retrieved,
interpolated and presented.
2.4.1. Temporal retrieval
All forecast parameters, both surface and upper air, based on 00and 12 UTC HRES and ENS,
are available at 3-hourly intervals up to +144 hours and at6-hourly intervals from +150 to
+240 hours. The parameters are available hourly up to +90 hoursto members of the Boundary
Conditions (BC) optional programme. Also available to BCprogramme members are two
additional cycles, at 06 and 18 UTC, with all forecastparameters, both surface and upper air
available hourly up to +90h.
Precipitation forecasts are provided as values accumulated fromthe start of the forecast
integration. The range of the daily variation of the forecast 2m temperature and wind gust is
best estimated by retrieving the forecast maximum and minimumvalues. In both cases the
valid time is defined as the time at the end of the period. Thecombination of accumulated and
instantaneous forecast information can occasionally lead toinconsistencies, for instance,
during the passage of a cold front: whereas there might bealmost cloud-free conditions at the
end of the interval, they will be timed together withsignificant precipitation amounts
accumulated over the wholetime interval.
2.4.2. Spatial retrieval
ECMWF forecast products can be retrieved at a wide range ofspatial resolutions, from
regular and rotated lat-lon grids to the original regular andreduced Gaussian grid. The data
can be retrieved from model, pressure, isentropic oriso-potential vorticity (PV) levels,
depending on the parameter.
Temperature, wind and geopotential forecast information isstored in spectral components but
can be interpolated to any specified latitude-longitude grid.This interpolation can also be
applied to near-surface parameters, although direct use of theoriginal reduced Gaussian grid
point values is strongly recommended, especially forprecipitation and other surface fluxes to
avoid the undesired effects of interpolation.
2.4.3. Orography
Because valleys and mountain peaks are smoothed out by the modelorography the directmodel output of 2 m temperature may representan altitude significantly different from the
real one. A more representative height might be found at one ofthe nearby grid points. Any
remaining discrepancy can be overcome by a correction using theStandard Atmosphere lapse
rate or statistical adaptation (see AppendixB-6).
2.4.4. The bi-linear interpolation
Since 1979 ECMWF has used a bi-linear interpolation techniquebecause of its efficiency. It
uses the 2 x 2 grid points closest to the selected interpolationlocation and takes a weighted
average to arrive at the interpolated value (seeFigure 5).
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Figure 5: Bi-linear interpolation of four model grid points(black crosses) starts by linear interpolation
between each pair of grid points (red circles). These two, ineither the latitudinal or longitudinal
direction, are then used for interpolation to the requestedlocation (filled circle), weighted according totheir distance fromeach of the model grid points.
The weights are based on the distance of the interpolatedlocation from each of the model grid
points. Although linear in both directions, the bi-linearinterpolation is not linear but
quadratic, except along lines which connect the model gridpoints (seeFigure 6).
Figure 6: Example of bilinear interpolation for any locationwithin the grid box. The interpolated value
for the centre is 1.25, but may take any value between 0 and 2elsewhere.
Every interpolation technique has its advantages anddisadvantages. When the interpolation
grid length is significantly coarser than the model grid,small-scale variability might
misleadingly appear to represent larger scales. If, for example,the interpolation is made to a
location close to one of the grid points, it will more or lesstake this value, even if it happens
to represent a small-scale extreme. Only if the interpolationpoint is in the centre, does an
interpolated value represent the mean over the grid-boxarea.
For the dissemination, all fields are bi-linearly interpolatedto a 0.125 lat/lon grid,
corresponding to a 13.5 km resolution in the meridionaldirection.
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Figure 7: For a given interpolation grid (red circles) theproportion of model information taken into
account depends on the model grid resolution (black crosses).When the interpolated grid is twice the
model grid length (or less), all model grid values will be usedin the interpolation.
When the model grid is lessthan half the interpolation gridlength, the proportion of used grid
points decreases (see Figure 7). If, for example, the model gridlength is a quarter of the
interpolation grid, only a quarter of the model grid points aretaken into account. This has the
undesired effect of not conserving area totals, which makes itunacceptable for use for surface
fields, such as precipitation.
