Introduction

Litterfall is a key parameter in the biogeochemical cycle linking the tree part to the water and soil part. Both the biomass of the litter and its chemical content (including heavy metals) are needed to quantify the annual return of elements and organic matter to the soil. Litter decomposition is a major pathway of nutrient fluxes and determines the organic matter input to forest soils and has a strong influence on forest productivity and soil nutrient status.

Effects of anthropogenic and natural factors, such as climate change, could influence both litterfall production and its seasonal progression. Processes like carbon cycling and carbon sequestration are closely related to stand leaf area index (LAI) and litterfall.

Changes in litterfall are responses to disturbances caused by biotic factors such as insect pests and/or environmental factors like spring frost, drought, wind, or pollution. Litterfall production is a quantitative parameter of stand vitality and gives additional information to the visual assessment of canopy condition already observed in each plot. Direct observation of abnormalities of the leaves can be performed on the collected litter (leaf size, fungi, and necrosis) for symptomatology.

Litterfall can also provide temporal and quantitative information about phenological development of the stand. The quantification of the foliage amount, flowering and fruiting patterns allows direct measurements of year-to-year variation in phenology as a reaction to short term weather patterns, long term climate, and tree vitality.

Litterfall area of leaves is also one of the components of direct estimate of LAI, the stand leaf area per ground area expressed in m 2 m -2 . LAI describes a fundamental property of the plant canopy in its interaction with the atmosphere, especially radiation, energy, momentum and gas exchange [START_REF] Monteith | Principles of Environmental Physics[END_REF]. LAI plays a key role in the interception of radiation, canopy interception (rainfall and deposition), in the carbon assimilation and water evapotranspiration during the diurnal and seasonal cycles, and in the pathways and rates of biogeochemical cycling within the canopy-soil system [START_REF] Bonan | Land-atmosphere interactions for climate system models: coupling biophysical, biogeochemical, and ecosystem dynamical processes[END_REF][START_REF] Van Cleve | Productivity and nutrient cycling in taiga forest ecosystems[END_REF][START_REF] Vesterdal | Carbon and nitrogen in forest floor and mineral soil under six common European tree species[END_REF]. Finally, various soil-vegetation-atmosphere models use LAI [START_REF] Sellers | A simple biosphere model (SiB) for use with general circulation models[END_REF]and Bonan, 1993). For evergreen species the annual litter represents the turn-over of needle/leaf area. For deciduous species, litterfall collection throughout one year and sorting among species is probably the most accurate way of measuring total LAI, and of calculating the contribution of each species to the total (e.g. Breda, 2003). This measure can be used as an alternative to mid season instrument based methods of LAI estimation within the plot (e. [START_REF] Thimonier | Estimating leaf area index in different types of mature forest stands in Switzerland: a comparison of methods[END_REF], or as an annual addition to a base line obtained by selected destructive harvesting of trees around the plot. LAI for one species is not simply related to its density or basal area contribution to the stand and cannot be derived from dendrometrical stand information alone.

Scope and application

This part of the Manual aims to provide sufficient methodological advice to allow participating National Focal Centres to sample and prepare an accurate measurement of the quantity and quality of litterfall, from selected plots of the ICP Forests intensive monitoring system. Harmonization of procedures of collection and chemical analysis is essential to ensure comparability of the chemical composition of litterfall, and accurate assessment of LAI. Only data obtained by the methodologies described in this chapter will be accepted for submission into the international database of the ICP Forests programme.

www.icp-forests.org/Manual.htm An overview on the variables assessed in the litterfall survey is given in Table 1. Litterfall chemistry is optional on standard Level II plots but mandatory on Level II core plots.

Objectives

The main objectives of litterfall sampling and analysis are to quantify litterfall production and its chemical composition over time. This will enable:

Quantification of litterfall amounts at any one plot, to be expressed in g m -2 (or kg ha -1 ).

The option to assess the local seasonal variation of litterfall components at any one forest plot, and between plots of different species. (N.B. Annual totals only need to be reported)

Accurate measurement of litterfall chemical quality, to be prepared from oven dried and bulked annual samples, or the means of periodic analysis, and expressed as concentrations of specific elements.

Measurement of specific leaf area of deciduous species on each 'core' plot of the intensive monitoring network in each year, allowing a direct assessment of LAI in m 2 m -2 as an alternative to field based methods.

Evaluation of the data will then allow for Comparisons of litterfall quantity variation across latitudinal and longitudinal gradients by species Investigation of relationships with insect vectors, weather phenomena, soil changes and climate variation by inter-plot comparisons Greater understanding of the role of litterfall in nutrient cycling, across gradients of temperature, soil moisture and soil type, and in particular to improve knowledge of the N, P and C cycles.

Accurate estimates of the effects of year on year variation of leaf area for use with assessments of water budgets on forest plots with differing soils across a variation of climate types.

Sampling requirements and field systems

Litterfall sorting is time-consuming and hence an expensive analysis. Within the ICP Forests monitoring system, fine sorting of the fractions is mandatory only on Level II core plots where meteorology, soil water, soil solution, and phenology are also performed (see Table 2). On standard Level II plots litterfall collection is optional. When it is carried out on Level II plots, at least a less detailed level of sorting to determine foliar and non-foliar litterfall mass is recommended. Plot data should be recorded and submitted on Form *.LFP (see ICP Forests Manual Part XVII Data handling and data submission forms)

Field sampling design

Number of replicates

It is recommended to sample litterfall from at least 10 collectors per plot under uniform forest canopy, but up to 20 or 30 collectors under mixed species or in larger plots with uneven topography. Leaves from deciduous trees are more susceptible to turbulent air movement than www.icp-forests.org/Manual.htm conifer needles. This effect may be mitigated either by increasing the number of litterfall traps (e.g. 10 traps for coniferous species and 20 traps for deciduous species) or by increasing the collecting area of each trap (especially for species with large leaves e.g. Populus).

