Anna-Veera Seppänen
email: anna-veera.seppanen@inserm.fr

Florence Bodeau-Livinec

ES Draper, BN Elaine M Boyle

Anna-Karin Edstedt-Bonamy

Marina Cuttini

Liis Toome

Rolf F Maier

Eva Cloet

Corine Koopman-Esseboom

Pernille Pedersen

Janusz Gadzinowski

Henrique Barros

Jennifer Zeitlin

Group

G Martens

P Martens

Eastern Region (K Boerch Reempts Van

A Hasselager

L Huusom

O Pryds

T Weber

L Estonia

H Toome

Varendi

Northern Region

P Y Ancel

B Blondel

A Burguet

P H Jarreau

P Truffert

B Misselwitz

Saarland (L Gortner S Schmidt

Emilia Romagna

D Baronciani

G Gargano

R Agostino

D Dilallo

Marche (V Carnielli F Franco

A Van Heijst

J Nijman

J Mazela

Portugal : Lisbon

Tagus Valley

L M Graça

Northern region (C Rodrigues M C Machado

T Rodrigues

A K Bonamy

M Norman

A C Fenton

Dwa Milligan

Paris Inserm

M Bonet

Specialist health care services use in a European cohort of infants born very preterm

AIM Children born very preterm require additional specialist care because of the health and developmental risks associated with preterm birth, but information on their health service use is sparse. We sought to describe the use of specialist services by children born very preterm in Europe.

METHOD We analysed data from the multi-regional, population-based Effective Perinatal Intensive Care in Europe (EPICE) cohort of births before 32 weeks' gestation in 11 European countries. Perinatal data were abstracted from medical records and parents completed a questionnaire at 2 years corrected age (4322 children; 2 026 females, 2 296 males; median gestational age 29wks, interquartile range [IQR] 27-31wks; median birthweight 1230g, IQR 970-1511g). We compared parent-reported use of specialist services by country, perinatal risk (based on gestational age, small for gestational age, and neonatal morbidities), maternal education, and birthplace.

RESULTS

Seventy-six per cent of the children had consulted at least one specialist, ranging across countries from 53.7% to 100%. Ophthalmologists (53.4%) and physiotherapists (48.0%) were most frequently consulted, but individual specialists varied greatly by country. Perinatal risk was associated with specialist use, but the gradient differed across countries. Children with more educated mothers had higher proportions of specialist use in three countries.

INTERPRETATION Large variations in the use of specialist services across Europe were not explained by perinatal risk and raise questions about the strengths and limits of existing models of care.

What this paper adds

 Use of specialist services by children born very preterm varied across Europe.  This variation was observed for types and number of specialists consulted.

 Perinatal risk was associated with specialist care, but did not explain country-level differences.

 In some countries, mothers' educational level affected use of specialist services.

Children born very preterm (<32wks' gestation) face higher risks of motor impairment, including cerebral palsy, vision and hearing loss, language and developmental delay, and behavioural and cognitive difficulties compared to children born at later gestational ages. [START_REF] Larroque | Neurodevelopmental disabilities and special care of 5-year-old children born before 33 weeks of gestation (the EPIPAGE study): a longitudinal cohort study[END_REF][START_REF] Saigal | An overview of mortality and sequelae of preterm birth from infancy to adulthood[END_REF][START_REF] Vohr | Language and hearing outcomes of preterm infants[END_REF][START_REF]Cognitive and behavioural outcomes following very preterm birth[END_REF][START_REF] Pierrat | Neurodevelopmental outcome at 2 years for preterm children born at 22 to 34 weeks' gestation in France in 2011: EPIPAGE-2 cohort study[END_REF] These risks rise with declining gestational age at birth. [START_REF] Larroque | Neurodevelopmental disabilities and special care of 5-year-old children born before 33 weeks of gestation (the EPIPAGE study): a longitudinal cohort study[END_REF][START_REF] Saigal | An overview of mortality and sequelae of preterm birth from infancy to adulthood[END_REF] Between 21% and 35% of children born extremely preterm (22-27wks) have been shown to have moderate to severe neurological disability in childhood. [START_REF] Saigal | An overview of mortality and sequelae of preterm birth from infancy to adulthood[END_REF] Other perinatal factors also affect the probability of health difficulties later in life, most importantly, the presence of severe neonatal morbidities at discharge from the neonatal unit. [START_REF] Saigal | An overview of mortality and sequelae of preterm birth from infancy to adulthood[END_REF] Up to 40% of infants born extremely preterm and 7% to 12% of infants born between 28 weeks and 31 weeks' gestation have a severe morbidity at discharge. [START_REF] Bonamy | Wide variation in severe neonatal morbidity among very preterm infants in European regions[END_REF][START_REF] Ancel | Survival and morbidity of preterm children born at 22 through 34 weeks' gestation in France in 2011: results of the EPIPAGE-2 cohort study[END_REF] However, many children without severe morbidities also experience developmental problems. [START_REF] Beaino | Predictors of the risk of cognitive deficiency in very preterm infants: the EPIPAGE prospective cohort[END_REF] Social factors may affect long-term prognosis, and children from socially disadvantaged families have more adverse outcomes in, for example, language development, [START_REF] Wild | The effect of socioeconomic status on the language outcome of preterm infants at toddler age[END_REF] cognition, [START_REF] Beaino | Predictors of the risk of cognitive deficiency in very preterm infants: the EPIPAGE prospective cohort[END_REF] and cerebral palsy. [START_REF] Dolk | Socio-economic inequalities in cerebral palsy prevalence in the United Kingdom: a register-based study[END_REF] Equitable and timely access to high-quality health services is needed to ensure appropriate care for emerging health problems in this population. Studies show that health service use is higher in infants born very preterm compared to children born at term 2 and in children with developmental disabilities compared to those without. [START_REF] Arim | Children with neurodevelopmental disorders and disabilities: a population-based study of healthcare service utilization using administrative data[END_REF] Use of occupational and physical therapies is higher in children born very preterm at 18 months corrected age [START_REF] Brok | Agreement between Cochrane Neonatal reviews and clinical practice guidelines for newborns in Denmark: a cross-sectional study[END_REF] and up to the age of 10 years to 12 years. [START_REF] Farooqi | Chronic conditions, functional limitations, and special health care needs in 10-to 12-year-old children born at 23 to 25 weeks' gestation in the 1990s: a Swedish national prospective follow-up study[END_REF] The type and number of services used depends primarily on gestational age at birth [START_REF] Larroque | Neurodevelopmental disabilities and special care of 5-year-old children born before 33 weeks of gestation (the EPIPAGE study): a longitudinal cohort study[END_REF][START_REF]Cognitive and behavioural outcomes following very preterm birth[END_REF] and the severity of disabilities. [START_REF] Larroque | Neurodevelopmental disabilities and special care of 5-year-old children born before 33 weeks of gestation (the EPIPAGE study): a longitudinal cohort study[END_REF] In the French Epidemiological Study on Small Gestational Ages (EPIPAGE) 1 cohort, one third of children born very preterm used specialized care, including occupational, speech and physiotherapy, and psychologist or psychiatrist consultations at 5 years of age. [START_REF] Larroque | Neurodevelopmental disabilities and special care of 5-year-old children born before 33 weeks of gestation (the EPIPAGE study): a longitudinal cohort study[END_REF] Other studies suggest that families' socio-economic characteristics affect children's use of health care services. Unfavourable social circumstances have been associated with increased outpatient service use in children born very preterm in Canada. [START_REF] Luu | Continuing utilisation of specialised health services in extremely preterm infants[END_REF] In the USA, low maternal education, poverty, and ethnic group have been associated with less access to early intervention services for high-risk infants. [START_REF] Barfield | Using linked data to assess patterns of early intervention (EI) referral among very low birth weight infants[END_REF] Socio-economic characteristics have also been associated with the type of service providers consulted. [START_REF] Raspa | Service provider combinations and the delivery of early intervention services to children and families[END_REF] While existing recommendations specify that paediatric specialist consultations, as well as sensory, developmental, and behavioral screening are needed for infants born preterm, [START_REF] Phillips | Multidisciplinary guidelines for the care of late preterm infants[END_REF][START_REF] Academy | Committee on Fetus and Newborn. Hospital discharge of the high-risk neonate[END_REF] clear evidence-based guidelines governing post-discharge care do not exist. The importance of establishing more solid evidence-based and common guidelines has been highlighted by parent organizations and professional societies [START_REF] Efcni | Caring for Tomorrow: EFCNI white paper on maternal and newborn health and aftercare services[END_REF][START_REF] Lancet | The unfinished agenda of preterm births[END_REF] but first, more information is needed about current practices. Existing studies provide an overview of the services used, but they are limited in their geographical coverage. Health service use may reflect both prevention and follow-up policies as well as how the health care system is organized, and are, therefore, highly context specific.

In this study, the objective was to compare the use of specialist services by children born very preterm (<32wks' gestation) across Europe. The focus was on care received after discharge from hospital up to 2 years' corrected age and on investigating the differences by children's perinatal risk and mothers' social characteristics, across regions from 11 countries.

METHOD

Study population

The EPICE cohort included 10 329 stillbirths, terminations of pregnancies, and live births before 32 weeks' gestation (Fig. S1, online supporting information). Out of 7 900 live births, 6 792 infants (86.0%) survived to discharge from the neonatal unit. Families whose child died before 2 years' corrected age (n=31) were not contacted for follow-up. Of the 6 761 children alive at 2 years, 2 336 (34.6%) did not participate in the study. The Northern region in the UK (380 children alive at 2 years) was excluded from the analyses because of concern about bias linked to a low response rate (27.1%). After excluding the UK Northern region, the loss to follow-up varied between 0.7% and 53.0% across the countries (p<0.001). The final study sample included 4 322 children (67.7% of those eligible).

