Assimilation of TCvitals -- still an problem in 2014?

Mike Fiorino, NOAA ESRL, Boulder CO 

23 November 2014

IWTC VIII is fast approaching and the head of the data assimilation group, Prof. Sharan Majumdar University of Miami asked me:

1) With the advancement of ensemble Kalman filters and 4-d schemes (and
   various hybrids thereof), is it still essential to assimilate TCvitals?
   If so, why?  Are there limitations in the DA methodology that make it
   necessary to assimilate position, central pressure etc?

2) Have some quantitative studies been done to show the impact of
   including TCvitals data in the assimilation?  Do you have a figure or
   reference that illustrates this?

3) Are there better ways to assimilate TCvitals than is being done now?

probably: 1) better field surgery to relocate the model background storm to the TCvitals position; 2) assimilation of 1-h TCvitals (through interpolation); and 3) direct assimilation of motion.  and in all cases: LESS is MORE.

4) Are we missing the appropriate observations that would make TCvitals
   unnecessary, and if so, what types of observations would we need?
   [For example, would ocean surface wind vectors in convective systems
   help?] 
observations that support the assimilation of TCvitals, e.g., IR imagery wind retrievals (Slocum and Fiorino 2011) and other retrievals from MTCSWA (Knaff et al. 20??)

This blog gives some preliminary answers; from what I consider a fairly unique view point.

Early work with TCvitals

In 1977 I was working on my M.S. at Penn State under Tom Warner and Rick Anthes.  They gave me a tape from NCEP (NMC at the time) with operational analyses for the time period of hurricane Eloise of 1975.  To say these analyses were dreadful, compared to today (hard to believe but the Eloise case is almost 40 y old), would be a gross understatement, yet I was charged with using MM0 (version 0.? of MM5 at the time) to make forecasts for Eloise. 

A quick inspection of the fields showed no TC and RH that went to 0 at the equator.  I remember calling Dr. Hovermale and saying (tongue-in-cheek), "Dr. Hovermale, did you know the relative humidity is almost 0 in the tropics?"  He said, "we have to do that to prevent the PE (the baroclinic operational model of the day) from blowing up with grid point storms.  NB: the issue of MRFocanes has a long history at NCEP...

To forecast Eloise I had to do a lot of 'data improvement' which now would be correctly called a kind of 'Data Assimilation.'  My DA scheme was a far cry from current technology, but the first problem was getting a vortex into the large-scale analyses.  There truly were very few obs to analyze Eloise, unlike today, but I did know the TCvitals -- best track position and intensity (TCvitals now include more variables such as radius of 34/50/65 kt winds).

It should not be controversial that TCvitals are the 0th-order TC observation.  The standard common complaint is that they are not objective, yet if one considers what a meteorological observation really is, I argue they are as valid as any other observation.  The problem with TCvitals is not what they are, but their error.

TCvital Observations

Let's go back to basics.  What is an observation?  My definition is that it is the result of an analysis process of *measurements*.  Consider satellite wind vectors.  The measurement are images, the analysis process is a computer code written by humans (i.e., has errors) that compares a sequence of images, and produces a meteorological observation of wind.  For TCvitals, the measurements are images, synop...and the analysis process is the forecaster.  While one can complain that the TCvitals analysis process (the human) is variable in quality, the process is constrained by things like Dvorak and forecaster training.  Thus, I maintain that TCvitals are valid observations that differ from
others TC obs in that they have a more uncertainty and a more variable error.

To not make a first-order objective of a TC DA system the correct analysis of TCvitals is to me strange.  Even if not assimilated, the TC vortex analysis will certainly be judged by the model-analyzed TCvitals.

Question 1 assumes there are sufficient non-TCvitals obs to correctly analyze the model TC vortex 'close enough' to the TCvitals position.  In the observing system of 2014, there will be situations where sufficient obs do exist, but what is 'close enough?'  An initial position error
(IPE) that is within the uncertainty of the (working) best track?  Initial intensity error (IIE, btw this means 'no' in Japanese)?  How about the wind radii?  The issue of 'close enough' begs the question of
how do we assess the quality of any TC vortex analysis.

Even if TCvital assimilation were unnecessary, TCvitals are the key TC obs used to verify both the DA and forecast.

