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Ground based evaluation of cloud forecasts. Robin Hogan Ewan O’Connor, Anthony Illingworth University of Reading, UK Clouds radar collaboration meeting 17 Nov 09. Project. Aim: to retrieve and evaluate the crucial cloud variables in forecast and climate models

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ground based evaluation of cloud forecasts
Ground based evaluation of cloud forecasts.

Robin Hogan

Ewan O’Connor, Anthony Illingworth

University of Reading, UK

Clouds radar collaboration meeting 17 Nov 09

  • Aim: to retrieve and evaluate the crucial cloud variables in forecast and climate models
    • 8+ models: global, mesoscale and high-resolution forecast models
    • Variables: cloud fraction, LWC, IWC, plus a number of others
    • Sites: 4 across Europe plus worldwide ARM sites
    • Period: several years to avoid unrepresentative case studies
  • Current status
    • Funded by US Department of Energy Climate Change Prediction Program to apply to ARM data worldwide
    • Application to FP7 Infrastructure - bid 3 Dec 09

joint with EUSAAR (trace gases) + Earlinet (lidar/aerosol)

ACTRIS: Aerosol Clouds and Trace gases Research Infrastructure Network.

level 1b
Level 1b
  • Minimum instrument requirements at each site
    • Cloud radar, lidar, microwave radiometer, rain gauge, model or sondes
  • Radar
  • Lidar
level 1c
Level 1c
  • Instrument Synergy product
    • Example of target classification and data quality fields:





level 2a 2b
Level 2a/2b
  • Cloud products on (L2a) observational and (L2b) model grid
    • Water content and cloud fraction

L2a IWC on radar/lidar grid

L2b Cloud fraction on model grid

cloud fraction
Cloud fraction



Met Office

Mesoscale Model


Global Model





Swedish RCA model

cloud fraction in 7 models
Cloud fraction in 7 models
  • All models except DWD underestimate mid-level cloud
  • Some have separate “radiatively inactive” snow (ECMWF, DWD); Met Office has combined ice and snow but still underestimates cloud fraction
  • Wide range of low cloud amounts in models
  • Not enough overcast boxes, particularly in Met Office model
  • Mean & PDF for 2004 for Chilbolton, Paris and Cabauw

0-7 km

Illingworth et al. (BAMS 2007)

comparison of nae 12km and 4km model
Comparison of NAE (12km) and 4km model

3 months data. 2009.

Ideally global and 1.5km model as well.

Compare 12km with 4km and also 4km averaged 3x3 boxes.

Is the performance any better at 4km?

Can make more overcast skies?

Any improvement on mid level cloud?

What about low level clouds?

What about getting the right cloud in the right place at

the right time - skill scores?


NAE 12km

Mean fraction too low

Equitable threat score:

Falls with fraction

threshold and age

of forecast.


4km 3 x 3

Mean fraction too low

Equitable threat score:

Spin up 0-5 hrs


4km each box

Mean fraction too low

Equitable threat score:

Same as 3x3.



NAE 12km 6-11hr

Can’t make overcast



4km (3x3) 6-11hr

Can’t make overcast



4km (each box) 6-11hr

Can’t make overcast

BL clouds – worse!


IWC 4km 3X3

Improved pdf

mid level cloud

Still missing

the higher iwc.

diurnal cycle composite of clouds
Diurnal cycle composite of clouds

Barrett, Hogan & O’Connor (GRL 2009)

Radar and lidar provide cloud boundaries and cloud properties above site


Local mixing scheme: too little entrainment


Prognostic TKE scheme: no diurnal evolution

All other models have a non-local mixing scheme in unstable conditions and an explicit formulation for entrainment at cloud top: better performance over the diurnal cycle

contingency tables
Contingency tables

Model cloud

Model clear-sky

Observed cloud Observed clear-sky

For given set of observed events, only 2 degrees of freedom in all possible forecasts (e.g. a & b), because 2 quantities fixed:

- Number of events that occurred n =a +b +c +d

- Base rate (observed frequency of occurrence) p =(a +c)/n

desirable properties of verification measures
Desirable properties of verification measures
  • “Equitable”: all random forecasts receive expected score zero
    • Constant forecasts of occurrence or non-occurrence also score zero
    • Note that forecasting the right cloud climatology versus height but with no other skill should also score zero
  • Useful for rare events
    • Almost all measures are “degenerate” in that they asymptote to 0 or 1 for vanishingly rare events

