optimized advection of radar reflectivities

Atmospheric Research 100 (2011) 213–225

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Atmospheric Research

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Optimized advection of radar reflectivities

Martin Ridal⁎, Magnus Lindskog, Nils Gustafsson, Günther HaaseSwedish Meteorological and Hydrological Institute, S-601 76 Norrköping, Sweden

a r t i c l e i n f o

⁎ Corresponding author.E-mail address: [email protected] (M. Ridal).

0169-8095/$ – see front matter © 2010 Elsevier B.V.doi:10.1016/j.atmosres.2010.12.016

a b s t r a c t

Article history:Received 29 April 2009Received in revised form 1 November 2010Accepted 10 December 2010

A nowcasting system for generation of short-range precipitation forecasts has been developedat the Swedish Meteorological and Hydrological Institute (SMHI). The methodology consists ofutilising a time-series of radar reflectivity composites for deriving an advection field, whichwillgive a better representation of the motion of the precipitation pattern compared to a modelwind field. The advection field is derived applying a 4-dimensional variational data assimilationtechnique. The resulting field is then used for a semi-Lagrangian advection of the latest availablereflectivity field forward in time. During the forecast, the advected field is gradually replacedby a numerical weather prediction forecast in order to include the onset of convection andadvection into the radar coverage area. In an idealised examplewith simulated observations thefunctionality of themethod is demonstrated. For a case study of a full scale example the resultingprecipitation forecast shows large improvements compared to the operational numericalweather prediction model used at SMHI, especially for forecasts up to three hours, where thelargest influence from the radar advection occurs. In an objective validation of the structure,amplitude and location of modelled precipitation, where the forecasts are compared to radarobservations, these findings are confirmed. The same validation of model runs over a longertime period also clearly indicates that the amplitude, structure and location of the precipitationpatterns are significantly improved as compared to a short-range forecast from the operationalforecast model used at SMHI.

© 2010 Elsevier B.V. All rights reserved.

Keywords:NowcastingRadarAdvectionVariational data assimilation

1. Introduction

The interest andneed for short-rangeprecipitation forecastsare constantly increasing. Users like road service companies,agriculture and hydro-power companies are more and moredependent on accurate precipitation forecasts since largeeconomic values can be lost. Weather radars provide reflectiv-ity informationwith a high spatial and temporal resolution andare ideal to exploit for these purposes. Precipitation rates canbe derived from radar reflectivities and the information froma network of radars may be combined into composites.

Numerical weather prediction (NWP) models are power-ful tools for medium to long range precipitation forecasts.The crossover point at which nowcasting is better than

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NWP forecasts is constantly moving towards shorter timescales depending on the spatial scale of interest. However,data assimilation systems still suffer from limited knowledgeof couplings/balances between moisture and dynamics. Thiscauses model spin-up problems, which affect forecastsof moisture, clouds and precipitation for forecast lead timesof 1–12 hours. Including observed radar reflectivities in thedata assimilation together with better initialisation ofmoisturebalance and new moisture control variables (Holm et al.2002) can reduce this spin-up. There is however still room fordeveloping innovative nowcasting methods for forecast leadtimes of 1–6 hours in operational environments. Most opera-tional NWP models also suffer from a spatial resolution that istoo coarse to resolve many important features e.g. heavyprecipitation in small to medium scale river catchments. Forinstance, would the HYPE (Hydrological Predictions for theEnvironment) model developed at the SwedishMeteorologicaland Hydrological Institute (SMHI) (Lindström et al. 2010),

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Fig. 1.Operational HIRLAM-11model domain (rectangle) and radar coverageused for KNEP (circles).

214 M. Ridal et al. / Atmospheric Research 100 (2011) 213–225

benefit from improved precipitation forecasts for 0–6 hourslead times.

Short forecasts, by extrapolating precipitation data fromsingle radars or composites, have been made for some time(e.g. Austin and Bellon, 1974; Browning and Collier, 1982),but the range of predictability for such forecasts is verylimited. Combining the high resolution radar data andnowcasting methods with the features of NWP models hasproven to be very powerful for forecast lead times of 1–6 h,e.g. in the Nimrod system (Golding, 1998), the MAPLE system(Germann and Zawadzki, 2002, 2004) or in the probabilisticSTEPS model (Bowler et al., 2006). A comprehensive study ofthe skill of different nowcasting systems for the convectivescale has been compiled by Wilson et al. (2010).

