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Assimilation and Modeling of the Atmospheric
Hydrological Cycle in the ECMWF Forecasting System
Erik Andersson, Peter Bauer, Anton Beljaars, Frederic Chevallier, Elías Hólm,
Marta Janisková, Per Kållberg, Graeme Kelly, Philippe Lopez, Anthony
Mcnally, et al.
To cite this version:
Erik Andersson, Peter Bauer, Anton Beljaars, Frederic Chevallier, Elías Hólm, et al.. Assimilation
and Modeling of the Atmospheric Hydrological Cycle in the ECMWF Forecasting System. Bulletin
of the American Meteorological Society, American Meteorological Society, 2005, 86 (3), pp.387-402.
�10.1175/BAMS-86-3-387�. �hal-02946358�
ASSIMILATION AND MODELING
OF THE ATMOSPHERIC
HYDROLOGICAL CYCLE IN THE
ECMWF FORECASTING SYSTEM
BY ERIK A N D E R S S O N , PETER B A U E R , A N T O N BELJAARS, FREDERIC CHEVALLIER, ELIAS H O L M , M A R T A J A N I S K O V A , PER K A L L B E R G , G R A E M E K E L L Y , PHILIPPE L O P E Z , A N T H O N Y M C N A L L Y , E M M A N U E L M O R E A U , A D R I A N J. S I M M O N S , J E A N - N O E L T H E P A U T , A N D A D R I A N M . T O M P K I N S
ECMWF's preparations for cloud and rain assimilation encompass development of
linearized physics, improved satellite data utilization, a new humidity analysis,
and another look at the "spindown" problem.
E
uropean, American, and Japanese satelliteagen-cies have a n u m b e r of Earth-observation missions with the objective of providing improved mea-surements of c o m p o n e n t s of the global hydrological cycle—clouds, precipitation, soil moisture, a n d water v a p o r — f r o m a range of operational platforms in b o t h polar a n d geostationary orbits. Significant develop-m e n t of data assidevelop-milation develop-m e t h o d s will be necessary to m a k e full use of b o t h the existing and n e w types of o b s e r v a t i o n s of t h e w a t e r cycle. T h e s m a l l - s c a l e
A F F I L I A T I O N S : ANDERSSON, BAUER, BELJAARS, CHEVALLIER, HOLM, JANISKOVA, KALLBERG, KELLY, LOPEZ, MCNALLY, MOREAU, SIMMONS, THEPAUT, AND TOMPKINS—ECMWF, Reading, U n i t e d K i n g d o m C O R R E S P O N D I N G A U T H O R : Dr. E. Andersson, ECMWF, Shinfield Park, Reading, RG2 9 A X , U n i t e d K i n g d o m
E-mail: e r i k . a n d e r s s o n @ e c m w f . i n t D O I : 10.1 I 7 5 / B A M S - 8 6 - 3 - 3 8 7 In final form 10 September 2004 ©2005 American Meteorological Society
variability in a t m o s p h e r i c h u m i d i t y a n d its s t r o n g d e p e n d e n c e o n physics a n d d y n a m i c s n e e d to be represented accurately in the assimilation systems. In this p a p e r we r e p o r t o n a c o m p r e h e n s i v e research p r o g r a m at the E C M W F (see appendix for definitions of all a c r o n y m s a n d abbreviations) devoted to cloud a n d rain assimilation a n d h u m i d i t y analysis. The aim is to explore the i n f o r m a t i o n contained in radiances obtained f r o m microwave a n d infrared sounders a n d i m a g e r s in clear, c l o u d y , a n d p r e c i p i t a t i n g skies. Current radiance assimilation methods (McNally et al. 1999,2000) leave important data gaps in areas of clouds a n d precipitation, as illustrated in Fig. 1 for the infra-red (Fig. la) and microwave (Figs. lb,c). The assimila-tion is therefore relatively ineffective in correcting for forecast errors in cloudy and rainy regions. To extend direct radiance assimilation to all-sky conditions re-quires upgrades to the assimilation system itself, a n d that fast radiative transfer m o d e l s be extended a n d e n h a n c e d to i n c o r p o r a t e t h e effects of clouds a n d precipitation.
AMERICAN METEOROLOGICAL SOCIETY MARCH 2005 BAFIS* | 387
FIG. I. T h e u s e o f s a t e l l i t e r a d i a n c e d a t a in c u r r e n t d a t a a s s i m i l a t i o n s y s t e m s is r e s t r i c t e d b y c l o u d s a n d p r e c i p i t a t i o n . T h e i d e n t i f i c a t i o n o f " c l e a r - s k y " d e p e n d s o n t h e m e a s u r e m e n t s ' s e n s i t i v i t y t o c l o u d l i q u i d w a t e r . T h i s f i g u r e s h o w s d a t a c o v e r a g e f o r t h e u s e d ( c y a n ) a n d d i s c a r d e d ( y e l l o w ) d a t a in E C M W F ' s o p e r a t i o n a l 4 D V A R s y s t e m , f o r 2 0 0 3 0 1 2 6 , p l o t t e d o n a 2 3 3 0 U T C G M S c l o u d i m a g e , ( a ) I n f r a r e d t r o p o s p h e r i c m e a s u r e m e n t s ( H I R S c h a n n e l - 7 ) a r e u s e d o n l y i n c l o u d f r e e a r e a s , l e a v i n g l a r g e d a t a v o i d s , ( b ) M i c r o w a v e t e m p e r a t u r e s o u n d i n g m e a s u r e m e n t s ( A M S U A c h a n -n e l - 6 ) a r e u s e d i -n m o s t -n o -n p r e c i p i t a t i -n g a r e a s ( p r o v i d e d s u r f a c e e m i s s i v i t y e f f e c t s a r e a c c u r a t e l y m o d e l e d ) , ( c ) M o i s t u r e - s o u n d i n g m i c r o w a v e d a t a ( S S M / I c h a n n e l - 7 ) a r e u s e d t h r o u g h c i r r u s b u t n o t i n a r e a s w i t h t h i c k c l o u d s o r p r e c i p i t a t i o n . C u r r e n t r e s e a r c h a i m s a t e x t e n d i n g t h e d i r e c t r a d i a n c e a s s i m i l a t i o n m e t h o d s i n c l o u d y a n d r a i n y s i t u a t i o n s . M O D E L I N G A S P E C T S A N D V A L I D A T I O N A G A I N S T I N S I T U D A T A . M o i s t p r o c e s s e s a r e obviously i m p o r t a n t for the modeling of clouds, pre-cipitation, radiation, and latent heat release. The mois-ture field depends on parameterized physical processes (Tiedtke et al. 1988; Gregory 1996; Tiedke 1993; Jakob and Klein 1999; Beljaars and Viterbo 1998), which can have substantial uncertainties, but it also depends on the large-scale motion, particularly the vertical motion. O n e way of assessing the model is by looking at sys-tematic differences between forecasts a n d analyses. Cross sections of the m o n t h l y m e a n relative h u m i d i t y difference are shown in Figs. 2a and 2b for day-1 and day-5 operational forecasts, respectively. T h e m a i n difference is in the Tropics, where the model is drier than the analysis. This is associated with a spindown (rapid a d j u s t m e n t to lower values) of precipitation (Fig. 2c) and a spindown of the Hadley circulation, as can be seen f r o m the systematic difference in vertical velocity b e t w e e n f o r e c a s t s a n d analysis (Fig. 2d). Because of the additional latent heat release in the Tropics during the first 12 h of the forecasts (which pro-vides the background for the next analysis), the Hadley circulation is stronger in the analyses t h a n in the fore-casts. It is important to note that the differences in rela-tive h u m i d i t y (Fig. 2a) between forecasts and analyses are up to about 5%, which is fairly small. At this stage it is difficult to say whether the model or the analysis is biased, because most current observing systems do not have an absolute calibration within 5%. Although the imbalance in moisture between analysis and model is
small, the spindown is damaging to the analysis as it maintains an overly active hydrological cycle during the data assimilation. The associated latent heat release and the divergent o u t f l o w f r o m the affected regions are likely also overestimated, leading to temperature and wind biases in the tropical analyses.