Extreme dependency score

  • Stephenson et al. (2008) explained this behavior:
    • Almost all scores have a meaningless limit as “base rate” p  0
    • HSS tends to zero and LOR tends to infinity
  • They proposed the Extreme Dependency Score:
    • where n = a + b + c + d
  • It can be shown that this score tends to a meaningful limit:
symmetric extreme dependency score
Symmetric extreme dependency score
  • EDS problems:
    • Easy to hedge (unless calibrated)
    • Not equitable
  • Solved by defining a symmetric version:
    • All the benefits of EDS, none of the drawbacks!

Hogan, O’Connor and Illingworth (2009 QJRMS)

skill versus height
Skill versus height
  • Most scores not reliable near the tropopause because cloud fraction tends to zero




  • New score reveals:
    • Skill tends to slowly decrease at tropopause
    • Mid-level clouds (4-5 km) most skilfully predicted, particularly by Met Office
    • Boundary-layer clouds least skilfully predicted



what is the origin of the term ets
What is the origin of the term “ETS”?
  • First use of “Equitable Threat Score”: Mesinger & Black (1992)
    • A modification of the “Threat Score” a/(a+b+c)
    • They cited Gandin and Murphy’s equitability requirement that constant forecasts score zero (which ETS does) although it doesn’t satisfy requirement that non-constant random forecasts have expected score 0
    • ETS now one of most widely used verification measures in meteorology
  • An example of rediscovery
    • Gilbert (1884) discussed a/(a+b+c) as a possible verification measure in the context of Finley’s (1884) tornado forecasts
    • Gilbert noted deficiencies of this and also proposed exactly the same formula as ETS, 108 years before!
  • Suggest that ETS is referred to as the Gilbert Skill Score (GSS)
    • Or use the Heidke Skill Score, which is unconditionally equitable and is uniquely related to ETS = HSS / (2 – HSS)

Hogan, Ferro, Jolliffe and Stephenson (WAF, in press)




Clouds in the 4km v 12km NAE.

Diurnal cycle of BL clouds in various models.

Problems with the ETS (now GSS) – use SEDS


BL clouds in models drizzle all the time.

New observations from CloudSat/Calipso

compared with FWD model from ECMWF.



-22dBZ  0.4g/m3 or 0.001mm/hr

(1mm per month: 0.6 W/m2).


LWP 100 g/m2  0dBZ

160 times too much drizzle!

Drizzle rate 0.03mm/hr.

{20 W/m2, 300m layer cools 0.3/hr}




LWP 100 g/m2  -22dBZ




ECMWF rain flux parameterisation

Autoconversion of cloud mixing ratio qcl to rain mixing ration qr

=K qcl

Threshold term: turns off autoconversion for value below qcl,crit = 0.3 g kg-1

Without threshold term: dqr /dt  q cl

LWP of 1000g/m2  0.6 mm/hr

LWP of 100gm2  0.06 mm/hr

Add threshold assume adiabatic 0.03mm/hr (0dBZ)

So why not increase qcl.crit to stop all the drizzle forming?


This will increase the lwp of all water clouds,

make them too bright and destroy the global radiation balance.



Evidence that the clouds in ECMWF are more adiabatic than observed?


Cloud amount


Observed 25% adiabatic? Modelled 50% adiabatic?


100% adiabatic  0.03mm/hr 0dBZ 300m deep/ max LWC 0.6gm3

50% adiabatic  0.02mm/hr 450m deep/max LWC 0.45g/m3

25% adiabatic  0.01mm/hr -8dBZ 700m deep/max LWC 0.3g/m3 CSAT gate 500m.


joint pdfs of cloud fraction
Raw (1 hr) resolution

1 year from Murgtal


Joint PDFs of cloud fraction





  • 6-hr averaging

…or use a simple contingency table

skill bias diagrams
Skill-Bias diagrams

Reality (n=16, p=1/4)


