1- near-optimized filtered forecasts (noff) using wavelet analysis (o-maple)

1- Near-Optimized Filtered Forecasts (NOFF) using wavelet analysis (O-MAPLE)

2- Probabilistic MAPLE (Probability of rain occurrence at different thresholds)

3- Model-MAPLE merging using optimal weights

McGill-NIMR Phase III (2009) Goals

Summary of Phase I & II

1- Adaptation of the McGill Variational Echo Tracking (VET) algorithm to Korea radar composites

2- Nowcasting algorithm using the Semi-Lagrangian advection scheme based on the VET motion field

3- Verification in terms of CSI, POD, FAR, ETS, Cross-correlation and RMS using a 4-month data set

4- Sensitivity tests (vector density, dBZ threshold, time interval,

weights for smoothing and conservation of reflectivity constraints) to determine the optimum VET input parameters

Verification results in terms of CSI obtained from the 4-month data sample.Reveals the poor forecastibility of higher rainfall rates with time Ex: CSI (10 mm/h) < 20% for forecasts > 1 hour

Conclusion: remove the unpredictable scales by optimal smoothing of the rainfall field with time.

Near-Optimized Filtered ForecastsTurner et al. JAM (2004)

- Wavelength length scale Lw = 2m∆x for 0 ≤ m ≤ mmax and ∆x=grid length

- Wavelet spectrum S(m): Normalized difference between pairs of points Lw apart on the same map.

- The wavelet cospectrum Co(m) involves different maps .

- A map can be reconstructed as the sum, over all scales, of the product of the wavelet transform coefficients with the corresponding wavelet smoothed image.

- Optimum weights w(m,T) that optimally dampen the features of scale m so as to minimize the errors between the forecast and the observation map at time T:

w(m,T) =Cofo(m)/Sf(m) OFF filters

where Cofo is the cospectrum between the forecast and observed maps and

Sf(m) is the spectrum of the forecast map.

- Nearly optimum (NOFF) weights can be derived in real-time from the OFF weights of a previous forecast, (1 h), and then applying the known spatial-time interdependence, that is, w(L,T) = w (2L,2T)

Left, composite map at T0, (0500 KST 1-July-2006), and the 20-min, 1-h, 2-h, 3-h and 4-h “regular” forecasts

Right, the corresponding “filtered” NOFF forecasts with mmax=8

20-min

T0 map at 0500 KST 1-July-2006

1-h

2-h

3-h

4-h

mmax=7mmax=8

mmax=6 mmax=5

Boundary artefacts on 4-h forecasts with large mmax reduced or eliminated with smaller mmax

Boundary artefacts

1-h

2-h

mmax=8

mmax=8

mmax=6

mmax=6

Comparison of NOFF forecasts generated with mmax=8 with those generated with mmax=6

Comparison of NOFF forecasts generated with mmax=8 with those generated with mmax=6

3-h

4-h

mmax=8

mmax=8

mmax=6

mmax=6

As expected, the NOFF forecasts yield better scores in terms of ADIF, RMS and of the cross-correlation coefficient .

(4-month data sample: July & Nov. ’06, Feb & May ‘07)

Surprisingly, unlike the results of Turner et al. (2004) with U.S. data,NOFF forecasts showed a significant improvement in terms of alsothe CSI parameter.

Probability Forecasts

- Because of the combined uncertainty of the forecast displacement and, especially,of the evolution of the reflectivity field, nowcasting cannot produce accurate, deterministic forecasts for higher rainfall rates or for long periods of time.

- Filtered forecasts is an honest response to this limitation but may not satisfy some end-users because the precipitation structure is gradually removed with lead time.

Solution: Probability forecasts complement the “regular ” and the “NOFF” forecasts by indicating the probability of observing a precipitation rate above a few selected thresholds.

The area A = L2 over which the probability is computed increases with lead time T according to the space-time slope relationship

L (km) = T(min) (L is limited to 160 km)

Left, composite map at T0, (0500 KST 1-July-2006), and the 20-min, 1-h, 2-h, 3-h and 4-h “regular” forecasts

Right, the corresponding “combo probability” maps derived from the reflectivity distribution over an area A=L2 such that L(km)=T(min), T being the forecast length in minutes.

20-min

T0 map at 0500 KST 1-July-2006

1-h

2-h

3-h

4-h

Probability forecasts generated using the space-time relationship L = T0.8. No upper limit needs to be imposed on L because L=80 km for a 4-h forecast

Radar nowcasts have better skill initially as they assimilate the precipitation field,but lose skill as storm evolution is not considered in the Lagrangian advection.