Boundary layer moisture is an i m p o r t a n t aspect of the model for two reasons. First, together with surface wind speed, it controls the surface evaporation. Second, b o u n d a r y layer moisture is the d o m i n a n t contribution to vertically integrated (total c o l u m n ) water v a p o r (TCWV). The latter aspect is i m p o r t a n t in the context of m i c r o w a v e satellite observations, which provide good estimates of T C W V . An example is given in Fig. 3, where the short-range forecast (Fig. 3a) is c o m p a r e d
to 1DVAR1 retrievals (Fig. 3b; Phalippou 1996) and to
a m o d e l - i n d e p e n d e n t retrieval (Fig. 3c) (Alishouse et al. 1990). The patterns in the three panels are remark-ably similar, suggesting that the observations have a high degree of realism and that the physics and the dy-namics of the m o d e l do a reasonable job. However, there is again a small systematic difference between the observations and the model. The difference is about
0.5 kg m~2 globally averaged, corresponding to about
1 In recent years variational methods have gained popularity in
data assimilation applications using satellite radiance data. In 1DVAR, independent vertical columns are considered. In 3DVAR, the entire model domain is analyzed at once, and in 4DVAR time sequences of observations and model states are considered.
388 I BAfft MARCH 2005
FIG. 2 . C o l o r c o d e d , z o n a l - a v e r a g e m o n t h l y m e a n d i f f e r e n c e b e t w e e n f o r e c a s t s a n d v e r i f y i n g a n a l y s e s f o r r e l a t i v e h u m i d i t y ( % ) ( a ) d a y I a n d ( b ) d a y 5 , A p r 2 0 0 2 , f r o m E C M W F ' s o p e r a t i o n a l f o r e c a s t i n g s y s t e m ( s h a d i n g i n t e r v a l 1%). B l u e ( y e l l o w ) s h a d i n g i n d i c a t e s t h a t t h e f o r e c a s t is less ( m o r e ) h u m i d t h a n t h e a n a l y s i s . T h e c o r r e s p o n d i n g a v e r a g e r e l a t i v e h u m i d i t y o f t h e a n a l y s i s is s h o w n i n b l a c k c o n t o u r s ( c o n t o u r i n t e r v a l 5 % ) . ( c ) T h e e v o l u t i o n o f p r e -c i p i t a t i o n ( m m d a y- 1, b l a c k l i n e ) a n d e v a p o r a t i o n ( m m d a y- 1, g r e e n ) i n t h e t r o p i c a l b a n d b e t w e e n 3 0 ° N a n d 3 0 ° S d u r i n g t h e 1 0 - d a y f o r e c a s t s , a l s o a v e r a g e d o v e r A p r 2 0 0 2 . T h e r e is e x c e s s i v e p r e c i p i t a t i o n d u r i n g t h e f i r s t 12 h o f t h e f o r e c a s t s . B e c a u s e o f t h e a s s o c i a t e d l a t e n t h e a t r e l e a s e t h e H a d l e y c i r c u l a t i o n is s t r o n g e r in t h e a n a l y s i s t h a n i n t h e f o r e c a s t s , ( d ) T h e d i f f e r e n c e i n v e r t i c a l v e l o c i t y ( P a s_ l) c o r r e s p o n d i n g t o ( a ) ( s h a d i n g i n t e r v a l 0 . 0 0 5 P a s_ l) . B l u e ( y e l l o w ) s h a d i n g i n d i c a t e s t h a t t h e f o r e c a s t u p w a r d v e l o c i t y is h i g h e r ( l o w e r ) t h a n t h e a n a l y s i s . T h e a v e r a g e d a n a l y -sis is s h o w n i n b l a c k c o n t o u r s ( i n t e r v a l 0 . 0 2 5 P a s_ l) .
2% of the global m e a n (27 kg n r2) . The discrepancy is
small and may be due to model bias or due to biases in the observing or retrieval systems.
The second m a j o r factor controlling T C W V is the b o u n d a r y layer depth. D u r i n g the EPIC experiment, r a d i o s o n d e s were l a u n c h e d f r o m a ship near 20°S, 85°W. A c o m p a r i s o n b e t w e e n averaged s o n d e a n d model profiles is shown in Fig. 4. The sharp inversion is the result of a subtle balance between large-scale sub-siding m o t i o n and turbulent e n t r a i n m e n t at the top of the cloud layer at the inversion. The model inversion is less sharp than observed a n d the model b o u n d a r y layer is slightly lower than observed. This has conse-quences for T C W V because in this situation, T C W V is to a good approximation equal to the b o u n d a r y layer depth multiplied by the boundary layer specific h u m i d -ity. Hence, relative errors in b o t h p a r a m e t e r s cause equal relative error in T C W V .
Boundary layer moisture over land is strongly af-fected by land surface processes t h r o u g h evaporation f r o m the surface (Viterbo and Beljaars 1995; V a n den H u r k et al. 2000). S u m m e r precipitation over land is also strongly influenced by land evaporation, which involves a positive feedback: high precipitation leads to
m o r e soil moisture, which enhances evaporation feed-ing back into high precipitation (Beljaars et al. 1996). To control this positive feedback it is necessary to have a g o o d soil m o i s t u r e d a t a a s s i m i l a t i o n s c h e m e . Significant work has been done in the past (Viterbo and Courtier 1995; Douville et al. 2000) to optimize the use of S Y N O P observations. C u r r e n t l y t h e E U - f u n d e d ELD AS project is underway to further improve the use of SYNOP data and to accommodate other data sources: radiation, precipitation, surface skin temperatures from satellites, and f u t u r e microwave data (SMOS).
T H E T R O P I C A L H U M I D I T Y A N A L Y S I S I N ERA-40. The ERA-40 analyses can be viewed as com-prising three periods that are characterized in terms of the observations that can influence the humidity analy-sis. Period A starts in 1957, and has only the conven-tional in situ surface and radiosonde m e a s u r e m e n t s available. Period B, f r o m 1973, uses the in situ mea-surements and infrared radiances, but not SSM/I data. The infrared data are f r o m VTPR instruments f r o m 1973 to 1978 and f r o m HIRS instruments beyond 1978. In period C, f r o m 1987 onward, in situ measurements, HIRS i n f r a r e d radiances, a n d 1DVAR retrievals of
A M E R I C A N METEOROLOGICAL SOCIETY M A R C H 2005 BAPIS* | 3 8 9
FIG. 3. T o t a l - c o l u m n w a t e r v a p o r ( k g m~2, s e e l e g e n d ) f o r t h e ( a ) m o d e l b a c k g r o u n d ( a s h o r t f o r e c a s t ) , ( b ) a I D V A R
r e t r i e v a l , ( c ) a n d a m o d e l - i n d e p e n d e n t r e t r i e v a l a l g o r i t h m f o r 2 9 Jul 2 0 0 2 , u s i n g d a t a f r o m t h e S S M / I i n s t r u m e n t . T h e t h r e e e s t i m a t e s o f a t m o s p h e r i c h u m i d i t y s h o w g o o d c o r r e s p o n d e n c e . B i a s e s a r e w i t h i n 2 % g l o b a l l y .
T C W V f r o m SSM/I r a d i a n c e s are all a s s i m i l a t e d . Diagnosis of hydrological aspects of the ERA-40 prod-ucts has been carried out. These studies have shown some p r o n o u n c e d differences in the behavior of the three periods that are almost certainly related mainly to the changes in data used rather than to natural earth-system changes.
I n f o r m a t i o n on the precipitation a n d evaporation averaged over land and sea, for each of the three peri-ods, is shown in Table 1, based on values provided by the Max Planck Institute for Meteorology, H a m b u r g , a partner in the ERA-40 project. ERA-40 results (based on 6-h forecasts) are c o m p a r e d with those f r o m ERA-15 for period C, with those f r o m the N C E P reanalysis for periods A and B and other relevant datasets (see caption). The period C ERA-40 precipitation for the years 1989-95 is substantially larger than that given by any of the verifying datasets, and
substantially larger than the ERA-15 precipitation for the years 1989-93. Precipitation exceeds evapora-tion over sea as well as land. Period B precipitation is also relatively high, t h o u g h not as high as in pe-riod C. Again, precipitation ex-ceeds evaporation over sea as well as land. Only in period A (when no satellite data were available for as-similation) is the oceanic precipi-tation, averaged globally, of the order of that given in the obser-vational datasets for the various periods, and less than the oceanic evaporation.
