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Mean Geoptential for Cluster 4
Object-oriented verification of WRF forecasts from 2005
SPC/NSSL Spring Program
Mike Baldwin
Purdue University
References
• Baldwin et al. (2005): Development of an automated classification procedure for rainfall systems. Mon. Wea. Rev.
• Baldwin et al. (2006): Challenges in comparing realistic, high-resolution spatial fields from convective-scale grids. Symposium on the Challenges of Severe Convective Storms 2006 AMS Annual Meeting
• Baldwin et al. (2003): Development of an events-oriented verification system using data mining and image processing algorithms. AMS 2003 Annual Meeting 3rd Conf. Artificial Intelligence
Types of data
• gridded fields of precipitation or reflectivity
• GRIB format has been used
• program expects models and observations to be on the same grid
Basic strategy
• compare forecast “objects” with observed “objects”• objects are described by a set of attributes related to
morphology, location, intensity, etc.• multi-variate “distance” can be defined to measure
differences between “objects” combining all attributes• “good” forecasts will have small “distances”• “bad” forecasts will have large “distances”• errors for specific attributes for pairs of matching fcst/obs
objects can be analyzed
Method
• find areas of contiguous precipitation greater than a threshold
• expand those areas by ~20% and connect objects that are within 20km of each other
• characterize objects by location, mean, variance, size, measures of shape
• compare every forecast object to every observed object valid at the same time
Strengths of approach
• Attributes related to rainfall intensity and auto-correlation ellipticity were able to classify precipitation systems by morphology (linear/cellular/stratiform)
• Can define “similar” and “different” objects using as many attributes as deemed important or interesting
• Allows for event-based verification– categorical– errors for specific classes of precipitation events
Weaknesses of approach
• not satisfied with threshold-based object ID procedure
• sensitivity to choice of threshold
• currently no way to determine extent of “overlap” between objects
• does not include temporal evolution, just doing snapshots
Weaknesses, continued…
• Not clear how to “match” fcst & obs objects– how far off does a fcst have to be to be considered a
false alarm?
• How to weigh different attributes? – 250km spatial distance same as 5mm precipitation
distance?
• Do attribute distributions matter?– Forecast of heavy rain and observation of heavy rain
is a good forecast, even if magnitude off by 50%– 50% error in light rain forecast is more significant
ExampleSTAGE II WRF2 CAPS
1 mm threshold
STAGE II WRF2 CAPS
5 mm threshold
STAGE II WRF2 CAPS
analyze objects > (50 km)2
WRF2 CAPSSTAGE II
Area=12700 km2
mean(ppt)=6.5
ppt= 14.5
max corr @ 25km =0.06
2 corr @ 25 km =0.97
@ 25 km = 107°
lat = 39.6°N
lon = 95.1°W
Area=55200 km2
mean(ppt)=8.2
ppt= 30.6
max corr @ 25km =0.54
2 corr @ 25 km =0.83
@ 25 km = 107°
lat = 40.7°N
lon = 97.3°W
ExampleSTAGE II WRF2 CAPS
Area=12700 km2
mean(ppt)=6.5
ppt= 14.5
max corr @ 25km =0.06
2 corr @ 25 km =0.97
@ 25 km = 107°
lat = 39.6°N
lon = 95.1°W
Area=55200 km2
mean(ppt)=8.2
ppt= 30.6
max corr @ 25km =0.54
2 corr @ 25 km =0.83
@ 25 km = 107°
lat = 40.7°N
lon = 97.3°W
analyze objects > (50 km)2
WRF2 CAPSSTAGE II
Area=20000 km2
mean(ppt)=22.6
ppt= 535.5
max corr @ 25km =0.47
2 corr @ 25 km =0.82
@ 25 km = 149°
lat = 34.3°N
lon = 101.3°W
Area=60000 km2
mean(ppt)=9.8
ppt= 57.7
max corr @ 25km =0.43
2 corr @ 25 km =0.57
@ 25 km = 21°
lat = 40.0°N
lon = 99.6°W
ExampleSTAGE II WRF2 CAPS
Area=20000 km2
mean(ppt)=22.6
ppt= 535.5
max corr @ 25km =0.47
2 corr @ 25 km =0.82
@ 25 km = 149°
lat = 34.3°N
lon = 101.3°W
Area=60000 km2
mean(ppt)=9.8
ppt= 57.7
max corr @ 25km =0.43
2 corr @ 25 km =0.57
@ 25 km = 21°
lat = 40.0°N
lon = 99.6°W
New auto-correlation attributes
• Replaced ellipticity of AC contours with 2nd derivative of correlation in vicinity of max corr at specific lags (~25, 50, 75 km every ~10°)
Example
• Find contiguous regions of reflectivity
• Expand areas by 15%
• Connect regions within 20km
Example
• Analyze objects > 150 points (~3000 km2)
• Result: 5 objects
• Next, determine attributes for each object
Attributes
• Each object is characterized by a vector of attributes, with a wide variety of units, ranges of values, etc.
