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Transcript of Page 1© Crown copyright 2004 The use of an intensity-scale technique for assessing operational...
© Crown copyright 2004 Page 1
The use of an intensity-scale technique for assessing operational mesoscale precipitation
forecasts
Marion Mittermaier and Clive Wilson
© Crown copyright 2004 Page 2
Outline
1. An intensity-scale technique (Casati et al. 2004)2. Model output and data description3. Value added by higher resolution for a severe
flooding event (Boscastle, August 2004)4. A modified sign-test statistic for highlighting
persistent/prevalent errors at the monthly time scale.
5. Radar vs gauge as “truth”6. Concluding remarks
1. An intensity-scale technique
….. best illustrated with an example ….
(from Casati, 2004)
Radar Model forecast
from Casati (2004)
Radar > 1 mm Forecast > 1 mm Binary error image
X > u X < u
Y > u Hits a
False Alarms
b a+b
Y < u Misses c
Correct Rejections
dc+d
a+c b+d a+b+c+d=n
© Crown copyright 2004 Page 5
MSE skill score
,
, , ,
1u u random uu
u best u random u random
MSE MSE MSESS LMSE MSE MSE
1
0
-1
-2
-3
-4
luSS ,
threshold (mm/h)
spat
ial s
cale
(km
)
[from Casati (2004)]
Axes multiples of 2
© Crown copyright 2004 Page 6
2. Model output and data description
Mesoscale version of the Unified Model (MES) runs 4 times a day at ~12 km over the UK (for Unified Model description see Davies et al., QJRMS, 2005)
Newly implemented 4-km model now runs twice a day over the UK (see Bornemann et al, this conference)
Radar-rainfall accumulations available on a 5 km x 5 km national grid
~2700 rain gauges have been used to produce a daily gridded rainfall product also on a 5 km x 5 km grid
© Crown copyright 2004 Page 7
3. Boscastle: the benefit of higher resolution?
How does one assess added benefit?
Output from the MES and 4 km model isn’t directly comparable Basis of comparison should ideally be the same.
Solution:
Average the 4 km model output to the 12 km grid and compare against the same 12-km averaged radar rainfall product.
…. consider 6-hr rainfall between 12-18Z from the 00Z run …
On 16.08.2004 over 180 mm were recorded by one gauge in a 5-hr period during a highly localised flooding event.
12-18Z
12-18Z
12-18Z
4 km 00Z 6 hr rainfall
MES 00Z 6 hr rainfall
4 km 00Z avg 6 hr rainfall E
rror
sca
le (k
m)
2x
16x
1 mm 64 mm
2x
16x
Max radar = 44 mm
68 mm 7 mm46 mm
Rainfall threshold (mm)
© Crown copyright 2004 Page 9
Distribution-free test as normality of errors can’t be assumed.
B = number of +ve skill scores for a given scale and intensity during a given time interval, e.g. 1 month.
Hypotheses:
H0 : SS >= 0 (implicit positive and skillful)
H1 : SS < 0 (less skill than a random forecast)
H0 is rejected if b <= bn,where B ~ bi(n, 0.5) for small samples (n < 40), = 0.025
The value of (n – B) / n is shaded in intensity-phase space for each scale and intensity where H0 is rejected.
4. A modified sign-test statistic
© Crown copyright 2004 Page 10
Added benefit: comparison of prevalent errors at the monthly time scale
(sub-)“grid” scale errors are more prevalent at trace rainfall totals for the 4 km model
prevalent errors at twice and four times the MES grid length for thresholds > 16 mm are less for the 4 km model (captures large totals better)
May 2005 MES vs radar May 2005 4 km avg vs radar
X X X X X X X X X X X X X X
X X XX X
X X
X48 km
32 mm
© Crown copyright 2004 Page 11
5. Radar vs gauge as “truth”
Slight shifts in the distribution of prevalent errors at the monthly time scale
Overall pattern very similar Radar-rainfall fields preferred as they are truly spatial with a
greater observation frequency
August 2004 MES vs radar August 2004 MES vs gauge
X X X X X X X X X X
X X XX X X
X X XX X X
© Crown copyright 2004 Page 12
6. Concluding remarks
1. The 4 km model contains much more detail (even when averaged to 12 km)
2. Detail does not necessarily equal accuracy! Raw model output needs to be averaged
3. Scale-intensity analyses show that the need for averaging is (almost) independent of grid length (there is always grid noise, regardless)
4. The difference between error analyses produced using radar (true spatial) and gauge (point-interpolated) fields is minimal. Recommend that radar fields are used also because of the high observation frequency.
Questions?
12-18Z
12-18Z
12-18Z
Radar 12Z 6 hr rainfall
MES 12Z 6 hr rainfall
4 km 12Z avg 6 hr rainfall E
rror
sca
le (k
m)
Rainfall threshold (mm)
19 June 2005Flash flooding caused by thunderstorms overNorth Yorkshire
Haar Wavelet filter
deviation from mean value
mean value
+
+
mean value on all the domain Casati et al., 2004, Met Apps
© Crown copyright 2004 Page 16
• Wavelets are locally defined real functions characterised by a location and a spatial scale.• Any real function can be expressed as a linear combination of wavelets, i.e. as a sum of components with different spatial scales. • Wavelet transforms deal with discontinuities better than Fourier transforms do
Haar mother wavelet 1
-1
0 1 2 4 n n+1
An intensity-scale technique using wavelets
wavelet decomposition of the binary errorScale
L
lluu EE
1,
from Casati (2004)