The hydrological balance of the ERA-40 data assimilation cycles
in-cludes a c o m p o n e n t with n o physical counterpart: the systematic addition or removal of atmospheric mois-ture by the humidity analysis. The lack of physical bal-ance in the hydrological cycle represented by the ERA-40 products for the latter two periods of the reanalysis is due to the assimilation system's use of satellite data to correct what is perceived to be a too-dry background model state over the tropical oceans. The assimilating model rejects almost all of the moisture added by the analysis. The resulting excessive tropical oceanic pre-cipitation is arguably the most serious problem diag-nosed in ERA-40.
M a p s of analysis i n c r e m e n t s f r o m ERA-40, a n d additional observing-system experiments, confirm that the period C analyses are generally m o i s t e n e d over tropical oceans by the assimilation of HIRS and SSM/I data. Figure 5 presents time series of tropical means of
FIG. 4 . S a t e l l i t e i n s t r u m e n t s ( e . g . , S S M / I ) p r o v i d e g o o d m e a s u r e m e n t s o f t h e t o t a l - c o l u m n w a t e r v a p o r o v e r o c e a n . I n t h e s u b t r o p i c a l s u b s i d e n c e r e g i o n s , e r r o r s in m o d e l e d T C W V c a n b e d o m i n a t e d b y e r r o r s in t h e b o u n d -a r y l -a y e r h e i g h t . S h o w n -a r e 6 - d -a y -a v e r -a g e s o f r -a d i o s o n d e o b s e r v -a t i o n s ( f u l l l i n e s ) a n d c o r r e s p o n d i n g a v e r a g e s o f E C M W F m o d e l p r o f i l e s ( d a s h e d ) o f ( a ) p o t e n t i a l t e m p e r a t u r e a n d ( b ) s p e c i f i c h u m i d i t y a t t h e " I M E T - S t r a t u s l o c a t i o n , " 2 0 ° S , 8 5 ° W . T h e f i g u r e w a s k i n d l y p r o v i d e d b y C h r i s B r e t h e r t o n , U n i v e r s i t y o f W a s h i n g t o n . 390 I BAH5- M A R C H 2005
TABLE 1. G l o b a l p r e c i p i t a t i o n a n d e v a p o r a t i o n o v e r l a n d a n d o c e a n f o r t h e y e a r s 1 9 5 8 - 6 1 , 1 9 7 3 - 7 5 , a n d 1 9 8 9 - 9 5 i n I 01 5 k g y r_ l f r o m t h e r e a n a l y s e s p e r f o r m e d a t N C E P a n d E C M W F ( E R A 1 5 a n d E R A -4 0 ) a n d f r o m o t h e r d a t a s o u r c e s : G P C C ( R u d o l f e t al. 1 9 9 6 ) , G P C P ( H u f f m a n e t a l . 1 9 9 7 ) , C M A P ( X i e a n d A r k i n 1 9 9 7 ) , a n d C R U ( N e w e t al. 2 0 0 0 ) . F o r t h e t w o e a r l i e r p e r i o d s o f E R A - 4 0 o n l y C R U d a t a o v e r l a n d e x c l u d i n g A n t a r c t i c a a r e a v a i l a b l e as o b s e r v a t i o n s . A l s o s h o w n a r e c l i m a t o l o g i c a l e s t i -m a t e s ( B a u -m g a r t n e r a n d R e i c h e l 1 9 7 5 , h e r e a f t e r B R ) . T h e E R A - 1 5 r e s u l t s a r e f o r 1 9 8 9 - 9 3 o n l y . P e r i o d A L a n d O c e a n ( 1 9 5 8 - 6 1 ) P r e c i p E v a p P r e c i p E v a p E R A - 4 0 9 2 7 1 4 0 1 4 7 2 N C E P 1 17 9 6 4 0 9 4 5 3 C R U 1 0 3 — — — B R 1 1 1 7 1 3 8 5 4 2 4 P e r i o d B L a n d O c e a n ( 1 9 7 3 - 7 5 ) P r e c i p E v a p P r e c i p E v a p E R A - 4 0 1 2 3 7 2 4 5 4 4 4 6 N C E P 1 1 7 9 4 3 8 4 4 2 9 C R U 1 0 3 — — — B R 1 1 1 7 1 3 8 5 4 2 4 P e r i o d C L a n d O c e a n ( 1 9 8 9 - 9 5 ) P r e c i p E v a p P r e c i p E v a p E R A - 4 0 1 16 7 6 4 7 6 4 4 8 E R A - 1 5 1 14 8 3 3 9 0 4 3 4 G P C C 9 7 — — — G P C P 1 0 6 — 3 7 6 — C M A P 9 8 — 3 9 4 — B R I I 1 7 1 3 8 5 4 2 4
the T C W V increment, the precipitation f r o m 6-h back-g r o u n d forecasts, a n d the T C W V itself for the entire ERA-40 period f r o m 1957 to 2002. A substantial j u m p in the precipitation rate can be seen over the second half of 1991. After a slight decline, the rate rises sharply again toward the end of 1994, with high rates (averag-ing a r o u n d 5.5 m m d a y1) m a i n t a i n e d t h r o u g h o u t
1995-2002. This temporal variation in precipitation rate closely follows the temporal variation in the T C W V increment. The results f r o m January 1958 to June 1965 show only weak drying increments f r o m the assimila-tion of in situ tropical data. Precipitaassimila-tion rates are in
the range of 3.6-4.0 m m day-1. The increments since
1991 a m o u n t to about 1% of the T C W V , added to the analysis every 6 h. Most of the added moisture is rained out, as it must be for the T C W V to keep reasonable values. The T C W V is nevertheless, on average, a r o u n d
10% higher in period C than in period A, generally in-creasing and reaching particularly high values during the strong 1998 El Nino event. The substantial increase in ERA-40 rain rates in the second half of 1991 was due in part to misinterpreted effects of volcanic aerosols on HIRS infrared radiances following the eruption of Mt. Pinatubo.
Various deficiencies of the assimilation system have been suggested as causes of the large tropical rain rates seen in the short-range ERA-40 and operational fore-casts. Problems with the bias correction of the satellite radiances, the vertical structure of the increments pro-duced by the analysis scheme, and the model repre-sentation of tropical moist processes are all possible c a n d i d a t e s , a n d s o m e sensitivity has b e e n seen to changes in these areas. If tropical circulations in assimi-lation cycles are too intense, there will be a tendency for descent regions to be too dry. It is in just these cloud-free regions that the satellite humidity data tend to be used, and the observations act to moisten what they see to be an overly dry atmosphere. The mois-ture added in the descent regions m a y then be fed into the precipitating ascent regions, where it can fuel the maintenance of the too-strong circulations. If this is indeed a significant factor, then assimilation of rain-affected microwave radiances (next section) would of-fer a better control of the tropical circulation.
S A T E L L I T E R E M O T E S E N S I N G O F H U M I D -I T Y . -In recent years, several N W P centers have shown the benefit of assimilating water v a p o r i n f o r m a t i o n f r o m satellites in operational forecasting systems. Due to the scarcity of conventional upper-air data to con-strain the m o d e l h u m i d i t y fields over the oceans, satellite data indeed offer a valuable source of i n f o r m a -tion that is being exploited. It has been s h o w n that
assimilated humidity information reduces analysis bi-ases a n d produces a large impact that can be retained in the forecast for several days, in experiments with HIRS (McNally a n d Vesperini 1996), SSM/I (Gerard a n d Saunders 1999), a n d M E T E O S A T ( M u n r o et al. 2004; Kopken et al. 2004) radiances. It should be m e n -tioned that the development of variational m e t h o d s facilitated the transition f r o m using retrievals to di-rect radiance assimilation in 3DVAR (Andersson et al. 1994,1998; Derber and W u 1998; McNally et al. 1999, 2000; English et al. 2000) a n d 4 D V A R (Rabier et al. 2000), allowing a c o n t i n u o u s i m p r o v e m e n t in the as-similation of i n f o r m a t i o n f r o m satellite i n s t r u m e n t s (Simmons and Hollingsworth 2002). Currently, a wide range of operational satellite systems provides h u m i d -ity i n f o r m a t i o n . Table 2 lists t h e data available at E C M W F for m o n i t o r i n g or assimilation, a n d shows data counts a n d the m a i n characteristics of each in-strument. The m a i n s h o r t c o m i n g of the i n s t r u m e n t s
AMERICAN METEOROLOGICAL SOCIETY MARCH 2005 BAPIS* | 3 9 1
FIG. 5. T h e m o i s t u r e a n a l y s i s a n d v a r i a t i o n s in t h e a v a i l a b i l i t y o f h u m i d -i t y d a t a c a n h a v e a s t r o n g -i n f l u e n c e o n t h e a n a l y z e d p r e c -i p -i t a t -i o n -in t h e T r o p i c s . T h e f i g u r e s h o w s t i m e s e r i e s o f t r o p i c a l - m e a n i n c r e m e n t s in ( a ) t o t a l - c o l u m n w a t e r v a p o r ( k g m- 2) , ( b ) p r e c i p i t a t i o n r a t e in 6 h f o r e -c a s t s ( m m d a y- 1) , a n d ( c ) a n a l y z e d T C W V ( k g r r r2) , a v e r a g e d o v e r all a n a l y s i s c y c l e s f o r e a c h m o n t h f r o m 1 9 5 8 t o 2 0 0 2 o f E C M W F ' s r e a n a l y -sis ( E R A - 4 0 ) . T h e t r o p i c a l p r e c i p i t a t i o n c o r r e l a t e s s t r o n g l y w i t h t h e m e a n T C W V i n c r e m e n t s , w h i c h v a r y o v e r t h e p e r i o d d u e t o v a r i a t i o n s in t h e a v a i l a b i l i t y o f s a t e l l i t e h u m i d i t y d a t a .