NWP precipitation forecasts perform poorly initially as the precipitation fieldis not well captured but are better in the longer term as they capture storm evolution.

Could ENSEMBLES of radar and NWP forecasts provide better forecasts bycompensating for each other’s shortcomings ? What is the optimum algorithm for combining the radar nowcasts and NWP forecasts ?

Merging of Radar data with NWP output

Forecast time (hr)

CSI

Basic NWP-RADAR Merging Technique(Kilambi & Zawadzki, 2005, 32nd Radar Conf)

- Determine the climatological skill of NWP forecasts and of radar nowcasts

- For scores like CSI where increasing magnitude implies an increase in skill, let the weight for a given forecast method m, (RADAR or NWP), and for a lead time t be Wm,t = [1/(1-(CSIm,t)p)]-1

where the exponent p =2.5 magnifies the difference between the two methods.

Ex: CSI ratio of (0.6/0.4) yields a weight ratio of 3.45 to 1.

- The combined value is the weighted average of the NWP and RADar estimates:

=[NWP*Wnwp,t’ + RAD*Wrad,t]/[Wnwp,t’ + Wrad,t)

The model lead time t’ is generally longer than t for the radar because models are executed less frequently. (But model skill scores are nearly independent of time for the time intervals of interest)

An example of a 2-h KLAPS forecast of a 10-min accumulation made at 0600 UTC on 14-July-2009 and valid for 0800 UTC.

Same KLAPS data as in the previous slide, but converted into a rainfall rate map (mm/h) and over the same domain and map projection used for MAPLE.

Composite radar map for the corresponding time (1700 KST, 14 July 2009)

Relatively good comparison withCSI(0.5 mm/h)=0.40 andCross-correl=0.313 but large ratio KLAPS/RADAR=2.34

KLAPS

RADAR

KLAPS Spin-up Time

Relative rainfall generated by KLAPS forecasts in July 2009 as a function of theforecast length. The amount generated by the 60-min forecasts is taken as reference.The spin-up time is reached within 30 minutes.

Comparisons of KLAPS and of MAPLEforecasts for July 2009 in terms of the indicated skill scores.Bias-corrected results (by dividing by 1.83) are also provided for KLAPS

KLAPS skill does not reach MAPLE’s skill even after 6 hours. Therefore, theKLAPS-MAPLE merging is not expected toyield improved forecasts.

2-h KLAPS forecast valid for 0200 KST,9-July-2009, showing a total absence of the stratiform precipitation seen on thecomposite radar map below but with an excess in convection.

Composite radar map for the corresponding time

CSI(0.5 mm/h)=0.16Cross-correl=0.026 KLAPS/RADAR=1.35

KLAPS

RADAR

More KLAPS-RADAR Comparisons

2-h KLAPS forecast valid for 1700 KST, 9-July-2009


CSI(0.5 mm/h)=0.41Cross-correl=0.374

KLAPS/RADAR=4.64

Better results than 15 hours earlier, but large KLAPS overestimation from excessive convection.

KLAPS

RADAR



CSI(0.5 mm/h)=0.27Cross-correl=0.302

KLAPS/RADAR=0.82

Good scores but extensive light precip. on radar not captured by KLAPS. Vice-versa for convection.

KLAPS

RADAR



CSI(0.5 mm/h)=0.03Cross-correl=-0.023

KLAPS/RADAR=0.24

No skill three hours later. Light precip. not present on KLAPS forecast. Note possible phase error.

KLAPS

RADAR




KLAPS/RADAR=0.12

Again, light precip. not on KLAPS.Phase error on the convection.

RADAR

KLAPS




KLAPS/RADAR=0.80

Light & moderate precip. seen on radar but not on KLAPS. Too many convective cells on KLAPS.

KLAPS

RADAR

Automatic Weather Stations of the Korean Network.

Conclusions and Proposed Future Work

1- Near-Optimal Filtered Forecasts (NOFF) have been applied to Korean radar

composites that filter the unpredictable scales with increasing lead time,

resulting in significant improved verification scores, including the CSI.

2- Probability maps for various thresholds have been generated and a suggested method of display has been illustrated.

3- A comparison of KLAPS forecasts with radar composites has been made for July 2009. Scores are not as good has hoped for because of the tendency for KLAPS to generate excessive convection at the expense of light or moderate precipitation. Some phase or spatial errors have been noticed.

4- A comparison of KLAPS and of MAPLE forecasts with an independent data set, ie., the Korean AWS network, is proposed as part of a continuing McGill-NIMR collaboration in order to better assess their respective weights in a merged KLAPS-MAPLE forecast.

1- near-optimized filtered forecasts (noff) using wavelet analysis (o-maple)

Documents