Size: area (number of grid boxes)
Location: lat, lon (degrees)
Intensity: mean, variance of reflectivity in object
Shape: difference between max-min auto-corr at 50, 100, 150 km lags
Orientation: angle of max auto-corr at 50, 100, 150 km lags
Object comparison
• each object is represented by a vector of attributes: x = (x1, x2, … ,xn)T
• similarity/dissimilarity measures – measure the amount of resemblance or distance between two vectors
• Euclidean distance: 2
1
),(
n
iii yxyxd
LEPS
• Distance = 1 equates to difference between “largest” and “smallest” object for a particular attribute
• Linear for uniform dist (lat, lon, )
• Have to be careful with
• L1-norm: AC diff = 0.4
Fo=.08
Fo=.47
n
iii yxyxd
1
),(
How to match observed and forecast objects?
= false alarm
F1
O2
O3
= missed event
Objects might “match” more than once…
If di* > dT then false alarm
If d*j > dT : missed event
…for each observed object, choose closest forecast object
dij = ‘distance’ between F i and O j
…for each forecast object, choose closest observed object
O1
F2
Example of object verf
Fcst_1
ARW 2km (CAPS) Radar mosaic
Obs_2Fcst_2
Obs_1
Object identification procedure identifies 4 forecast objects and 5 observed objects
Distances between objects
• Use dT = 4 as threshold
• Match objects, find false alarms, missed events
O_34 O_37 O_50 O_77 O_79
F_25 5.84 4.16 8.94 9.03 11.53
F_27 6.35 2.54 7.18 6.32 9.25
F_52 7.43 9.11 4.15 9.19 5.45
F_81 9.39 6.35 6.36 2.77 5.24
= .07 = .08
= .04 = .22
= .04 = -.07
median position errors
matching obs object given a forecast object
NMM4
ARW2 ARW4
Average distances for matching fcst and obs objects
• 1-30h fcsts, 10 May – 03 June 2004
• Eta (12km) = 2.12
• WRF-CAPS = 1.97
• WRF-NCAR = 1.98
• WRF-NMM = 2.02
With set of matching obs and fcsts
• Nachamkin (2004) compositing ideas– errors given fcst event– errors given obs event
• Distributions of errors for specific attributes
• Use classification to stratify errors by convective mode
Automated rainfall object identification
• Contiguous regions of measurable rainfall (similar to Ebert and McBride 2000)
Connected component labeling
• Pure contiguous rainfall areas result in 34 unique “objects” in this example
Expand areas by 15%, connect regions that are within ~20 km
• Results in 5 objects
Useful characterization
• Attributes related to rainfall intensity and auto-correlation ellipticity were able to produce groups of stratiform, cellular, linear rainfall systems in cluster analysis experiments (Baldwin et al. 2005)
New auto-correlation attributes
• Replaced ellipticity of AC contours with 2nd derivative of correlation in vicinity of max corr at specific lags (50, 100, 150km, every 10°)
How to measure “distance” between objects
• How to weigh different attributes?– Is 250km spatial distance same as 5mm precipitation
distance?
• Do attribute distributions matter?– Is 55mm-50mm same as 6mm-1mm?
• How to standardize attributes?– X'=(x-min)/(max-min)– X'=(x-mean)/– Linear error in probability space (LEPS)
Estimate of dT threshold
• Compute distance between each observed object and all others at the same time
• dT = 25th percentile = 2.5
• Forecasts have similar distributions
25th %-ile
Fcst_1
NCAR WRF 4km
Stage II radar ppt
Attributes
Area=70000 km2
mean(dBZ)=0.97
dBZ= 1.26
corr(50)=1.17
corr(100)=0.99
corr(150)=0.84
=173°
=173°
=173°
lat = 40.2°N
lon = 92.5°W
Fcst_2 Obs_1 Obs_2
Area=70000 km2
mean(ppt)=0.60
ppt= 0.67
corr(50)=0.36
corr(100)=0.52
corr(150)=0.49
=85°
=75°
=65°
lat = 44.9°N
lon =84.5°W
Area=135000
mean(ppt)=0.45
ppt= 0.57
corr(50)=0.37
corr(100)=0.54
corr(150)=0.58
=171°
=11°
=11°
lat = 39.9°N
lon = 91.2°W
Area=285000
mean(ppt)=0.32
ppt= 0.44
corr(50)=0.27
corr(100)=0.42
corr(150)=0.48
=95°
=85°
=85°
lat = 47.3°N
lon = 84.7°W
Obs_2
Obs_1