Estimation of the Added Value of the Absolute Calibration of GPS Radio Occultation Data for Numerical Weather Prediction

Transcription

1 APRIL 2015 A P A R I C I O A N D L A R O C H E 1259 Estimation of the Ae Value of the Absolute Calibration of GPS Raio Occultation Data for Numerical Weather Preiction JOSEP M. APARICIO AND STÉPHANE LAROCHE Data Assimilation an Satellite Meteorology, Environment Canaa, Dorval, Quebec, Canaa (Manuscript receive 30 April 2014, in final form 3 October 2014) ABSTRACT An analysis of the impact of GPS raio occultation observations on Environment Canaa s global eterministic weather preiction system is presente. Raio occultation ata, as any other source of weather observations, have a irect impact on the analyses. Since they are assimilate assuming that they are well calibrate, they also impact the bias correction scheme employe for other ata, such as satellite raiances. The authors estimate the relative impact of occultation ata obtaine from, first, their assimilation as atmospheric measurements an, secon, their influence on the bias correction for raiance ata. This assessment is performe using several implementations of the thermoynamic relationships involve, an also allowing or blocking this influence to the raiance bias correction scheme. The current implementation of occultation operators at Environment Canaa is presente, collecting upgraes that have been etaile elsewhere, such as the equation of state of air an the expression of refractivity. The performance of the system with an without assimilation of occultations is reviewe uner conitions representative of current operations. Several enial runs are prepare, withrawing only the occultation ata from the assimilation, but keeping their influence on the raiance bias correction, or assimilating occultations but enying their impact on the bias correction proceure, an a complete enial. It is shown that the impact of occultations on the analysis is significant through both paths assimilation an raiance bias correction albeit the first is larger. The authors conclue that the traceability link of the ensemble of occultations has an ae value, beyon the value of each atum as an atmospheric measurement. 1. Introuction GPS raio occultation (GPSRO) ata have been a successful aition to the sources of observational ata for numerical weather preiction (NWP). Positive results were confirme at various meteorological centers (e.g., Healy an Thépaut 2006; Cucurull et al. 2007; Aparicio an Deblone 2008; Rennie 2008). GPSRO probes with high vertical resolution regions that are otherwise poorly sample, or where most ata are of low vertical resolution, most notably over the oceans an polar areas. This qualitative iversification of sampling an resolution yiels overall positive results through a better escription of the global circulation. The improvement is less obvious Denotes Open Access content. Corresponing author aress: Josep M. Aparicio, Environment Canaa, 2121 Trans-Canaa Hwy., Dorval QC H9P 1J3, Canaa. josep.aparicio@ec.gc.ca in regions that were alreay well sample, as over the continental Northern Hemisphere. The potential ae value of these ata probably goes beyon this improvement in coverage an vertical resolution. The long-term stability of the ata an their traceability to funamental stanars are recognize assets (Anthes et al. 2000). Exploiting this property may have a profoun influence on an assimilation system, but also poses challenges beyon those of merely assimilating the ata. Several other sources of ata, notably satellite raiances, require a bias correction proceure before being reay for assimilation. This bias correction requires reference information that must be provie externally, an normally consists of both the physical processes that etermine the climatology of the moel an ata that o not require calibration. Because of their traceability, raio occultation ata are goo caniates to participate in this proceure, in aition to measurements by raiosones, aircraft, an certain surface instruments. The amount of reference calibrating ata is only a small fraction of DOI: /MWR-D

2 1260 M O N T H L Y W E A T H E R R E V I E W VOLUME 143 all available ata, an their istribution is particularly uneven. Raio occultations have been a major aition to this subset, both ue to their volume an their istribution. This stuy escribes a series of efforts towar the assessment of this potential as a calibrate source, an its exploitation, on top of alreay obtaine goo results erive from the iversification an ensification of the sampling of the atmosphere. These efforts are part of a broaer upgrae of the assimilation of GPSRO ata at Environment Canaa (EC). There are strong inications that GPSRO contributes significantly to the estimation of raiance bias corrections, when these are allowe to float an ajust, as shown, for instance, in Aparicio an Deblone (2008), Healy (2008), Poli et al. (2010), an Cucurull et al. (2014). Wewillhereestimateifthis impact translates into measurable forecast value, in the form of better preictability. The first implementation performe at EC was escribe in Aparicio an Deblone (2008). The istribution of the impact inicates that a large fraction correspons to the qualitatively ifferent properties an istribution of these ata, with respect to other assimilate ata types. These ata offer global coverage an vertically well-resolve profiles, although limite horizontal resolution. It is complementary to raiance ata, which offers also global coverage an has goo horizontal resolution, but limite vertical resolution. It is also complementary to the raiosone network, which also provies ata vertically well resolve, but its istribution is very irregular at a global scale. Fully exploiting the theoretical ae value of an absolutely calibrate an traceable ata source, on top of this iversifie sampling, an a variety of other ata types is challenging (Aparicio et al. 2008). Certain types of measurements assimilate in NWP systems are alreay consiere to be well calibrate an traceable to funamental stanars, notably some measurements obtaine from raiosones, aircrafts an surface stations. Despite being assume to be well calibrate, none is perfect, an some resiual inaccuracy is to be expecte. An effective raiance bias correction will epen on the compatibility between the ifferent calibrations of these ata types. Raiosones, aircrafts, an surface stations ultimately epen on laboratory-calibrate conventional local measurements (temperature, moisture, an pressure). This is entirely ifferent from GPSRO, which is nonlocal, remote, an provies a nonconventional measurement (refractivity). Since the traceability chain is very inepenent, this compatibility