has been their p o o r vertical resolution, which makes the distribution of h u m i d i t y i n f o r m a t i o n in the verti-cal a delicate problem.
A n o t h e r i m p o r t a n t aspect of the assimilation of humidity-sensitive radiances concerns the quality of the RT model calculating radiances f r o m the N W P model variables. Direct assimilation of radiances (rather than retrievals) is preferred because it ensures consistency between different satellite observations a n d because the description of observation errors is easier in terms
of radiances. However, great care has to be taken to properly h a n d l e sys-tematic errors in the observations and in the RT model through bias correc-t i o n p r o c e d u r e s ( H a r r i s a n d Kelly 2001). In Europe, the development of RT codes for N W P is c o o r d i n a t e d within EUMETSAT's NWP-Satellite Application Facility. Recently an im-p r o v e d v e r s i o n of t h e R T T O V (Saunders et al. 1999) fast regression-based RT model has been developed (Saunders et al. 2002; Matricardi et al. 2004). The new version addresses sig-nificant deficiencies highlighted by G a r a n d et al. (2001) in i n t e r c o m -p a r i s o n s with accurate line-by-line computations. This new version is also an essential step toward accurate as-similation of radiances f r o m the wa-ter vapor channels of MSG, AIRS, and IASI (Matricardi and Saunders 1999; Matricardi 2003). For SSM/I it is im-portant that RTTOV now includes the fast sea s u r f a c e e m i s s i v i t y m o d e l F A S T E M - 2 (English a n d H e w i s o n 1998), a n d it t h u s s u p e r s e d e s t h e older RTSSMI ( P h a l i p o u 1993). In Fig. 6 we c o m p a r e the distributions of b a c k g r o u n d , bias-corrected back-g r o u n d , a n d a n a l y s i s d e p a r t u r e s f r o m R T S S M I ( t o p ) a n d R T T O V (lower panels) for a 5-day period in May 2002. For all seven SSM/I chan-nels (only the 37-GHz chanchan-nels are shown) the background departures and t h e biases are significantly smaller when RTTOV is used. This improve-m e n t is a result of the better paraimprove-m- param-eterization of seawater permittivity as well as the inclusion of nonspecular re-flection contributions with increasing surface roughness (Ellison et al. 2003). The SSM/I i n s t r u m e n t measures horizontally and vertically polarized radiance at three frequencies (19, 37, a n d 85 GHz) and vertically polarized radiances at 22 GHz. These channels show a differential sensitivity to the integrated atmospheric water vapor content and wind-induced sea surface roughness. This information was assimilated t h r o u g h 1DVAR retrievals of T C W V a n d wind speed (Phalipou 1996). The largest analysis changes caused by the assimilation of this information occurred in the Tropics a n d in the Southern H e m i
-392 I BAI15- M A R C H 2005
sphere. Here, the data caused a significant moistening of the analysis, which is difficult to verify due to the absence of an extensive conventional observing sys-t e m m e a s u r i n g T C W V . H o w e v e r , earlier s sys-t u d i e s (McNally a n d Vesperini 1996) have s h o w n a g o o d agreement between T C W V f r o m SSM/I and the h u -midity i n f o r m a t i o n f r o m other satellite i n s t r u m e n t s such as HIRS. The use of SSM/I 1DVAR retrievals has recently been replaced by direct assimilation of SSM/I radiances in the 4 D V A R system (Bauer et al. 2002), restricted to clear-sky and thin cloud conditions. Single-cycle experiments showed that the T C W V increments are fairly comparable between 1DVAR and direct ra-diance assimilation. Longer cycling experiments con-firmed these results. The hydrological budget remained almost unchanged, as did the spindown of precipita-tion rate.
Recognizing the importance of global humidity in-formation, space agencies have invested in a n u m b e r of new and planned satellite missions that will further enhance the capability to observe the highly variable d i s t r i b u t i o n of h u m i d i t y in t h e a t m o s p h e r e : AIRS o n b o a r d Aqua ( l a u n c h e d in J u n e 2002) a n d IASI onboard M E T O P (expected in 2005) provide a substan-tial increase of water vapor information compared with the traditional infrared radiometers. A first conserva-tive AIRS assimilation strategy, restricted to cloud-free c o n d i t i o n s (McNally a n d W a t t s 2003), was
imple-m e n t e d at E C M W F in October 2003 (Table 2). Future investigations will be directed toward exploring m o r e of the rich information in data f r o m this class of high-s p e c t r a l - r e high-s o l u t i o n i n high-s t r u m e n t high-s in t h e p r e high-s e n c e of clouds (Chevallier et al. 2004). The SEVIRI instrument o n b o a r d MSG has 4 times as m a n y channels as the current METEOSAT instruments. Extra window chan-nels should improve the cloud detection and the qual-ity of the MSG clear-sky radiance product. The avail-ability of two water vapor channels (7.3 and 6.2 jum) modestly increases the vertical resolution. The first sat-ellite in this new series (MSG-1) was launched in Au-gust 2002, a n d data are beginning to become available for analysis. The SSMI/S on board DMSP-16 (launched O c t o b e r 2003) c o m b i n e s A M S U - A , AMSU-B, a n d SSM/I sensing capabilities in a single instrument. The combined availability of imaging and sounding chan-nels will improve the vertical resolution with respect to water vapor structures. Passive limb sounders (such as MIPAS on b o a r d ENVISAT) a n d active GPS radio-occultation measurements (e.g., GRAS, COSMIC) can provide high vertical resolution measurements of wa-ter vapor. These new and planned missions are very promising, but also challenging, since they raise poten-tially difficult assimilation problems in the horizontal.