Sampling scheme

As litterfall is a canopy parameter, and not a tree one, litterfall traps should be distributed all over the plot area. It is recommended that the traps are set up in a design enabling comparisons with deposition and soil water results. The traps are fixed and may be placed randomly or systematically e.g. at regular intervals and in sufficient number to represent the whole plot and not only the dominant tree species.

Sampling equipment

The countries are free to select the type of traps for the monitoring of litterfall. Figure 1 gives examples of two litterfall trap designs.

It is recommended that the litterfall traps are not fixed too close to the ground, to ensure adequate water drainage. The opening area of the collectors must be horizontal, and if necessary, special trap fixation should be prepared for mountainous plots. A top height between 1.0 and 1.3 m should ensure that there is clearance from the ground on the up-slope side, whilst still allowing capture of leaves from shrub vegetation. Canopy leaves and other litterfall inputs can be collected in nets or litter bags which are attached to a frame of durable material, with a known catching area (minimum 0.18 m 2 but preferably over 0.25 m 2 ).The total sampling area must be sufficiently large to be able to determine litter amount and quality. There may be a need to trim tall ground vegetation from just beneath the trap itself, to avoid interference with the nets/bags, which is acceptable as long as the trap position is not within the ecological survey area. For tree species with very large individual leaves e.g. Populus, the collecting area of individual traps must be increased (i.e. up to 0.5 m 2 ). It is recommended that the litter bags or collecting funnels are at least 0.5 m deep to prevent litter from blowing out of the traps. Deposition of litter into these traps due to lateral movements by wind is assumed to be minimal. The material of the mesh must not interact with the litterfall sample. Litter nets/bags of inert materials like cotton, polyethylene or nylon are suitable materials, not interfering with the major ions present in litter. However, natural materials like fine cotton stitching will decay quickly on site under sustained high temperature and moisture levels. The mesh size of the bags must be large enough to allow for easy drainage of water. It is recommended to adapt mesh size to the dimension of smallest elements, i.e. for needles from coniferous species up to 0.5 mm, but if there is interest in the finest 'frass' material (caterpillar droppings), then the texture needs to be much smaller. During the winter season in areas of heavy snowfall, traps may lowered on to the ground to avoid breakage of the collector structures, preferably on to a plastic mesh sheet to avoid direct contact with the soil.

Mesh trap

Frequency of sampling

It is recommended that litterfall be collected at least monthly and even bi-weekly in periods of heavy fall, which may be co-incident with heavy rainfall. This is to avoid pre-collection decomposition in the traps and chemical leaching of the material during rain episodes. It is particularly vital to obtaining true weights of the fine flower and bud components in spring, which very quickly become compressed and unidentifiable. The samples may be pooled to periodic or annual totals -the litterfall year for reporting purposes should run from spring to spring i.e. beginning of April (yr 1) to the end of March (yr 2). In regions with snow in the winter or which are remote, it may be impossible to collect samples at regular intervals. Litterfall may then be collected once before the winter period and once after snowmelt, as frost will limit both drainage and litter decomposition. Total values for this period should then be subdivided proportionally to the months passed since the last collection.

Sample collection, transport and storage -quality control in the field

The collection bags must be carefully labelled with site number, trap number and date before removing them from the site. It is recommended that a record sheet is taken to the field at each bag change to record any unusual conditions or missing samples, and that this should be sent in each time with the bags and be stored in suitable files in the analysing laboratory. If collection is made from fixed nets by hand then powder-free vinyl gloves should be worn to lessen sample contamination ahead of chemical analysis. Alternatively, suspended bags may be replaced at each visit, and possibly cleaned and re-used.

Ideally all samples should be transferred immediately to the laboratory, preferably in cool boxes, or if necessary temporarily stored at 4 °C, but not frozen.

Laboratory measurements

Variables to be assessed

The variables of interest concern quantity (mass measurements) and chemical quality of litter, and the possibility to measure specific leaf area (SLA) values from the foliar fraction. In standard Level II plots the litterfall survey is optional, but at least litterfall quantity is recommended, along with www.icp-forests.org/Manual.htm measures of dry mass (Table 1), but in the Level II designated 'core' plots chemical analysis is requested of finer fractions (see section 5.3, Table 2).

A procedural flow diagram to facilitate assessment of all these variables is given in Figure 2.

Reception

Litter samples should be checked and counted into the lab on arrival, using non-contaminating gloves, and the paper work filed. This is a vital part of the quality control of samples from the field to the laboratory.

If the samples are damp, this may be an opportunity to measure leaf area for pines, which are particularly difficult when dry, as the longer needles tend to warp and twist. Incoming samples should then be kept damp, but cooled, and processed as soon as possible so that decay does not start. In all cases samples are easier to sort when dried, and could be left covered for several days in a warm, dry place to air dry -alternatively they may be oven dried at temperatures below 70 0 C for at least 24 hours. Any insect life in the bags should be noted, and identified if in large numbers.

Part

Litter sorting and quantity measurement

All litter sorting into fractions should be made wearing non-contaminatory gloves, both for personal safety and to allow chemical analysis afterwards. If the samples are dusty, a light weight face mask should also be worn during lab work. Paper bags can be used to contain the various fractions during oven drying at temperatures at maximum 70 0 C.

Any litter collected from Level II plots should be sorted into at least foliar and non-foliar fractions for reporting purposes. If the plot has been designated as Level II core plot, then litter should be further separated into the fractions shown in Table 2. It is assumed that large branches >2 cm diameter, not often captured within the litter traps, will be recorded as part of the deadwood estimates of the plot, as taken during ecological surveys.