requires that each of these two classes of realizations be accoringly accurate. We escribe in this article the moifications mae to our first implementation. These are oriente to improve the quality of the realization of the traceability link for GPSRO ata, an from it, to provie a larger impact from their assimilation. Portions of these evelopments have been escribe in Aparicio et al. (2009), an Aparicio an Laroche (2011, hereafter AL11). This article provies aitional etails of the present approach at EC, after these moifications are collecte into a coherent implementation. Their impact in the performance of EC s global NWP system is then stuie. The sprea of the impact of the same ata, assimilate uner ifferent implementation choices is estimate. Since EC s operational system has evolve significantly since GPSRO was introuce, a supplementary objective of the present stuy is to provie an upate estimation, through enial experiments, of the net impact of GPSRO ata uner the present operational conitions at EC. Here, we examine the relative impact of GPSRO ata through both its assimilation, an its impact in the estimation of raiance bias corrections. We explore partial enials of GPSRO, first in the ata assimilation only, while keeping the bias corrections of the control run; an, secon, in the bias correction proceure, but keeping the assimilation, an also a complete enial, where GPSRO ata have been entirely eliminate from the system. 2. Present implementation of GPSRO assimilation at EC a. The GPSRO ata Raio occultation observations provie information about the fiel of inex of refraction. This information may be provie in several forms, incluing the bening angle as a function of the impact parameter, the refractivity as a function of altitue, or others. In all cases, a user must be able to escribe an manipulate the scalar fiel of refractivity N(x), which inclues the representations of the position x an the refractivity N. The current implementation of GPSRO operators at EC can hanle refractivity an bening angle profiles, with refractivity being the operational configuration. For the present purpose, the ifference is not relevant, an the implementation of bening angle will be escribe elsewhere. In the following, we consier the N(x) expression to generically escribe any technical representation of refractive observables within a forwar operator, regarless of whether refractivity is the final goal, or further transformations, to bening angle or others, are require. b. General concepts Let us assume a parcel of moist air of pressure P, ensity r, absolute temperature T, an specific moisture q (mass of water per unit mass of moist air). We also use

3 APRIL 2015 A P A R I C I O A N D L A R O C H E 1261 TABLE 1. Constants require for the expression of the compressibility of moist air. Value Units a KPa 21 a Pa 21 a K 21 Pa 21 b KPa 21 b Pa 21 c KPa 21 c Pa K 2 Pa 22 e K 2 Pa 22 the expressions t for the Celsius temperature an x for the molar fraction of water vapor. We assume that air consists of two fractions: the ry air of molar mass m an the water vapor of molar mass m w. When necessary, we will use the values m an m w (both in g mol 21 )(AL11). The total ensity is the sum of the ensities of the ry air an water vapor fractions r 5 r 1 r w. Therefore, t 5 T K an m x 5 q [m w 1 (m 2 m w )q]. (1) If air were exactly an ieal gas, its equation of state woul be expresse as P i 5 (r R 1 r w R w )T [ (rr Ty i ), (2) where R an R w are the gas constants for pure ry air an pure water vapor, respectively, associate to their molar mass. Equation (2) efines the virtual temperature Ty i of the moist air, if assume ieal, which can be expresse as Ty i 5 T 1 1 q m 2 m w. (3) m w Moist air is close to ieal, but not exactly, so we express its equation of state as P 5 P i Z, where Z is the compressibility factor. For this stuy, following Aparicio et al. (2009) an AL11, we have aopte the compressibility factor given by Picar et al. (2008), which is applicable to atmospheric conitions: Z P T [a 0 1 a 1 t 1 a 2 t2 1 (b 0 1 b 1 t)x 1 (c 0 1 c 1 t)x 2 ] 1 P2 T 2 ( 1 ex2 ). (4) The constants are liste in Table 1. We therefore express, instea of (2), the nonieal equation of state as P 5 rr T y, (5) where we have introuce a nonieal virtual temperature: T y 5 T 1 1 q m 2 m w Z. (6) m w The quantity T y absorbs both the moisture an the compressibility factor into an equation of state (5) for air. From the point of view of the hyrostatic behavior of a parcel of air, it can be then treate as if it were ry an ieal with temperature T y. c. The position operator In a generic NWP system, a vertical profile of the atmosphere at a specific location is escribe by some local state vector, containing several quantities as a function of some vertical coorinate. In the EC s NWP moel, the vertical coorinate is a hybri quantity, strongly linke to pressure, an altitue is a erive quantity. In a generic case, both altitue an pressure may be functions of the vertical coorinate an other state variables. In all cases, an operator linking altitue an pressure is require. This section presents thealtitueoperator,regarless of the irection in which it must be applie. We assume hyrostatic equilibrium: P 52gr, (7) h where h is the geometric altitue an g is the acceleration of gravity. Integrating this equation requires a bounary conition, which a backgroun moel normally provies as the surface pressure P s at the altitue of the moel topography h T. It also requires some closure through the equation of state, as in (5). Another element that is require is the quantity g. It inclues both gravitation an the rotation of the noninertial Earth-fixe reference frame. The value of g is not a constant, an varies with altitue h, an with latitue f, both ue to the istance to Earth s center, an to Earth s rotation. Smaller variations are also foun ue to local anomalies. The latter are substantially smaller an, hence, neglecte. Only the ellipsoial altitue an latitue epenences are retaine. We use the fiel propose by the WGS-84 Earth ellipsoi moel (National Imagery an Mapping Agency 2000). That report presents an expression for the acceleration at the surface g s, which is exact for a rotating ellipsoi in equilibrium: 1 1 k sin 2 f g s 5 g e q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi. (8) 1 2 e 2 sin 2 f