Answer to #1

TCvital assimilation is not a technical DA issue -- 4DVAR, EnKF etc are *not* sufficient, nor are the non-TCvital obs.  Current DA schemes are adequate, what is not adequate are the obs that can sufficiently analyze the entire TC vortex.  And so we come to issue of verification...and a proposal for assessing the quality/skill of any TC DA and forecast model.

The bottom-line metric is position error (PE) and intensity error (IE) which come from a comparison of a model tracker to a best track - either 'working' (real-time, operational) or the final, reanalyzed best track.  These 'three numbers' are a bulk/gross measure of the entire model forecast field and thus cannot assess any individual process (e.g., precipitation) involved with TC motion and intensification.  However, the 3-numbers do measure net quality and are obviously the most important output for forecasting.

Answer to #2 to Answer #1

An old friend Bob Kistler, the father of the first NCEP reanalysis, wisely said that 'forecasting is the acid test of an analysis.'  In the next section we'll take a look at the current models that use a variety
of schemes to assimilate TC vitals, specifically:

Table 1. Main operational NWP models circa 2014 and TCvitals assimilation

model	ATCF ID	domain	TCvital Assimilation
ECMWF HRES	EDET	global	none
NCEP GFS	AVNO	global	'relocation' of the TC in the background (first quess) to the TCvital position
NCEP HWRF	HWRF	limited-area	relocation as in the GFS + adjustment of the *analyzed* TC vortex so the tracker intensity matches the TCvitals
NCEP GFDL	GFDL	limited-area	spinup of a symmetric version of model, add beta-gyre asymmetries to the 2-D vortex to make a 3-D vortex, then blend into the total initial fields
UKMO	EGRR	global	retrieve 1-D wind profiles from the TCvitals (synthetic obs) and assimilate
USN NAVGEM	NVGM/NGX	global	similar to UKMO except more retrievals and spectral smoothing of the background near the vortex
USN COAMPS	COTC	limited-area	similar to NAVGEM, but experimenting with vortex blending as in the GFDL and nudging

What is interesting about the current state of TCvital assimilation is that they all use elements from my M.S. thesis (Fiorino 1978 and Fiorino and Warner 1981) and/or 'bogussing' as originally proposed by Anderson and Hollingsworth (1978) at ECMWF -- ECMWF never implemented because the method was considered too artificial.  And this sentiment would prevail during my time at ECMWF where I developed a reduced retrieval scheme to assimilate TCvitals in the ERA-40 reanalysi.  Whilst ECMWF did you not use my reduced TC wind retievals, JMA did in their first global reanalysis JRA-25 (Katsushika et al., 2009) and in their second JRA-55.

The ECMWF HRES model (hi-resolution deterministic run) is the obvious to control for comparison of the current quality of TCvital assimilation.

We now look at the performance of the above models for 2014 in the atLANTic (LANT), Eastern north PACific (EPAC) and Western north PACific (WPAC).

First consider Position Error (PE - sometimes erroneously called track error) in the three basins.

2014 LANT activity was ~35% below normal (see http://ruc.noaa.gov/hfip/tcact) -- broad generalizations cannot be made.  However, the results are based on the latest versions of the models and while the growth curves in earlier years are not the same, the relationship between IPE and IIE and 12-36 h errors are similar.

Figure 1 gives the heterogeneous mean PE for the 00/12 UTC forecasts only.  Since the focus is on how a model's mean error changes and not model intercomparison, we do not make the cases homogeneous between the models.  The number of cases is not very dissimilar (except for ECMWF and UKMO which long intergrations are made only at 00/12 UTC), but homogeneous comparisons can make surprising changes in the mean error -- the means are sensitive to case selection.

Figure 1.  LANT mean FE for the models in table 1for taus 0-36 h.  Cases are heterogeneous to emphasize a model's change in error from t=0 and the early forecasts where the initial vortex would be expected to affect the forecasts.

Models with strong assimilation of TCvitals (HWRF and GFDL) have the lowest IPE.  ECMWF has higher IPE than the GFS, but the GFS relocates the background vortex to the TCvitals position.  The large IPE for NAVGEM is surprising to me, ditto for the UKMO.  Despite the 'good' assimilation of TCvitals in HWRF/GFDL (lowest IPE), the PE grows quickly whereas ECMWF shows a much slower growth.  To emphasize error growth we calculate the % improvement relative to GFS as this global model provides initial and lateral boundary conditions for all the limited-area models in the LANT in Figure 2 below.