Under-prediction No bias Over-prediction

Best possible forecast








Random unbiased forecast

Constant forecast of occurrence

Constant forecast of


Worst possible forecast

Hedging“Issuing a forecast that differs from your true belief in order to improve your score” (e.g. Jolliffe 2008)
  • Hit rate H=a/(a+c)
    • Fraction of events correctly forecast
    • Easily hedged by randomly changing some forecasts of non-occurrence to occurrence





Defined by Gandin and Murphy (1992):

  • Requirement 1: An equitable verification measure awards all random forecasting systems, including those that always forecast the same value, the same expected score
    • Inequitable measures rank some random forecasts above skillful ones
  • Requirement 2: An equitable verification measure S must be expressible as the linear weighted sum of the elements of the contingency table, i.e. S = (Saa +Sbb +Scc +Sdd) / n
    • This can safely be discarded: it is incompatible with other desirable properties, e.g. usefulness for rare events
  • Gandin and Murphy reported that only the Peirce Skill Score and linear transforms of it is equitable by their requirements
    • PSS = Hit Rate minus False Alarm Rate = a/(a+c) – b/(b+d)
    • What about all the other measures reported to be equitable?
some reportedly equitable measures
Some reportedly equitable measures

HSS = [x-E(x)] / [n-E(x)]; x = a+d ETS = [a-E(a)] / [a+b+c-E(a)]

E(a) = (a+b)(a+c)/nis the expected value of a for an unbiased random forecasting system

Simple attempts to hedge will fail for all these measures

LOR = ln[ad/bc] ORSS = [ad/bc – 1] / [ad/bc + 1]

Random and constant forecasts all score zero, so these measures are all equitable, right?

skill versus cloud fraction threshold
Skill versus cloud-fraction threshold
  • Consider 7 models evaluated over 3 European sites in 2003-2004



  • LOR implies skill increases for larger cloud-fraction threshold
  • HSS implies skill decreases significantly for larger cloud-fraction threshold
extreme dependency score
Extreme dependency score
  • Stephenson et al. (2008) explained this behavior:
    • Almost all scores have a meaningless limit as “base rate” p  0
    • HSS tends to zero and LOR tends to infinity
  • They proposed the Extreme Dependency Score:
    • where n = a + b + c + d
  • It can be shown that this score tends to a meaningful limit:
    • Rewrite in terms of hit rate H =a/(a +c) and base rate p =(a +c)/n :
    • Then assume a power-law dependence of H on p as p  0:
    • In the limit p  0 we find
    • This is useful because random forecasts have Hit rate converging to zero at the same rate as base rate: d=1 so EDS=0
    • Perfect forecasts have constant Hit rate with base rate: d=0 so EDS=1
skill versus cloud fraction threshold1
Skill versus cloud-fraction threshold




  • SEDS has much flatter behaviour for all models (except for Met Office which underestimates high cloud occurrence significantly)
a surprise
A surprise?
  • Is mid-level cloud well forecast???
    • Frequency of occurrence of these clouds is commonly too low (e.g. from Cloudnet: Illingworth et al. 2007)
    • Specification of cloud phase cited as a problem
    • Higher skill could be because large-scale ascent has largest amplitude here, so cloud response to large-scale dynamics most clear at mid levels
    • Higher skill for Met Office models (global and mesoscale) because they have the arguably most sophisticated microphysics, with separate liquid and ice water content (Wilson and Ballard 1999)?
  • Low skill for boundary-layer cloud is not a surprise!
    • Well known problem for forecasting (Martin et al. 2000)
    • Occurrence and height a subtle function of subsidence rate, stability, free-troposphere humidity, surface fluxes, entrainment rate...
key properties for estimating life
Key properties for estimating ½ life
  • We wish to model the score S versus forecast lead time t as:
    • where t1/2 is forecast “half-life”
  • We need linearity
    • Some measures “saturate” at high skill end (e.g. Yule’s Q / ORSS)
    • Leads to misleadingly long half-life
  • ...and equitability
    • The formula above assumes that score tends to zero for very long forecasts, which will only occur if the measure is equitable
which measures are equitable
Expected values of a–d for a random forecasting system may score zero:

S[E(a), E(b), E(c), E(d)] = 0

But expected score may not be zero!

E[S(a,b,c,d)] = S P(a,b,c,d)S(a,b,c,d)

Width of random probability distribution decreases for larger sample size n

A measure is only equitable if positive and negative scores cancel

Which measures are equitable?