4 1262 M O N T H L Y W E A T H E R R E V I E W VOLUME 143 TABLE 2. Constants require for the escription of the gravity fiel of the WGS-84 Earth ellipsoi moel. Name Value Units a Semimajor axis m f Flattening 1/ g e Theoretical gravity at the m s 22 equator k Theoretical gravity constant e 2 First eccentricity, square m Theoretical rotation constant Constants g e, k, an e applicable for Earth, as well as its equatorial semimajor axis a an flattening f, are efine by the WGS-84 specification, an summarize in Table 2. For nonzero but small altitues, h a, this specification recommens a secon-orer expansion, which we assume to be sufficiently accurate to be applie to the entire atmosphere, an is the expression that we retain for the gravity acceleration: g 5 g s a (1 1 f 1 m 2 2f sin2 f)h 1 3 a 2 h2. (9) The hyrostatic equation with bounary conition is therefore expresse as P h 52g P, (10) R T y P(h T ) 5 P s, (11) where T y, h T, an P s are obtaine from the backgroun fiel, an g is from the WGS-84 specification.. The forwar operator of refractivity Several relationships between refractivity, pressure, temperature, an moisture have been propose in the literature. Our former implementation (Aparicio an Deblone 2008) use Rüeger (2002, hereafter R02). For this stuy, two other expressions, Smith an Weintraub (1953, hereafter SW53), an AL11 are also teste. For completeness, we mention here the ifferent expressions that have been teste for this work. These expressions use hectopascal (hpa) units for pressures, kelvin (K) for temperatures, kilogram per cubic meter (kg m 23 ) for ensities, an N-units for refractivity. For R02, which ha been the initial operational expression at Environment Canaa: N 5 77:6890P/T 1 71:2952P w /T 1 3: P w /T 2. (12) The SW53 expression is N 5 77:6P/T 1 3: P w /T 2. (13) Our current operational implementation uses AL11, whose expression is with TABLE 3. Constants require for the refractivity expression. Value Units a m 3 kg 21 a m 3 kg 21 a m 3 kg 21 a m 3 kg 21 N 5 N 0 ( N 0 /6) (14) N 0 5 a 1 r 1 a 2 r t 1 a 3 r w 1 a 4 r w t, (15) where the expression s parameters are collecte in Table 3, an where t K/T 2 1. It is important to mention here that AL11 suggeste that an expression of refractivity shoul be presente in terms of the partial ensities of ry air an water vapor, in contrast to virtually all other available expressions, an in particular those of SW53 an R02, which use partial pressures while implicitly assuming that those partial pressures are well efine, aitive, an proportional to the respective mole fractions. The reason provie in AL11 is the nonieal behavior of moist air. The partial ensities of a mixture are well-efine quantities, inepenently of the ieality of the equation of state of the mixture, an are aitive. By contrast, partial pressures are clearly efine, observable, an aitive only if the mixture is an ieal gas. Air presents only small eviations from a perfect gas. However, by construction an use of the partial pressure of water vapor P w, both SW53 an R02 implicitly assume that air is an ieal gas. For the tests performe here with SW53 an R02, we cannot avoi the evaluation of this quantity, which we choose as P w 5 x w P, where x w is the molar fraction of water vapor. Equation (14) oes not assume that the air is an ieal gas. Its partial ensities are relate to the total pressure an water vapor fraction consistently with the nonieality applie elsewhere in this implementation, an in particular uring the evaluation of the hyrostatic equation (4). e. The estimation of observation error statistics It is ifficult to give a proper estimation of the a priori error istribution for GPSRO ata. Values formally offere by ata proviers vary in their characteristics,

5 APRIL 2015 A P A R I C I O A N D L A R O C H E 1263 incluing only a eclaration of intent, or imprecisely ocumente values. Some ata are provie without an estimation of the error istribution, although the ata appear to be valuable. As a result, we o not rely on estimates of error statistics offere by the proviers. However, these values are essential to etermine the relative weights given to the backgroun fiel an observational ata. Therefore, a proceure was chosen, which ynamically etermines a useful value for the a priori stanar eviation of the observation error (Aparicio an Deblone 2008). In the specific case of GPSRO, ata are naturally associate into vertical profiles. Profiles are measure an processe as an ensemble, an it is, therefore, to be expecte that accuracy, precision, an resolution are collective properties of a profile, rather than iniviual properties of each atum, even if these properties may vary along the profile. We, therefore, estimate the a priori observation error istributions through entire profiles. Let us assume a profile of observe values O i. If the observable is refractivity, this means a set fn i (h i ); i 5 1,..., ng, but the proceure may be equally applie to profiles of bening angles fa i (a i ); i 5 1,..., ng, or other variables. The application of the forwar moel to a backgroun fiel allows the evaluation of the corresponing backgroun values B i for each observation. We can then efine the relative increment in observation space, an normalize them to allow a better comparison at ifferent altitues: Z i 5 O i 2 B i B i. (16) We also efine the following weights, with a Gaussian shape as a function of altitue: w ij 5 exp[2(h j 2 h i ) 2 /H 2 ], (17) where H is some scale height, which we arbitrarily set to H 5 5 km, an evaluate with them the weighte rootmean square (RMS) of the increments: å w ij Zj 2 z 2 i 5 j. (18) å w ij j This is an estimate of the average normalize ifference between observations an the backgroun fiel, at altitues similar to that of each observation i. For refractivity, typical values of z i are of the orer of 0.01, or 1% relative ifference between ata an backgroun. Minimal values typically occur in the upper troposphere FIG. 1. Observation minus backgroun (O 2 B) increment for one occultation profile, an value of the estimate error E that is ynamically evaluate an attribute to the observations through the algorithm escribe in section 2, shown in refractivity an bening angle space. Both increment an error are normalize to the backgroun value: (O 2 B)/B, an E/B. Note that the horizontal scaling iffers between the plots. an lower stratosphere, aroun or 0.5%, but often reach 3% 5% in the lower troposphere, especially if it is moist. Reversing the normalization, we obtain a list of values associate with each atum: «i 5 z i B i. (19) We choose to use these moving vertical average RMSs against the backgroun fiel «i, as a priori error estimates of the observations. For robustness, a lower boun of is applie to z i everywhere, before evaluating «i. An example of the estimate ispersion of the error «i is shown in Fig. 1, where the algorithm is applie to both the bening angle an refractivity ata of the same profile. It is to be note that, by construction, these values are not intrinsic properties of exclusively the input ata, but also epen on the backgroun fiel.