Figure 2. LANT 2014 % improvement relative to the GFS

HWRF and GFDL have much lower IPE v GFS, but by 12h the errors are higher than the GFS.  More significantly ECMWF had similar IPE to the GFS but its error grows slower.  From tau 12-36 h the ECMWF errors are 12-28 % lower than the GFS.

This simple comparison shows that the assimilation of TCvitals does not improve the early forecasts despite low IPE. 

Let's continue to EPAC/WPAC and only the % improvement as in Fig. 2

Figure 3.  As in Fig. 2 except for EPAC

Figure 4. As in Fig. 2 except for WPAC

The results are similar to the LANT:  1) the USN models are poor performers; 2) HWRF/GFDL have better IPE compared to GFS but the early forecasts are not better; and 3) ECMWF has much higher IPE than the GFS but as soon as 12 h its track forecasts are superior.

#2: From the comparisons above, we could conclude that TCvital assimilation is not good idea for track prediction.  Alternatively, we could say that too much TCvital assimilation (HWRF/GFDL) is adding error in the initial TC vortex on scales (> 500 km) much larger than the inner core (~50 km) and thereby distorting the motion (Fiorino and Elsberry, 1989).

Next consider the third number of the three-number metric -- intensity or the maximum surface wind speed.










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WPAC 2013 -- GFS-based Models v ECMWF

 TC Performance of GFS-based US Models v ECMWF 

2013 WPAC season

Mike Fiorino, NOAA ESRL, Boulder CO 
05 November 2013

Now the that 2013 in the western North Pacific (WPAC) basin is nearly over, I've prepared preliminary error statistics for the tropical cyclone (TC) forecasts of three GFS-based US models v the ECMWF HRES (the 10-d, High-RESolution deterministic run of the IFS).  

These results are preliminary for two reasons:

1. as of time of this writing two systems are active:  30W and 31W (haiyan).  31W is the 7th typhoon to undergo 'ED' - explosive deepening which is defined as a 50 kt change in 24 h.  When you add in RI - rapid intensification (30 kt / 24 h) storms, 11 of 31 typhoons have made large intensity changes.  Further,  with the recent promotion of 31W, there have been 5 'supertyphoon' -- max winds >= 130 kt
2. I use the 'working' best track for verification vice the 'final' best track.  The final, post-season reanalysis of the fix data that makes the true or final best track is typically not available until around Feb/Mar for NHC whereas JTWC finalizes the best track during the season.

The models considered are (ATCF 4-char name in caps):

• HWRF - a three-grid, high-resolution limited-area model that use the GFS for initial and lateral boundary conditions. the grids have a horizontal resolution (dx) of 27:9:3 km
• AVNO - the GFS global model dx~21 km (a spectral model formerly know as the 'aviation' run)
• FIM9 - the ESRL global model dx=15 km (finite-volume, flow-following icosahedral dynamical core)
• EDET - ECMWF HRES, dx~15 km (a spectral model with 129 layers)

Table 1. test of tables from google docs

a	b
e	d

from google doc + snagit grab

First consider the mean forecast (track) error, defined as the great-circle distance between the best track and forecast position, but before looking at the stats, the verification system needs to be reviewed.   

There were cases of tracker failures (inability to accurately locate the model TC) that had to be eliminated to avoid skewing the statistics.  These failures are obvious when plotting the tracks, as is done in operations, and are few in number in WPAC.  Details are given in appendix A.

Figure 1.  WPAC 2013 mean forecast error [nmi]

There are no clear winners in that no single model has lower numbers at all forecast times or 'taus'.  For the longer taus 96 and 120 h (day4 D4 & D5) there is greater separation because of fewer storms going into the mean --  one bad storm can ruin the mean.  We'll dig into the details later...