The various fractions should be dried separately at maximum 70°C until constant weight is achieved (at least 24 hrs for fine fractions and leaves, but longer for substantial woody debris), and weighed to 2 decimal places (g). Annual totals will be reported on Form *.LFM, but there is also the facility to report mass/m 2 with other time periods as both start and end date are to be recorded in form .LFM. Storage may then be made until the annual total of material is accumulated (see flow chart Fig 2 .).The monthly mass of the various fractions can then be totalised from April to March to achieve annual litterfall mass at the plot in kg m -2 , and submitted to the data centre on form*.LFM (Part XVII). Stored material may then be pooled at the end of the year, well mixed and subsamples taken for assessment of the weight of 100 leaves or 1000 needles (minimum requirement). Two further subsamples of the annual total can then be taken for chemical analysis (5.3) and more detailed specific leaf area (SLA) assessment if desired (see Chapter 5.4). In the case of foliar material from the main canopy species, it is recommended that a series of replicates should be prepared from the pooled total to allow some assessment of both the chemical and SLA variability of the material, although only the mean is required for reporting Part XIII version 5/2010 13 purposes. However, litter material present in only small quantities at the end of the year, such as flowers (or bud scales), may be pooled across all the traps and chemically analysed as one total sample.

Quality of litterfall -chemical analysis

The chemical analysis of litter is similar to that of the foliar component. For techniques and analytical methods in more detail see Part XII of the ICP Forests Manual on Sampling and Analysis of Needles and Leaves. Analysis will be made on an annual sample of the various fractions, determined by pooling the monthly collection through the year (April -March).

For chemical analysis the litterfall samples are dried to constant weight in an oven at maximum 70°C, and samples are ground to a homogeneous powder in a suitable mill. For large twig fractions and tough seed cases and cones, this may mean a two-stage pre-treatment to achieve chipped material of a suitable size for laboratory grinding. All chemical element concentrations should be reported moisture corrected from dry ground material mass by drying subsamples to 105°C. For Quality control recommendations see section 6.

Reporting on annual chemistry of element concentrations should be made on Form *.LFM and *.LFO.

Specific Leaf area measurements for Leaf Area Index estimation

Introduction

The litterfall based method is an optional approach for leaf area index (LAI) estimation which has been frequently used in the past for broadleaf stands (Breda, 2003[START_REF] Thimonier | Estimating leaf area index in different types of mature forest stands in Switzerland: a comparison of methods[END_REF]. The most suitable definition of LAI is half the total green leaf area (one-sided area for broad leaves) in the plant canopy per unit ground area [START_REF] Chen | Defining leaf area index of plant canopies with branch architecture[END_REF]. The leaf area subtended by deciduous trees for each year can be computed from total leaf litter dry biomass of that species in that year (March-February) per m 2 , multiplied by a ratio to convert dry weight to leaf area. This ratio of leaf area (A): dry mass (m) is named Specific Leaf Area and its alternative expression is as LMA (leaf mass per area): SLA = A/m (cm 2 per g.) LMA = m/A (g per cm 2 )

Canopy leaf area (LAI) is the composite measure from all tree and tall shrub species in the plot and can only be obtained from litterfall if foliar SLA is determined for each of the component species. SLA can be measured leaf by leaf, as may be needed in photosynthesis or porometry research, or in bulk as an annual value smoothing out the variations of the individuals. However, this requires suitable laboratory equipment for accurate leaf area measurement, such as the Delta-T scanner or the Li-cor CI-203 laser area machine.

Methodology

SLA can be made on both fresh weight and dry weight bases, but the latter gives better standardisation between sites. It has to be determined for each main canopy species from a random subsample of litter leaves (at least100 leaves from different traps). Preferentially, several replicates form one years leaf litter total should be analysed to obtain a measure of the variability of the material from the site accruing through the year.

If litterfall leaves are dry, either naturally following abscission, or through storage or oven treatment, they will be more fragile than green leaves. If they are taken wet, or have been some time in the litter trap, they are likely to be dirtier than freshly fallen leaves, and may need to be cleaned and flattened before leaf area measurement. The option to retain or cut off petioles may not be present in litter leaves, but if canopy representative measures of SLA are needed, leaves as complete as possible need to be measured, or at least have a balance of mid rib and petiole. The exception to this would be in cases where measurements of area eaten are required.

Where a bulk only measurement of SLA is required, a known number of leaves can be selected and dry weighted before other treatment is undertaken. These must all then be measured to obtain cumulative area, and other mean measures (such as leaf size) can then be calculated.

For dried litter leaves either folded or curled, a soaking technique may be required to ensure sufficient flexibility for measurement. This is possible for most broadleaves, though excessive soaking leaches out humic acids and weight loss may ensue. Occasionally for very thin leaves (e.g. Fraxinus excelsior), area losses may also occur. Test on each species collected should be conducted to establish a standard treatment with a known effect. In the case of dehisced Fagus sylvatica leaves, which dry folded into a concertina, a brief soaking in hot water (60-70°C) has been found to flatten leaves sufficiently for measurement, but weight losses of 5% have been recorded after longer overnight soaking. However, for Quercus robur and Q.petraea leaves weight loss is minimal over the same time period. For thinner leaves such as Corylus avellana, or Fraxinus, a soak of an hour or so will be sufficient, as weight losses of up to 15% have been recorded after long soaking. Any weight loss due to a soaking procedure should be incorporated into the SLA calculation as a correction factor before LAI is calculated from the litterfall weights. The use of flattening devices, such as a plant press, has been found helpful to ensuring accurate expansion of soaked broadleaves.

For short conifer needles which have dried (e.g. Picea sp), area measurement is often obtainable after only prelimonary cleaning, as they remain woody in nature and do not change area. However, finer needles (e.g. Larix sp) are difficult to prepare, and twist on drying. These would need a short soak and would be best measured on a leaf area machine where they can be laid on a flat bed under slight pressure. Longer needles (e.g. some Pinus sp) also twist on drying, and are difficult to soak out, as they then break up. Area measurements are best made from these if they can be kept damp from abscission.

All samples should then be dried at maximum 70°C for 24 hours before weighing for calculation of SLA. Previously soaked leaves must not be used for chemical analysis.

Quality Assurance and Quality Control

The quality of the litterfall analytical data is controlled by regular Interlaboratory comparison ring tests of plant material by the Forest Foliar Co-ordinating Centre. It is anticipated that there will be increasing need for these tests on non-foliar litter material, in order to establish the limits of expected and acceptable variation, as and when such material is available in sufficient quantity and homogeneity. All countries wishing to report litterfall chemistry should regularly take part in laboratory inter-comparisons.