C L O U D A N D R A I N A S S I M I L A T I O N . O p e r a tional N W P centers have a growing interest in
assimi-TABLE 2. L i s t o f p r o c e s s e d a n d u s e d h u m i d i t y s e n s i t i v e r a d i a n c e s a t e l l i t e d a t a i n E C M W F p r e o p e r a t i o n a l t e s t s , f o r t h e d a t e 20030701-0000 U T C . T h e t e s t s y s t e m b e c a m e t h e o p e r a t i o n a l s y s t e m o n 7 O c t 2003. I n s t r u m e n t S p a c e c r a f t T o t a l n u m b e r p r o c e s s e d N o . o f u s e d d a t a N o . o f c h a n n e l s , a v a i l a b l e a n d ( u s e d ) H u m i d i t y s e n s i t i v i t y o f u s e d d a t a
Imager, METEOSAT-5 181,000 20,000 2(1) Upper
geostationary METEOSAT-7 3 12,000 43,000 Infrared troposphere
orbit GOES-9 899,000 37,000
GOES-10 553,000 26,000
GOES-12 496,000 17,000
HIRS, NOAA-14 64,000 0 19(6) Mostly upper
polar orbiting NOAA-15 63,000 0 Infrared troposphere
NOAA-16 1,684,000 88,000
NOAA-17 1,423,000 77,000
AMSU-B, NOAA-IS 402,000 0 5(3) Upper and
mid-polar orbiting NOAA-16 399,000 34,000 Microwave troposphere
NOAA-17 403,000 33,000
SSMI, DMSP-13 88,000 38,000 7(7) Total column
polar orbiting DMSP-14 89,000 33,000 Microwave
DMSP-15 88,000 39,000
AIRS, Aqua 52,242,000 1,915,000 2378 (230) Upper and
mid-polar orbiting (EOS-PM) Infrared troposphere
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FIG. 6. A c c u r a t e r a d i a t i v e t r a n s f e r m o d e l s a r e r e q u i r e d t o s i m u l a t e t h e s a t e l l i t e -m e a s u r e d r a d i a n c e s f r o -m t e -m p e r a t u r e , h u -m i d i t y , a n d o t h e r q u a n t i t i e s p r o v i d e d b y t h e f o r e c a s t m o d e l . D i f f e r e n c e s b e t w e e n o b s e r v e d a n d s i m u l a t e d r a d i a n c e s a r e e x t e n s i v e l y m o n i t o r e d . R e c e n t i m p r o v e m e n t s in t h e a c c u r a c y o f R T m o d e l -i n g [ c o m p a r -i n g R T S S M I ( o l d ) a g a -i n s t R T T O V ( n e w ) ] -is -i l l u s t r a t e d f o r t h e 3 7 - G H z S S M / I c h a n n e l s in v e r t i c a l ( V ) a n d h o r i z o n t a l ( H ) p o l a r i z a t i o n : ( a ) V , o l d R T ; ( b ) H , o l d R T ; ( c ) V , n e w R T ; a n d ( d ) H , n e w R T m o d e l . T h e t h r e e c u r v e s s h o w o b s e r v a t i o n m i n u s s h o r t r a n g e f o r e c a s t w i t h o u t ( g r e e n ) a n d w i t h ( b l a c k ) , b i a s c o r -r e c t i o n , a n d o b s e -r v a t i o n m i n u s a n a l y s i s d e p a -r t u -r e s ( b l u e ) .
T C W V , which led to simu-lated surface rain rates that better matched the observa-tions. The resulting 1DVAR T C W V retrievals were then assimilated in 4DVAR. This m e t h o d is r e f e r r e d t o as " 1 D V A R + 4 D V A R " ( M a r e c a l a n d M a h f o u f 2003). The second approach is direct assimilation of sur-face rain rate observations in the 4D VAR system, and is re-ferred to as "Direct 4DVAR" assimilation of rain rates. T h e o b s e r v a t i o n s in t h e above studies were rain-rate retrievals f r o m satellite mi-c r o w a v e m e a s u r e m e n t s from TMI and SSM/I (Bauer et al. 2001).
Global 1 - m o n t h assimi-l a t i o n e x p e r i m e n t s u s i n g b o t h t h e a b o v e m e t h o d s have been conducted at full r e s o l u t i o n (T511 f o r e c a s t m o d e l with analysis incre-m e n t s at T159). The results (Marecal et al. 2001, 2002) s h o w t h a t t h e E C M W F
lating satellite observations in cloudy and rainy regions ( T r e a d o n 1997; T s u y u k i 1997; M a c p h e r s o n 2001; Marecal and Mahfouf 2002). Measurements in cloudy regions contain valuable information on temperature, humidity, a n d w i n d that is f u n d a m e n t a l l y different f r o m clear-sky areas. Regions where forecast error is most sensitive to initial-condition error are often cloudy (McNally 2002). C u r r e n t satellites already p r o v i d e some cloud-related information that is not generally assimilated in operational analyses. Variational assimi-lation schemes can, in principle, handle cloud and pre-cipitation observations. However, these data represent features a n d processes that are m o r e d i s c o n t i n u o u s and have smaller spatial and temporal scales than most currently used data. Several aspects of the data assimi-lation systems will need to be revised, as increased ac-curacy and efficiency m a y be required.
Marecal and Mahfouf (2002) have compared the per-formance of two different methods for assimilating sur-face rainfall observations in the E C M W F 4DVAR sys-tem. In the first approach, a I D VAR technique (Marecal and Mahfouf 2000) was used to generate increments of
m o d e l can h a v e o p p o s i t e h u m i d i t y biases in rainy and n o n r a i n y areas, by about 5 % - 1 0 % in T C W V ( w i t h o p p o s i t e s i g n s in t h e midlatitudes and Tropics). W h e n satellite data are used only in nonrainy conditions, extrapolation of informa-tion into the rainy areas often degrades the analysis there by increasing the bias further. This provides a strong motivation to extend the use of satellite humidity data to all-sky conditions. A n o t h e r i m p o r t a n t result is that the strong nonlinearities in the observation op-erators for rain rates—that is, the moist convection scheme—led to convergence problems in the 4DVAR solution algorithm. T h e 1DVAR + 4 D V A R m e t h o d p a r t l y a v o i d s t h i s p r o b l e m b y t r e a t i n g t h o s e nonlinearities outside of 4DVAR. In m a n y respects the most attractive assimilation approach would be direct radiance assimilation of cloud- and rain-affected mi-crowave radiances. However, this requires substantial development of 1) linearized versions of cloud and con-vection schemes, 2) accurate RT models for cloudy and precipitating skies, and 3) further developments of the 4DVAR system. This is currently our main develop-m e n t strategy, as outlined in the following sections.
394 I BAI15- M A R C H 2005
Revised convection and cloud schemes. A modified version of E C M W F ' s o p e r a t i o n a l convection scheme has been developed for an i m p r o v e d v a r i a t i o n a l a s s i m i l a t i o n of cloud a n d precipitation ob-servations. While the scheme shares the f u n d a m e n t a l fea-tures of the original mass-flux scheme (Tiedtke 1993), it be-haves m o r e linearly with re-spect to changes in t h e key parameters. All types of con-vection (shallow, midlevel, a n d deep) are treated simi-larly. In particular, t h e link b e t w e e n the m o d e l c o n t r o l variables a n d t h e s u b g r i d -scale convective quantities is expressed t h r o u g h a single f o r m u l a t i o n t h a t d e p e n d s on the relaxation of CAPE in time. T h e initial characteris-tics of t h e u p d r a f t s are n o w d e t e r m i n e d f r o m s u r f a c e h e a t f l u x e s . T h e t o t a l e n -t r a i n m e n -t is a f u n c -t i o n of the height above cloud base, while t h e d e t r a i n m e n t rate is set e q u a l to t h e e n t r a i n -m e n t rate, e x c e p t close t o cloud t o p w h e r e a c o n s t a n t d e t r a i n m e n t is a p p l i e d . S i m p l i f i e d c a l c u l a t i o n s of d o w n d r a f t s a n d convective m o m e n t u m t r a n s p o r t are also i n c l u d e d in the m o d i f i e d p a r a m e t e r i z a t i o n .
T h e n e w convection scheme has first been validated in the single-column version of the E C M W F m o d e l a n d t h e n in the full 3D m o d e l for periods of u p to 4 m o n t h s . In the context of such s t a n d a r d forecasts, t h e n e w pa-r a m e t e pa-r i z a t i o n behaves similapa-rly to the m o pa-r e sophis-ticated o p e r a t i o n a l s c h e m e . It h a s b e e n verified t h a t the d o m a i n of validity of the linear a s s u m p t i o n (Fillion a n d M a h f o u f 2003) n o w e x t e n d s to larger p e r t u r b a -t i o n s — -t o p e r -t u r b a -t i o n s of -the size of -typical analysis i n c r e m e n t s .