Data on use of specialist health services

Data on the use of health services were collected through the parent-report questionnaire at 2 years' corrected age. Parents were asked whether their child had seen any of the health care providers included on a prespecified list, or whether their child had seen any other health care professionals which could be answered by a free-text response. The prespecified list of providers was developed in English, then translated and adapted to local health care systems; the providers thus differed slightly across countries (Table SI, online supporting information). This analysis focused on the most commonly used services provided by specialist physicians and other health care professionals that are not routinely provided by a general practitioner or paediatrician. Free-text responses were abstracted and the most common specialist services were described. Services for similar health problems, such as psychologist and psychiatrist, were analysed together. A variable 'any specialist' was defined as having consulted, at least once since first discharge from the neonatal unit, any of the prespecified specialists for all countries. Information on paediatricians was included to assess if these consultations were more frequent where specialist use was lower.

Data on perinatal risk factors and socio-economic status

Perinatal and child characteristics included gestational age in weeks, sex, small for gestational age (birthweight <10th centile for gestational age and sex, using references developed for the cohort), [START_REF] Mikolajczyk | A global reference for fetal-weight and birthweight percentiles[END_REF] any congenital anomaly, bronchopulmonary dysplasia (based on need for supplemental oxygen or ventilation at 36 weeks' postmenstrual age), retinopathy of prematurity (stages III-V, diagnosed before discharge), intraventricular haemorrhage (grades III and IV) or cystic periventricular leukomalacia, and necrotising enterocolitis needing surgery.

The mothers' highest achieved educational level was collected in the 2-year questionnaire using the International Standard Classification of Education 2011 definition and categorized as (1) high school (upper secondary) or below and (2) more than high school (postsecondary or more). Whether the mother was foreign-born was also self-reported. The mother's age at delivery was obtained from medical records.

Statistical analysis

First, responders were compared with non-responders regarding child characteristics, perinatal risk, and mother's sociodemographic factors. The use of specialist services was then described across the countries and by perinatal risk. Three risk groups were defined, based on perinatal characteristics associated with the risk of developing developmental or health problems in childhood: [START_REF] Saigal | An overview of mortality and sequelae of preterm birth from infancy to adulthood[END_REF][START_REF] Beaino | Predictors of the risk of cognitive deficiency in very preterm infants: the EPIPAGE prospective cohort[END_REF] (1) a high-risk group born before 28 weeks and/or with a severe neonatal morbidity (bronchopulmonary dysplasia, retinopathy of prematurity, intraventricular haemorrhage/cystic periventricular leukomalacia, or necrotising enterocolitis needing surgery) and/or a severe congenital anomaly; (2) a low-risk group born at 30 weeks or 31 weeks, not small for gestational age, without congenital anomalies, and without severe neonatal morbidity, and (3) a moderaterisk group including all other children, not classified as high or low risk. Proportions were compared using X 2 test for trend of odds and the mean number of different specialists seen across these risk groups was compared using the Kruskal-Wallis test.

To assess the effect of social factors, specialist use was compared by maternal education (high school or less vs more than high school) and birthplace (foreign vs native-born). Direct standardization was used to account for the distribution of perinatal risk within each country.

Binomial regression models were used to obtain p-values for the risk differences in any specialist service use across the educational groups and between foreign and native-born mothers, adjusting for perinatal risk. Adjusted mean numbers of specialists were predicted holding risk constant at the mean across social groups. p-values were obtained by negative binomial regressions, a method appropriate for Poisson-distributed data where the variance is greater than the mean, [START_REF] Hilbe | Negative Binomial Regression[END_REF] and the Wald test, adjusted for perinatal risk. For both adjusted models, a clustered sandwich estimator was used to take into consideration intrafamily correlation for multiples.

Sensitivity analyses were performed to assess the impact of non-response on the estimates of service use using inverse probability weighting. The weights were derived using sociodemographic and medical characteristics to estimate the probability of responding to the 2-year questionnaire, following methods previously used for this cohort. [START_REF] Bonnet | Low breastfeeding continuation to 6 months for very preterm infants: a European multiregional cohort study[END_REF] All analysis was performed using STATA 14.0 (Stata Corp., College Station, TX, USA).

RESULTS

The population at 2 years' corrected age consisted of 2 026 females and 2 296 males, with a median gestational age of 29 weeks (interquartile range, [IQR] 27-31; Table I) and a median birthweight of 1230g (IQR 970-1511g). Bronchopulmonary dysplasia was present in 12.6% of the children, severe and non-severe congenital anomaly in 1.1% and 7.3% respectively, retinopathy of prematurity in 3.8%, intraventricular haemorrhage/cystic periventricular leukomalacia in 6.1%, and necrotising enterocolitis needing surgery in 1.6%. Based on gestational age and perinatal factors, 26.9% were classified into the low-risk group, 38.8% into the moderate-risk group, and 34.3% into the high-risk group. Mothers had a median age of 31 years (IQR 27-35y) and a majority had more than high school education (53.6%). Among nonresponders at 2 years, mothers were younger (<24y) and more often foreign-born with singleton pregnancies (Table SII, online supporting information). The questionnaires were completed by the mother (85.9%), father (6.0%), both (2.9%), or other responders (e.g. grandparents, 5.2%).

Overall, the highest reported specialist service use was for ophthalmologists and physiotherapists or motor development therapists (Table II). However, there was wide variation across countries: the use of ophthalmologists ranged from 23.9% in the Danish region to 99.3% in Estonia (overall 53.4%), and physiotherapists ranged from 29.5% in the UK regions to 96.4% in Estonia (overall 48.0%). Respiratory and asthma specialists were the third most used service (23.6% overall) but with a higher use of respiratory physiotherapy in French regions (63.5%).

Psychologist/psychiatrist visits were more frequent in Estonia (42.0%) and in the Polish region (42.1%). Consultations with dieticians were reported more often in the UK (25.8%) and Swedish (27.9%) regions. Hearing specialists (including ear-nose-throat, audiology, and hearing screening) were reported as free-text answers in all countries except Estonia, where hearing examinations were prespecified and frequently reported (83.3%). However, the item in Estonia referred to the examination (not the specialist) and may have been provided in other settings. Use of any of the prespecified specialists varied from 53.7% (Italian regions) to 100% (Estonia). Consultations with paediatricians showed variability by country, but were not systematically higher when specialist service use was low.

Perinatal risk was associated with increased specialist use (Table III). In the lowest risk group, 64.3% had seen at least one specialist compared to 85.7% of the high-risk children (p<0.001). On average 1.1 specialists were reported for low-risk, 1.4 for moderate-risk, and 1.9 for high-risk children (p<0.001). This increase was seen in all countries except the Netherlands and Denmark.

Overall, the proportion of children having consulted at least one specialist was slightly higher for mothers with more than high school education (77.6% vs 74.2%; p=0.009), after standardizing for risk group (Table IV). Significant differences by maternal educational level were found in Belgium, Germany, and Portugal. Differences were found between foreign and native-born mothers in France (any specialist use) and Germany (number of different specialists), after adjusting for risk.

The sensitivity analysis using inverse probability weights revealed slightly lower use of all services when loss to follow-up was taken into consideration (Table SIII, online supporting information). However, service use and differences between countries were otherwise very similar. The analysis by risk and educational groups yielded similar associations (data not shown).

DISCUSSION

This study provides a previously unavailable overview of specialist service use among children born very preterm in their first 2 years of life in 11 European countries. A large variability existed in the reported use of services across the countries, with use of any specialist varying from 54% to 100%. Higher perinatal risk was associated with increased specialist consultations and number of specialists. Maternal education was associated with specialist use in regions from three countries. These results reveal highly diverse approaches to the use of specialists in care of children born very preterm across Europe and the challenges of benchmarking care across countries, even when they share similar standards of living and universal health care coverage.

Our findings corroborate previous studies showing a high use of specialist services by children born preterm, much higher than the 16% in children born at 39 weeks or 40 weeks in a previous study. [START_REF] Larroque | Neurodevelopmental disabilities and special care of 5-year-old children born before 33 weeks of gestation (the EPIPAGE study): a longitudinal cohort study[END_REF] It also confirms the documented association with perinatal risk factors. [START_REF] Larroque | Neurodevelopmental disabilities and special care of 5-year-old children born before 33 weeks of gestation (the EPIPAGE study): a longitudinal cohort study[END_REF][START_REF] Luu | Continuing utilisation of specialised health services in extremely preterm infants[END_REF][START_REF] Forrest | Predictors of children's healthcare use: the value of child versus parental perspectives on healthcare needs[END_REF] However, perinatal risk did not explain differences between countries, as these persisted after risk adjustment. This variation may be explained by differences in policies for the follow-up of infants born very preterm. For instance, Estonia, where almost all children had seen a specialist, has established national follow-up policies and a comprehensive programme including specialist care for all children born before 32 weeks. In the UK, Denmark, and Italy, where national protocols have not yet been established for follow-up of children born very preterm, specialist service use was lower, even when perinatal risk was high, possibly reflecting a focus on treatment more than prevention. Studying the content of established follow-up programmes and their ability to refer children to specialists could give a better picture of the role of specialists in screening, prevention, and treatment. Variation across countries may also reflect differences in how paediatric primary care is organized more generally, and the accessibility of paediatric services. Systems with varying provision of paediatric services exist across Europe. [START_REF] Van Esso | Paediatric primary care in Europe: variation between countries[END_REF] However, there was no clear pattern across the countries with respect to using paediatric versus specialist services.

The two most commonly used services were ophthalmologist and physiotherapist, as reported previously. [START_REF] Brok | Agreement between Cochrane Neonatal reviews and clinical practice guidelines for newborns in Denmark: a cross-sectional study[END_REF] Some services were more country specific, such as respiratory physiotherapy in France, speech therapy in Estonia, dietician in Sweden and the UK, and neurologist and psychologist/psychiatrist in Estonia and Poland. In France, respiratory physiotherapy is commonly used in the general paediatric population. [START_REF] Arnoux | Chest X-ray and acute bronchiolitis: Are these indications decreasing?[END_REF] Speech/language therapy, which is used for feeding difficulties in this age group, were also mentioned by parents, although they were not prespecified in the questionnaire and should be included in future studies.