Guidelines for QA/QC procedures in the laboratory are given in the Manual part XVI on laboratory QA/QC. Documentary proof of the QA/QC adopted in each laboratory should be submitted, together with the annual results, to the European-level data centre.

Plausibility limits

Data completeness

Table1 outlines for all the chemical variables the conditions under which they are mandatory or optional to report. When a country/federal state decides to report optional variables, they should be fulfilling the data quality requirements outlined in the methodology.

Data handling, submission procedures and forms

Forms for data submission lab quality information and explanatory items are found in Manual part XVII -Data handling and data submission forms in this Manual (and electronically on the ICP Forests web page, at http://www.icp-forests.org/ Manual.htm). The quality information from the labs has to be sent together with the relevant data submission forms to the data centre using form LF.LQA.

Bonan G.B. 1993. Importance of leaf area index and forest type when estimating photosynthesis in boreal forests. Remote Sensing of Environment 43:303-314.

Figure 1 :

 1 Figure 1: Potential collector design

Figure 2 :

 2 Figure 2: Procedural flow diagram for variable assessment

Table 1 :

 1 Status of variables for measurements at various levels

	Form Variable	Level I Level II Level II
					core
	Biomass measures
	LFM	Dry weight per m 2 [kg/m 2 ]	n	o	m
		for total litter biomass
	LFM	Dry weight per m 2 [kg/m 2 ]	n	o	m
		for foliar litter biomass
	LFM	Dry weight per m 2 [kg/m 2 ]	n	o	m
		for other litter biomass
	LFM	Dry mass of 100 leaves	n	o	o
		or of 1000 needles [g]
	LFM	Area of 100 leaves or of 1000 needles [m 2 ]	n	o	o
	Chemical analyses
	LFM	C [g/100g]	n	o	m
	LFM	N [mg/g]	n	o	m
	LFM	S [mg/g]	n	o	m
	LFM	P [mg/g]	n	o	m
	LFM	Ca [mg/g]	n	o	m
	LFM	Mg [mg/g]	n	o	m
	LFM	K [mg/g]	n	o	m
	LFO	Zn [μg/g]	n	o	o
	LFO	Mn [μg/g]	n	o	o
	LFO	Fe [μg/g]	n	o	o
	LFO	Cu [μg/g]	n	o	o
	LFO	Pb [μg/g]	n	o	o
	LFO	B [μg/g]	n	o	o
	LFO	Cd [ng/g]	n	o	o
	o -optional m -mandatory n -not assessed
	Litterfall sampling is strongly recommended on Level II sites where meteorology data is available.

Table 2 :

 2 Fractionation of litterfall

	Fraction of Litterfall	Level II	Level II core
			plot
	Total litter biomass kg/m 2 (all species)	o	m
	Foliar litter total (all species)	o	m
	Foliar litter (main species )	o	m
	Foliar litter (other tree species)	o	m
	Non foliar litter total (all species)	o	m
	Flowers total (including catkins)	o	o
	Flowers (main species)	o	o
	Flowers (other species)	o	o
	Fruits/seeds total (all species)	o	m
	Fruits/seeds total incl. green cones (main species)	o	m
	Fruit capsules + empty cones (main species)	o	o (m*)
	Rest of fruiting	o	o
	Fruits /seeds total incl. green cones (other species)	o	m
	Fruit capsules + empty cones (other tree species)	o	o
	Bud scales	o	o
	Wood fraction (Twigs <2 cm D/branches/bark)	o	o
	Fines and frass (<1mm)	o	o
	Other biomass (lichen, moss etc)	o	o
	o = optional, m = mandatory
	m* mandatory only for the main tree species = Fagus sylvatica

  Table3summarises the current suggested plausibility limits on the reported chemical composition of litterfall samples. It is anticipated that these limits will be frequently revised as increasing numbers of litterfall results become available in the central database, and the full range in chemical composition of the different fractions of litterfall is established.

	Part XIII
	version 5/2010

Table 3 : Plausible range of element concentrations in the foliar-litter of different species

 3 (indicative values in grey).Source: Forest Foliar Co-ordinating Centre. ICP Forests

	Tree Species
	(Foliar litter)	Limit C	S	N	P	K	Ca	Mg	Zn	Mn	Fe	Cu	B
			mg/g	mg/g mg/g	mg/g mg/g mg/g mg/g μg/g	μg/g μg/g	μg/g μg/g
	Betula pendula	low	290		7.30	0.20 0.30 5.,00 1.00 105.00 600 45.0	6
		high 330		21.00	1.20 1.40 12.50 2.00 170.00 3000 300.0 19	38
	Castanea sativa low	390		9.00	0.20 0.20 4.50 1.40 35.00 700		5
		high 420		13.00	0.70 0.55 10.50 2.00 45.00 2500 90.0	13	100
	Fagus sylvatica	low	460	1	9.00	0.50 2.00 4.00 0.80 25.00 650 70.0	4	2
		high 510	2.2	19.00	1.90 8.00 17.00 2.00 35.00 1600 140.0 7	40
	Fraxinus
	excelsior	low	470		12.00	0.75 0.40 20.00 2.00 15.00 110 120.0 7
		high 470		18.00	1.50 1.40 25.00 3.50 20.00 200 200.0 9	50
	Quercus frainetto low		1.1	8.00	1.10 4.50 14.00 1.20
	(Q. conferta)	high		1.1	11.70	1.30 5.20 18.30 1.40
	Quercus petraea low	460		8.00	0.30 2.00 7.00 1.30 14.00 700 50.0	5
		high 510		12.00	0.60 4.00 10.00 2.00 25.00 1700 200.0 8	35
	Quercus robur	low	460	0.85 10.00	0.82 4.00 5.00 1.00 15.00 1000 90.0	6	7
	(Q. pedunculata) high 510	1.7	19.00	2.00 8,00 13.00 2.00 25.00 1200 150.0 7	35
	Abies
	cephalonica	low			8.00		2.70 11.00 1.00
		high			13.00		8.30 24.00 1.50
	Picea abies	low		1	6.50	0.60 1.00 2.50 0.70
	(P. excelsa)	high 520	1.5	12.60	1.20 4.20 16.00 2.20
	Picea sitchensis low	440	1	6.00	0.60 1.50 4.00 0.60 15.00 250 40.0	2
		high 530	1.1	13.00	1.10 3.00 11.00 1.00 35.00 1400 120.0 4	35
	Pinus sylvestris	low	490	0.62 5.00	0.40 1.00 2.00 0.50 20.00 180 35.0	2
		high 530	0.62 10.00	0.80 3.00 11.00 0.80 45.00 800 150.0 5	45