ETS & ORSS are asymmetric

n = 16

n = 80

asyptotic equitability
Asyptotic equitability
  • Consider first unbiased forecasts of events that occur with probability p = ½
  • Expected value of “Equitable Threat Score” by a random forecasting system decreases below 0.01 only when n > 30
  • This behaviour we term asymptotic equitability
  • Other measures are never equitable, e.g. Critical Success Index CSI = a/(a+b+c), also known as Threat Score
what about rarer events
What about rarer events?
  • “Equitable Threat Score” still virtually equitable for n > 30
  • ORSS, EDS and SEDS approach zero much more slowly with n
    • For events that occur 2% of the time (e.g. Finley’s tornado forecasts), need n > 25,000 before magnitude of expected score is less than 0.01
    • But these measures are supposed to be useful for rare events!
possible solutions
Possible solutions
  • Ensure n is large enough that E(a) > 10
  • Inequitable scores can be scaled to make them equitable:
    • This opens the way to a new class of non-linear equitable measures

Report confidence intervals and “p-values” (the probability of a score being achieved by chance)

properties of various measures
Properties of various measures
  • Truly equitable
  • Asymptotically equitable
  • Not equitable
skill versus lead time
Skill versus lead time



  • Only possible for UK Met Office 12-km model and German DWD 7-km model
    • Steady decrease of skill with lead time
    • Both models appear to improve between 2004 and 2007
  • Generally, UK model best over UK, German best over Germany
    • An exception is Murgtal in 2007 (Met Office model wins)
forecast half life
Forecast “half life”

Met Office DWD



3.0 d

  • Fit an inverse-exponential:
    • S0 is the initial score and t1/2 is the half-life
  • Noticeably longer half-life fitted after 36 hours
    • Same thing found for Met Office rainfall forecast (Roberts 2008)
    • First timescale due to data assimilation and convective events
    • Second due to more predictable large-scale weather systems

2.7 days

2.6 days

3.2 d

3.1 days

2.9 days

4.0 days

2.7 days

3.1 d

2.9 days

2.4 days

4.3 days

2.9 days

4.3 days

2.7 days

why is half life less for clouds than pressure
Why is half-life less for clouds than pressure?
  • Different spatial scales? Convection?
    • Average temporally before calculating skill scores:
    • Absolute score and half-life increase with number of hours averaged
geopotential height anomaly vertical velocity
Geopotential height anomaly Vertical velocity
  • Cloud is noisier than geopotential height Z because it is separated by around two orders of differentiation:
    • Cloud ~ vertical wind ~ relative vorticity ~ 2streamfunction ~ 2pressure
    • Suggests cloud observations should be used routinely to evaluate models
satellite observations icesat
Satellite observations: IceSAT
  • Cloud observations from IceSAT 0.5-micron lidar (first data Feb 2004)
  • Global coverage but lidar attenuated by thick clouds: direct model comparison difficult

Lidar apparent backscatter coefficient (m-1 sr-1)


Optically thick liquid cloud obscures view of any clouds beneath

Solution: forward-model the measurements (including attenuation) using the ECMWF variables

global cloud fraction comparison
Global cloud fraction comparison

ECMWF raw cloud fraction

  • Results for October 2003
    • Tropical convection peaks too high
    • Too much polar cloud
    • Elsewhere agreement is good
  • Results can be ambiguous
    • An apparent low cloud underestimate could be a real error, or could be due to high cloud above being too thick

ECMWF processed cloud fraction

IceSAT cloud fraction

Wilkinson, Hogan, Illingworth and Benedetti (MWR 2008)

testing the model skill from space
Testing the model skill from space

Tropical skill appears to peak at mid-levels but cloud very infrequent here

Clearly need to apply SEDS to cloud estimated from lidar & radar!

Highest skill in north mid-latitude and polar upper troposphere

Unreliable region

Is some of reduction of skill at low levels because of lidar attenuation?