A second measure of forecast performance is storm 'intensity' or a comparison of the model max surface wind speed (Vmax) to 'observed' from the (working) best track.  The standard metric for intensity is the mean absolute error (no directionality), but from a modeling perspective the mean error itself, i.e., the bias, may be more important.  Although bias is not commonly displayed, I do below:

Figure 2.  WPAC 2013 intensity or Vmax eror: lines are the mean absolute error and the bars the mean error or bias

The bars show bias and the lines the mean absolute error.  In some ways the numbers are typical but other not:

• HWRF has the highest spatial resolution (3km) and takes great care in initializing the model vortex.  Consequently, the model has near zero initial bias and shows only a slight over intensified bias out to 120 h (5 kt). More remarkable is the mean abs error of 15 kt at 72 h.  One of the best statistical-dynamical intensity aids is LGEM (Logistic Growth Equation Model) and this aid serves as a baseline for performance.  In a head-to-head comparison at 72 h: HWRF: 16|1 kt v LGEM: 19|-12 kt [MM|BB where MM is the mean abs error and BB is the bias].  A 15 kt mean abs error is simply excellent and these statistics are among the best I have ever seen for any model, numerical or statistical, in WPAC.
• The initial ECMWF mean|bias is 20|-18 kt.  These statistics imply a very poor analysis of the cyclone intensity.  The bias does decrease in time and is only -3 kt at tau 120 h.  This drop in bias is typical for the ECMWF model and in the past there were cases where the bias goes positive at 120 h.  The basic conclusion is that the ECMWF data assimilation system does a (very) poor job in analyzing the TC vortex.
•  The two GFS-based global models: AVNO and FIM9 both under analyze and under predict TC intensity.  The mean abs error is about 5 kt higher than HWRF at all taus and most of the error comes from a negative (weak-storm) bias.
• Large intensity errors do not imply large track errors.  The key result of my PhD work at the Naval Postgraduate School (Fiorino and Elsberry 1989) was that the TC inner-core, where the intensity change occurs, does not affect the dynamics of vortex motion, i.e., the scales that dominate the motion process are much larger the the TC inner core (~50 km).  Nonetheless, the large intensity error in the ECMWF model may reflect vortex structure errors on larger scales.  We will explore this relationship in a separate blog...
• FIM9 with higher horizontal resolution than the GFS (AVNO) has less bias than AVNO despite the tracker using the same grid (0.5 deg global).  The higher model resolution does permit more intense cyclones and if we tracked at the native resolution, the bias would probably be less...

One way to compensate for large intensity errors in the numerical models when forecasting, is to apply statistical post-processing.  The scheme used at both JTWC and NHC is to calculate an initial 'offset' and then add a portion of the inital offset to the forecast.  The offset is defined as the intensity analyzed in operations minus the model initial intensity.  This operational intensity is generally not the same as the working best track, but since all intensity is analyzed to the nearest 5 kt, does not make much of a practical difference, but does result a some initial intensity error.  For global models, I apply 100% offset at tau 0 and 0% at tau 72 h, with a linear variation between 0-72 h.  The limited-area models set the 0% at tau 24 h.

Here are the bias-corrected statistics:

Figure 3. WPAC 2013 intensity or Vmax eror with bias correction. lines are the mean absolute error and the bars the mean error or bias

The big initial under bias for ECMWF has been eliminated and the correction has greatly reduced the size of the bias from tau 0-48 h and the mean abs errors. Still, the global model errors are higher the HWRF (and LGEM, not shown).

Appendix A - details of the stats

  
Figure 1 plots these numbers

                      000    012    024    036    048    072    096    120  
           HWRF      10.1   31.0   43.7   58.0   74.9  106.2  165.4  276.9
           AVNO      13.5   27.0   39.5   54.8   76.2  113.5  172.6  237.5
           FIM9      14.7   25.5   40.6   56.8   74.9  110.9  165.1  212.3
           EDET      22.0   27.2   39.2   55.5   68.4  108.5  178.2  247.3
           CONW       7.5   28.3   45.0   63.5   78.8  118.6  155.9  220.2
         #CASES       206    189    172    151    132    95     60     36    
 #Tossed( HWRF)       2      1      1      1     
 #Tossed( AVNO)       1      1      1      1     
 #Tossed( FIM9)       1      1     
 #Tossed( EDET)       1      2      2     

#Tossed is the number of cases removed at that forecast tau

model runs that were filtered:

BE filter Cases for: HWRF
stmid     dtg         tau     BE[nmi]
02W.2013  2013022018   12     221
14W.2013  2013083100   12     253

BE filter Cases for: AVNO
stmid     dtg         tau     BE[nmi]
14W.2013  2013082912   12     203

BE filter Cases for: FIM9
stmid     dtg         tau     BE[nmi]
02W.2013  2013022100    0     173
02W.2013  2013022100   12     335

BE filter Cases for: EDET
stmid     dtg         tau     BE[nmi]
08W.2013  2013071700    0      190
08W.2013  2013071612   12     217

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FIM9 2013 LANT/EPAC

FIM9 Track Performance during 2013 LANT/EPAC seasons

Mike Fiorino, NOAA ESRL, Boulder CO 

Craig Mattocks, the new TECHDEV lead at NHC (I was in this position from 2006-2009) made an interesting comment in an email of 25 Oct 2013:

... "I have heard good things from the Hurricane Specialists this year about the FIM(9), especially the track accuracy."