www.icp-forests.org/Manual.htm


). In July 2008 two outbreaks were reported by the Moroccan veterinary services to the World Organization for animal Health (OIE). This notification was based on clinical and basic laboratory diagnostics carried out in Morocco. In CIRAD, Partial sequencing of the amplicons from infected tissue samples from the Moroccan epizootic confirmed that the causative agent was PPRV of lineage IV -a lineage circulating in the Middle East and Asia but not reported before from Africa.

Introduction

Due to the status of OIE reference laboratory, CIRAD received blood and organs samples from sick animals sent by the laboratory of vaccines BIOPHARMA Morocco during the first weeks of the outbreaks. A mission with experts in PPR was organised by FAO in August 2008 in this country. New organ samples were collected. Sera were analysed by C-ELISA based either on anti-N (CIRAD) or anti-H Mabs (Pirbright). Detection of PPRV RNA was performed by RT-PCR [START_REF] Couacy-Hymann | Rapid and sensitive detection of peste des petits ruminants virus by a polymerase chain reaction assay[END_REF]. PCR products were directly used for sequencing for phylogenetic analysis [START_REF] Kwiatek | Peste des Petits Ruminants (PPR) Outbreak in Tajikistan[END_REF]. Taqman real-time PCR (unpublished) was performed using the AgPath-ID one-step RT-PCR kit (Applied Biosystem). Both tests are using specific PPR primers/probe targeting the 3' end of the N gene. In Morocco, a full-scale campaign of vaccination of sheep and goats started on September 22nd using PPR vaccine produced by BIOPHARMA laboratory with the attenuated Nigeria 75/1 strain obtained from CIRAD and developed in collaboration with IAH.

Material and Methods

Twenty one out of 24 sera were positive or doubtful in both tests. Three out of 10 blood samples and 18 out of 24 organ samples were found positive at least in real-time PCR assay. Sequencing of part of the N PPR gene was done on 6 of those samples and the sequences obtain were compared with the other PPR strain sequences from our library. Inclusion of the Moroccan strains in the phylogenetic tree permitted its classification into lineage IV (Fig 3).

Results

Fig 1 : Extent of PPR in the world

PPR first incursion in Morocco

Conclusion and discussion

The occurrence of PPR outbreaks in Morocco allowed us to genetically characterize the causal strain and this was shown to be of lineage IV together with other Asian and Middle-East strains whereas the others strains from Africa cluster in three lineages (I -III). The study demonstrate the value of the partial sequence of the N gene as traceability marker of strains to conduct epidemiological field studies. Combined with emergency response it maximizes the prevention of viral spread from infected area.

Fig

  Fig 2 : geographical distribution of outbreaks in November 2008

Fig 3 : 1 1

 31 Fig 3 : Majority rule consensus tree of PPRV based on the alignment of the nucleotide sequences of the N protein gene («Neighbour-joining method »)

Acknowledgements

This study was partially granted by the EU EPIZONE network of excellence


domain: sdv sde

text:
Sylvain Dupont

Yves Brunet

Large-Eddy Simulation of turbulent wind flow over heterogeneous landscape

come   L'archive ouverte pluridisciplinaire

Rural landscapes are often characterized by a large spatial variability due to the presence of clearings, roads, forest or crop patches of various heights, etc., from which topographic effect are added. Such fragmentation induces three-dimensional variability in micrometeorological fields (wind, temperature, humidity) that may lead to the formation of local meteorological events (advective flows, fog, etc.). Although at this fine scale these surface heterogeneities are almost sub-grid scale heterogeneities in mesoscale models, they could influence physical processes within the all atmospheric boundary layer. As a consequence, modelling micrometeorological fields is important for improving subgrid scale parameterization of surface heterogeneities in weather forecasting system but also for many environmental applications such as forest management, wind energy applications, forest-atmosphere scalar exchange, forest fire propagation, etc. Wind modelling at fine scale has remained until now limited because of the complexity of accounting in airflow models for surface heterogeneities.

In a first step to improve our knowledge on the impact of surface heterogeneities and small topography on micrometeorology, we focused on turbulent wind flow in neutral atmosphere by modifying the atmospheric model ARPS (Advanced Regional Prediction System) so as to simulate turbulent flow at very fine scale within and above heterogeneous vegetation canopies using a Large-Eddy Simulation (LES) approach. Conversely to usual approaches, LES not only allows to have access to the average wind flow but also to its non-stationary character, i.e. turbulent structures known as `coherent' which dominate the turbulent flows and which ensure a large part of the exchanges (mass, heat, momentum) between the vegetation and the above atmosphere.

We will present a review of the recent validation and application of this model over two types of surface heterogeneities representative of the rural landscape, forest leading edge and forested hill. In these two configurations, we have analyzed in details the dynamic of the wind flow as well as that of turbulent structures in order to characterise canopy-atmosphere exchanges along these heterogeneities. The next step to this work will consist in introducing a SVAT (Soil-Vegetation-Atmosphere-Transfer) model within ARPS in order to simulate in details the variability of the temperature and humidity fields at landscape scale. In the end, such model should be able to improve the simulation of local meteorological events.