Children of more educated mothers were more likely to see a specialist in three of the 11 countries, which has similarly been reported for out-patient services in children born very preterm. [START_REF] Luu | Continuing utilisation of specialised health services in extremely preterm infants[END_REF] The absence of these differences in the remaining countries might be explained by the organisation of care, such as having systematic follow-up in place, or referral or targeting practices focussing on socially disadvantaged families, and constitute areas for further investigation. Ensuring access to specialized health services for socially disadvantaged families is essential as these families are more likely to have a child born very preterm [START_REF] Bonet | Neighbourhood deprivation and very preterm birth in an English and French cohort[END_REF] and there is evidence that they may benefit more from some services. [START_REF] Spittle | The role of social risk in an early preventative care programme for infants born very preterm: a randomized controlled trial[END_REF] Conversely, being foreign-born or not speaking the language may act as a barrier to contact with service providers. [START_REF] Clements | Maternal socio-economic and race/ethnic characteristics associated with early intervention participation[END_REF] Reassuringly, few differences were found between foreign and native-born women in this study.

The strengths of this study include its population-based design, geographic spread, and standardized protocol across 11 European countries. However, with limited detail collected about the frequency of consultations and whether they were for prevention or treatment, we could not consider the appropriateness of the care, nor whether specialist care was provided as part of other health services, such as motor development tests that are sometimes performed at maternal and child health centres. Neither could we distinguish private from public providers, nor assess if services had out-of-pocket costs. Another limitation was loss to follow-up, which varied across regions. Comparison of non-responders with responders showed that younger and foreign-born mothers were underrepresented, but proportions of medical risk factors were very similar in both groups. Consideration of non-response using inverse probability weighting lowered estimates of specialist use, suggesting that non-responders were less likely to use health services, but associations with risk and educational level did not change. Finally, recall bias might have affected the accuracy of the answers, but there is no reason to believe that recall bias was differential across regions as the protocol and questionnaires were standardized.

In conclusion, these data show high heterogeneity in specialist health service use among children born very preterm across European regions using a standardized parent-report instrument in 10 languages. This heterogeneity cautions about generalizing research results on health care use from one country to others, and calls attention to the diverse models of care within Europe. Further studies on specialist service use in relation to health outcomes, use of emergency and in-patient services, parental experiences of care, and health care costs should investigate the advantages and drawbacks of these models in order to inform guidelines that are applicable across diverse health systems.

  Data source Data were collected as part of the Effective Perinatal Intensive Care in Europe (EPICE) project, a population-based cohort of very preterm births in 19 regions in 11 European countries: Belgium (Flanders); Denmark (Eastern region); Estonia (entire country); France (Burgundy, Ile-de-France, and Northern region); Germany (Hesse and Saarland); Italy (Emilia-Romagna, Lazio, and Marche); the Netherlands (Central and Eastern region), Poland (Wielkopolska); Portugal (Lisbon and Northern region); Sweden (greater Stockholm) and the United Kingdom (East Midlands, Northern, and Yorkshire and the Humber regions). Regions were selected based on geographic location, organizational diversity, on-site infrastructure, and expertise for implementing the protocol. Still and live births between 22 weeks' and 31 weeks and 6 days' gestation were included from all maternity hospitals over 12 months between April 2011 and September 2012. In France, the inclusions were performed over 6 months. Perinatal data were abstracted from obstetric and neonatal records until the initial discharge from hospital, by medical staff or trained investigators. At 2 years' corrected age, parents were sent a questionnaire on the development and health of their child. Consistency and reliability were addressed in the design phase of the study; questionnaires included previously validated questions when possible and common definitions that were translated and pretested in each country. Consent to participate in the EPICE cohort was obtained from all mothers included in the follow-up study, including for the collection of perinatal and follow-up data. Each region obtained approval from their local ethics board and/or hospital committee according to national legislations before the start of data collection. The study was also approved by the French Advisory Committee on Use of Health Data in Medical Research and the French National Commission for Data Protection and Liberties.

Figure S1 :

 S1 Figure S1: Flow-chart illustrating the participation in the study.

Table SI :

 SI Specialist services as defined in each country specific questionnaire

Table SII :

 SII Responder and non-responder characteristics

Table SIII :

 SIII Use of specialist services by country using inversed probability weighting, sorted by total use of services

Table I :

 I Sample characteristicsData reported as n (proportion) or in bold type for median [IQR]. a Percentages are calculated on all cases excluding missing values, as indicated. b Lower: over 29 weeks' gestation, without small for gestational age, severe neonatal morbidities, and congenital anomaly; Moderate: not classified as higher or lower risk; Higher: below 28 weeks' gestation or at least one neonatal morbidity or severe congenital anomaly. IQR, interquartile range.

		n a	n (%) or median [IQR]
	Gestational age in completed weeks	4322	29 [27-31]
	<26		324 (7.5)
	26-27		759 (17.6)
	28-29		1152 (26.7)
	30-31		2087 (48.3)
	Birthweight, g	4322	1230 [970-1511]
	Multiple birth
	Singleton	4322	2890 (66.9)
	Twins		1259 (29.1)
	Triplets or more		173 (4.0)
	Sex: female	4322	2026 (46.9)
	Small for gestational age	4322
	Yes (<10 th centile)		1413 (32.8)
	No (>10 th centile)		2909 (67.3)
	Congenital anomaly	4321
	Severe		49 (1.1)
	Non-severe		317 (7.3)
	None		3955 (91.5)
	Bronchopulmonary dysplasia at 36 weeks' postmenstrual age	4225	533 (12.6)
	Retinopathy of prematurity stages III-V	4272	161 (3.8)
	Intraventricular haemorrhage grade III or IV	4278	260 (6.1)
	Necrotising enterocolitis needing surgery or cystic periventricular leukomalacia Perinatal risk b	4322 4215	67 (1.6)
	Lower		1132 (26.9)
	Moderate		1636 (38.8)
	Higher		1447 (34.3)
	Mother's age at delivery (y)	4322	31 [27-35]
	<24		537 (12.4)
	25-34		2515 (58.2)
	≥35		1260 (29.4)
	Foreign-born mother	4308	956 (22.2)
	Mother's educational level	4168
	High school or less		1936 (46.5)
	More than high school		2232 (53.6)

Table II :

 II Use of specialist services by country (sorted by total use of services)

							Prespecified services a			Free text responses
	Regions from	Total	Paedia-trician, %	Any of the prespecified services, %	Ophthal-mologist, %	Physiotherap ist or motor development therapist, %	Respiratory, lung or asthma specialist or pulmonologist, %	Develop-mental psychologist or psychiatrist, %	Dietician or nutritio-nist, %	Hearing specialist, % examination ear-nose-throat/ audiology/ hearing	Neurologist, %	Osteo-path, %	Speech therapist, %

Table III :

 III Use of specialist services (proportion of any specialist and mean number of different services used) by country and level of medical riskData reported as number of children in each category, proportion of children having seen any of the prespecified services and mean number of different prespecified services seen.

				Lower			Moderate			Higher
	Regions from	Total	Number of children	Any service, %	Mean number of services	Number of children	Any service, %	Mean number of services	Number of children	Any service, %	Mean services number of	p a	p b
	Belgium	308	98	48.9	0.7	101	60.8	0.9	85	81.5	1.5	<0.001	<0.001
	Denmark	180	33	50.0	0.7	64	59.4	0.9	69	72.5	1.1	0.022	0.053
	Estonia	138	36	100.0	2.2	52	100.0	2.8	50	100.0	2.6	-	0.003
	France	986	234	87.3	1.5	400	92.7	1.8	306	97.3	2.3	<0.001	<0.001
	Germany	435	104	81.7	1.3	182	89.8	1.5	149	92.4	1.8	0.012	<0.001
	Italy	731	215	42.3	0.6	284	51.9	0.8	225	66.1	1.3	<0.001	<0.001
	Netherlands	229	53	81.1	1.4	86	82.6	1.3	89	88.6	1.5	0.200	0.194
	Poland	199	53	96.1	2.1	62	91.8	2.3	83	96.4	2.9	0.798	<0.001
	Portugal	408	98	64.8	1.1	173	80.4	1.4	137	89.2	2.0	<0.001	<0.001
	Sweden	165	44	37.2	0.7	63	75.4	1.4	54	100.0	2.9	<0.001	<0.001
	UK	543	164	44.9	0.6	169	51.2	0.8	200	76.8	1.6	<0.001	<0.001
	Total	4322	1132	64.3	1.1	1636	75.1	1.4	1447	85.7	1.9	<0.001	<0.001

a X 2 test for trend of odds. b Kruskal-Wallis test for p-value for mean number of services. Regions are: Belgium (Flanders); Denmark (Eastern region); Estonia (entire country); France (Burgundy, Ile-de-France, and Northern region); Germany (Hesse and Saarland); Italy (Emilia-Romagna, Lazio, and Marche); the Netherlands (Central and Eastern region), Poland (Wielkopolska); Portugal (Lisbon and Northern region); Sweden (greater Stockholm); and the UK (East Midlands and Yorkshire and the Humber regions).