6 1264 M O N T H L Y W E A T H E R R E V I E W VOLUME 143 This estimate combines observation error (measurement or representativity), an backgroun error. If the observation contribution is ominant, the proceure leas to weights for the ata very close to optimum. Otherwise, the algorithm will attribute a lower than optimum weight, which is conservative. However, this oes not necessarily lea to significantly suboptimal performance. We are here concerne with the optimal use of GPSRO as a stream of ata, rather than the optimal use of any iniviual atum. If the assimilation is suboptimal at any given moment, because the backgroun error inflates the above-mentione estimate of the ata error statistics, the resiual suboptimal improvement will at least reuce the backgroun error, an thus the error estimate of future ata, progressively increasing the weight of the GPSRO stream until an equilibrium is reache. This evolution towar an equilibrium can be seen through the O 2 B statistics of GPSRO ata, which are the basis for the above estimate. The RMS evolve to become clearly smaller in GPSROassimilating experiments than in GPSRO-enie ones (Aparicio an Deblone 2008), until no further benefit is gaine. We assume that at this equilibrium we will be close to the optimum weight for GPSRO ata that the system is able to use with net benefit. Once there, tests to improve performance with several criteria base on fixe error statistics, faile to provie significantly better results. Given that the results were goo, an not trivially outperforme, this algorithm was retaine for operational use (Aparicio an Deblone 2008). With a set of fixe a priori errors, the restoring tenency that pulls the analysis towar the true atmosphere becomes stiffer when the eviation of the backgroun state is larger. By comparison, with the above ynamic algorithm, since the assume a priori observation error also grows with backgroun error, the restoring tenency provie by GPSRO woul still be flexible, even at large backgroun errors. Thus, if this ynamic algorithm is use, GPSRO will guarantee only weakly that the experiment will not iverge from the true atmosphere. Experience, however, has never shown symptoms of ivergence, neither in experimental nor in operational ata assimilation cycles. This is not surprising since many other observations whose a priori errors are fixe are proviing this restoring stiffness. Besies, this property is not new: proceures base on fixe a priori errors, which are applie to other ata types, are also normally built to be flexible when the backgroun eviation is large, for instance through quality control softening of the cost function, or eletion of ata that present large observation minus backgroun ifferences. On the other han, this ynamic error estimation has allowe, without algorithmic moification, an evolution of the average a priori error with the assimilation system, as the forecast skill improve over several upgraes of the NWP system. GPSRO s accuracy, known only very approximately at the initial implementation, has been emonstrate at progressive levels. Although this goo potential was suspecte uring the initial implementation, it coul not be sufficiently substantiate. The assimilation system has, uring this evolution, provie increasing proof of the accuracy of GPSRO, allowe smaller a priori errors, an in turn extracte progressively larger benefit from it. Also, an most importantly, ynamic error estimation has proven to be able to correctly ientify, an properly hanle, infrequent events where ata were abnormally inaccurate, such as perios with significant receiver navigation errors, or large ionospheric contamination, before the proviers flag them as below nominal. In these cases, the profile fits poorly with the backgroun, an the ata receive an appropriately low weight. To summarize, we o not claim that ynamic error estimation of GPSRO is statistically optimal, or that it coul not be outperforme. It is, instea, an approach that has successfully hanle a new technology, an that has aapte to the evolution of the assimilation system, in a way that was sufficiently close to optimal to be useful. We, therefore, report it here for completeness. f. Data screening Besies general sanity checks for vali values, the following rules are applie. We mention the rationale behin each of them. Height must be at least 1 km above MSL. Data below may suffer from unmoele phenomena: reflections, superrefraction, etc. Height must be at least 1 km above terrain. Data below may suffer from iffraction an reflections. Height must be below 40 km above MSL. Refractivity profiles are not expecte to be accurate in the upper levels (contamination by ionospheric signatures, receiver navigation error, presence of gravity waves, an upper initialization of the Abel transform). Vertical thinning: Proceeing upwar, after one value is accepte, no value is accepte uring the next 1 km. Data values are probably correlate at smaller scales. Tests of assimilation at higher vertical ensity have not shown consistently better results. Values with absolute eviations larger than 0.05 in (O 2 B)/B for refractivity are rejecte. These values o appear, but are often questionable, an are associate with extremely irregular structures in the low troposphere or gravity waves in the upper stratosphere. In both cases, it is unavisable to assimilate them.