2.4.5. The subsampling procedure
Data may be requested on grids much coarser than 0.125 or 13.5km. Then a subsample of
the 0.125 resolution grid points is selected. If, for example,interpolated values in 0.5, 1.0 or
1.5 resolutions are requested, every 4th, 8th or 12thinterpolated value will be selected and
disseminated (seeFigure 8).
Figure 8: When the requested interpolation grid length is, forexample 0.5, every 4 thof the bi-linearly
interpolated values (red circles) in a 0.125 resolution isselected.
This will have the undesired effect that model grid point valueswhich, essentially represent
small scales, may by chance appear to represent much largerscales (seeFigure 9).
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Figure 9: Example of the effect of inappropriate interpolationof precipitation fields. To the left the
forecast is interpolated in a 0.25 x 0.25 grid, to the right ina 1.5 x 1.5 grid.
2.4.6. Interpolating land and sea points
When the interpolation of the 2 m temperature or 10 m wind takesplace over or near a coast
line, the interpolation makes use of the land-sea mask (seeSection2.1.4) to decide whether
the four grid points are land or sea points (see Figure 10).This determines whether the
interpolated value should be regarded as a land or sea point. Inthis way there will be no
undesired smoothing of gradients along coast lines.
Figure 10: A rather detailed coast line (grey line) is definedby the model high-resolution grid
(crosses). In the interpolation to a coarser grid, only the fournearest grid points to the interpolated
position are used. Depending on whether they are predominantlyof land or sea character, they will
unambiguously define an interpolated land (green) or sea (blue)point.
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Systematic differences between HRES and ENS (see chapter 3) can,for example, occur in
connection with strong gradients along coasts, small islands orin mountainous regions. Any
such discrepancy is most clearly apparent during the first fewdays, when the spread is
normally small (seeFigure 11 andFigure 12).
Figure 11: EPSgram for Kontiolahti in eastern Finland, 22 April2011 12 UTC. The systematicdifference between the HRES (blue line)and the ensemble Control forecast (red line) is around 5C.
Kontiolahti lies close to a small lake resolved in HRES but notin the ENS (for more details about
EPSgrams see Section 5.2).
Figure 12: The difference in 2 m temperature between the HRESand the ensemble Control forecast for
23 April 2011 00 UTC + 12h. The maximum and minimum differencesare indicated as integers. The
interval is 2C. The differences are largest where thediscrepancy between the HRES and ENS land-sea
mask or orography is largest.
At grid points along coastlines the marine influence may beoverestimated and statistical
interpretation schemes can be beneficial, in particular fortemperature forecasts (see Appendix
B-6).
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2.5. The relation between grid point values and observations
The reduced Gaussian grid values, like all other grid values,should not be considered as
representing the weather conditions at the exact location of thegrid point, but as a time-space
average within a two- or threedimensional grid box (Gber et al,2008). The discrepancybetween the grid-point value and theverifying observed average can be both systematic and
non-systematic. The systematic errors reflect the limitations ofthe models ability to simulate
the physical and dynamic properties of the system; thenon-systematic errors reflect synoptic
phase and intensity errors (seeFigure 13).
Figure 13:The comparison between NWP model output andobservations ought ideally to follow a two-
step procedure: first from grid-point average to observationarea average. The systematic errors are
then due to model shortcomings; the non-systematic stem fromsynoptic phase and intensity errors. In
the next step, the systematic errors between observation averageand point observation result fromstation representativeness and thenon-systematic from sub-grid scale variability.
When the NWP model output is compared with point observations,additional systematic and
non-systematic errors are introduced, due to theunrepresentativeness of the location and the
observations sub-grid variability (seeFigure 14).
Figure 14: In reality, the comparison between NWP andobservations must for simplicity bypass thearea average stage. Thisresults in the systematic and non-systematic errors emanating fromdistinctly
different sources.