The COST 731 Action deals with the quantification offorecast uncertainty in meteo-hydrological forecast systems(Rossa et al., 2010, 2011-this issue). To improve precipitationforecasts advanced nowcasting and data assimilation schemes(mainly based on radar data) have been developed as part ofthe meteo-hydrological forecast chain.

A system for nowcasting and short-range forecasts ofprecipitation, KNEP (Swedish acronym for short-range precip-itation forecasts) using radar reflectivities, has been developedat SMHI. KNEP is based on the early work by Andersson (1993).It uses a variational approach to track the movement ofindividual precipitation systems from a time sequence ofradar composites following the ideas of GermannandZawadzki(2002, 2004, 2006). The advection field that is in bestcorrespondence with the movements of the individual precip-itation systems is determined. KNEP is built on componentsof the HIRLAM (HIgh Resolution Limited Area Model) NWPvariational data assimilation system (Gustafsson et al., 2001;Lindskog et al., 2001; Huang et al., 2002). The elementsobtained from the HIRLAM 4-dimensional variational dataassimilation (4D-Var) include a background error constraintand advanced observation handling. Once the advection fieldis determined, the latest available radar reflectivity field isadvected forward in time 3–6 hours by applying a semi-Lagrangian advection scheme (Hortal 2002). Semi-Lagrangianadvection allows for a dynamic advection compared to now-casting models that use extrapolation and it is more accuratethan Eulerian advection. After the advection the resultingprecipitation field is gradually replaced by a short-range NWPprecipitation forecast. This is necessary in order to handle theprecipitation formation or decay by physical or dynamicalprocesses during the nowcasting period. This blending of fieldsis made using a linearly weighted average between the twofields. Other, more sophisticated methods like morphingtechniques include phase corrections to the fields (e.g. Wonget al., 2009 or Atencia et al., 2010). These methods take intoaccount that a precipitation field can be correct in amplitude(precipitation amount) but slightly wrong in location. Amethod including phase correction would move the precipita-tion field in the blending. Our method would instead give asmoothed precipitation field of less amplitude.

The purpose of this paper is to describe the methodologyand functionality of this newly developed nowcasting system.In Section 2 the radar data used as input for the model ispresented, in Section 3 themethodology is described in detail,followed in Section 4, by examples of results from experi-ments with both synthetic and real data. A validation of the

method is presented in Section 5 and the main results aresummarised and conclusions are given in Section 6.

2. Radar data

The radar data used within this study originate from theNordic Weather Radar Network (NORDRAD). NORDRAD con-sists of around 35 C-band Doppler weather radars in Norway,Sweden, Finland, Denmark, Estonia and Latvia. The coverage ofthe radars used for KNEP is illustrated by the gray circles inFig. 1. Note that the radars from the Baltic countries are notincluded. Surface reflectivity composites have a horizontalresolution of 2 km and are available every 15 min. One-hourradar-based accumulated precipitation products are alsogenerated at the same horizontal resolution using an adjust-ment technique employing gauge observations.

The generation of reflectivity composites involves severalquality control steps. A beam propagation model (BPM) isused to correct for topographical beam blockages. The BPMsimulates the radar's field of view based on information onthe radar scan geometry, the vertical refractivity gradient andthe topography (Bech et al., 2007). Correction matrices areapplied to each individual radar scan assuming atmosphericstandard propagation. A multisource method employingoperationally-classified cloud-type products derived fromMeteosat-8 data has been implemented in the compositeprocessing chain for identification and removal of non-precipitation echoes (Michelson, 2006). Currently, radarechoesare removed only in areas classified as being cloud-free. Finally,a gauge-adjustment technique is applied to generate surfacereflectivity products (Michelson and Koistinen, 2000). Asummary of the radar data quality in the Nordic countries hasbeen published by e.g. Saltikoff et al. (2004, 2010) and Haase et

215M. Ridal et al. / Atmospheric Research 100 (2011) 213–225

al. (2005). The operational Z–R relation used to convert surfacereflectivity into surface precipitation is:

Z = 200R1:5

where Z is expressed in mm6/m3 and R is in mm/h.