To see if the 'good things' can be seen in the standard metric of track skill, I looked at the  errors in the atLANTic (LANT) and Eastern north PACific (EPAC) using the working best tracks.

2013 atLANTic mean forecast ('track') error for HWRF, GFS, FIM9

For forecast times (as they say in .mil 'taus') 0-72 h, FIM9 did have slightly higher errors than the GFS.  Note the considerably poorer performance of HWRF which is telling because all three models used the exact same initial (and lateral boundary for HWRF) conditions.  The errors at tau 120h only represent the performance for one storm (09L - HU Humberto). 

At tau 72 h there are more storms:

2013 LANT tau 72 storm-by-storm mean forecast error [nmi]

Most of the GFS improvement over the FIM9 at tau 72 h comes from storm 11L - TS Jerry (7 cases), whereas the FIM9 was better for storms 04L, 05L and 10L with 1,3,4 cases respectively.  

The statistics don't show a clear advantage of FIM9 over the GFS in the LANT, yet the hurricane specialists were impressed(?).  Do we need a better way to measure 'good things.' 

The results in the EPAC are different:

2013 EPAC mean forecast error [nmi] for HWRF, GFS, FIM9

Here we find the FIM9 has lower errors than both HWRF and GFS at all taus.  Also note how the GFS errors grow faster than in FIM9.  One speculation is that while both GFS and FIM9 share a common set of physics, their dynamical cores are substantially different. The precipitation fields in my TCgen site http://ruc.noaa.gov/hfip/tcgen look different with GFS generally having more intense and smaller-scale precipitation events.

It's also impressive that HWRF has lower errors at the longer taus (72-120h) compared to its host global model the GFS.  This error growth is counter intuitive in that the lateral boundaries in HWRF should cause greater errors.  Further investigation is needed, but given the better errors for FIM9 maybe it is in EPAC that the specialists are impressed...

For completeness here are the mean tau 72 errors by storm:

2013 EPAC storm-by-storm tau 72 mean forecast errors [nmi]

Storms 03E (5 cases) and 05E (3 cases) are noteworthy in that FIM9 has lowest errors for 03E but higher errors for 05E

Let's combine the basins for stats in EPAC & LANT:

EPAC & LANT 2013 mean forecast errors [nmi] HWRF v GFS v FIM9

No comparison is complete without including the 'gold standard' of TC track prediction - ECMWF HRES (this is how ECMWF refers to their hi-resolution deterministic run).  There were 8 cases of serious errors in the ECMWF trackers - failure to track the observed storm initially and making large track changes in the first 24 h (with implied speed of motion > 100 kt).  The main problem storm was 02L in which the tracker jumped into the EPAC from the Bay of Campeche.  These errors will be the subject of an upcoming post...but my verification code had to be improved to toss out these cases.  Fortunately no cases > 48 h were removed and most of the bad tracks were for tau 0-24.

For EPAC/LANT combined:

EPAC & LANT 2013 mean forecast error HWRF v GFS v FIM v ECMWF

 ECMWF is clearly the gold standard at tau 48-120 h

The results in the LANT are in some ways more dramatic:

LANT 2013 mean forecast error [nmi] HWRF v GFS v FIM9 v ECMWF

The large initial position errors and the relative poorer performance for tau 0-24 are explained by deficiencies in the ECMWF tracker and no special treatment of TCs in their data assimilation system.  However, the stats at tau 48 and 72 are hugely better than the US models.  A mean forecast error of 90 nmi may be a record low.  When I started in this business in the late 1970s the typical 72-h mean error was around 350 nmi!!!!

In EPAC we find a similar pattern - ECMWF better at the medium and long-range taus (72-120 h)

EPAC 2013 mean forecast error [nmi] HWRF v GFS v FIM9 v ECMWF