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Systematic errors due to model deficiencies and/or observationalrepresentativeness can be
partly corrected by statistical means (see AppendixB-6).Non-systematic synoptic errors can
be dampened by different ensemble approaches (see Chapter4), butthe errors due to sub-grid
variability can only be remedied by new model versions withhigher numerical resolutions. Amodel-independent estimate of thesub-grid noise can be made by verifying the
observations from one observing station as forecasts for aneighbouring observing station.
A typical value for hom*ogenous terrain is about 1C with typicaldistances of 50-150 km.
2.6. Some characteristics of NWP output
Output from NWP models does not behave in a simple or regularway due to the non-linear
nature of the forecast system.
2.6.1. Forecast error growth
Forecast error growth is, on average, largest at the beginningof the forecast. At longerforecast ranges it levels offasymptotically towards the error level of persistenceforecasts,
pure guesses or the difference between two randomly chosenatmospheric states (see Figure
15). This error level is significantly higher than the averageerror level for a simple
climatological average used as a forecast (see AppendixA-2 fordetails).
Figure 15: A schematic illustration of the forecast errordevelopment of a state-of-the-art NWP (full
curve), persistence and guesses (dotted curve), whose errorsconverge to a higher error saturation
level than modified forecasts, which converge at a lower level(dashed curve).
2.6.2. Downstream spread of influence
Influences in the forecasts, both good and bad, often travelfaster downstream than the
synoptic systems themselves. A two-day forecast over Europe maybe affected by the initial
conditions over most of the North Atlantic, a five-day forecastalso by the initial conditions
over the North American continent and easternmost North Pacific.There is also an ever
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present influence from the subtropical and tropical latitudes,particularly when a subtropical
depression, tropical storm or hurricane enters the westerlies(seeFigure 16).
Figure 16: Schematic illustration of the typical propagation offorecast errors over the northern
hemisphere towards Europe in situations with generally zonalflow. The errors propagate mainly along
the storm track, which during the warm season is displacedpolewards. Forecast errors or jumpiness
at D+3 typically have their origin over the eastern part of theNorth American continent, at D+5 over
the western part or the eastern part of the North Pacific. Inrare cases, forecast failures at D+7 have
been traced back even further. During all seasons, but inparticular during the summer and autumn,
forecast errors associated with disturbances in the tropics orsubtropics can move into the zonal
westerlies.
Hence, if the short-range forecast is initially poor (good) overthe area of interest, this does
not mean that the medium-range forecast for the same area isnecessarily poor (good). Any
attempt to judge the medium-range performance a priori from theshort-range performance
ought to be made over large upstream areas and also involve theupper-air flow (Bright and
Nutter, 2004).
2.6.3. The relation between scale and predictive skill
It is known from theory and synoptic experience that the largerthe scale of an atmospheric
system, the longer its timescale and the more predictable itnormally is (seeFigure 17).
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Figure 17: A schematic illustration of the relationship betweenatmospheric scale and timescale. The
typical predictability is currently approximately twice thetimescale, but might ultimately be three times
the timescale
Small baroclinic systems or fronts are well forecast to aroundD+2, cyclonic systems to
around D+4 and the long planetary waves defining weather regimesto around D+8.
Exceptions are features that are coupled to the orography, suchas lee-troughs, or to the
underlying surface, such as heat lows. The predictable scalesalso show the largest
consistency from one run to the next.
Figure 18 shows 1000 hPa forecasts from the operational model.The forecast details differ
between the forecasts but large-scale systems, such as a lowclose to Ireland, a high over
central Europe and a trough over the Baltic States are commonfeatures.
The +144 h forecast from 14 August predicted a south-westerlygale over the British Isles six
days later. It would, however, have been unwise to make such adetailed interpretation of the
forecast, considering the typical skill at that range. Only astatement of windy, unsettled and
cyclonic conditions would have been justified. Such a cautiousinterpretation would have
avoided any embarrassing forecast jump, when the subsequent +132h and +120 h runs
showed a weaker circulation. The same cautious approach wouldhave minimized the forecast
jump with the arrival of the +108 h forecast.