Table IV :

 IV Use of specialist services (proportion of any specialist and mean number of different specialists seen) by country, maternal education level and birthplace, adjusted by medical risk Data reported as number of children in each category, proportion of children having seen any of the prespecified services and mean number of different prespecified services seen. a Proportions adjusted by level of medical risk by direct standardization. b Adjusted predictions of mean number of services holding risk constant at mean across social groups. c p-value for risk difference adjusted for perinatal risk and clustering for multiples, using binomial regression. d p-value for difference in mean number of specialists seen adjusted by risk and clustering for multiples, using Wald test

							Use of specialist services by educational level and birthplace, adjusted for risk
	Regions from		High school or less	More than high school				Foreign-born		Native
			Number	Any	Mean	Number	Any	Mean	p c	p d	Number	Any	Mean	Number	Any	Mean	p c	p d
		Total	of	service	number	of	service	number			of	servic	number	of	service	number
			children	(%) a	of	children	(%) a	of			children	e (%) a	of	children	(%) a	of
					services b			services b					services b			services b
	Belgium	308	128	57.1	0.8	174	67.8	1.0	0.036	0.197 58	67.2	0.9	250	62.2	0.9	0.836 0.615
	Denmark	180	27	65.2	1.1	150	63.4	0.9	0.968	0.467 18	43.1	1.0	162	63.9	0.9	0.485 0.767
	Estonia	138	46	100.0	2.7	89	100.0	2.5	-	0.104 9	100.0 2.6	129	100.0	2.6	-	0.757
	France	986	428	91.9	1.9	481	94.0	1.9	0.295	0.434 335	90.3	1.8	646	94.1	1.9	0.045 0.439
	Germany	435	221	88.1	1.5	200	93.0	1.7	0.008	0.186 122	82.1	1.3	311	91.0	1.7	0.145 0.006
	Italy	731	459	54.6	0.8	266	51.0	0.8	0.406	0.512 188	53.2	0.8	543	53.5	0.8	0.994 0.935
	Netherlands	229	39	87.5	1.6	187	84.0	1.4	0.873	0.173 27	76.2	1.2	202	85.4	1.4	0.377 0.269
	Poland	199	114	93.8	2.4	83	97.6	2.6	0.081	0.069 1	-	2.2	198	-	2.5	-	0.062
	Portugal	408	228	74.7	1.4	175	86.2	1.7	0.011	0.013 76	84.1	1.6	332	78.8	1.5	0.828 0.408
	Sweden	165	71	70.6	1.4	93	75.3	1.5	0.396	0.537 48	66.4	1.3	117	75.5	1.5	0.280 0.535
	UK	543	175	56.7	0.9	334	59.9	1.0	0.519	0.693 74	51.0	0.9	462	59.8	1.0	0.229 0.378
	Total	4322	1936	74.2	1.4	2232	77.6	1.5	0.009	0.170 956	75.1	1.4	3352	76.2	1.4	0.456 0.227
	after negative binomial regression. Regions are: Belgium (Flanders); Denmark (Eastern region); Estonia (entire country); France (Burgundy, Ile-de-France, and Northern region); Germany (Hesse
	and Saarland); Italy (Emilia-Romagna, Lazio, and Marche); the Netherlands (Central and Eastern region), Poland (Wielkopolska); Portugal (Lisbon and Northern region); Sweden (greater
	Stockholm); and the UK (East Midlands and Yorkshire and the Humber regions).

Table SI :

 SI Specialist services as defined in each country specific questionnaire. Only freetext answers obtained where crossed out cells.

	Pre-specified services and/or free-text answers	UK	FRANCE	SWEDEN	DENMARK	GERMANY	BELGIUM & THE NETHERLANDS	PORTUGAL	ITALY	POLAND	ESTONIA
	Paediatrician	Paediatrician	Un(e) pédiatre Paediatrician	Barnläkare Paediatrician	Børnelaege Paediatrician	Kinderärztin/ Kinderarzt Paediatrician	Kinderarts Paediatrician	Pediatra Paediatrician	Pediatra (oltre le visite di controllo presso la neonatologia) Paediatrician (outside check-up visit at neonatal unit)	Pediatra Paediatrician	Lastearst väljaspool eelnevaid asutusi Pediatrician outside the follow-up clinic
	Physiotherapist or motor	Physiotherapist/ Motor development therapist	Des séances de kinésithérapie motrice Physiotherapy sessios	Sjukgymnast Physiotherapist	Fysioterapeut Physiotherapist	Physiotherapeut(in)/ Krankengymnast(in) Physiotherapist	Fysiotherapeut Physiotherapist	Fisioterapeuta/ Terapeuta de desenvolvimento motor	Fisioterapista/ Terapista della motricità (oltre le visite di controllo presso la neo-natologia)	Fizjoterapeuta/ Rehabilitant	Füsioterapeut
	development therapist	Motor development therapist	Un(e) psycho-motricien(ne) Psychomotor therapist				Therapeut voor motorische ontwikkeling Motor development therapist	Physiotherapist/ Motor development therapist	Physiotherapist/Motor development therapist (outside check-up visit at neonatal unit)	Physiotherapist/ Rehabilitation	Physiotherapist
	Resporatory, lung or asthma specialist, allergologist, pulmonologist	Respiratory/ Asthma specialist	Des séances de kinési-thérapie respiratoire Respiratory physiotherapy	Andningsmottagning eller lungmottagning specialist Respiratory or lung	Lungespecialist / astmaspecialist asthma specialist Lung specialist/	Lungenspezialist(in)/ Asthmaspezialist(in) asthma specialist Lung specialist/	Ademhalings-/astmaspecialist specialist Respiratory/ asthma	Imuno-alergologista/ pneumologista pulmonologist Immuno-allergist /	Specialista in malattie respiratorie (oltre le visite di controllo presso la neo-natologia) Specialist

in respiratory diseases (outside check-up visit at neonatal unit)

										Pulmonolog Pulmonologist	Kopsuarst Allergologist/ pulmonolmogist
	Psychologist or developmental psychologist	Developmental or behavioural psychologist	Un(e) psychologue Psychologist	Psykolog Psychologist	Udviklings-eller adfaerdspsykolog Developmental or behavioural psychologist	Entwicklungspsycholo gin Develomental psychologist	Ontwikkelings-of gedragspsycholoog Developmental or behavioural psychologist	Psicólogo (do comportamento ou do desenvolvimento) or development) Psychologist (behavior	Psicologo dello sviluppo in età evolutiva (oltre le visite di controllo presso la neonatologia) neonatal unit) (outside check-up visit at Developmental psychologist	Psycholog Psychologist	Lastepsühholoog Child psychologist
	Psychiatrist	Psychiatrist	Un(e) psychiatre Psychiatrist	Psykiater Psychiatrist	Børnepsykiater Child psychiatrist	Psychiater(in) Psychiatrist	Psychiater Psychiatrist	Psiquiatra Psychiatrist		Psychiatra Psychiatrist	Lastepsühhiaater Child psychiatrist
									Dietista (oltre le visite di controllo
	Dietician or nutritionist	Dietician	Un(e) diététicien(ne) Dietician	Dietist Dietician	Diaetist Dietician	Ernährungsberater(in) Dietician	Diëtist(e) Dietician	Nutricionista/Dietista Nutritionist/Dietist	presso la neonatologia) Dietician (outside check-up visit	Dietetyk Dietician	Dieetõde Dietician
									at neonatal unit)
			Un(e) orthoptiste/
	Ophthalmologist or eye specialist	Ophthalmologist	ophtalmologiste (spécialiste des yeux) Optometrist/ ophthalmologist (eye	Ögonläkare /Ortoptist Ophthalmologist/ orthoptist	Øjenspecialist Ophthalmologist	Augenärztin/ Augenarzt eye doctor Ophthalmologist /	Oogspecialist Ophthalmologist	Oftalmologista Ophthalmologist	Oculista (oltre le visite di controllo presso la neonatologia) neonatal unit) Oculist (outside check-up visit at	Okulista Oculist	Silmaarst Ophthalmologist
			specialist)
									Neuropsichiatra infantile /
	Neurologist	Neurologist	Un(e) neurologue Neurologist	« Neurologist » asked questionnaires in some	Neurologist Neurolog	Child neurologist Neuropädiater(in)		Neurologist Neurologista	Neurologo (oltre le visite di controllo presso la neonatologia)

Child neuro-psychologist / Neurologist (outside check-up visit at neonatal unit) Neurolog Neurologist Lasteneuroloog Child neurologist Speech therapist

		Logopeed
		Speech therapist
	Hearing examination/ ear specialist/ ENT/audiology	Kuulmisuuringud Hearing examinations
	Osteopath	Ostéopathe Osteopath

Table SII :

 SII Responder and non-responder characteristics

		Responders at 2 years	Non-responders at 2
		(N=4322)	years (N=2059)
		n(%) or median [IQR]	n(%) or median [IQR]
	Gestational age, weeks	29 [27-31]	30 [28-31]
	<26	324 (7.5)	175 (8.5)
	26-27	759 (17.6)	297 (14.4)
	28-29	1152 (26.7)	554 (26.9)
	30-31	2087 (48.3)	1033 (50.2)
	Total	4322 (100.0)	2059 (100.0)
	Birth weight, grams	1230 [970-1511]	1250 [985-1525]
	Multiple birth
	Singleton	2890 (66.9)	1456 (70.8)
	Twins or triplets	1432 (33.1)	602 (29.3)
	Total	4322 (100.0)	2058 (100.0)
	Sex of child
	Male	2296 (53.1)	1115 (54.2)
	Female	2026 (46.9)	943 (45.8)
	Undetermined	0 (0.0)	1 (0.1)
	Total	4322 (100.0)	2059 (100.0)
	Small for gestational age
	No (>10 th percentile)	2909 (67.3)	1401 (68.1)
	Yes (<10 th percentile)	1413 (32.7)	657 (31.9)
	Total	4322 (100.0)	2058 (100.0)
	Congenital anomaly
	None	3957 (91.6)	1898 (92.2)
	Non-severe	315 (7.3)	138 (6.7)
	Severe	49 (1.1)	23 (1.1)
	Total	4321 (100.0)	2059 (100.0)
	Bronchopulmonary dysplasia at 36 weeks postmenstrual age
	No	3692 (87.4)	1740 (86.3)
	Yes	533 (12.6)	276 (13.7)
	Total	4225 (100.0)	2016 (100.0)
	Retinopathy of prematurity stages III-V
	No	4111 (96.2)	1952 (96.6)
	Yes	161 (3.8)	68 (3.4)
	Total	4272 (100.0)	2020 (100.0)
	Intraventricular haemorrhage grades III-IV or cystic periventricular leukomalacia
	No	4018 (93.9)	1882 (92.8)
	Yes	260 (6.1)	146 (7.2)
	Total	4278 (100.0)	2028 (100.0)
	Necrotising enterocolitis with surgery
	No	4255 (98.5)	2020 (98.1)
	Yes	67 (1.6)	39 (1.9)
	Total	4322 (100.0)	2059 (100.0)
	Overall perinatal risk
	Low	1132 (26.9)	575 (28.7)
	Moderate	1636 (38.8)	764 (38.2)
	High	1447 (34.3)	662 (33.1)
	Total	4215 (100.0)	2001 (100.0)