3. The KNEP model

KNEP is built on components of the HIRLAM NWPvariational data assimilation system (Gustafsson et al.,2001; Lindskog et al., 2001; Huang et al., 2002). One of theoperational HIRLAM versions at SMHI produces forecasts ata horizontal resolution of roughly 11 km and for 60 verticallevels. The horizontal extent of the radar composites used,described in Section 2, fits within this operational HIRLAMdomain. This is illustrated in Fig. 1, which shows the radarcoverage and the HIRLAM model domain as a frame. In orderto handle the precipitation formation or decay by physicalor dynamical processes during the nowcasting period theextrapolated radar field is gradually replaced by a short-rangeHIRLAM forecast. Another reason for this is that there mightbe advection of precipitation into the area covered by theradars during the extrapolation time.

The KNEP model thus consists of three steps. First, a dataassimilation step is performed inwhich radar reflectivities areassimilated in order to capture themotion of the precipitationpatterns. This will produce a field of motion vectors. Second, asemi-Lagrangian advection step is performed, i.e. the forecastis calculated, using the motion vectors obtained from the dataassimilation step. Finally, in a postprocessing step, by simplyusing a linearly weighted average, a gradual replacement ofthe radar based forecast with a NWP forecast is carried out.These three steps are discussed inmore detail in the followingsubsections.

3.1. 4-Dimensional data assimilation

The variational approach to determine the advection fieldthat will be used for the advection is based on the HIRLAM4-dimensional variational data assimilation. It consists infinding the model state vector, x0, including a 2-dimensionaltime invariant advection field (u,v) and an initial reflectivityfield ψ0 that minimizes the following cost function, J:

Jðx0Þ = Jbðx0Þ + Joðx0Þ =12

x0−xbð ÞTB−1 x0−xbð Þ

+12ðHMx0−ψobsÞTR−1ðHMx0−ψobsÞ

Here Jb measures the distance to a background modelstate, xb, and Jo measures the distance to the reflectivityobservations, ψobs. The time invariant background state is afirst guess of the 2-dimensional advection field, valid atthe beginning of the assimilation window, and a constantreflectivity field. M is the advection model that propagatesψ forward in time, to the time of the observations. Notethat at time t, ψt=Hxt, where H is the observation operator.In our case H simply consists of horizontal interpolation ofthe model state reflectivity to the positions of the reflectivityobservations, ψobs. B is the matrix containing the spatial

covariances of the background error field (u, v, and ψ) and Ris the matrix containing the covariances of the reflectivityobservation errors. The denotation T indicates the transpose,or adjoint, of an operator.

The background advection field is a wind field taken fromthe latest available SMHI operational HIRLAM forecast. Thebackground field is used to prevent short-lived convectivecells or other randomly occurring echoes to affect theresulting advection field. Echoes that are present during allof the assimilation period, on the other hand, like stationaryorographic precipitation, will generate a zero wind field sincethe background error is set rather high. An example of howthe background wind field is affected is shown in Section 4.1.The background wind field is taken from a vertical levelof approximately 850 hPa. This level was chosen since it isfairly close to the ground but still elevated enough not to beaffected too much by the surface. Tests have shown however,that the background level is not so important for the resultingadvection field.

The background reflectivity field is set to a constant value.This value is arbitrary. The observations ψobs, consist of six2-dimensional radar reflectivity composites, spread evenlyin time within a 1.5 hour assimilation window.

The background error covariances are based on the onesderived for the HIRLAM model by applying the NMC method(Parrish and Derber, 1992). Horizontal advection and reflec-tivity error correlations are represented. The reflectivityerror correlations are taken from the moisture backgrounderror correlations at vertical level of roughly 850 hPa. Cross-correlations between reflectivity background error and advec-tion field background errors are not represented. Backgrounderror standard deviations for the advection field and thereflectivity field have been scaled. This scaling is based onestimated relative uncertainties in the background advectionfield, the background reflectivity field and the reflectivityobservations. Through the scaling it is implicitly assumed thatmuch larger uncertainties are associatedwith the backgroundreflectivity and advection fields, than with the reflectivityobservations. The errors of the reflectivity observations arethus assumedmuch smaller than the errors of the backgroundfield. Furthermore the reflectivity observation errors areassumed horizontally uncorrelated. The main reason is thedifficulty of estimating these error correlations. When usingradar data spatial observation error correlations are usuallyavoided through the creation of super observations or datathinning in assimilation systems (e.g. Salonen et al. 2009). Toalleviate the potential effect of correlated observation errors(Liu and Rabier 2002) we will consider such an approach infuture versions of KNEP.