For t h e p u r p o s e of rain a n d cloud assimilation, a n e w statistical diagnostic cloud s c h e m e has b e e n de-v e l o p e d ( T o m p k i n s a n d J a n i s k o de-v a 2004). T h e n e w s c h e m e includes a p a r a m e t e r i z a t i o n of large-scale pre-cipitation f o r m a t i o n based o n S u n d q u i s t et al. (1989) a n d a n e w p a r a m e t e r i z a t i o n of precipitation evapora-tion based o n the subgrid-scale variability of total
wa-FIG. 7. ( t o p ) Analysis and ( b o t t o m ) forecast i m p a c t c o m p a r i n g (left) rain r a t e
and ( r i g h t ) radiance assimilation, (a), ( b ) Analysis i n c r e m e n t s of t o t a l - c o l u m n w a t e r v a p o r ( c o l o r scale, kg m~2), w i n d v e c t o r i n c r e m e n t s a t 8 5 0 h P a ( a r r o w s ) ,
a n d surface pressure (isolines) for t r o p i c a l cyclone Z O E on 1200 U T C 26 D e c 2 0 0 2 . (c), ( d ) 24-h forecast differences ( r a i n assimilation - c o n t r o l ) of t o t a l col-u m n w a t e r v a p o r ( c o l o r scale and w i n d v e c t o r i n c r e m e n t s a t 8 5 0 h P a ( a r r o w s ) .
ter. T h e s c h e m e also e m p l o y s a diagnostic version of t h e s o u r c e t e r m associated w i t h convective d e t r a i n -m e n t , f r o -m Tiedtke (1993). First results indicate t h a t the largest i m p r o v e m e n t s are achieved in the Tropics. T h e u p d a t e d cloud a n d convection schemes have been used in the e x p e r i m e n t s described in the following.
Assimilation of rain-affected microwave radiances. T h e assimilation of rain-affected m i c r o w a v e radiances re-quires the development of a fast RT m o d e l (Bauer 2002; M o r e a u et al. 2002) that a c c o u n t s for scattering effects d u e to r a i n d r o p s a n d ice particles. Similarly, a tool to c o m p u t e c l o u d - a f f e c t e d i n f r a r e d r a d i a n c e s has b e e n developed. Both m o d e l s h a v e b e e n u s e d to evaluate t h e E C M W F m o i s t p h y s i c s (Chevallier et al. 2001; Chevallier a n d Kelly 2002; Chevallier a n d Bauer 2003). T h e 1DVAR assimilation of rain-affected radiances has b e e n c o m p a r e d w i t h assimilation of rain rates fo r t h e case of S u p e r t y p h o o n Mitag in M a r c h 2002 (using T M I data) a n d for a m i d l a t i t u d e f r o n t in J a n u a r y 2002
(us-AMERICAN METEOROLOGICAL SOCIETY M A R C H 2005 BAPIS* | 3 9 5
ing SSM/I). Both 1 D V A R m e t h o d s succeeded in p r o -d u c i n g reasonable a n -d c o h e r e n t t e m p e r a t u r e a n -d spe-cific h u m i d i t y i n c r e m e n t s that correct the s i m u l a t e d r a d i a n c e s t o w a r d t h e satellite o b s e r v a t i o n s ( M o r e a u et al. 2004) or i m p r o v e the m o d e l ' s surface rain rates. T h e c o m p u t a t i o n a l cost is less for r a i n - r a t e assimila-tion as the RT calculaassimila-tions are n o t required in that case. H o w e v e r , t h e following issues have to b e considered:
1) with rain-rate assimilation, precipitation c a n n o t be activated w h e r e the b a c k g r o u n d rain rate is zero as there is t h e n n o sensitivity of rain rate with respect to h u m i d i t y ;
2) r a i n r a t e assimilation is d e p e n d e n t o n t h e p e r f o r -m a n c e of the selected r a i n - r a t e retrieval a l g o r i t h -m that m a y b e based o n a s s u m p t i o n s that are n o t con-sistent w i t h t h e N W P m o d e l physics;
3) t h e c o m b i n e d sensitivity of radiances t o water va-por, cloud water, ice a n d precipitation allows a m o r e general application a n d avoids aliasing; a n d 4) assimilating radiances p e r m i t s a m o r e flexible
se-lection of m i c r o w a v e c h a n n e l s available f r o m a given i n s t r u m e n t , t h u s m a k i n g the t r a n s f e r of t h e m e t h o d b e t w e e n d i f f e r e n t i n s t r u m e n t s relatively s t r a i g h t f o r w a r d .
Figures 7a a n d 7b s h o w an e x a m p l e of the analysis in-c r e m e n t s of T C W V , lower-level (850 h P a ) w i n d vein-c- vec-tors, a n d surface pressure f r o m a single 4 D V A R analy-sis using the above-described T C W V retrievals f r o m r a i n - r a t e a n d r a d i a n c e observations, respectively. T h e case is Tropical Cyclone Zoe o n 1200 U T C 26 D e c e m -b e r 2002. T h e panels p r e s e n t t h e analyses assimilating rain rates (Fig. 7, left panels) a n d radiances (Fig. 7, right panels) using T M I observations. T h e T M I data are t h e only observations that are assimilated over t h e m a i n p a r t of t h e s t o r m . T h e m a i n signal is a n o r t h e a s t w a r d d i s p l a c e m e n t of the cyclone as well as an intensifica-tion of the central low pressure b y 5 - 1 0 hPa. T h e radi-ance assimilation p r o d u c e s larger i n c r e m e n t s w i t h a s t r o n g e r m o i s t e n i n g in t h e eastern p a r t of the cyclone as well as larger w i n d i n c r e m e n t s , despite t h e s o m e -w h a t lo-wer data coverage (not s h o -w n here). T h e m a i n reason for this is t h e better differential sensitivity of radiances to cloud a n d rainwater that is still effective in heavy p r e c i p i t a t i o n d u e to the usage of t h e 10.7-GHz T M I channels. T h e fact t h a t t h e assimilation of pre-cipitation observations displaces the m o d e l clouds a n d rain (apart f r o m m o d i f y i n g the system's intensity) en-sures that this i n f o r m a t i o n is carried i n t o the forecast for a p e r i o d of time. Figures 7c a n d 7d illustrate this effect for the 24-h forecast. T h e y s h o w t h e difference between the rain assimilation a n d a control experiment
in t h e 24-h forecasts of T C W V a n d t h e 8 5 0 - h P a w i n d vector. T h e initial d i s p l a c e m e n t of the system gener-ates "dipoles" of p o s i t i v e - n e g a t i v e T C W V differences d u e to the T C W V g r a d i e n t b e t w e e n the inside a n d t h e outside of the s t o r m . T h e forecast differences are simi-lar in m a g n i t u d e to the analysis increments . It can t h u s b e expected that t h e assimilation of rain i n f o r m a t i o n will h a v e a substantial i m p a c t o n b o t h analyses a n d forecasts.
T h e above-described strategies for the assimilation of rain-affected m i c r o w a v e radiances can be e x t e n d e d to the assimilation of cloud i n f o r m a t i o n f r o m i n f r a r e d observations, p r o v i d e d a suitable r a d i a t i o n m o d e l is available. Preliminary I D V A R studies have been based o n observations f r o m HIRS (Chevallier et al. 2002) a n d o n b r o a d b a n d l o n g wave fluxes f r o m t h e A R M field c a m p a i g n (Janiskova et al. 2002b). It has b e e n s h o w n t h a t t h e I D V A R retrieval is capable of g e n e r a t i n g a n d r e m o v i n g clouds as necessary.
Required improvements of the 4DVAR system. Regarding t h e assimilation system itself, a n i m p o r t a n t r e q u i r e -m e n t is a b e t t e r c o n s i s t e n c y b e t w e e n t h e linear (low resolution) a n d nonlinear (full resolution) models used in 4 D V A R ( C o u r t i e r et al. 1994) in t e r m s of resolu-tion, m o i s t physics, a n d t i m e i n t e g r a t i o n s c h e m e for h u m i d i t y . In a revised 4 D V A R - s o l u t i o n a l g o r i t h m i m p l e m e n t e d in J a n u a r y 2003, t h e l o w - r e s o l u t i o n lin-earization t r a j e c t o r y is c r e a t e d t h r o u g h i n t e r p o l a t i o n of the h i g h - r e s o l u t i o n fields (Tremole t 2004). This en-sures t h a t m o d e l profiles are similar at h i g h a n d low r e s o l u t i o n , a n d t h a t physical processes (i.e., t h o s e as-sociated w i t h c l o u d a n d rain) are active at similar lo-c a t i o n s at b o t h resolutions. T h e revision will also al-low f u r t h e r increases in analysis r e s o l u t i o n (to T 2 5 5 a n d b e y o n d ) , w h e n a p p r o p r i a t e , d e p e n d i n g o n t h e availability of a c c u r a t e linear physics ( M a h f o u f 1999; Janiskova et al. 2002a) a n d o n t h e availability of h i g h resolution observations. T h e inclusion of physical p r o -c e s s e s as o b s e r v a t i o n o p e r a t o r s will i n -c r e a s e t h e n o n l i n e a r i t y of t h e assimilation p r o b l e m (Chevallier et al. 2004) a n d m o r e f r e q u e n t relinearization m a y b e necessary.