Data reported as median [IQR: interquartile range] or n(proportion)

Table SII ,

 SII continued: Responder and non-responder characteristics

		Responders at 2 years	Non-responders at 2
		(N=4322)	years (N=2059)
		n(%) or median [IQR]	n(%) or median [IQR]
	Mother's age in years at delivery	31 [27-35]	29 [25-34]
	<24	537 (12.4)	488 (23.7)
	25-34	2515 (58.2)	1098 (53.3)
	≥35	1270 (29.4)	473 (23.0)
	Total	4322 (100.0)	2059 (100.0)
	Mother's country of birth
	Foreign-born	956 (22.2)	500 (38.4)
	Native	3352 (77.8)	802 (61.6)
	Total	4308 (100.0)	1302 (100.0)
	Mother's educational level a
	High school or less b	1936 (46.5)
	More than high school c	2232 (53.6)
	Total	4168 (100.0)
	Country
	Belgium	308 (7.1)	345 (16.8)
	Denmark	180 (4.2)	106 (5.2)
	Estonia	138 (3.2)	1 (0.1)
	France	986 (22.8)	117 (5.7)
	Germany	435 (10.1)	222 (10.8)
	Italy	731 (16.9)	237 (11.5)
	The Netherlands	229 (5.3)	101 (4.9)
	Poland	199 (4.6)	50 (2.4)
	Portugal	408 (9.4)	197 (9.6)
	Sweden	165 (3.8)	75 (3.6)
	UK	543 (12.6)	608 (29.5)
	Total	4322 (100.0)	2059 (100.0)

Data reported as median [IQR: interquartile range] or n(proportion)

a Not available for non-responders at 2 years b ISCED levels 0-3 (early childhood education to upper secondary) c ISCED levels 4-8 (post-secondary to doctoral)

ACKNOWLEDGMENTS

The research received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement No 259882 and received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 633724.


Behrang Moradi

Nicolas Daclin

Vincent Chapurlat

Formalization, Evaluation of non-functional properties for system of system engineering: Application to Resilience

come   L'archive ouverte pluridisciplinaire

Formalization, Evaluation of non-functional properties for system of system engineering: Application to Resilience

Behrang MORADI, Nicolas DACLIN, Vincent CHAPURLAT (firstname.lastname@mines-ales.fr)

LGI2P, Ecole des Mines d'Alès

Systems of Systems Engineering

A system of system (SoS) is an integration of a finite number of constituent systems which are independent and operable, and which are networked together for a period of time to achieve a certain higher goal. 1 [Jamshidi, 2009]. SoS are composed of separate constituent systems and have a majority of the following five characteristics 2 [START_REF] Maier | Principles of System of System Architecture[END_REF]]: Operational independenceconstituent has a purpose of its own and can be operated independently, without the need to interact with other systems. Managerial independence -constituent are controlled by different authorities (or system owners), they not only have operational independence but are, actually, operated independently. Emergent behaviorbehaviors are only exhibited at the SoS level and cannot be achieved by any of the constituent systems operating independently of the other constituent systems.

Evolutionary development -SoS is not created once and for all, but evolves as constituent systems, or functions thereof, are added, removed, or modified. Geographical distributionthe concern of SoSE is primarily with the information exchange between constituent systems.

Relationships amongst Resilience and System Lifecycle Properties (Ilities) :

 The "-ilities" are properties that often manifest and determine value after a system is put into initial use (e.g. resilience, interoperability, robustness).  Resilience is an important "-ilitiesand must be mastered and maximized with engineering systems of systems. Hypothesis 1: The resilience can be evaluated by defining and analysing its relations within the "-ilities" "ecosystem".

Fig. 1 .

 1 Fig.1. A Transport System-of-Systems

Fig. 2 .

 2 Fig.2. Illustration of essential resilience capabilities.

Fig. 3 . 2 :

 32 Fig. 3. Correlation network of ilities based on a normalized 2-tubel keyword analysis 6 [De Weck, Ross, Rhodes,2012]

Fig. 4 . 3 :

 43 Fig. 4. Framework of evaluation of resilience


Lianyi Guo

Zhihong Jiang
email: zhjiang@nuist.edu.cn

Mei Ding

Weilin Chen

Laurent Li

Prof Zhihong Jiang

Downscaling and projection of summer rainfall in Eastern China using a nonhomogeneous hidden Markov model

Keywords: Nonhomogeneous hidden Markov model, Statistical downscaling, Daily precipitation, Future projection, Global warming of 1.5℃ and 2℃

A nonhomogeneous hidden Markov model (NHMM) is used to stochastically simulate summer (June-August) daily precipitations in the middle and low reaches of the Yangtze River in Eastern China, with driving forcing from three global climate models (GCMs). Simulations cover the historical period from 1961 to 2005 and from 2006 to 2100 following the RCP4.5 scenario. The model is firstly evaluated against data from the regional observation network. Results show that NHMM effectively enhances the ability of GCMs in simulating summer daily rainfall in the region. For future projection at different time horizons of the 21st century, the spectral distribution of regional precipitations (in function of their intensity) shows consistent changes with a decrease of occurrence probability for light rain (< 10mm/day) and an increase for heavy rain (> 10mm/day). Among variables of interest, total precipitation (PRCPTOT), precipitation intensity (SDII), number of rainy days for daily precipitation exceeding 10mm (R10mm) and 95th percentile of precipitation (P95), all show a gradually increasing trend in the 21st century, and geographically an eastward gradient with smaller increase (or even weak decrease) for the west and larger increase for the east. It is noted that obvious changes occur in eastern region with 95% significance level, and PRCPTOT or R10mm increases by 40%~60% in the late 21st century. Further quantitative assessment is performed for global warming of 1.5℃ and 2℃. The halfdegree additional warming makes R10mm change by -3.7%, 2.4% and 12.1% over western, central and eastern regions, respectively.

Introduction

The middle and low reach of the Yangtze River in Eastern China is strongly influenced by the Asian monsoon. The annual precipitation in this zone is about 1000mm and two-thirds fall in summer. The region suffers frequent extreme climate events causing serious losses of lives and properties. It is therefore important for us to investigate future evolution of such events under global warming. Furthermore, the 2015 Paris Agreement aims to limit the global warming to well below 2℃ above the pre-industrial and to pursue efforts to limit it to 1.5℃ (UNFCC, 2015). Particularly, the half-degree warming from 1.5°C to 2.0°C becomes an issue for international geopolitics, since some recent studies concluded that it may drastically augment the occurrence frequencies and impacts of extreme events [START_REF] Schaeffer | Long-term sea-level rise implied by 1.5 ℃ and 2 ℃ warming levels[END_REF][START_REF] Knutti | A scientific critique of the two-degree climate change target[END_REF].

Global climate model (GCM) which can well simulate large-scale climate variables is often used to make future climate change projection in China. However, GCM has shortcomings to well simulate regional climate, mainly due to its relatively coarse spatial resolution. It generally fails to reproduce mean and extreme precipitations [START_REF] Jiang | Ensemble projection of 1-3℃ warming in China[END_REF][START_REF] Xu | Projected changes of precipitation extremes in river basins over China[END_REF][START_REF] Jiang | Extreme climate events in China: IPCC-AR4 model evaluation and projection[END_REF][START_REF] Jiang | Extreme Precipitation Indices over China in CMIP5 models. Part 1: Models evaluation[END_REF][START_REF] Yang | Biases and Improvements in three Dynamical Downscaling Climate Simulations over China[END_REF]. Downscaling techniques are thus indispensable to transform outputs of GCM to reliable regional climate simulations. To do so, the statistical downscaling approach can be very appropriate, in particular, for simulating daily precipitation and with multiple realisations [START_REF] Alaya | Probabilistic Multisite Statistical Downscaling for Daily Precipitation Using a Bernoulli-Generalized Pareto Multivariate Autoregressive Model[END_REF][START_REF] Dayon | Transferability in the future climate of a statistical downscaling method for precipitation in France[END_REF][START_REF] Jha | A space and time scale-dependent nonlinear geostatistical approach for downscaling daily precipitation and temperature[END_REF][START_REF] Ding | Simulation and evaluation of summer daily precipitation based on nonhomogeneous hidden Markov model over the Yangtze-Huaihe River Basin[END_REF][START_REF] Hundecha | Inter-comparison of statistical downscaling methods for projection of extreme flow indices across Europe[END_REF][START_REF] Jones | Downscaling regional climate model outputs for the Caribbean using a weather generator[END_REF][START_REF] Wu | Projection of summer precipitation over the Yangtze-Huaihe River basin using multimodel statistical downscaling based on canonical correlation analysis[END_REF].