7 APRIL 2015 A P A R I C I O A N D L A R O C H E 1265 Assimilation of ata in the upper stratosphere is particularly problematic. Since GPSRO is a relatively fast measurement technique, besies other issues that coul potentially have a technical solution (such as imperfect ionospheric subtraction, satellite navigation errors, or the upper bounary conition), it measures the instantaneous profile of the atmosphere, with a scanning time smaller than the perio of gravity waves. Even if they were free of error, measurements obtaine in the presence of gravity waves o not represent the conitions of hyrostatic equilibrium of that column of air. However, the fiel that the assimilation system is trying to estimate is the state of hyrostatic equilibrium. Therefore, it woul not be appropriate to assimilate these upper ata, even if the other sources of error were absent. Concerning the lower height limit, here set at 1 km above MSL, other higher values have been teste. Notably, it is clear that the ata show large variations, an the frequent presence of negative bias in the low troposphere is well establishe (Ao et al. 2003). However, the net effect of increasing the lower height limit, which woul systematically withraw more ata in the low troposphere, was foun to be negative when verifie against raiosones, in all regions an at all forecast ranges teste, up to 5 ays. Other means of filtering the low troposphere, such as the rejection of ata with large O 2 B eviations (set at 5%), an the ynamic error estimation, were foun to be better at hanling lowtropospheric structures such as superrefraction than a more strict filter base exclusively on altitue. 3. Data assimilation experiments a. General setup A series of ata assimilation experiments carrie out with the operational EC global forecast system (Charron et al. 2012) is escribe in this section. The system uses the General Environmental Multiscale moel (GEM; C^oté et al. 1998a,b). The assimilation is performe with either a 3D-Var scheme, which ha been employe operationally before the implementation of 4D-Var (Gauthier et al. 2007). The 3D-Var scheme employe here evaluates the same backgroun trajectory as the operational 4D-Var [i.e., First-Guess at the Appropriate Time (FGAT)], an is chosen for this stuy because it is computationally cheaper than 4D-Var, although it retains nearly all its properties, an is appropriate for assessing the impact of small moifications. Also, we have teste the system uner an ensemble variational (EnVar) ata assimilation scheme, which is scheule to become operational by the en of 2014, an uses information from an external ensemble system to provie flow-epenent correlation information over the assimilation winow (Buehner et al. 2013). This test was only performe to verify that the general behavior of the system is consistent uner system upates representative of both the current operational system, an the immeiate future. The experiments were teste over several perios: 15 December February 2009 an 31 January 14 March A thir perio, 30 June 2 August 2011, was also teste for qualitative agreement over an upate version of the system, but is not shown in this paper. The 3D-Var scheme is use for the first two perios, whereas EnVar is use for the thir. These experiments cover several generations of the forecast system an etaile system configurations, incluing a wie range of moel resolutions an assimilate ata volumes. This variety of trial perios an ata assimilation schemes is expecte to unerline the consistent impact of raio occultations as anchor ata. Within each group of tests, control experiments have been spun up for several weeks before the start of the test perio, to ensure that the ynamic bias corrections for the raiances are in equilibrium at the beginning of the control experiment. All epartures from the control start at that point, an are allowe a further spinup to allow a transient perio of the state of their respective bias correction proceures. Statistical results are evaluate over the remaining perio. The list of experiments is given in Table 4. We explore various refractivity formulations, the role of the compressibility of air, an of the ynamical bias correction for raiances implemente in the EC global ata assimilation system. The observations use in these experiments are those that were operationally assimilate at EC uring each perio. They are from raiosones, ropsones, aircraft reports, lan stations, buoys, ships, National Oceanic an Atmospheric Aministration (NOAA) win profilers, atmospheric motion vectors from geostationary satellites an from the Moerate Resolution Imaging Spectroraiometer (MODIS) on boar Aqua an Terra polarorbiting satellites, GPSRO, Avance Scatterometer (ASCAT) ata, operational geostationary satellite imagers (GOES, Meteosat, MTSAT), the atmospheric infrare souner (AIRS), an Avance Microwave Souning Unit (AMSU) A an B sensors. All were kept ientical for the respective control experiments of each group (CTL, CTLB, an SL03). Variations are introuce only in the hanling of GPSRO ata. The secon perio teste inclues, with respect to the first, a number of system upgraes, an notably for this paper, a substantial increase (about twofol) in the volume of raiance ata assimilate, largely ue to moifications of their thinning, allowing a larger ata ensity in time an space. The thir perio s main

8 1266 M O N T H L Y W E A T H E R R E V I E W VOLUME 143 TABLE 4. List of experiments carrie out in this stuy that explore the best physical implementation. The summarize properties are the assimilation scheme (4D-Var, or 3D-Var with FGAT), the presence of raio occultation (RO) ata, the refractivity expression, the air equation of state (EOS, ieal or nonieal), an the experiment where the ynamic bias corrections (DynBC) for raiance ata are evaluate (itself, or another experiment). Refractivity an EOS are only applie in the GPSRO operators, an thus they o not apply to GPSRO-enie experiments. Expt Scheme RO assimilation Refractivity EOS DynBC Perio Operational 4D-Var Yes R02 Nonieal Itself Winter 2009 CTL 3D-Var FGAT Yes R02 Nonieal Itself Winter 2009 AL11 3D-Var FGAT Yes AL11 Ieal CTL Winter 2009 SW53 3D-Var FGAT Yes SW53 Ieal CTL Winter 2009 R02 3D-Var FGAT Yes R02 Ieal CTL Winter 2009 AL11 1 CMP 3D-Var FGAT Yes AL11 Nonieal CTL Winter 2009 AL11 1 CMP 1 DYN 3D-Var FGAT Yes AL11 Nonieal Itself Winter 2009 nogpsro 3D-Var FGAT No CTL Winter 2009 upgraes are the switch to the EnVar assimilation scheme, an an increase in moel resolution from 25 to 15 km. b. Bias correction As for all major global forecast systems, the largest volume of ata for EC s global system are satellite raiances, which are require to be bias correcte to provie a goo contribution to forecast skill (Eyre 1992). We specify EC s etails below, but the main principles that are relevant here are common to implementations in other major centers (e.g., Derber an Wu 1998; Harris an Kelly 2001; Dee an Uppala 2009; Auligné et al. 2007) that use ynamic raiance bias correction. We summarize here the main general issues. The bias correction proceure assumes that for several reasons raiance ata are biase, an tries to fit a number of floating parameters, to