The cost function is minimized iteratively. The minimiza-tion problem to be solved is non-linear, since the advectionmodel Mx0 depends non-linearly on the advection field(u and v included in M) and on the initial reflectivity field ψ0.To handle the non-linearities, the minimization problemis solved by successive re-linearizations in an outer minimi-zation loop and by solving a standard linear minimizationproblem of a quadratic cost function in each such outer loopiteration. The solution of the quadratic minimization problemmay be referred to as the minimization inner loop. For eachminimization inner loop, a tangent linear model Mx0 isapplied. This is obtained by linearization around the solution

Table 1The partitioning between radar advection field and NWP forecast over time.

Forecast time (hours) 1 2 3 4 5 6

Radar advection field 90% 80% 60% 40% 20% 10%NWP forecast 10% 20% 40% 60% 80% 90%


for the advection field (u,v) and the initial reflectivity (ψ)from the previous outer loop iteration. Let (x0)k be thesolution to be found from outer loop iteration k and let Mk−1

be the tangent-linear model obtained by linearization aroundthe model state xb+(x0)k−1. The inner loop minimizationcost function is given by:

Jððx0ÞkÞ = Jbððx0ÞkÞ + Joððx0ÞkÞ =12ððx0Þk−xbÞTB−1ððx0Þk−xbÞ

+12ðHðMðx0Þk−1 + Mk�1ððx0Þk−ðx0Þk−1ÞÞ

−ψobsÞTR−1ðHðMðx0Þk−1 + Mk�1ððx0Þk−ðx0Þk−1ÞÞ−ψobsÞ

For each iteration in solving the inner loop minimizationproblem, a calculation of the gradient of the cost functionwith respect to (x0)k valid at time t0 is required:

∇J = ∇Jb + ∇Jo = B−1ððx0Þk−xbÞ + ðMk�1ÞTHTR−1ðHðMðx0Þk−1

+ Mk�1ððx0Þk−ðx0Þk−1ÞÞ−ψobsÞ

Each inner loop iteration (in outer loop k) involve runninga tangent-linear advection model, Mk−1 (linearised aroundthe solution from outer loop k−1), 1.5 hours forward in timewithin the assimilation window. It also involves running thetranspose (or adjoint, (Mk−1)T) of the advection model1.5 hours backward in time. The procedure continues untilthe cost function has reached its minimum. If needed, afterthis we may carry out another minimization outer loopiteration. After convergence of the outer loop minimization,this means that the reflectivity observations have induced areflectivity field and an advection field that is ‘mostconsistent’ with the 2-dimensional observed reflectivitypattern and its variation in time. That advection field shouldthen later on be used to advect the latest available observedradar reflectivity composite a few hours forward in time.

It should be mentioned that what is meant by a modelstate being ‘most consistent’ with the radar observations isstrongly dependent on the pre-scribed error statistics for thebackground advection and reflectivity fields. It also dependson the error statistics for the reflectivity observations. Thesequantities describe how the observation information isdistributed in space and also to what extent the observationsinfluence the advection field and the reflectivity field,respectively.

3.2. Semi-Lagrangian advection

Semi-Lagrangian advection schemes combine attractivefeatures of Eulerian and Lagrangian advection schemes. In anEulerian advection scheme an observer watches the atmo-spheric flow from a fixed geographical point. In a Lagrangianadvection scheme the observerwatches the atmosphericflow,while travelling with the air-parcel. Eulerian schemes arewell suited for fixed Cartesian grids, while Lagrangian are not.On the other hand, Eulerian advection schemes need veryshort time-steps to prevent numerical instability. Significantlylonger time-steps may be applied in Lagrangian integrationschemes still maintaining stability and high numericalaccuracy. In semi-Lagrangian schemes a new set of air-parcelsis chosen each time step such that the air parcels arrive exactlyat the points of a regular Cartesian grid at the end of the time

step. To further improve the numerical stability, linear terms,affected by gravitational oscillations, may be treated in animplicit manner. Such a scheme is called semi-implicit semi-Lagrangian (Robert, 1981).