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Figure 18: A sequence of 1000 hPa forecast maps ranging from+156 h to +96 h, all verify on 20
August 2010, 00 UTC.
Smoothing out or, more correctly, filtering away small-scaledetails, in order to highlight the
predictable scale, does not necessarily have to be donesubjectively (by eye). There are also
various convenient ways to do it objectively. For example,retaining only the first 20 spectral
components filters away all scales smaller than 1000 km andbrings out the more predictable
large-scale pattern (seeFigure 19).
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Figure 19: Same as Figure 18 but based on the 20 largestspectral components.
Five of the six forecasts now show much larger coherence, with acyclonic feature
approaching the British Isles and a stationary high pressuresystem over central Europe.
Spectral filtering does not take into account how thepredictability varies due its flow
dependency: a small-scale feature near Portugal might be lesspredictable than an equally
sized feature over Finland. Section4.4.3 shows how the ensembleforecasting system would
treat the same synoptic situation in a more consistent andoptimal way.
2.6.4. Forecast jumpiness
Since every new forecast run is, on average, better than theprevious one, it is also different.
These differences occur because of new observations that modifyprevious analyses of the
atmospheric state and thereby the subsequent forecasts generatedfrom these analyses.
Usually, the differences in the forecasts are small or moderatebut can occasionally be quitelarge and appear as forecast jumps.This jumpiness is an unavoidable consequence of a
non-perfect dynamical forecast system and not a problemper se.Only when the forecasts are
perfect will there never be any jumpiness (Persson and Strauss,1995).
Just because the most recent forecast is, on average, betterthan the previous one, does not
mean that it is alwaysbetter. A more recent forecast can, asshown inFigure 20,frequently be
worse than a previous one; with increasing forecast range itbecomes increasingly likely that
the 12 or 24 hours older forecast is the better one. Chapter 4describes how forecasters can
handle forecast jumpiness by combining previous forecasts withthe most recent one.
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Figure 20: The likelihood that a 12-h or 24-h forecast is better(in terms of RMSE) than todays
forecast. The parameter is the MSLP for N Europe and the periodOctober 2009-September 2010. Theresult is almost identical, if ACCis used as the verification measure.
2.6.5. Flip-flopping forecasts
The order in which the jumpiness occurs can provide additionalinsights. According to
Table 1 the likelihood that precipitation occurs seems to beabout equal for the last two
forecasts being consistent (R R -) or the last threeflip-flopping (R - R).
Last 3forecasts
84,96,108h
Numericalprobability
Observedfrequency
Numberof
forecasts
- - - 0% 6% 598
- - R 33% 15% 66
- R - 33% 22% 46
R - - 33% 36% 59
- R R 67% 30% 43
R - R 67% 44% 27
R R - 67% 47% 43
R R R 100% 74% 157
Table 1: The percentage of cases when > 2mm/24 h has beenobserved, when up to threeconsecutive ECMWF runs (+84, +96 and+108h) have forecast >2mm/24 h for Volkel,
Netherlands October 2007-September 2010. Similar results arefound for other west and
north European locations and for other NWP medium-rangemodels.
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This might be because, although the last two forecasts are moreskilful than the earliest
forecast, they are also, on average, more correlated. What theearliest forecast might lack in
forecast skill, it compensates for by being less correlated withthe most recent forecast. The
agreement between two on average less correlated forecastscarries more weight than two onaverage more correlated.
2.6.6. Jumpiness and forecast skill
It is intuitively appealing to assume that a forecast is morereliable, if it has not changed
substantially from the previous run. Objective verifications,however, show a very small
correlation between forecast jumpiness and the quality of thelatestforecast (seeFigure 21).
The jumpiness relates rather to the skill of the average of theforecasts (see AppendixA-5).
Figure 21: The correlation between 24 hour forecast jumpinessand forecast error for 2 m temperature
forecasts for Heathrow at 12 UTC, October 2006 - March 2007.While the relationship between
jumpiness and error is low in the short range, it increases withforecast range and asymptotically
approaches the 0.50 correlation.