Elisabeth Tabone

Estelle Roux

Marlène Marquier

Hong Do

Thi Khanh

Clarisse Clain

Régis Goebel

Optimising biological control of sugarcane stem borer in Reunion Island: inducing diapause or quiescence in Trichogramma chilonis

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.


Fayu Wan
email: fayu.wan@nuist.edu.cn

Xiaoyu Huang

Preeti Thakur
email: pthakur@ggn.amity.edu

Atul Thakur
email: athakur1@ggn.amity.edu

Sébastien Lallechere
email: sebastien.lallechere@uca.fr

Blaise Elysée

Guy Ravelo

Sébastien Lalléchère

Blaise Ravelo
email: blaise.ravelo@nuist.edu.cn

Negative group delay experimentation with tee connector and cable structures

Keywords: Negative group delay (NGD), NGD analysis, NGD experimentation, Tee-cable network, Sparameter model

"Negative group delay experimentation with tee connector and cable structures", Eur. Phys. J. Appl.

INTRODUCTION

The group delay (GD) may affect the transmission signal quality in the communication systems [START_REF] Myoung | Effect of Group Delay in RF BPF on Impulse Radio Systems[END_REF][START_REF] Heffner | Accurate, automated measurement of differential group delay dispersion and principal state variation using Jones matrix eigen analysis[END_REF][START_REF] Kwon | Effect of Antenna Gain and Group Delay Variations on Pulse-Preserving Capabilities of Ultrawideband Antennas[END_REF][START_REF] Ravelo | Delay modelling of high-speed distributed interconnect for the signal integrity prediction[END_REF][START_REF] Hu | Propagation delays computation in GEO multi-beam satellite communications system[END_REF][START_REF] Weiss | Fundamental limitations in passive time-delay estimation-Part I: Narrow-band systems[END_REF]. In addition, with the dispersion effect [START_REF] Myoung | Effect of Group Delay in RF BPF on Impulse Radio Systems[END_REF], the group delay can become non flat in the operation frequency bands of RF and microwave components. Depending on the application area, such degradation effects are interpreted with different analytical parameters group- [START_REF] Myoung | Effect of Group Delay in RF BPF on Impulse Radio Systems[END_REF][START_REF] Heffner | Accurate, automated measurement of differential group delay dispersion and principal state variation using Jones matrix eigen analysis[END_REF], propagation- [START_REF] Kwon | Effect of Antenna Gain and Group Delay Variations on Pulse-Preserving Capabilities of Ultrawideband Antennas[END_REF][START_REF] Ravelo | Delay modelling of high-speed distributed interconnect for the signal integrity prediction[END_REF] and time- [START_REF] Hu | Propagation delays computation in GEO multi-beam satellite communications system[END_REF][START_REF] Weiss | Fundamental limitations in passive time-delay estimation-Part I: Narrow-band systems[END_REF] delays. Therefore, an efficient technique is necessary for estimating the influence of delays on the communication quality [START_REF] Hu | Propagation delays computation in GEO multi-beam satellite communications system[END_REF][START_REF] Weiss | Fundamental limitations in passive time-delay estimation-Part I: Narrow-band systems[END_REF]. In addition, effective technical solutions have been deployed to overcome the delay effects as the development of design methods dedicated to group delay equalizers [START_REF] Weinstein | Fundamental limitations in passive time-delay estimation-Part II: Wide-band systems[END_REF][START_REF] Ziska | Method for design of analog group delay equalizers[END_REF][START_REF] Žiska | Analog Group Delay Equalizers Design Based on Evolutionary Algorithm[END_REF], minimizer [START_REF] Gupta | Group-Delay Engineered Noncommensurate Transmission Line All-Pass Network for Analog Signal Processing[END_REF] and linearizer [START_REF] Pasolini | Multistage Decimators with Minimum Group Delay[END_REF] were proposed. So far, different techniques to design equalizers were introduced with typically all-pass network filters [START_REF] Keerthan | Design of cascaded all pass network with monotonous group delay response broadband radio frequency applications[END_REF]. Nevertheless, these types of equalizers have negative undesirable effects as the generation of additional positive group delays. The uncontrollable group delays are not good and may degrade the system performance.

An alternative technique of equalizer implementation using negative group delay (NGD) function was introduced in [START_REF] Ravelo | Neutralization of LC-and RC-Effects with Left-Handed and NGD Circuits[END_REF]. This type of NGD equalizer enables to realize outstanding solutions as the neutralization of undesirable RCand LC-effects generally degrading the signals propagating through the electrical interconnections [START_REF] Ravelo | Delay modelling of high-speed distributed interconnect for the signal integrity prediction[END_REF]. However, nowadays, in difference to the other classical functions, the NGD phenomenon is still not understandable for most of electronics, RF and microwave engineers. For this reason, the present paper investigates an experimentation of NGD phenomenon with a non-complicated electrical structure.