reuce or eliminate systematic biases between raiances an moel fiels. These parameters are frequently upate, although some inertia is introuce in this upate, so the parameter evolution will be slow compare to weather patterns. If raiance ata show bias against the moel fiels, the fit slowly ajusts to reuce it. Therefore, biascorrecte raiance ata are effectively allowe to float. This ajustment of the fit also affects the assimilation of future raiance ata, proucing a feeback over the following ays. This feeback, with moel ajusting to ata (assimilation), an ata are ajusting to the moel (bias correction), coul potentially rift inefinitely. Instea, this feeback amps towar a floating equilibrium where new raiance ata, once bias correcte, show very small bias, an the fit is stable over time. This equilibrium epens on properties of the moel such as its climate trens, an also of other ata also assimilate that are not allowe to float. The ensemble of moel properties an of those other ata, which amps the rift an etermines this equilibrium, is commonly sai to anchor the system. At EC, this raiance bias correction proceure is ynamic (Garan et al. 2005), with its parameters upate at every step of an assimilation sequence. For each analysis, the previous few ays, in this case 7, of innovations (i.e., observations minus short-range forecasts uring each 6-h assimilation winow) are use to estimate a fit to the observation biases, following the multiparametric fit approach propose by Harris an Kelly (2001). The resulting parameters of these bias corrections, therefore, epen on the ata assimilation experiment where the innovations are evaluate, an evolve with time. The bias corrections for the higher-peaking AMSU-A channels are however obtaine from a static bias correction scheme, which follows the same methoology, but o not evolve with time. They ha been fixe before each test perio an, within each perio, remain ientical in all experiments consiere here. These static channels are AMSU-A in the first two perios, an in the thir. The upper statically correcte channels o not ever prouce feeback. The control experiments presente here were alreay in equilibrium with the bias correction fits. Since the moifications applie in all experiments shown here are small, we assume that after allowing a small spinup perio, the bias correction evolution an feeback will also be near equilibrium. Previous experience shows that this is largely sufficient for small moifications like the ones explore here. Uner normal operation, a cycle evaluates its own fit for the evaluation of bias correction. This is what exposes it to potential rift, an why an anchor is important. We can alternatively use, in a given experiment, the history of ynamic bias correction parameters evaluate by a secon experiment for the same perio. If the two experiments are similar, the bias correction parameters of the secon will also be applicable to the first. These bias correction parameters also evolve with time, but in this latter case the first experiment cannot suffer any feeback, as the bias correction parameters are alreay fixe by the secon experiment.

9 APRIL 2015 A P A R I C I O A N D L A R O C H E 1267 Some of the experiments escribe here evaluate their own raiance bias corrections. In others, the corrections are taken from another experiment. We use this to allow or block the feeback mentione, an explore its impact. We will explore the impact of some moifications. The ability to use a fixe history of bias correction allows the separation of the impact of this moification between their irect contribution, at fixe bias corrections, an their inirect contribution through the ynamic bias correction, such as the following: System A: Performs its own ynamic bias correction. System B: Like A, plus some moification. Takes bias correction from A. System C: Same moification as in B. Performs its own ynamic bias correction. c. Test of ifferent refractivity expressions The refractivity expressions propose by AL11, SW53, an R02 for the assimilation of GPSRO ata were consiere for several experiments, hereafter labele as AL11, SW53, an R02, respectively. Air is here assume to be an ieal gas (its compressibility factor Z has the trivial value of 1). These experiments were run over the first perio mentione, in 2009 (see Table 4 for etails). These experiments use the same history of ynamic bias corrections for raiances estimate an applie in the 3D-Var control system, which in turn closely follows EC s 4D-VAR operational global forecast system at that time. Since the experiments o not calculate their own bias corrections, the bias correction feeback mentione above is blocke. The operational system at that time use the R02 refractivity expression, an applie a realistic (nontrivial) compressibility factor. Figure 2 shows the mean innovations for temperature from the global raiosone network for January 2009 from AL11, SW53, an R02. Most of the impact is below 400 hpa. The results for AL11 an SW53 are very close, whereas the refractivity formulation in R02 leas to a coler bias in the forecast temperature, which was escribe in Aparicio et al. (2009), an confirme by Healy (2011) an Cucurull (2010). The expression R02 provies a slightly larger ry refractivity for given conitions. The analysis fits this with a enser (coler by about 0.18C) low troposphere. This moifies the vertical thickness of the low troposphere. In altitue or geopotential level, the column appears to be shifte ownwar. In temperature versus pressure, only the low troposphere is affecte. Following Aparicio et al. (2009), the atmosphere woul inee be enser, but attributes the reason not to a coler temperature, but to nonieal gas effects. Pressure exerte by FIG. 2. Global average of the raiosone temperature O 2 B bias, for the three refractivity moels consiere (SW53, R02, an AL11). GPSRO altitues are evaluate with an ieal gas equation of state. Raiance bias corrections are the same in all three experiments, as etermine by an external control experiment. air is slightly smaller, for a given molar ensity, than an ieal gas. The best results are obtaine with the AL11 experiment. The warm bias peaking at 200 hpa in all experiments is ue to the aircraft temperature observations. Above 150 hpa, the GEM moel is known to be systematically coler than raiosone ata. Concerning the choice of the physical constitutive relations, namely, the equation of state an the refractivity expression, this inicates that results are improve when both the AL11 expression an the real-gas compressibility factor are use in the observation operator. This is consistent with the stuies of Aparicio et al. (2009) an AL11 that suggeste, inepenently of an NWP system, that these constitutive relations are of higher quality. It is also consistent with explorations of NWP performance uner several constitutive relations by Aparicio et al. (2008), Healy (2011), an Cucurull (2010). We note that not only the source ataset is ientical in all these runs, but also the assimilate ataset, after any filter, quality check, an bias correction. These are taken from an external control run. Thus, only the GPSRO forwar operator iffers between them.