For this study we have used the Stable Extrapolation Two-Time Level Extrapolation scheme (SETTLS) which is a semi-implicit numerical integration scheme (Hortal, 2002). Ascompared to earlier versions of semi-Lagrangian schemes ithas the advantage that extrapolation in time of the velocitiesused for the computation of trajectories, as well as non-linearmodel terms, is avoided. This fact makes it stable. The SETTLSscheme is used for advecting the latest available radarreflectivity composite (the last in the series used within the4D-Var procedure) 6 hours forward in timewith a time step of5 min. The time invariantmotion vectors described above, areused for the advection.Whenmaking a forecast from time t0 itis thus assumed that the advection field derived from a timeseries of radar composites from t0−1.5 h to t0 is representa-tive also for the period t0 to t0+6 h and that variations in timecan be neglected. Furthermore it is assumed that physicalprocesses causing formation or decay of precipitation may beneglected as compared to advection. These assumptions areconsidered to be valid if the forecast length is kept shorterthan a couple of hours.

3.3. Postprocessing

In a postprocessing step the radar extrapolation isgradually replaced by an NWP forecast. This step is necessaryin order to compensate for the effects of neglecting the time-variation of the advection field and the representation ofphysical processes. The effect of the latter is that undevelopedconvection, not present in the advected radar composite butdeveloping within the forecast time range, is not captured. Itis also a way to model precipitation that is advected into theradar coverage area during the forecast. In an operationalenvironment, the latest available HIRLAM forecast is used.

The blending is performed by a linearlyweighted average ofthe two precipitation fields. Different weights have been testedfor several situations. The results show that the radar advectionfield can be used up to 6 h formost cases. Theweights we havechosen to use are given in Table 1. In the first hour the radaradvection data dominates the final product with a gradualincrease of the influence of the NWP field with increasingforecast length. The optimum would be to define dynamicweights that depend on e.g. the precipitation patterns orthewind speed. Currently, however theweights are fixed for allsituations.

Since most end users of the product are interested in avery local area, the treatment of the area outside the radarcoverage is not so important. In Figs. 6–9 we have chosen toinclude the full NWP field outside the radar area since it givesa large scale view of the weather situation. Effects at the radarcoverage boundaries can be seen as a result of this.


4. Functionality

4.1. Simulated reflectivity observations

To illustrate the functionality of KNEP an idealisedexample is constructed. The background advection field isset uniform all over the domain, having a speed of 15 m/stowards east. The background reflectivity field is set to 0.1everywhere. Two simulated observations, both with the value150, are provided moving towards south-east with anapproximate speed of 7 m/s. The positions of the observationsin each assimilation window are illustrated in Fig. 2 togetherwith the background advection field.

Initially we tuned the error statistics for this individualcase to match the two observations. However, this leads tounrealistic values for cases with real data. The reason is thattwo single observations should not be allowed to affect themotion vectors too much. This will lead to unrealistic fieldsin the case of single or short-lived convective cells. Thus, thebackground field is given more weight. The resulting motionvectors are shown in Fig. 3. The advection field is clearlyaffected by the observations, which have decreased the speedof the advection field to about 11.5 m/s, illustrated by thecolouring in Fig. 3. The speed does not fully decrease to 7 m/s,which is in agreement with what we would be expected ifthis was a real situation. Due to the same reason the winddirection is only slightly directed more southward comparedto the initial field.We can also see how the background field isaffected away from the observations due to the horizontalscale of the background error correlations as mentioned inSection 3.1. The error statistics describe how the observationsare distributed in space.

8 9 10 11 12 1351

52

53

54

55

56

57

58

59

60

Fig. 2. Geographical location of two simulated observations every 15 min within thmoving parallel from north west towards south east. Note that the arrows only indicy-axis indicate the longitudes and latitudes respectively.

4.2. A full scale example

During the day of 27 March 2009 there was a precipitationsystem passing over southern Scandinavia from south westto north east, followed by showers. The system was rotatingcyclonically associated with a low pressure system locatedroughly between Great Britain and Denmark. The overallweather situation is illustrated in Fig. 4.

A forecast starting at 16 UTC is chosen as an example sinceit is illustrative in many ways. In this example six radar-composites, within a 1.5 hour interval from 14.30 to 16 UTC,were used as observations in the data assimilation step. Theresulting advection field is shown in Fig. 5A,B shows thefirst guess field from HIRLAM, which is a 10 hour forecastinitialised at 06 UTC. In the central and southern part ofSweden, it can be seen that the HIRLAM forecasted winds areweaker and directed more towards the west than the derivedadvection field. This is because the HIRLAM wind is blowingalong the isobars in the trough seen in Fig. 4, in which thefront is placed. The variationally derived advection field, onthe other hand, representsmore themotion of the front and istherefore directed more to the north. The derived field is thenused to advect the radar data composite from 27 March 2009at 16 UTC, 6 hours forward in time.