A N E W F O R M U L A T I O N O F T H E H U M I D I T Y
A N A L Y S I S . At the present level of analysis accuracy, the b a c k g r o u n d e r r o r s for all analysis variables except h u m i d i t y a p p e a r to have n e a r - n o r m a l d i s t r i b u t i o n s , which can be a p p r o x i m a t e d by Gaussian PDFs. T h e use of G a u s s i a n P D F s in a variational analysis results in a q u a d r a t i c cost f u n c t i o n , w h i c h can b e m i n i m i z e d the m o s t efficiently. Detailed studies have s h o w n t h a t h u m i d i t y has the least Gaussian a n d the least h o m o g e
-3 9 6 I BAI15- M A R C H 2005
n e o u s b a c k g r o u n d e r r o r s of all t h e analysis variables. This is d u e to t h e c o n d e n s a t i o n effects n e a r s a t u r a t i o n a n d t h e strict limit at zero h u m i d i t y . It is suspected t h a t this u n a c c o u n t e d n o n - G a u s s i a n b e h a v i o r is a m a j o r c o n t r i b u t o r to p r o b l e m s in t h e h u -m i d i t y analysis, w h i c h have r e q u i r e d ad h o c "fixes." T h e a i m of t h e p r e s e n t r e f o r m u l a t i o n is t o r e c t i f y s o m e of these s h o r t c o m i n g s of the h u m i d i t y analysis. W e h a v e a d o p t e d t h e a p -p r o a c h of Dee a n d da Silva (2003) to recast the h u m i d i t y analysis p r o b l e m in t e r m s of a t r a n s f o r m e d h u m i d i t y variable for w h i c h s h o r t - r a n g e fore-cast e r r o r s exhibit n e a r - n o r m a l dis-tribution.
Normalized relative humidity. A large set of 3 - h forecast differences, gen-erated by an ensemble of data assimi-l a t i o n s w i t h r a n d o m assimi-l y p e r t u r b e d o b s e r v a t i o n s (Fisher a n d A n d e r s s o n 2001; Fisher 2003), p r o v i d e d a m p l e d a t a f o r t h e s t u d y of s h o r t - r a n g e forecast e r r o r P D F s f o r h u m i d i t y , a n d v a r i o u s t r a n s -f o r m e d h u m i d i t y variables. It was -f o u n d t h a t w h e n e r r o r P D F s w e r e stratified a c c o r d i n g to t h e value of t h e relative h u m i d i t y t h e y w e r e easier to a p p r o x i m a t e w i t h a G a u s s i a n d i s t r i b u t i o n . Based o n these f i n d i n g s a n o r m a l i z e d relative h u m i d i t y variable was c h o s e n as t h e n e w c o n t r o l v a r i a b l e f o r t h e r e v i s e d h u m i d i t y analysis ( H o l m et al. 2002). T h e n o r m a l i z a t i o n f a c t o r is the s t a n d a r d deviation of the relative h u m i d i t y error, stratified according to the relative h u m i d i t y itself, with d e p e n d e n c e o n vertical level. T h e asymmetries in PDFs for c o n d i t i o n s n e a r zero h u m i d i t y a n d n e a r saturation are also a c c o u n t e d for (see H o l m et al. 2002 f o r a de-scription) t h r o u g h a n o n l i n e a r t r a n s f o r m a t i o n . T h e resulting e r r o r s t a n d a r d d e v i a t i o n s in t e r m s of either specific or relative h u m i d i t y are t h e r e b y strongly de-p e n d e n t o n t h e a t m o s de-p h e r i c state (Fig. 8). T h e figure s h o w s t h a t the resulting b a c k g r o u n d e r r o r in t e r m s of relative h u m i d i t y is lower (orange shading) w i t h i n t h e c o l d a i r o u t b r e a k a n d w i t h i n t h e s a t u r a t e d f r o n t a l -z o n e r e g i o n , a n d is h i g h e r ( g r e e n ) w i t h i n t h e d e p r e s s i o n .
T h e t r a n s f o r m e d h u m i d i t y variable has been imple-m e n t e d in t h e b a c k g r o u n d c o n s t r a i n t of 4 D V A R (op-erationally in O c t o b e r 2003). It has b e e n verified t h a t t h e n e w h u m i d i t y analysis in a b r o a d sense gives t h e correct weight to all h u m i d i t y sensitive r a d i a n c e data
FIG. 8. H u m i d i t y b a c k g r o u n d e r r o r s a t m o d e l level 4 4 ( ~ 7 0 0 h P a ) in t e r m s o f r e l a t i v e h u m i d i t y ( s h a d e d , s e e l e g e n d ) , 2 0 0 3 0 5 2 4 - 1 5 0 0 U T C . G e o p o t e n t i a l a t 1 0 0 0 h P a is c o n t o u r e d in b l a c k ( 4 - d m i n t e r v a l ) a n d t h e b l u e c o n t o u r s h o w s c l o u d f r a c t i o n = 0 . 5 . T h e n e w s t a t i s t i c a l m o d e l f o r h u m i d i t y b a c k g r o u n d e r r o r s assigns l o w ( o r a n g e ) r e l a t i v e h u m i d i t y e r r o r s t a n d a r d d e v i a t i o n s w i t h i n t h e c o l d a i r o u t b r e a k a n d w i t h i n t h e f r o n -t a l c l o u d s , a n d h i g h b a c k g r o u n d e r r o r s ( g r e e n ) , f o r e x a m p l e , w i -t h i n -t h e d e p r e s s i o n .
(listed in Table 2) a n d also to S Y N O P 2 - m relative-h u m i d i t y a n d radiosonde-specific relative-h u m i d i t y data. T relative-h e r a d i o s o n d e h u m i d i t y o b s e r v a t i o n s are c u r r e n t l y u s e d b e l o w 300 h P a only. Following t h e positive results of t h e N a s h (2002) review of r a d i o s o n d e h u m i d i t y sensor p e r f o r m a n c e , t h e use of several of t h e m a i n o p -e r a t i o n a l r a d i o s o n d -e typ-es abov-e 300 h P a was acti-v a t e d S e p t e m b e r 2004.
Tackling the spindown problem. T h e n e w h u m i d i t y analy-sis f o r m u l a t i o n a l o n e o n l y s l i g h t l y r e d u c e s t h e s p i n d o w n in tropical precipitation. T h e s p i n d o w n con-sists of fairly few, b u t strong, convective precipitation events at the start of the forecast ( 2 0 - 5 0 m m h_1 in T159 resolution e x p e r i m e n t s , n o t s h o w n ) . T o better u n d e r -s t a n d t h e n a t u r e of the -s p i n d o w n , -sen-sitivity experi-m e n t s w i t h experi-m i n o r c h a n g e s to t h e h u experi-m i d i t y analysis were p e r f o r m e d . In o n e such e x p e r i m e n t the analysis i n c r e m e n t s were c o n d i t i o n e d n o t to increase the rate of c o n d e n s a t i o n in h u m i d c o n d i t i o n s (relative h u m i d -ity > 80%). It was f o u n d that this change, which reduces t h e z o n a l - m e a n b o u n d a r y layer h u m i d i t y b y less t h a n 1% ( n o t s h o w n ) , r e m o v e s t h e s p i n d o w n in t r o p i c a l convective precipitation (Fig 9). T h e precipitation rate of the sensitivity e x p e r i m e n t r e m a i n s nearly c o n s t a n t in the Tropics d u r i n g the first 24 h of forecasts, whereas in the reference e x p e r i m e n t t h e r e is a r a p i d decrease
AMERICAN METEOROLOGICAL SOCIETY M A R C H 2005 BAPIS* | 3 9 7
FIG. 9. 6 - h o u r l y f o r e c a s t e v o l u t i o n o f z o n a l l y a v e r a g e d c o n v e c t i v e p r e c i p i t a t i o n d u r i n g t h e f i r s t 2 4 h ( s e e l e g e n d ) . T h e a v e r a g e is o v e r 18 f o r e c a s t s s t a r t i n g 6 h a p a r t o v e r a 3 - d a y p e r i o d . I n b o t h p a n e l s , f o r e c a s t s w e r e s t a r t e d f r o m a n a l y s e s p r o v i d e d b y t h e n e w h u m i d i t y f o r m u l a t i o n , ( b ) T h e r e f e r e n c e c a n b e c o m p a r e d t o ( a ) a s e n s i t i v i t y e x p e r i m e n t in w h i c h t h e a n a l y s i s i n c r e m e n t s w e r e c o n d i t i o n e d n o t t o i n c r e a s e t h e r a t e - o f - c o n d e n s a t i o n in h u m i d l o c a t i o n s ( r e l a t i v e h u m i d i t y > 8 0 % ) . T h e s e n s i t i v i t y e x p e r i m e n t s u c c e s s f u l l y r e m o v e s t h e s p i n d o w n o f t r o p i c a l c o n v e c t i v e r a i n f a l l . b e t w e e n t h e 0 - 6 - a n d 6 - 1 2 - h p e r i o d s . H u m i d i t y changes of this order (a few percent or less) are, as m e n t i o n e d in section 2, below the accuracy of the cur-rent best humidity observations (Nash 2002). The best radiosondes can have 5% relative h u m i d i t y biases in the b o u n d a r y layer. Further research on removing the s p i n d o w n in t h e T r o p i c s ( a n d s p i n u p in t h e extratropics) n o w concentrates on thermodynamical and dynamical balance constraints, since the observa-tions on their own cannot be depended on to correctly constrain the h u m i d i t y analysis.