10 1268 M O N T H L Y W E A T H E R R E V I E W VOLUME 143. Test of nontrivial compressibility As shown by Aparicio et al. (2009), the eviation of the compressibility factor of air, from the trivial value of 1, shoul be taken into account in the estimation of observation heights. The nontrivial compressibility is smaller than one: a parcel of air of given molar ensity an temperature exerts a pressure slightly smaller than an ieal gas. When this is neglecte, the system fits the observations reucing the temperature in the lower troposphere. This is mostly a hyrostatic effect. From (6), we can see that the virtual temperature an the hyrostatic pressure epen on the compressibility factor. By incorrectly setting the latter to 1, but telling the system that GPSRO is a trustable source of thermal ata, we effectively force the system to lower the temperature an fit the occultation profiles. An experiment (AL11 1 CMP) was therefore prepare, which combines the AL11 refractivity an consiers the real-gas compressibility factor in the hyrostatic equation of GPSRO s height operator. See Table 4 for etails. This is shown in Fig. 3, an confirms the proposal by Aparicio et al. (2009) to introuce nonieal gas behavior to evaluate the hyrostatic profiles. In the AL11 1 CMP experiment, GPSRO introuces a near-neutral thermal bias with respect to raiosones. Both AL11 an AL11 1 CMP use the bias-correcte raiances of the control experiment (which is R02 1 CMP 1 DYN). Since neither AL11 nor AL11 1 CMP experiments evaluate their raiance corrections, these moifications in the treatment of GPSRO refractivity or height cannot have any impact on the raiance bias correction. The ifference shown in Fig. 3 between these two experiments is exclusively ue to the irect impact of GPSRO on the system. We will then keep the treatment of GPSRO to the AL11 refractivity, nonieal gas (CMP), an see if allowing the ajustment of the raiance bias corrections to the new conitions, which is the normal moe of operation, leas to significant ifferences. This will be AL11 1 CMP 1 DYN. e. Test of ynamic bias correction feeback Since both the choice of the refractivity expression an the compressibility have an effect on the mean temperature profile, particularly in the troposphere, the bias corrections for raiances may also be impacte if these corrections were estimate ynamically from previous innovations in the ata assimilation cycles. We explore the size of this impact launching an experiment that evaluates its own ynamic bias corrections, instea of using the history from the control (CTL) experiment, therefore, allowing the cycle to receive a feeback from FIG. 3. Global average of the raiosone temperature O 2 B bias, for the AL11 refractivity moel. The three experiments have an ieal equation of state an external raiance bias correction (AL11), a nonieal equation of state an external raiance bias correction (AL11 1 CMP), an both a nonieal equation of state an self-consistent raiance bias correction (AL11 1 CMP 1 DYN), respectively. previous innovations of raiances, in aition to the ata assimilation itself. We label this new experiment as AL11 1 CMP 1 DYN. With this notation, the CTL experiment correspons to R02 1 CMP 1 DYN. Figure 3 shows the mean innovations for the AL11, AL11 1 CMP, an AL11 1 CMP 1 DYN experiments. The ifference between AL11 1 CMP an AL11 1 CMP 1 DYN is representative of the size of the bias correction feeback to a ifference in the implementation of the GPSRO operator (again, the control experiment use R02, not AL11), everything else being equal. Allowing the bias correction scheme to operate selfconsistently tens to reuce the overall bias in the entire column. This is possible because raiosones an GPSRO ata are in goo agreement, which allows a better bias correction. This agreement also supports the choice of the constitutive relations. The thermoynamic biases that remain are ominate by known issues with other ata types (e.g., aircraft temperature reports) an known forecast moel weaknesses. A better refractivity expression, as well as the implementation of the nonieal compressibility in the

11 APRIL 2015 A P A R I C I O A N D L A R O C H E 1269 observation operator also leas to forecast skill improvements, as shown in Fig. 4 for the geopotential height at 250 hpa over the globe. This fiel is particularly relevant in this stuy since it is representative of the air mass in the troposphere where most of the impacts of the compressibility factor Z, an the refractivity expression examine here, are foun. Note that the compressibility factor oes not affect as much (Aparicio et al. 2009) the interpretation of ata at layers where air is nonieal, as it affects the altitue of the column above, at layers where air is very close to ieal. In the top panel, ay-1 to ay-5 anomaly correlations are plotte for all mentione 2009 experiments, as well as for an experiment where the GPSRO ata are not assimilate (nogpsro). In this latter experiment, the raiance bias corrections are still those from the control experiment. The bottom panel shows the anomaly correlation loss incurre by the nogpsro run, when it is compare against each of the runs that implement GPSRO assimilation. A larger loss of enial implies that the assimilating run ha better performance. In these comparisons, it can be seen that at equal ata (incluing GPSRO ata), moel, an general setup, ifferent implementations of GPSRO assimilation (refractivity expressions, equation of state of air) lea to a very substantial sprea in skill gain, as much as a factor of 2 at 5 ays, an even larger at shorter lea times. The best results are obtaine with the AL11 1 CMP 1 DYN experiment, which has a higher anomaly correlation, an where a enial of GPSRO leas to larger loss. This sprea is a large fraction of the total impact from assimilating GPSRO ata, an implies that the net impact of GPSRO to the forecast skill of the system oes not epen only on the amount of ata available, but also on the fine etails of the thermoynamic interpretation of these ata. Both the compressibility an the use of a selfconsistent ynamic bias correction scheme for raiances improve the forecast skill, whereas the choice of the refractivity expression plays a minor role. It is interesting to note [see Fig. 4, curves(nogpsro)2 (AL11 1 CMP) an (nogpsro) 2 (AL11 1 CMP 1 DYN)] that a substantial fraction of the anomaly correlation gain available from the assimilation of GPSRO through the best choice of equation of state (nonieal) an refractivity (AL11) is obtaine through the use of ynamic bias correction. This means