2.6.7. Forecast trends cannot be extrapolated
Trends in the development of individual synoptic systems oversuccessive forecasts do not
provide any indication of their future development. If, duringits last runs, the NWP has
systematically changed the position and/or intensity of asynoptic feature, it does not mean
that the behaviour of the next forecast can be deduced by simpleextrapolation of previous
forecasts (Hamill, 2003).
2.6.8. Other state-of-the-art NWP models
What has been said so far applies, in principle, to all majorstate-of-the-art NWP models,
spectral- or grid-point-based, global or limited area,hydrostatic or non-hydrostatic. The
differences in their average forecast quality are lesssignificant than the daily variability of the
scores. Hence, the best NWP model, on average, is notnecessarily the best on a particular
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day. An NWP model that has recently performed significantlybetter (or worse) than other
models (of about the same average skill), is not likely tocontinue to do so.
However, as mentioned in Section2.6.2 and further discussed inSection4.2,it is as difficult
to determine the model of the day from one of several NWP modelforecasts as it is fromconsecutive forecasts from the same model.Forecasters are advised to treat forecasts from
different NWP models as a multi-model ensemble whose membersdiffer slightly in their
initial conditions and model characteristics. The betterforecasters learn to handle the NWP
output in this way, the better they will be able to manage theensemble forecasts, where these
problems are more consistently addressed (see Chapter 4).
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3. The forecast ensemble
The value of NWP forecasts would be greatly enhanced if thequality of the forecasts could be
assessed a priori; consequently, in parallel with improving theobservational network, the data
assimilation system and the models, methods of providing advanceknowledge on how certain(or uncertain) a particular forecast is andwhat possible alternative developments might occur
are being developed.
3.1. The rationale behind the ensemble
The ECMWF forecast ensemble is based upon the notion thaterroneous forecasts result from
a combination of initial analysis errors and model deficiencies,the former dominating during
the first five days or so. Analysis errors amplify most easilyin the sensitive parts of the
atmosphere, in particular where strong baroclinic systemsdevelop. These errors then move
downstream and amplify and thereby affect the large-scale flow.To estimate the effect of
possible initial analysis errors and the consequent uncertaintyof the forecasts, small changesto the 4D-Var analysis are made,creating an ensemble of many (currently 50) different,
perturbed, initial states. Model deficiencies are represented bya stochastic process. In order
to save computational time, the ensemble members are run with alower resolution version of
the IFS.
3.1.1. Qualitative use of the ensemble
If forecasts starting from these perturbed analyses agree moreor less with the forecast from
the non-perturbed analysis (the ensemble Control forecast), thenthe atmosphere can be
considered to be in a predictable state and any unknown analysiserrors would not have a
significant impact. In such a case, it would be possible toissue a categorical forecast withgreat certainty.
If, on the other hand, the perturbed forecasts (the ENS) deviatesignificantly from the Control
forecast and from each other, it can be concluded that theatmosphere is in a rather
unpredictable state. In this case, it would not be possible toissue a categorical forecast with
great certainty. However, the way in which the perturbedforecasts differ from each other may
provide valuable indications of which weather patterns arelikely to develop or, often equally
importantly, not develop.
3.1.2. Quantitative use of the ENS
The ENS provides the ensemble mean (EM) forecast (or theensemble median) where the less
predictable atmospheric scales tend to be averaged out. Theaccuracy of the EM can be
estimated a priori by the spread of the ensemble: the larger thespread, the larger the expected
EM error, on average.
More importantly, the ENS provides information from which theprobability of alternative
developments is calculated, in particular those related to riskof extreme or high-impact
weather.
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3.1.3. Characteristics of a good ensemble
a) The ensemble forecasts should display no mean errors (bias),otherwise the
probabilities will be biased as well.
b) The forecasts should have the ability to span the fullclimatological range, otherwise the
probabilities will either over- or under-forecast the risks ofanomalous or extreme weather
events.
c) Any systematic errors with respect to mean error orvariability can be detected by the
deterministic verification methods discussed in Appendix A. Theycan, however, also be
measured through the probabilistic verification methods outlinedinAppendix B.