C O N C L U D I N G R E M A R K S . T h e c u r r e n t s t a t u s o f assimilation and modeling of the hydrological cycle at E C M W F has been reviewed. The emphasis has been on remote sensing of h u m i d i t y f r o m current a n d fu-ture satellite systems, in clear-sky, cloudy, and precipi-tation conditions, through direct radiance assimilation. The improved accuracy and the increasing availability of satellite information on Earth's hydrological cycle have brought this topic firmly into focus in recent years. This is reflected in the research plans of m a n y N W P centers—for example, the British, French, Japanese, and C a n a d i a n meteorological services; the National Centers for Environmental Prediction (Washington, D.C.); G l o b a l M o d e l i n g a n d A s s i m i l a t i o n O f f i c e (Washington, D.C.); and Forecast Systems Laboratory (Boulder, CO), as detailed in the proceedings of a re-cent E C M W F / G E W E X workshop ( E C M W F 2002). It is expected that this work will lead to forecast improve-m e n t through iimprove-mproved analysis in the precipitating regions of developing midlatitude weather systems and tropical cyclones.
T h r o u g h c o m p a r i s o n with in situ data, we have shown that the model's per-f o r m a n c e w i t h r e s p e c t to b o u n d a r y layer h u m i d i t y is often within the absolute accuracy of most current h u -m i d i t y o b s e r v i n g s y s t e -m s (around 5% relative h u m i d -ity). F r o m experience with r e a n a l y s i s f o r t h e p e r i o d 1 9 5 7 - 2 0 0 2 ( t h e E R A - 4 0 project) we have f o u n d that these small biases in model a n d data nevertheless lead to excessive t r o p i c a l r a i n rates in analyses and short-range forecast, that is, the " s p i n d o w n " p r o b l e m . T h e ERA-40 dataset is thus not in hydrological balance with a nonclosure of about 10%, globally (see Table 1 and its discussion in the main text, and Betts et al. 2003a,b; Kallberg 2002; Troccoli and Kallberg 2004).
The operational status of satellite remote sensing of a t m o s p h e r i c h u m i d i t y h a s b e e n p r e s e n t e d . Currently, assimilated data include radiances f r o m the HIRS, AMSU-B, SSM/I, METEOSAT, GOES, and AIRS instruments, essentially in cloud-free conditions. A con-certed effort is n o w being m a d e to extend the radiance assimilation capability to cloudy and rainy conditions. Several approaches have been defined, with the ulti-mate goal being direct 4DVAR assimilation of cloud-a n d rcloud-ain-cloud-affected rcloud-adicloud-ances. This will involve severcloud-al new ingredients in the assimilation system, such as lin-earized moist physical processes, radiative t r a n s f e r models (including scattering in clouds a n d precipita-tion), and e n h a n c e m e n t s to the 4DVAR system itself, as outlined in the "Cloud and Rain Assimilation" sec-tion. Multiple column retrievals (a 1DVAR framework) have shown very encouraging results in a case study of T y p h o o n Mitag and Tropical Cyclone Zoe.
Several of the abovementioned aspects of the m o d -eling and assimilation of the atmospheric hydrological cycle are likely to benefit f r o m the recent development of a reformulated humidity analysis (previous section). The background term of the new formulation takes the wide-ranging variability of the h u m i d i t y background errors better into account. This improves the interpre-tation of h u m i d i t y data, and the inversion of informa-tion f r o m radiances to four-dimensional distribuinforma-tions of t e m p e r a t u r e a n d humidity. Results show that the long-standing problem with spindown of tropical
pre-398 I BAI15- M A R C H 2005
cipitation can be reduced. Ways to reduce inconsisten-cies between h u m i d i t y information f r o m different ob-serving systems, including an automatic bias correc-tion procedure, require further investigacorrec-tion.
A C K N O W L E D G E M E N T S . We owe many thanks to
our ECMWF colleagues for discussions, suggestions, and contributions to the manuscript. We acknowledge the ground-breaking work of Jean-Francois Mahfouf and Virginie Marecal, which demonstrated that rain assimila-tion is indeed feasible. Anthony Hollingsworth and Martin Miller provided valuable comments on an earlier version of the manuscript. Stefan Hagemann and Klaus Arpe at the Max Planck Institute for Meteorology, Hamburg, pro-vided diagnosis on the ERA-40 performance. Data for Fig. 4 were kindly provided by Chris Bretherton, University of Washington. Rob Hine skillfully improved the figures for publication.
A P P E N D I X . A c r o n y m s a n d a b b r e v i a t i o n s . 1D/3D/4DVAR one-/three-/four-dimensional
variational data assimilation Atmospheric Infrared Sounder Advanced Microwave Sounding Unit (A and B)
Name of EOS-PM Earth Observing System satellite (NASA)
Atmospheric Radiation Measure-ment program
Convective available potential energy
CPC Merged Analysis of Precipita-tion
Joint U.S.-Taiwan radio occultation mission
Climate Prediction Center Climate Research Unit
Defence Meteorological Satellite Program
European Centre for Medium-Range Weather Forecasts
European Land Data Assimiliation System
ESA's Environmental Monitoring Satellite
Eastern Pacific Investigation of Climate
ECMWF's 15- and 45-Year Reanalysis projects European Space Agency European Organisation for the Exploitation of Meteorological Satellites AIRS AMSU (A/B) Aqua ARM CAPE CMAP COSMIC CPC CRU DMSP ECMWF ELDAS ENVISAT EPIC ERA-15/ERA-40 ESA EUMETSAT
GOES Geostationary Operational Environ-mental Satellites (NOAA)
GMS Geostationary Meteorological Satellite
GPCC Global Precipitation Climatology Centre
GPCP Global Precipitation Climatology Project
GPS Global Positioning System GRAS The Global Navigation Satellite
System (GNSS) Receiver for Atmospheric Sounding
HIRS High-Resolution Infrared Radiation Sounder
IASI Infrared Atmospheric Sounding Interferometer
METEOSAT geostationary satellites (EUMETSAT)
METOP Meteorological Operational satellite (EUMETSAT)
MIPAS Michelson Interferometer for Passive Atmospheric Sounding (ESA) MSG METEOSAT Second Generation NASA National Aeronautics and Space
Administration
NCEP National Centers for Environmental Prediction
NOAA National Oceanic and Atmospheric Administration
NWP Numerical Weather Prediction PDF Probability density function RT radiative transfer
SEVIRI Spinning-Enhanced Visible and InfraRed Imager
SMOS Soil Moisture and Ocean Salinity Mission (ESA)
SSM/I Special Sensor Microwave Imager SYNOP data format for meteorological
surface stations
TCWV total column water vapor TMI TRMM Microwave Imager TRMM Tropical Rainfall Measuring Mission
(NASA)
VTPR Vertical Temperature Profile Radiometer (NASA)
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