Since the first experimentation of NGD phenomenon in 1990s, few groups of research are currently working on this counterintuitive topic. Nevertheless, various non mature attempts of applications in particular in the area of RF and microwave engineering were proposed [START_REF] Ravelo | Neutralization of LC-and RC-Effects with Left-Handed and NGD Circuits[END_REF][START_REF] Broomfield | Broadband Negative Group Delay Networks for Compensation of Oscillators, Filters and Communication Systems[END_REF][START_REF] Oh | Compensated circuit with characteristics of lossless double negative materials and its application to array antennas[END_REF][START_REF] Abunjaileh | A matched bridged tee network with positive phase derivative[END_REF][START_REF] Choi | Efficiency enhancement of feedforward amplifiers by employing a negative group delay circuit[END_REF][START_REF] Choi | Bandwidth enhancement of an analog feedback amplifier by employing a negative group delay circuit[END_REF][START_REF] Kandic | Bilateral gain-compensated negative group delay circuit[END_REF][START_REF] Bridges | Gain compensated symmetric loaded transmission line exhibiting bidirectional negative group delay[END_REF][START_REF] Meng | A Broadband Switch-Less Bi-Directional Amplifier with Negative-Group-Delay Matching Circuits[END_REF][START_REF] Wu | A Dual-Purpose Reconfigurable Negative Group Delay Circuit Based on Distributed Amplifiers[END_REF][START_REF] Mirzaei | Arbitrary-angle squint-free beamforming in series-fed antenna arrays using non-Foster elements synthesized by negative-group-delay networks[END_REF][START_REF] Wu | A Novel Arbitrary Terminated Unequal Coupler With Bandwidth-Enhanced Positive and Negative Group Delay Characteristics[END_REF][START_REF] Mortazawi | Negative group delay circuit[END_REF][START_REF] Bao | Device for negative group delay[END_REF]. As reported in [START_REF] Broomfield | Broadband Negative Group Delay Networks for Compensation of Oscillators, Filters and Communication Systems[END_REF], an NGD compensation method of oscillators, filters and communication systems was initiated [START_REF] Broomfield | Broadband Negative Group Delay Networks for Compensation of Oscillators, Filters and Communication Systems[END_REF]. Another compensation method of array antenna effect based on the NGD circuit fabricated with lossless double negative metamaterials can be found in [START_REF] Oh | Compensated circuit with characteristics of lossless double negative materials and its application to array antennas[END_REF]. Design of matched bridged tee network with positive phase slope was studied in [START_REF] Abunjaileh | A matched bridged tee network with positive phase derivative[END_REF]. But, the passive NGD circuits used in these applicative proposals suffer from attenuation losses. To alleviate this roadblock, alternative applications with NGD active circuits were proposed [START_REF] Choi | Efficiency enhancement of feedforward amplifiers by employing a negative group delay circuit[END_REF][START_REF] Choi | Bandwidth enhancement of an analog feedback amplifier by employing a negative group delay circuit[END_REF][START_REF] Kandic | Bilateral gain-compensated negative group delay circuit[END_REF][START_REF] Bridges | Gain compensated symmetric loaded transmission line exhibiting bidirectional negative group delay[END_REF][START_REF] Meng | A Broadband Switch-Less Bi-Directional Amplifier with Negative-Group-Delay Matching Circuits[END_REF][START_REF] Wu | A Dual-Purpose Reconfigurable Negative Group Delay Circuit Based on Distributed Amplifiers[END_REF]. For example, a design method of enhanced bandwidth feedforward amplifier using NGD resonator was presented in [START_REF] Choi | Efficiency enhancement of feedforward amplifiers by employing a negative group delay circuit[END_REF][START_REF] Choi | Bandwidth enhancement of an analog feedback amplifier by employing a negative group delay circuit[END_REF]. More recently, another design of bidirectional amplifier with NGD matching circuits was investigated in [START_REF] Kandic | Bilateral gain-compensated negative group delay circuit[END_REF][START_REF] Bridges | Gain compensated symmetric loaded transmission line exhibiting bidirectional negative group delay[END_REF][START_REF] Meng | A Broadband Switch-Less Bi-Directional Amplifier with Negative-Group-Delay Matching Circuits[END_REF]. A design method of distributed amplifier using reconfigurable NGD circuit is presented in [START_REF] Wu | A Dual-Purpose Reconfigurable Negative Group Delay Circuit Based on Distributed Amplifiers[END_REF]. Different antenna design applications were also proposed as the arbitrary-angle squintfree beamforming in series-fed antenna arrays using non-Foster NGD networks [START_REF] Mirzaei | Arbitrary-angle squint-free beamforming in series-fed antenna arrays using non-Foster elements synthesized by negative-group-delay networks[END_REF]. Then, design method of arbitrary terminated unequal coupler with bandwidth-enhancement by using NGD circuit is proposed in [START_REF] Wu | A Novel Arbitrary Terminated Unequal Coupler With Bandwidth-Enhanced Positive and Negative Group Delay Characteristics[END_REF].

Designs of NGD devices and circuits for RF and microwave front-and back-end chains based were also invented [START_REF] Mortazawi | Negative group delay circuit[END_REF][START_REF] Bao | Device for negative group delay[END_REF]. In spite of those applications, today, the NGD function can be classified as the most uncommon electronic function for most of researchers and engineers.

To feed our knowledge on the uncommon NGD phenomenon, a brief state-of-the-art is narrated in this paragraph.