3.2. Generation of the ENS
3.2.1.
Different perturbation techniquesThe small perturbations addedto the Control analysis to create 50 perturbed initialconditions
are computed by a combination of three methods:
a) A singular vector (SV) technique seeks perturbations on wind,temperature and pressure
that will maximizetheir impact on a 48 hour forecast, measuredby the total energy over
the hemisphere outside the tropics. The maximization does notmean that the SV only
intensifies weather systems; equally often it weakens them. Inaddition, the systems can
be slightly displaced. Since SV calculations are quite costly,they have to be run at a low,
T42, resolution corresponding to almost 500 km.
To specifically address uncertainties in the moisture processestypical of low latitudes, inparticular of tropical cyclones, aspecial version of the SV is created using a linearised
diabatic version of the model. These tropical SVs may alsoinfluence forecasts of extra-
tropical developments, when, for example, tropical cyclonesenter the mid-latitude some
days into the forecast and interact with the baroclinicdevelopments in the westerlies.
b) The perturbations are modified by using differences betweenthe members of an ensemble
of data assimilations (EDA). The EDA is an ensemble ofindependent 4D-Var data
assimilations where the main analysis error sources(observation, model and boundary
conditions errors) are represented by perturbing the relativequantities (observations,
forecast model and sea surface temperature, respectively)according to their estimated
accuracy.
c) Model uncertainty is represented by two different stochasticperturbation techniques. One,
stochastic physics, randomly perturbs the tendencies in thephysical parametrization
schemes. The other, stochastic backscatter, models the kineticenergy in the unresolved
scales by randomly perturbing the vorticity tendencies. Thewhole globe is perturbed,
including the tropics. The Control forecast is run withoutstochastic physics.
In the idealized schematics Figure 22, one can see how the4D-Var 12-hour assimilation
window (left part of the diagram) modifies the initialtrajectories of the EDA members (in
yellow) to reflect the information from the assimilatedobservations (black dots with error
bars). The analysis trajectories (in green) show the impact ofthe new observations on the
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ensemble: the spread of the ensemble has been reduced and a biashas been corrected by
reducing the magnitude of some of the highest values.
At the end of the assimilation window the EDA is used to provide(a) background error
information for the successive deterministic analysis update and(b) the initial perturbations of
the ensemble around the control analysis.
Figure 22 Schematic representation of the ensemble ofassimilations (EDA, green) and its link with the
forecast ensemble (ENS, blue). The yellow area represents thespread of forecasts starting from the
previous EDA analyses 12 hours earlier.
Once the different sets of SVs have been separately calculatedover the northern and southern
hemispheres and over the tropics between 30 N and 30 S, they arelinearly combined (using
coefficients randomly sampled from a Gaussian distribution) andadded to the EDA
perturbations to make a set of 25 global perturbations. Thesigns of these 25 global
perturbations are then reversed to obtain another set of 25mirrored global perturbations.
This yields a total of 50 global perturbations for 50alternative analyses and forecasts.
Consecutive members therefore have, pair-wise anti-symmetricperturbations. The anti
symmetry may, depending on the synoptic situation and thedistribution of the perturbations,
disappear after one day or so, but can occasionally be noticed3-4 days into the perturbed
forecasts (seeFigure 23 andFigure 24).
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Figure 23:1000 hPa perturbed analyses and forecasts of members 1and 2 from 15 August 2010, 12
UTC; the positive and negative perturbations in red and bluedashed lines respectively. At initial time
the perturbations are pair-wise anti symmetric, weakening ordeepening a shallow low-pressure system
on the westernmost Atlantic (upper images). 24 hours into theforecast, the perturbations in member 1
have led to the low splitting into two cyclonic pressuresystems, in member 2 to a significant deepening
of the single low pressure system.