In the postprocessing step, the advected precipitationfield is gradually replaced by the HIRLAM forecast from06 UTC, resulting in a blended product with a one hour timeresolution. After six hours the advected field is given verylittle weight and its influence is therefore very small on thefinal precipitation forecast.

In Fig. 6A the 16+01 KNEP forecast of accumulatedprecipitation in mm is shown. The corresponding 06+11

14 15 16 17 18 19

e assimilation window. The observations are illustrated by the small crosses,ate the background advection direction and a relative wind speed. The x- and

image of Fig.�2

Fig. 4. The weather situation over the North Atlantic and Europe, 27 March 2009 at 00 UTC .The map is produced by the UKMetOffice. See their website for furtherinformation.

Fig. 3. The resulting advection field after the data assimilation step. The arrows indicate the direction while the advection (wind) speed (m/s) is indicated by thecolours. The starting condition is illustrated in Fig. 2. The x- and y-axis indicate the longitudes and latitudes respectively.


image of Fig.�3

Fig. 5. Advection field derived from a time series of radar composites (A) and the corresponding HIRLAM wind forecast (B). Colour scale is m/s and the arrows arenot scaled, they just show the direction and relative wind speed. The x- and y-axis indicate the longitudes and latitudes respectively.


image of Fig.�5

Fig. 6. A: Radar advection forecast for a forecast length of 1 h from 27 March2009 at 16+01 UTC. The field is of 1 h accumulated precipitation consistingof 90% radar advection and 10% HIRLAM forecast. B: The correspondingradar composite translated to rain rate and valid at the same time. C: Theaccumulated precipitation between the 06+10 and 06+11 UTC HIRLAMforecast from the same day. This forecast is used in the final calculation of thefield in the upper left panel (10%).Colour scale is mm/h. The x- and y-axisindicate the longitudes and latitudes respectively.

Fig. 7. Same as Fig. 6 but for a forecast length of 3 h (16+03). The radaradvection forecast field (A) consists of 60% radar advection and 40% HIRLAMforecast. The HIRLAM forecast (C) is a one hour accumulation between the16+12 and 16+13 UTC forecasts. The x- and y-axis indicate the longitudesand latitudes respectively.


image of Fig.�6

image of Fig.�7


HIRLAM forecast is shown in Fig. 6C. The same forecast isused for the gradual replacement by an NWP forecast inthe final product. The field in Fig. 6A thus consists of 90%radar composite advection and 10% of the HIRLAM forecastshown in Fig. 6C. These two fields are compared with theradar composite in Fig. 6B, which also shows a one houraccumulation of precipitation valid at the same time. One canclearly see that the KNEP field is more similar to the radarcomposite with better positioning of the precipitation anda better small scale structure.

Fig. 7 shows the same situation as in Fig. 6 but after a 3 hourintegration forward in time (16+03). The HILRAM field isin this case the accumulated precipitation between 06+12and 06+13 forecasts. The corresponding radar observationis shown in Fig. 7B. Again the KNEP forecast, now including60% radar advection, shows a better agreement with theradar observation. After three hours however, we start tosee strange effects at the edges of the radar coverage area,where no radar data is advected into the area while the NWPforecast still has rather low weight. This is obvious in theBaltic Sea close to Baltic states.

The advection fields seen in Fig. 5 show that thevariationally derived field moves in a more northwarddirection. From the precipitation fields in Fig. 7 we see thatthe HIRLAM forecast (Fig. 7C) does not reach as far north asit should compared to the radar observation (Fig. 7B). TheKNEP field however, does reach a bit too far north, indicatingthat the motion direction is correct but perhaps the velocityof motion is a bit too strong.

It can also seem less obvious to use a forecast as long as13 h for the gradual replacement with NWP. One reason forthis is that we need to be sure that the forecast is available atthe start of the radar advection model in the operationalenvironment, in this case 16 UTC. Another reason is to avoidspin-up problems in the NWP precipitation field. Forconsistencywe therefore use forecasts from the same analysisthroughout the radar advection forecast time. For comparisonthe forecast closest in time, a seven hour forecast from12 UTC (12+07), is shown in Fig. 8. Compared to the forecast

Fig. 8. Same as Fig. 7C but precipitation accumulated between the 12+06and 12+07 UTC forecasts from 27 March 2009 at 12 UTC. The x- and y-axisindicate the longitudes and latitudes respectively.