The nonhomogeneous hidden Markov model (NHMM) is a good candidate for climate downscaling. It was firstly used by [START_REF] Hughes | A class of stochastic models for relating synoptic atmospheric patterns to regional hydrologic phenomena[END_REF] to construct a relationship between large-scale atmospheric information and regional precipitation. This climate downscaling procedure is based on the hypothesis that the occurrence probability of local weather is determined by large-scale fields, NHMM being able to determine the transition of local meteorological pattern on a daily timescale. Many interesting results were reported in the literature on using NHMM to conduct climate downscaling in different regions and obtained good effect [START_REF] Bates | Stochastic downscaling of numerical climate model simulations[END_REF]Charles et al., 1999;[START_REF] Greene | Downscaling projections of Indian monsoon rainfall using a non-homogeneous hidden Markov model[END_REF][START_REF] Tan | Non-homogeneous hidden Markov model for daily[END_REF][START_REF] Cioffi | Large scale climate and rainfall seasonality in a Mediterranean Area: Insights from a non-homogeneous Markov model applied to the Agro-Pontino plain[END_REF]. Fu et al. (2013a) used NHMM to generate an ensemble of stochastic daily rainfall projections for 30 stations across south-eastern Australia. [START_REF] Robertson | Downscaling of daily rainfall occurrence over northeast Brazil using a hidden Markov model[END_REF] applied NHMM to outputs of the global climate model ECHAM4.5 over Northeast Brazil and pointed out that the generated daily precipitation series have good statistical properties. Recently, we also applied NHMM to produce daily precipitation in the Yangtze-Huaihe River Basin with BCC-CSM1.1(m) global model. A preliminary evaluation was reported in [START_REF] Ding | Simulation and evaluation of summer daily precipitation based on nonhomogeneous hidden Markov model over the Yangtze-Huaihe River Basin[END_REF]. We found that our downscaling methodology with NHMM can effectively improve the daily precipitation properties on its spatial distribution, temporal variation and probability distribution function (PDF). The present work is an extension of [START_REF] Ding | Simulation and evaluation of summer daily precipitation based on nonhomogeneous hidden Markov model over the Yangtze-Huaihe River Basin[END_REF]. We want to extend the utilization of NHMM to outputs from multiple climate models, and further investigate fine features of regional response with high credibility. Meanwhile, we also strongly hope that our projected daily precipitation for future is useful and can be used for regional management and relevant researches for surface hydrology, agriculture and land use.

The outline of this paper is as follows. Section 2 describes data and methodology.

Section 3 presents a validation of NHMM applied to three global models. The future projection of indices' changes during twenty-first century and under the global warming of 1.5℃ and 2℃ are presented in Section 4. Finally, Section 5 provides a general discussion and conclusions.

Data and methodology

Datasets

To construct a performant statistical downscaling model, we selected 56 highquality stations in the middle and low reach of the Yangtze River (27.5-32°N, 110-122°E) A comparison with rainfalls directly from GCMs can reveal added value of the downscaling procedure. In a similar way, future climate projection is done for the three GCMs and for three periods at different horizons, 2016-2035, 2046-2065 and 2081-2100. It's noted that our NHMM, as described in [START_REF] Ding | Simulation and evaluation of summer daily precipitation based on nonhomogeneous hidden Markov model over the Yangtze-Huaihe River Basin[END_REF], was trained at a global grid of 2.5° by 2.5°. We need thus to interpolate predictors fields from GCMs into the grid of ERA-40 reanalysis with a bilinear interpolation scheme. In addition, the four large-scale predictors entering into the NHMM calculation are normalized anomalous fields, with 1961-1990 climatology removed at each point, and the standard deviation as a normalization factor.

Nonhomogeneous hidden Markov model (NHMM)

The NHMM is a double stochastic process consisting of hidden states that cannot be directly found and an observed state sequence. The model decomposes the daily precipitation field on a network of stations into a few discrete hidden states, which are modelled as a first-order Markov chain progressing in time. Each hidden state is associated with a distinct atmospheric circulation regime. The transition of hidden states is unavoidably affected by large-scale predictors. The hidden states of whatever day in the temporal sequence are jointly determined by those of the precedent day and currentday large-scale predictors. In such a way, the whole precipitation sequence is stochastically simulated. Without the external large-scale predictors, NHMM would become a simple hidden Markov model.

We can now use and to designate observed precipitations and hidden states on day ( = 1, 2 … ). Both are defined at stations over the study area, is time sequence length in days, i.e., 92 for boreal summer. If the number of hidden states is noted as , and then = { , … … }, where denotes each hidden state.

represents atmospheric circulation field on day and thus : = ( , … ) denotes the time series of circulation field from = 1 to = . The NHMM is defined with two assumptions [START_REF] Hughes | A class of stochastic models for relating synoptic atmospheric patterns to regional hydrologic phenomena[END_REF][START_REF] Hughes | A non-homogeneous hidden Markov model for precipitation occurrence[END_REF].

( | : , : , : ) = ( | ) (1)
( | : , : ) = ( | , ) (2)
The first assumption is that the multivariate precipitation at time is conditionally independent of all other variables, given the hidden states at time . The second assumption indicates that the hidden states on day depend only on the predictor vector for day and the hidden states on day -1. A flow chart demonstrating how NHMM practically works is shown in Fig. 1.

The modeling process for NHMM was introduced by [START_REF] Hughes | A class of stochastic models for relating synoptic atmospheric patterns to regional hydrologic phenomena[END_REF][START_REF] Hughes | A non-homogeneous hidden Markov model for precipitation occurrence[END_REF].

For the precipitation probability distribution function (conditional to the hidden states )

( | ), we establish a δ function and a double-exponential distribution function to describe the probability of non-rainfall and rainfall, respectively.

P( | = ) = ∏ ( = !| = ) " # = ∏ $ " #
(3)

$ = % & ! = 0 ( ) * ) + , -./ 0 )# ! > 0
Where ! is the observed precipitation at station 2 on day , is the hidden state on day , 2 = 1, 2 … , 3 = 1, 2 … , 4 is the number of exponentials, ) refers to the weight, and * ) denotes the exponential distribution function parameter.

To calculate the transition matrix ( | , ) , we use Bayes conditional probability theory to decompose it into a product of the baseline transition matrix 5 6

( P( = 7 = 6 8 and a function of the atmospheric predictors P( | = 6 , = ).

Considering that the relevant atmospheric predictors are usually derived variables of high-dimensional atmospheric fields, we can reasonably assume that are multivariate and normally distributed. This leads to the following model for ( | , ):

P( = | = 6 , ) ∝ P( = 7 = 6 8P( | = 6 , = ) = 5 6 exp [-( -> 6 )∑ ( -> 6 ) @ ] (4)
Here, > 6 is the mean of the atmospheric predictors associated with transitions from state 6 at day t -1 to state at day t. ∑ is the covariance matrix of the atmospheric predictors. To ensure identifiability of the parameters, the constraints ∑ 5 6 = 1 and

∑ > 6 = > 6 = 0 are imposed.
Parameter estimation is accomplished by the methodology of maximum likelihood.

Letting Θ denote the model parameters, the likelihood can be written as:

L(Θ) = P( : | : ) = ∑ P( : , : | : ) E F:G = ∑ P( | ) ∏ P( | , ) # E F:G ∏ P( | ) # (5)
The set of parameters Θ that maximize L(Θ) can be obtained with the widely-used Baum-Welch algorithm [START_REF] Rabiner | An introduction to hidden Markov models[END_REF], a variant of the iterative Expectation-Maximization (EM) algorithm [START_REF] Dempster | Maximum likelihood from incomplete data via EM algorithm[END_REF] for obtaining maximum likelihood parameter estimates for models with hidden variables and/or missing data.

The specific EM procedure that we used in this paper for NHMM parameter estimation is fully detailed in [START_REF] Robertson | Hidden Markov models for modeling daily rainfall occurrence over Brazil[END_REF].

After the calibration of NHMM, model parameters including the hidden states = { , … … } , the transition matrix P(S I | S I , X I ) and the precipitation probability distribution function (conditional to the hidden states S I ) P(R I | S I ) are fully determined. They remain unchanged for all rainfall simulations, including future climate conditions. As shown by the technical flowchart in Fig. 1, the first step of using NHMM is to generate a Markov chain of hidden states, S , S , … , S L , based on a sequence of daily atmospheric predictors, and the transition matrix P(S I | S I , X I ). The next step is to simulate daily precipitation, r, according to probabilities P(R I N = r|S I = q P ). In the case of future warming climate, atmospheric predictors corresponding to global warming would lead to modifications in the frequency of the hidden states with different rainfall amounts. Eventually more (or less) precipitation can be generated.

Therefore, the case of climate change for a future scenario is explicitly taken into account in the frequency of each hidden states.

The number of hidden states K is optimized by the Bayesian information criterion (BIC). The BIC score with K states is defined as:

BIC = 2U(V * ) -X log \]^ (6)
Where V * is the estimated maximum likelihood parameter vector, as is obtained through EM applied to the training data for a model with K states, U(V * ) is the likelihood of the model evaluated at V * and X is the number of parameters in the K-state model. The least BIC score corresponds to an optimal model exploring the training data.

After tests, an eight-state model (K = 8) is finally chosen for us [START_REF] Ding | Simulation and evaluation of summer daily precipitation based on nonhomogeneous hidden Markov model over the Yangtze-Huaihe River Basin[END_REF].

NHMM, applied to climate downscaling, needs appropriately-selected predictors.

Our previous paper [START_REF] Ding | Simulation and evaluation of summer daily precipitation based on nonhomogeneous hidden Markov model over the Yangtze-Huaihe River Basin[END_REF] shows that with four large-scale predictors, including sea level pressure, geopotential height at 500hPa, zonal wind at 500hPa and relative humidity at 500hPa, it is possible to establish a good NHMM to simulate summer daily precipitation over Eastern China. Actually, the basic principle of selecting predictors is that they must have a good correlation with precipitation (the predictand) and a clear physical meaning.