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Figure 24: Same asFigure 23 but for 15 August 2010 00 UTC. Inthis case the anti symmetry is stillclearly seen 24 hours into theforecast, member 1 having the low deepened and displaced into aslightlymore westerly position, member 2 having the low weakenedand displaced into a slightly more easterly
position.
3.2.2. Quality of the individual perturbed analyses
An unavoidable consequence of modifying the initial conditionsaround the most likely
estimate of the truth, the 4D-Var analyses, is that theperturbed analysis is on average slightly
degraded. The RMS distance from truth for a perturbed analysisis, in the ideal case, on
average 2 times the RMS distance of the unperturbed analysisfrom the truth (see Figure25).
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Figure 25: A schematic illustration of why the perturbed initialconditions will, on average, be further
from the true state than the Control analysis is. The analysisis known, as well as its average error, but
not the true state of the atmosphere (which can be anywhere onthe circle). Any perturbed analysis can
be very close to the truth, but is in a majority of the casesmuch further away: in the ideal case the
average distance is the analysis error times Consequently, theproportion of the perturbed analyses that are better than theControl
analysis for a specific locationand for a specific parameter,such as the 2 m temperature or
MSLP, is only 35% (see Figure 26); considering more than onegrid point lowers the
proportion even further.
Figure 26: Although the perturbed analyses differ on averagefrom the Control analysis as much as
Control from the truth, for a specific gridpoint only 35% of theperturbed analyses are closer to the
truth than the Control analysis.
If an ensemble member is closer to the truth than to the Controlin, for example, Paris, it
might not be so in Berlin. Indeed, the larger the area, the lesslikely that any of the perturbed
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members are better than the non-perturbed Control analysis(Palmer et al, 2006). For a region
the size of a small ECMWF Member State, only about 7% of theperturbed analyses are, on
average, better than the Control analysis, for the larger MemberStates this decreases to only
2% (seeFigure 27).
With respect to the forecasts, in the short range only a smallnumber of the perturbed forecasts
are, on average, more skilful than the Control forecast.However, with increasing forecast
range the average proportion of perturbed forecasts that arebetter than the Control forecast
increases, eventually asymptoting to 50%.
Figure 27: Schematic representation of the percentage ofperturbed forecasts with lower RMS error
than the Control forecast for regions of different sizes:northern hemisphere, Europe, a typical small
Member State and a specific location. With increasing forecastrange, fewer and fewer perturbed
members are worse than the Control (from Palmer et al 2006).
3.2.3. Quality of the individual perturbed forecasts
Since the perturbed analyses have, ideally on average, 41%larger analysis errors than
Control, this makes the individual ensemble forecasts on averageless skilful than the
unperturbed Control forecast. The difference in predictive skillvaries with season and
geographical location, but is about one day (seeFigure 28).
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Figure 28: Schematic image of the RMS error of the ensemblemembers, ensemble mean and Control
forecast as a function of lead-time. The asymptoticpredictability limit is defined as the average
difference between two randomly chosen atmospheric states. In aperfect ensemble system the RMS
error of an average ensemble member is times the error of theensemble mean.However, what the perturbed forecasts may lack inindividual skill, they compensate for by
their large number, their ability to form good median orensemble mean values and reliable
probability estimations. The information should therefore beused in its totality, i.e. from all
the members in the ensemble. The low proportion of perturbedforecast members better
than the Control in the short range makes the task of trying toselect the member of the day
very difficult and, perhaps, impossible. There are no knownmethods to a priori identify the
best ensemble member beyond the first day or so (see Sections2.6.2 and 4.2).
3.3.
The ensemble at different lead times
To use computer resources cost-efficiently, the horizontalresolution of the ensemble is
reduced at day 10, and the remainder of the forecast (out to 15or 32 days) is run at half the
horizontal resolution of the first 10 days.
3.3.1. The 10-day range
In spite of its coarser resolution, which is half that of HRES,the ensemble Control forecast
performs very similarly to HRES with respect to synopticpatterns. Differences are most
noticeable for small-scale extreme weather events, where HRES isable to generate,
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