Fig. 9. Same as Fig. 6 but for a forecast length of 5 h (16++5). The radaradvection forecast field (A) consists of 20% radar advection and 80% HIRLAMforecast. The HIRLAM forecast (C) is a one hour accumulation between the06+14 and 06+15 h forecast. The x- and y-axis indicate the longitudes andlatitudes respectively.

image of Fig.�8

image of Fig.�9

Table 3SAL verification comparing radar observations against HIRLAM forecasts as inan operational environment valid at the same time as the forecasts in Table 2.

Forecast time S A L

06+11 UTC 1.718 0.349 0.15306+13 UTC 1.709 0.463 0.17806+15 UTC 1.801 0.523 0.131


in Fig. 7C there are no dramatic differences, except for theintense precipitation over Denmark which is better describedin the later forecast (Fig. 8).

Finally the resulting fields after 5 hours integrationforward in time (16+05) are shown in Fig. 9. At this timethere is only 20% radar advection included in the final KNEPproduct (Fig. 9A). We can also see that the KNEP forecast andthe HIRLAM (06+15) forecast are very similar. Compared tothe radar observation valid at the same time (Fig. 9B) it is notpossible to say which one of the two forecasts is more similarto the radar composite.

5. Verification

For this study we have used a rather novel verification toolcalled SAL (Wernli et al., 2008). This method compares radarcomposites to a model field by identifying so called objects.The objects are areas where the precipitation is above athreshold value. This value is determined from the maximumamount of precipitation in the area. The comparisons are thenmade for the structure, amplitude and location of the objectsin the model fields and the radar composites.

The values for structure (S) and amplitude (A) can varyfrom −2 to 2, where 0 is a perfect agreement with theobservations. Positive values for S imply more stratiformprecipitation patterns in the model, compared to theobservations, while negative values result from moresmall scale patterns in the model. Positive values for Aindicate that there is a too large amount of precipitation inthe model compared to the observations, while negativevalues indicate the opposite. The values for location (L) canvary from 0 to 2, where 0 indicates that the centre ofmass for all model objects is in perfect agreement with thecentre of mass for all observed objects. The larger the valuefor L, the more displaced the modelled object is from theobserved.

For the example in Section 4.2, from 27 March 2009 at16 UTC, a verification using SAL gives the presented inTables 2, 3 and 4. The verifications are made inside theradar coverage area and the threshold value for identifying anobject is 1/15 of the maximum value of precipitation withinthis domain. The threshold value is the same as used byWernli et al. (2008).

The first thing to notice is that the values for L make verylittle sense. The reason for this is that we compare fields withdifferent horizontal resolutions. If an object in one field is asmoothed version of the other, as indicated by the positive Svalues, it is likely that the location is given a better value thanif we compare fields with similar resolution.

For S and A on the other hand, we see a clear improvementusing the KNEP forecast, Table 2, compared to the HIRLAM

Table 2SAL verification comparing radar observations against KNEP forecasts on 27March 2009.

Forecast time S A L

16+01 UTC 1.314 0.149 0.17816+03 UTC 1.624 0.308 0.18716+05 UTC 1.789 0.474 0.136

Table 4SAL verification comparing radar observations against the HIRLAM forecastsclosest in time to the start of the KNEP forecast.

Forecast time S A L

12+05 UTC 1.757 0.262 0.16312+07 UTC 1.676 0.405 0.18912+09 UTC 1.677 0.525 0.127

forecasts, Tables 3 and 4. The positive values for S indicatethat the models give more stratiform precipitation ascompared to the radar observations. This is not surprisingsince the radar observations can observe more small scalefeatures. We see, especially for the short forecasts, that thestructures are improved by KNEP with more small scalefeatures compared to HIRLAM. After 5 h, there is not muchimprovement but this forecast includes 80% HIRLAM so thevalues are expected to be similar. In fact the HIRLAM forecastclosest in time, Table 4, is better that the KNEP forecast. Itshould be remembered however, that the KNEP forecast after5 h consists 80% of the HIRLAM forecast initialised at 06 UTC.

The positive amplitude values indicate that the modelsoverestimate the amount of precipitation as compared to theradar observations. Here we see a clear improvement usingKNEP for all forecast lengths.