In practice, the selection is as follows. We firstly calculated the leading principal component of summer precipitation from the 56 stations available in the middle and low reach of the Yangtze River. The leading PC was then used to calculate the temporal correlation coefficients with eighteen atmospheric variables including sea level pressure, atmospheric geopotential height, temperature, relative humidity, and wind fields. The obtained correlation maps could help us to determine potential predictors to select and their spatial domains which include major areas passing the 95% significance test. The second step of our practice consists of actually testing the performance of NHMM by using different combinations of potential predictors. We evaluated the model ability by examining the temporal variability and spatial distribution of its simulations.

Finally the optimal model was obtained with the following predictors (with their relevant domain): sea level pressure (12.5-35°N, 105-120°E), geopotential height at 500hPa (10-25°N, 95-170°E), zonal wind at 500hPa (25-32.5°N, 95-140°E) and relative humidity at 500hPa (27.5-32.5°N, 105-125°E).

To reduce the dimensionality of the selected predictors, a principal component analysis (PCA) is applied to the combined normalized fields of the four predictors. The first twenty six principal components, explaining up to 90% of the total variance, are selected as "actual predictors" of the model.

Furthermore, since our NHMM was established with the 2.5°-grid of ERA-40 and its four variables as predictors, the same four variables extracted from GCMs outputs need to be firstly interpolated into the 2.5°-grid. They are then normalized by their standard deviations of the period

Precipitation indices and evaluation methods

In order to measure the climate characteristics of simulated precipitations, five indices including precipitation means and extremes are used [START_REF] Jiang | Extreme climate events in China: IPCC-AR4 model evaluation and projection[END_REF]. They are all calculated with the diagnostic software provided by the Statistical and Regional Dynamical Downscaling of Extremes for European Regions (STARDEX) [START_REF] Haylock | Downscaling heavy precipitation over the United Kingdom: a comparison of dynamical and statistical methods and their future scenarios[END_REF]. Their definition is presented in Table 1.

Performance metrics include a parameter assessing the distribution of daily precipitations, skill Score ( `)a0b ), and the Taylor diagram describing the spatial pattern of a geophysical variable [START_REF] Perkins | Evaluation of the AR4 climate models' simulated daily maximum temperature, minimum temperature, and precipitation over Australia using probability density functions[END_REF][START_REF] Liu | Evaluation of two statistical downscaling models for daily precipitation over an arid basin in China[END_REF]Fu et al., 2013b;[START_REF] Taylor | Summarizing multiple aspects of model performance in a single diagram[END_REF].

`)a0b was proposed in [START_REF] Perkins | Evaluation of the AR4 climate models' simulated daily maximum temperature, minimum temperature, and precipitation over Australia using probability density functions[END_REF] to measure the coincidence of two PDF curves by calculating the cumulative minimum value of the two distributions.

`)a0b = ∑ c3d3efe( g # h , a ) (7)
Where h and a are the modelled and observed 3th probability values of each bins and i is the number of bins. It varies from 0 (no overlapping at all) to 1 (total matching between the two distributions).

Taylor Diagram [START_REF] Taylor | Summarizing multiple aspects of model performance in a single diagram[END_REF] provides a statistical summary of patterns similarity between simulations and observations in terms of spatial correlation coefficient, centered root-mean-square (RMS) difference, and ratio of spatial standard deviations. A perfect simulation would have the value of 1 for the centered pattern root mean square error (RMSE), and 0 for the spatial correlation. The ratio of spatial standard deviations would be 1.

Time windows for 1.5℃ and 2℃ global warming targets

As defined in the Paris climate Agreement, the 1.5℃ and 2℃ global warming thresholds are relative to the pre-industrial level. The period 1861-1900 is selected as a common pre-industrial period in this study. The emission scenario is RCP4.5. Time page 12

series of global averaged temperature anomalies are firstly smoothed by a 21-year moving average before selecting the year for which the 1.5℃ or 2℃ threshold is firstly reached. Finally a period of 21 years in total is defined with 10 years before and after the nominative year, as shown in Table 2. This way of defining the time windows is consistent and comparable with a few recent studies, e.g., [START_REF] Hu | Temperature and precipitation projection at 1.5℃ and 2.0℃ increase in global mean temperature[END_REF] and [START_REF] Shi | Changes in temperature extremes over China under 1.5 ℃ and 2 ℃ global warming targets[END_REF], on China's regional climate change corresponding to 1.5°C and 2°C warming levels. We need to point out that the climate reference period is from 1986 to 2005, defined as present-day climate, although the 1.5℃ and 2℃ warming targets are relative to the pre-industrial. The global mean surface air temperature increases by 0.9°C from pre-industrial to present-day in the ensemble mean of our three GCMs. The net warming for the cases of 1.5°C and 2°C warming levels would be of 0.6℃ and 1.1℃ respectively.

Climate properties of extreme precipitations in GCMs and NHMM

In our previous study, we used ERA-40 large-scale circulation from 1991 to 2002 in the construction and calibration of NHMM to stochastically simulate summer (1 June to 31 August) daily precipitations in Eastern China. NHMM showed a very good skill in simulating the probability distribution of precipitations, their spatial distribution patterns and their interannual variability [START_REF] Ding | Simulation and evaluation of summer daily precipitation based on nonhomogeneous hidden Markov model over the Yangtze-Huaihe River Basin[END_REF]. In this paper, we will further evaluate the performance of NHMM, but in the context of its application to outputs of three GCMs. We put emphasis on the added value of NHMM compared to the performance of original GCMs. Since this evaluation is done for present-day climate, it also provides a reference for projecting future extreme rainfall changes.

Statistical properties of daily precipitation

To assess the ability of NHMM and that of the three driving GCMs, we first show the Quantile-Quantile plots performed on daily precipitation for four major stations in the region. As shown in Fig. 2, there is a systematic bias in the distribution of daily precipitations in GCMs. For any quantile, the simulated rainfall amount is significantly lower than the observed one. The largest difference is above 60mm (Fig. 2a and Fig. 2c).

After downscaling with NHMM, models are rather close to observation with an absolute error smaller than 20mm. It indicates that NHMM indeed improves the statistical behaviors of daily precipitation. For daily precipitation rate below 50mm, NHMM is highly consistent with observation at Nanjing and Wuhan. Similarly, NHMM does a good job for daily rainfall rate below 40mm at Hangzhou and Hefei. For heavy rain greater than 50mm, the simulation by NHMM at Nanjing, Hangzhou and Hefei is generally smaller than observation, while at Wuhan and for precipitation greater than 80mm, the simulation is larger than observation.

In terms of differences among models, the ability of simulation below 70mm in MPI-ESM-MR gets closer to observation than other two models and the multi-model ensemble, while for daily rainfall greater than 70mm, BCC-CSM1.1(m) is slightly better than other models. The simulation capability of the multi-model ensemble generally keeps at middle level among the three models. After downscaling with NHMM, the outputs of all the three models and the multi-model ensemble tend to coincide. We almost cannot distinguish them from each other in Fig. 2.

We now examine all the stations in the region. Fig. 3 gives box-and-whisker plots showing the distributions of `)a0b at the 56 stations. When `)a0b are closer to 1, the simulated distribution for all stations is closer to the observed one. It is clear that NHMM improves significantly the ability of all the three models and the multi-model ensemble in simulating the distribution of daily precipitation. Detailed results show that the medians of `)a0b for BCC-CSM1.1(m), IPSL-CM5A-MR, MPI-ESM-MR and multi-model ensemble are 0.68, 0.68, 0.83 and 0.75, respectively. After downscaling with NHMM, the medians of `)a0b increase to 0.91, 0.90, 0.90, and 0.91, respectively.

In general, the `)a0b for each station almost is above 0.85, in which the largest `)a0b is up to 0.96. The ranges of `)a0b are significantly decreased among different stations.

If we examine individual models and the multi-model ensemble, MPI-ESM-MR

gives the best results on `)a0b , while BCC-CSM1.1(m) and IPSL-CM5A-MR show the largest improvement after NHMM downscaling with the medians of S jklmn increasing to more than 0.9 (Fig. 3).

Spatial distribution of precipitation indices

In this section we turn our attention to the performance reproducing the spatial pattern by NHMM along with the mean and extreme precipitation indices.

Change in daily precipitation distribution

We can now calculate the probability distribution functions of daily precipitations with different intensities from all the 56 stations in our region. This is repeated for present-day and the three future periods respectively. Instead of making visual inspection among the four curves (not shown), we can quantify the variations from present-day to future horizons by calculating the ratio of probabilities for each bin of intensities. This concept is close to the probability ratio (PR) introduced and used by [START_REF] Stott | Human contribution to the European heatwave of 2003[END_REF] and [START_REF] Fischer | Anthropogenic contribution to global occurrence of heavyprecipitation and high-temperature extremes[END_REF] to measure the risk variation. Fig. 5 shows PR of daily precipitation distribution, calculated for the whole domain with data from the multi-model ensemble for three periods of the 21st century, [2017][2018][2019][2020][2021][2022][2023][2024][2025][2026][2027][2028][2029][2030][2031][2032][2033][2034][2035][2036][2046][2047][2048][2049][2050][2051][2052][2053][2054][2055][2056][2057][2058][2059][2060][2061][2062][2063][2064][2065] and 2080-2100. Generally speaking, PR of light rain (0.1-9.9mm) shows a decreasing trend, while that of strong rainfalls (larger than 9.9mm per day) increases. The rate of PR seems to slow down when the time goes on (a saturation effect). Specifically, for light rain (0.1-9.9mm/day), PR in average during 2017-2036, 2046-2065 and 2080-2100 is 0.983, 0.966 and 0.962, respectively, relative to 1986-2005. For moderate rain (10-24.9mm/day), the occurrence probabilities increase by a factor of 1.005, 1.014 and 1.016, respectively. For heavy rain (25-49.9mm/day), the occurrence probabilities increase by a factor of 1.026, 1.047 and 1.053, respectively. For the rainstorm (50-99.9mm), the occurrence probabilities increase by a factor of 1.027, 1.052 and 1.055, respectively. For heavy rainstorm (more than 99.9mm), the occurrence probabilities increase by a factor of 1.026, 1.045 and 1.047, respectively. In general, summer daily precipitation in the middle and low reach of the Yangtze River has a higher occurrence probability for strong rainfalls (> 10 mm/day) and a weaker probability for light rainfalls (< 10 mm/day).