Lowest skill: tropical boundary-layer clouds

Wilkinson, Hogan, Illingworth and Benedetti (MWR 2008)

ccpp project
CCPP project
  • US Dept of Energy Climate Change Prediction Program recently funded 5-year consortium project centred at Brookhaven, NY
    • Implement updated Cloudnet processing system at Atmospheric Radiation Measurement (ARM) radar-lidar sites worldwide
    • Ingests ARM’s cloud boundary diagnosis, but uses Cloudnet for stats
    • New diagnostics being tested
  • Testing of NWP models
    • NCEP, ECMWF, Met Office, Meteo-France...
    • Over a decade of data at several sites: have cloud forecasts improved over this time?
  • Single-column model testbed
    • SCM versions of many GCMs will be run over ARM sites by Roel Neggers
    • Different parameterization schemes tested
    • Verification measures can be used to judge improvements
summary and outlook
Summary and outlook
  • Model comparisons reveal:
    • Half-life of a cloud forecast is between 2.5 and 4 days, much less than ~9 days for ECMWF 500-hPa geopotential height forecast
    • In Europe, higher skill for mid-level cloud and lower for boundary-layer cloud, but larger seasonal contrast in Southern US
  • Findings applicable to other verification problems:
    • “Symmetric Extreme Dependency Score” is a reliable measure of skill for both common and rare events (given we have large enough sample)
    • Many measures regarded as equitable are only so for very large samples, including the “Equitable Threat Score”, but they can be rescaled
  • Future work (in addition to CCPP):
    • CloudSat & Calipso: what is the skill of cloud forecasts globally?
    • What is half-life of ECMWF cloud forecasts? (Need more data!)
    • Near-real-time evaluation for rapid feedback to NWP centres?
    • Dept of Meteorology Lunchtime Seminar, 1pm Tuesday 3rd Nov: “Faster and more accurate representation of clouds and gases in GCM radiation schemes”
monthly skill versus time
Monthly skill versus time
  • Measure of the skill of forecasting cloud fraction>0.05
    • Comparing models using similar forecast lead time
    • Compared with the persistence forecast (yesterday’s measurements)
  • Lower skill in summer convective events
statistics from amf
Statistics from AMF
  • Murgtal, Germany, 2007
    • 140-day comparison with Met Office 12-km model
  • Dataset released to the COPS community
    • Includes German DWD model at multiple resolutions and forecast lead times
possible skill scores
Possible skill scores
  • “Cloud” deemed to occur when cloud fraction f is larger than some threshold fthresh
  • To ensure equitability and linearity, we can use the concept of the “generalized skill score” = (x-xrandom)/(xperfect-xrandom)
    • Where “x ” is any number derived from the joint PDF
    • Resulting scores vary linearly from random=0 to perfect=1
  • Simplest example: Heidke skill score (HSS) uses x=a+d
    • We will use this as a reference to test other scores
  • Brier skill score uses x=mean squared cloud-fraction difference, Linear Brier skill score (LBSS) uses x=mean absolute difference
    • Sensitive to errors in model for all values of cloud fraction
alternative approach
Alternative approach
  • How valid is it to estimate 3D cloud fraction from 2D slice?
    • Henderson and Pincus (2009) imply that it is reasonable, although presumably not in convective conditions
  • Alternative: treat cloud fraction as a probability forecast
    • Each time the model forecasts a particular cloud fraction, calculate the fraction of time that cloud was observed instantaneously over the site
    • Leads to a Reliability Diagram:


No resolution

No skill

Jakob et al. (2004)


ECMWF cloud fraction after processing

IceSAT cloud fraction

ECMWF raw cloud fraction

Simulate lidar backscatter:

  • Create subcolumns with max-rand overlap
  • Forward-model lidar backscatter from ECMWF water content & particle size
  • Remove signals below lidar sensitivity
testing the model climatology
Testing the model climatology

Error due to uncertain extinction-to-backscatter ratio

Reduction in model due to lidar attenuation


4. ECMWF rain flux parameterisation

Autoconversion of cloud mixing ratio qcl to rain mixing ration qr

=K qcl

Threshold term: turns off autoconversion for value below qcl,crit = 0.3 g kg-1

Without threshold term: dqr /dt  q cl

LWP of 1000g/m2  0.6 mm/hr

LWP of 100gm2  0.06 mm/hr

Add threshold assume adiabatic 0.03mm/hr (0dBZ)

So why not increase qcl.crit to stop all the drizzle forming?


This will increase the lwp of all water clouds,

make them too bright and destroy the global radiation balance.