that a substantial part of the benefit of GPSRO appears through their participation in the calibration of raiances, an not exclusively through their irect assimilation. It is interesting to note, in view of both the anomaly correlations of ifferent cycles, Fig. 4, an the agreement with raiosone ata, Figs. 2 an 3, that the forecast skill is better in those cycles where the agreement FIG. 4. (a) Anomaly correlation for temperature at 250 hpa of the ifferent experiments of the first perio, in winter 2009, which explore the ifferent constituent relationships an impact on the bias correction. (b) The anomaly correlation loss of the nogpsro enial experiment, with respect to each experiment that oes inclue GPSRO. Larger enial losses imply better performance of the experiment incluing GPSRO. The approximate error for the curves grows from at ay 1, to at ay 5. with raiosones is better. As shoul have been expecte, this suggests that agreement between anchor atasets has a significant forecast skill value. This consistency shoul be unerstoo as incluing not only the ata, but also the physical relationships between the ifferent kins of ata. In the GPSRO case, these are notably the equation of state an refractivity expression. Elsewhere in the system, this may suggest that the quality of other constitutive relationships may have a similar impact on skill. 4. Direct an inirect impact of GPSRO ata Having reache the conclusion that for both theoretical reasons, an practical tests, the best anchoring is obtaine with the constitutive relations AL11, for the refractivity, an with nonieal gas pressure in the hyrostatic equation, we explore the paths for this anchore information to flow into the NWP system, an impact its performance. This was one launching GPSRO enial

12 1270 M O N T H L Y W E A T H E R R E V I E W VOLUME 143 TABLE 5. List of experiments presente in this work that explore the impact of the assimilate information through the ifferent paths (irect assimilation, an anchoring of the raiance bias correction). The summarize properties are the assimilation scheme, the assimilation of raio occultation (RO) ata, an the experiment where the ynamic bias corrections (DynBC) for raiance ata are evaluate (itself, another experiment). Refractivity an the equation of state (EOS) are only applie in the GPSRO operators, an thus they o not apply to GPSRO-enie experiments. Expt Scheme RO assimilation Refractivity EOS DynBC Perio CTLB 3D-Var FGAT Yes AL11 Nonieal Itself Winter 2011 noro-x 3D-Var FGAT No CTLB Winter 2011 RO-X 3D-Var FGAT Yes AL11 Nonieal noro Winter 2011 noro 3D-Var FGAT No Itself Winter 2011 experiments, which also allowe the evaluation of the general impact of GPSRO uner conitions representative of the upate operational system. As inicate by the experiments mentione above, GPSRO not only has a irect impact through its assimilation, but also an inirect impact through the estimation of raiance bias corrections, as suggeste by the ifference between AL11 1 CMP an AL11 1 CMP 1 DYN. a. Experimental setup A set of four experiments was prepare, covering a contingency table: with an without assimilation of GPSRO ata, an with an without the impact of GPSRO ata on the raiance bias corrections. That is one control, two partial enial experiments, an one full enial experiment. To verify the robustness of the above results, this was one in a new perio, in the boreal winter of 2011, an with an upate version of the NWP system an ata ensemble, to verify that the qualitative results are maintaine. See Table 5 for the set of four experiments. The NWP system normally evaluates the bias correction coefficients for raiance ata from its own observation minus backgroun statistics. However, we may use the coefficients store from another experiment. 1) CTLB: follows the operational cycle of that time, but using 3D-Var as ata assimilation scheme. Its raiance bias correction coefficients are store. 2) nogpsro: enies GPSRO ata for all purposes, but is otherwise ientical to CTLB. Its raiance bias correction coefficients are also store. Full enial. 3) nogpsro-x: without GPSRO assimilation, but takes the history of raiance bias correction coefficients from the recore CTLB. Assimilation enial. 4) GPSRO-X: with GPSRO assimilation, but takes the history of raiance bias correction coefficients from the recore nogpsro. Denial of the bias correction feeback. b. Results The robustness of the result was teste an confirme by preparing the above mentione sets of four experiments on two ifferent perios, incluing full implementation of GPSRO, full enial, an two partially enie experiments. The general setup of the NWP system was comparable, an was representative of current operational stanars. Between each block, significant upgraes have been implemente. In Fig. 5, the evolutions of two particular channels (AMSU-A 8 an 10, in NOAA-16) over the course of two experiments are shown. These are the histories of the self-consistent experiments CTLB (with GPSRO) an the enial (noro), from the secon block of experiments (boreal winter, 2011). See Table 5 for etails. The eparture between the two histories of bias correction estimations can be seen. As with other channels, the approximate size of the ifference between experiments is of the orer of a few hunreths of a kelvin. The same behavior can be seen in a similar set of experiments with an upate version of the system (for boreal summer 2011, not shown). It shoul be note that the eparture between experiments is very slow, an on time scales substantially longer than the internal variability within each experiment. This internal variability shows most activity at aily to weekly time scales. The ifference of bias correction between the GPSRO allowe an enie experiments is very close to linear over the entire perio. With no evient saturation, it is to be expecte that longer experiments woul show an increase eparture. Since the eparture was still linear after 40 ays, the experiments were not continue, as it woul have been prohibitively expensive (several months) to wait for saturation. Figure 6 shows the skill loss of GPSRO enial over several experiments, incluing full enial. The skill loss was compare over the ifferent perios an etaile configurations, an foun to be consistent, up to an incluing the most recent experiments in a one month perio of boreal summer 2011 (not shown), which use an upgrae NWP system with EnVar assimilation, an that is an avance caniate to become operational uring It can be seen in Fig. 6, that most of the skill impact from GPSRO ata results from their participation in the