Change in geographic distribution of precipitation indices

The spatial distribution of PRCPTOT and SDII changes for 2017-2036, 2046-2065 and 2080-2100, relative to 1986-2005, is shown in Fig. 6. In the early 21st century, both PRCPTOT and SDII increase at major stations in the east, with relative changes keeping below 20% and 10%, respectively, while the two indices decrease in the west.

In the middle 21st century, larger variations appear for the two indices, compared to the former period. For example, PRCPTOT across the coastal area increases by 40%. In the late 21st century, PRCPTOT and SDII show more dry areas for stations in the west, while the difference between the west and the east tends to amplify. It's noted that the increase of PRCPTOT is generally stronger than that in SDII.

Fig. 7 shows relative changes of extreme precipitation indices R10mm, P95 and CDD. The trend of R10mm is similar to that of P95, but opposite to that of CDD. In the early 21st century, R10mm and P95 at major stations increase with the relative changes keeping below 20% and 10%, respectively, while CDD generally decreases. In the middle 21st century, larger variations appear in the three indices and at more stations in the east. R10mm and P95 increase by more than 20% and 10%, and CDD decreases by over 20%. In the late 21st century, the increase of R10mm across the eastern region is up to over 40% and the decrease of CDD keeps more than 20%, while CDD over the western area decreases by less than 20%. To sum up, extreme and local characteristic of future summer rainfall over the Yangtze-Huaihe River Basin will show a gradual increase with smaller increase (or even weak decrease) in western region and larger increase in eastern region.

Response of extreme precipitation under the global warming of 1.5℃ and 2℃

Considering there is a general gradient from west to east in our region of investigation, we divided the 56 stations into three groups (west, middle and east) with roughly equal number of stations. Statistics for each group are given in Fig. 8 in the form of box-whisker plots.

For both R10mm and P95, there is a slight decrease in the west, but there are increases in the middle and east. Changes in 2°C are generally amplified compared to those in 1.5°C warming. The additional half-degree warming from 1.5℃ to 2℃ implies changes of -3.7% (-0.3%), 2.4% (-0.1%) and 12.1% (2.7%) for R10mm (P95) and for the west, middle and east respectively. For CDD, we observe a reverse gradient from west to east.

The additional half-degree warming induces an increase of 2.1% in the west, but decreases of -4.6% and -7.2% in other two regions. (2) Future rainfall changes are projected based on NHMM for three future periods, 2017-2036, 2046-2065 and 2080-2100, under

Summary and discussion

R T-1 R T R t R 2 R 1 S 1 S 2 X 1 X 2 S t

  from June 1 to August 31 from the China Meteorological Administration (CMA) network with daily rainfall records from 1961 to 1990. Daily atmospheric circulation fields are from ERA-40 reanalysis with 2.5°×2.5° resolution from the European Centre for Medium-Range Weather Forecasts (ECMWF). They are used, together with rainfall from stations, to establish the NHMM statistical downscaling model. Large-scale predictors are sea level pressure (12.5-35°N, 105-120°E), geopotential height at 500hPa (10-25°N, 95-170°E), zonal wind at 500hPa (25-32.5°N, 95-140°E) and relative humidity at 500hPa (27.5-32.5°N, 105-125°E) (Ding et al. 2016). Three GCMs used in the NHMM are BCC-CSM1.1(m) (1.125°×1.125°) from China National Climate Center, IPSL-CM5A-MR (2.50°×1.27°) from French Pierre Simon Laplace Institute and MPI-ESM-MR (1.88°×1.87°) from Germany Max Planck Institute. Large-scale atmospheric predictors from GCMs from 1986 to 2005 are firstly applied into the NHMM. Simulated daily precipitations are carefully compared against observations from the same period, which provides a verification of the statistical model.

Fig. 4

 4 shows the Taylor diagram for the five precipitation indices in the three global models and the multi-model ensemble to comprehensively evaluate the spatial distribution. The same is shown for results with the application of NHMM. There is generally a weak ability in GCMs. Specifically, the spatial correlation coefficients of major indices between the simulations and observations are less than 0.4 and the maximum does not exceed 0.6; the standard deviations are relatively scattered; the RMSEs are generally greater than 0.75. After downscaling, NHMM improves significantly the spatial distribution of precipitation indices. Except CDD that does not show improvement with NHMM, other precipitation indices observe their spatial correlation coefficients increasing to more than 0.8; the standard deviations remain between 0.9 and 1.3; the RMSEs decrease to less than 0.75. Among the different indices measuring spatial patterns of precipitation, there is a greater improvement in simulating PRCPTOT and R10mm with spatial correlation coefficients larger than 0.9 and RMSEs smaller than 0.5. Again, CDD shows its weakest score compared to other indices. The first-order Markov chain, obviously, cannot well capture this persistent behavior of weather sequences. Burger et al. (2012), by comparing different statistical downscaling methods, also conclude that most of them fail to reproduce CDD. To sum up, NHMM effectively enhances the ability of models in simulating summer daily precipitation and spatial distribution over the Yangtze-Huaihe River Basin. It provides a basis for projecting future change of daily precipitation under warmer climate using this method. After downscaling, the PDF curves of the simulations get closer to the observations. The median of skill score for BCC-CSM1.1(m), IPSL-CM5A-MR, MPI-ESM-MR and multi-model ensemble is increased by 0.23, 0.22, 0.07 and 0.16, respectively. The ranges of the `)a0b are significantly decreased among different stations. The spatial correlation coefficients of PRCPTOT, SDII, R10mm and P95 are improved from less than 0.6 to more than 0.8, and the root mean square errors of the above four are generally decreased to 0.75 or less, in which PRCPTOT and R10mm have the optimal improvement. 4 Future projections In view of the added value of NHMM compared to performance of initial GCMs, we apply the established NHMM to further project future change in daily precipitation or extreme precipitation during 2017-2036, 2046-2065 and 2080-2100 under the RCP4.5 emission scenario, as well as the global warming period of 1.5℃ and 2℃.

  important economic and geopolitical issues in relation to the global warming levels of 1.5℃ and 2.0℃ in the Paris Agreement, we put particular attention to responses of extreme precipitation in our region of investigation under the two warming targets. Precipitation indices in terms of geographic distributions are quite similar to what is shown in Fig. 7, R10mm, P95 and CDD have a spatially coherent change with wetter trend in eastern region and drier trend in western region under 1.5℃ warming target, while these trends are more significant under 2℃ target. Considering the fact that Accepted manuscript. Guo et al. 2018 International J. of Climatology https://doi.org/10.1002/joc.5882 page 18

A

  statistical climate downscaling based on NHMM was constructed and used to simulate summer daily precipitation in Central and Eastern China. The nonhomogeneous term was the large-scale atmospheric circulation from three global climate models, i.e., BCC-CSM1.1(m), IPSL-CM5A-MR and MPI-ESM-MR. NHMM became thus a powerful tool to perform relevant climate downscaling, including future projection of summer daily rainfall under the RCP4.5 emission scenario. Main conclusions are the following. (1) NHMM effectively enhances the ability of global climate models in simulating summer daily rainfall in the middle and low reach of the Yangtze River in Eastern China. Absolute errors of daily precipitation distribution shown in Quantile-Quantile plots are largely reduced, from about 60mm in global models to generally below 20mm in NHMM downscaling. The improvement is also confirmed with quantitative measures, the skill score. Spatial correlation coefficients of PRCPTOT, SDII, R10mm and P95 are improved from less than 0.6 to more than 0.8. The RMSEs of the above four indices are generally decreased to 0.75 or less. CDD shows little improvement in NHMM, due to certainly inadequacy of the first-order Markov chain for long-lasting phenomenon.

Fig. 1 .

 1 Fig. 1. Schematic of NHMM and its progressing in time.

Fig. 3 .Fig. 5 .Fig. 6 .

 356 Fig. 3. Box-and-whisker plot showing the distribution of `)a0b at 56 stations before (blue, i.e. in GCMs) and after (red) NHMM downscaling.

Fig. 7 .

 7 Fig. 7. Same as Fig. 6, but for R10mm (a, d, g), P95 (b, e, h) and CDD (c, f, i).

Fig. 8 .

 8 Fig. 8. Boxplots showing the distribution of relative changes (in %) of R10mm (a), P95

Table 1 .

 1 There are also uncertainties in relation to future emission scenarios and to GCMs themselves. To reduce uncertainties of climate downscaling and projection, multiple models and multiple approaches need to be further promoted. Finally, in terms of NHMM improvement, we need to study model sensitivity in function of tunable parameters or to compare it with other statistical theories and approaches, already used in the East Asian monsoon region. Indicator, acronym, definition and unit of five indices used in this study

	the RCP4.5 scenario. Our study area

Accepted manuscript.

Guo et al. 2018

International J. of Climatology https://doi.org/10.1002/joc.5882

Acknowledgments. We thank the editor and anonymous reviewers for their constructive comments. We acknowledge the PCMDI for collecting and archiving the CMIP5 model output and the World Climate Research Programme's Working Group on Coupled Modelling. This study was jointly supported by the National Key Research and Development Program of China (2017YFA0603804, 2016YFA0600402) and the State Key Program of National Natural Science Foundation of China (41230528).