The examples and SAL verification numbers shown aboveare just three individual examples and the numbers are notnecessarily representative. In order to extend the statisticalbasis, KNEP has been run over a period of 44 days, duringAugust and September 2008. This period covers severalweather types including both convective activity as well asfrontal precipitation. The verification is made for the threehour forecast from 00, 06, 12 and 18 each day giving 176forecast–observation pairs. The results for KNEP are pre-sented in Fig. 10, while the corresponding verification forHIRLAM is presented in Fig. 11. These figures show thatthe structure of the KNEP forecasts (including the gradualNWP influence) is more centred around zero than theHIRLAM forecast. The dashed lines indicate the 25% and75% percentiles. This indicates that the precipitation in theHIRLAM forecast is more stratiform and that the KNEPforecasts contain more small scale features. The amplitudeis narrower around zero for KNEP, indicating that theprecipitation amounts are more similar to the radar observa-tions. It is also obvious that the colours of the circles in thetwo figures are darker blue for the KNEP forecasts, indicatinga better location of the precipitation objects.

It should be noted that cases with very low precipitationor very few identified objects are not included. These cases

Fig. 10. SAL verification for the radar advection forecast using radar observations over 44 days. Three hour forecasts from 00, 06, 12 and 18 are included. The valuesfor location (L) are colour scaled. The dashed lines indicates the 25 and 75 percentiles for the amplitude (A) and the structure (S).


may otherwise lead to large errors since the number ofcompared objects is very small.

6. Concluding remarks

A system for deriving the advection field from radarechoes, consistent with the latest available time-series ofradar reflectivity composites has been developed. Themethodology utilises components of the HIRLAM 4D-Var,including data assimilation, semi-Lagrangian advection and apostprocessing step in which the radar advection forecast isgradually replaced by a NWP forecast. The last step is neededin order to capture developing convection or advection ofprecipitation across the radar coverage boundaries.

The functionality of the system, called KNEP, has beendemonstrated in an idealised experiment, using a time-seriesof two reflectivity observations, as well as in a realistic fullscale assimilation experiment. Verification shows that thereare large benefits by using KNEP compared to the operationalHIRLAM 11 km forecast model with the strongest impact forthe short forecast lengths, 1–4 h. For forecast lengths of 5–6 hthe resulting fields from KNEP consist to a very large degree(more than 80%) of HIRLAM fields through the gradualreplacement. The impact is therefore not as clear but there isstill some benefit using KNEP.

The verification of the three hour forecasts over a longertime period containing both convective and frontal precipi-

tation has also been made with satisfying results. The KNEPforecasts show large improvements, with more small scaleprecipitations, compared to the operational HIRLAM 11 kmforecasts.

In the further development of KNEP, it would be highlydesirable to improve the removal of non-precipitation echoes.We would also like to include the effect of a gradualreplacement of the advection field during the forecast in thesame way as for precipitation. The advection field would thenbe replaced gradually by anNWPwind forecast. This is slightlymore complicated than for the precipitation as it has to bedone during the forecast and not in a postprocessing step. Theway the blending of fields is made in the postprocessingalso needs to be refined, e.g. by phase correction techniquesor some other form of object displacement.

A version of KNEPwith very high time resolution does alsoexist. This version, which advects the precipitation only onehour, gives an output every 15 min, i.e. the same as the timeresolution of the input radar fields. It is desirable for usersto have the radar images and the forecast with the sametime resolution. In this version we cannot, presently, do thegradual replacement with an NWP forecast since theoperational forecast output at SMHI has the time frequencyof one hour. Without blending we do not want to extend theforecast to more than 1 or 1.5 h.

Finally it should be mentioned that the advection systemis rather general and the principle could be used for a wide

image of Fig.�10

Fig. 11. SAL verification for the HIRLAM using radar observations over 44 days. Three hour forecasts from 00, 06, 12 and 18 are included. The values for location (L)are colour scaled. The dashed lines indicates the 25 and 75 percentiles for the amplitude (A) and the structure (S).


range of applications, e.g. using satellite images instead ofradar reflectivities or forecasting advection of oil patterns,by generating the advection field from a time-sequence ofobservations of the oil pattern.

Acknowledgements

The authors would like to acknowledge Ulf Andrae andLisa Bengtsson for valuable assistance regarding GRIBhandling and the SAL software. We would also like to thankPer Undén for constructive comments on the manuscript.This work was performed in the framework of COST-731(Propagation of uncertainty in advanced meteo-hydrologicalforecast systems) and the SAMP project.

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