Basically, the NGD phenomenon can be identified with its outstanding signature of the apparition of output signal in advance of smoothed input [START_REF] Ravelo | Demonstration of negative signal delay with short-duration transient pulse[END_REF]. Knowing the initial interpretation of the group delay [START_REF] Zakarevicius | Group Delay Estimation with Wideband Signals[END_REF][START_REF] Yegnanarayana | Significance of group delay functions in signal reconstruction from spectral magnitude or phase[END_REF], it can be understood that the NGD phenomenon can be generated systematically when a linear circuit transmission phase presents a positive slope when the frequency increases [START_REF] Zakarevicius | Group Delay Estimation with Wideband Signals[END_REF][START_REF] Yegnanarayana | Significance of group delay functions in signal reconstruction from spectral magnitude or phase[END_REF]. The first NGD synthesizer with typically RLC-resonator passive network was investigated in [START_REF] Lucyszyn | Analog Reflection Topology Building Blocks for Adaptive Microwave Signal Processing Applications[END_REF][START_REF] Lucyszyn | Negative Group Delay Synthesiser[END_REF]. One decade later, NGD passive resonant circuits inspired from double negative metamaterial structures were designed [START_REF] Eleftheriades | Transmission Line for Negative Refractive Index Media and Associated Implementations without Excess Resonators[END_REF][START_REF] Siddiqui | Periodically Loaded Transmission Line with Effective Negative Refractive Index and Negative Group Velocity[END_REF][START_REF] Siddiqui | Time-Domain Measurement of Negative-Index Transmission-Line Metamaterials[END_REF]. The NGD function meaning in time-domain with the negative delay was theoretically investigated and experimented in [START_REF] Ravelo | Demonstration of negative signal delay with short-duration transient pulse[END_REF]. However, it was emphasized in [START_REF] Kandic | Asymptotic Limits of Negative Group Delay in Active Resonator-Based Distributed Circuits[END_REF] that the NGD circuit must operate with limited time-advance. Nevertheless, last decade, some innovative circuits operate with NGD phenomenon were developed [START_REF] Mirzaei | Realizing Non-Foster Reactive Elements Using Negative-Group-Delay Networks[END_REF][START_REF] Wu | Maximally Flat Negative Group-Delay Circuit: A Microwave Transversal Filter Approach[END_REF][START_REF] Barroso | Negative group velocity in resistive lossy lefthanded transmission lines[END_REF][START_REF] Chaudhary | Microstrip Line Negative Group Delay Filters for Microwave Circuits[END_REF][START_REF] Chaudhary | Distributed Transmission Line Negative Group Delay Circuit with Improved Signal Attenuation[END_REF][START_REF] Liu | Compact transmission-type negative group delay circuit with low attenuation[END_REF][START_REF] Ravelo | Negative Group-Delay Phenomenon Analysis with Distributed Parallel Interconnect Line[END_REF][START_REF] Ravelo | Tee power divider and combiner based negative group delay topology[END_REF][START_REF] Ravelo | Theory on Coupled Line Coupler-Based Negative Group Delay Microwave Circuit[END_REF][START_REF] Das | Lossy Coupling Matrix Synthesis Approach for the Realization of Negative Group Delay Response[END_REF][START_REF] Shao | A compact transmission line self-matched negative group delay microwave circuit[END_REF]. Non-Foster reactive elements NGD passive networks were proposed [START_REF] Mirzaei | Realizing Non-Foster Reactive Elements Using Negative-Group-Delay Networks[END_REF]. Maximally flat NGD active circuit by exploiting the transversal filter concept is proposed [START_REF] Wu | Maximally Flat Negative Group-Delay Circuit: A Microwave Transversal Filter Approach[END_REF]. Then, design of passive NGD lumped circuit with modified lossy left-handed metamaterial structure is proposed in [START_REF] Barroso | Negative group velocity in resistive lossy lefthanded transmission lines[END_REF].

Mostly, the NGD circuits using lumped passive elements are significantly lossy. Therefore, NGD circuits with distributed transmission lines (TLs) were proposed [START_REF] Chaudhary | Microstrip Line Negative Group Delay Filters for Microwave Circuits[END_REF][START_REF] Chaudhary | Distributed Transmission Line Negative Group Delay Circuit with Improved Signal Attenuation[END_REF][START_REF] Liu | Compact transmission-type negative group delay circuit with low attenuation[END_REF][START_REF] Ravelo | Negative Group-Delay Phenomenon Analysis with Distributed Parallel Interconnect Line[END_REF][START_REF] Ravelo | Tee power divider and combiner based negative group delay topology[END_REF][START_REF] Ravelo | Theory on Coupled Line Coupler-Based Negative Group Delay Microwave Circuit[END_REF][START_REF] Das | Lossy Coupling Matrix Synthesis Approach for the Realization of Negative Group Delay Response[END_REF]. Transmission type NGD distributed passive circuits were also introduced [START_REF] Chaudhary | Microstrip Line Negative Group Delay Filters for Microwave Circuits[END_REF][START_REF] Chaudhary | Distributed Transmission Line Negative Group Delay Circuit with Improved Signal Attenuation[END_REF][START_REF] Liu | Compact transmission-type negative group delay circuit with low attenuation[END_REF]. Another NGD distributed passive circuits based on the coupling effect were proposed in [START_REF] Ravelo | Theory on Coupled Line Coupler-Based Negative Group Delay Microwave Circuit[END_REF][START_REF] Das | Lossy Coupling Matrix Synthesis Approach for the Realization of Negative Group Delay Response[END_REF]. This tremendous progress of NGD design should be accompanied to pedagogical experimental open technique to make the topic more familiar to non-specialists.

As discussed previously, further illustrative theory and experimentation is necessary to illustrate and explain the NGD phenomenon. More research work must be performed to open the NGD topic to non-specialist including RF and microwave engineering community. Simpler NGD topology operating with lower loss and good access matching remains an open topic of research. For this reason, the present paper introduces an easy to understand NGD investigation. To do this, particularly simple structure constituted by SMA Tee-Connectors and SMA cables operating as a bandpass NGD function is presented. In difference to the previous NGD study [START_REF] Ravelo | Neutralization of LC-and RC-Effects with Left-Handed and NGD Circuits[END_REF][START_REF] Broomfield | Broadband Negative Group Delay Networks for Compensation of Oscillators, Filters and Communication Systems[END_REF][START_REF] Oh | Compensated circuit with characteristics of lossless double negative materials and its application to array antennas[END_REF][START_REF] Abunjaileh | A matched bridged tee network with positive phase derivative[END_REF][START_REF] Choi | Efficiency enhancement of feedforward amplifiers by employing a negative group delay circuit[END_REF][START_REF] Choi | Bandwidth enhancement of an analog feedback amplifier by employing a negative group delay circuit[END_REF][START_REF] Kandic | Bilateral gain-compensated negative group delay circuit[END_REF][START_REF] Bridges | Gain compensated symmetric loaded transmission line exhibiting bidirectional negative group delay[END_REF][START_REF] Meng | A Broadband Switch-Less Bi-Directional Amplifier with Negative-Group-Delay Matching Circuits[END_REF][START_REF] Wu | A Dual-Purpose Reconfigurable Negative Group Delay Circuit Based on Distributed Amplifiers[END_REF][START_REF] Mirzaei | Arbitrary-angle squint-free beamforming in series-fed antenna arrays using non-Foster elements synthesized by negative-group-delay networks[END_REF][START_REF] Wu | A Novel Arbitrary Terminated Unequal Coupler With Bandwidth-Enhanced Positive and Negative Group Delay Characteristics[END_REF][START_REF] Mortazawi | Negative group delay circuit[END_REF][START_REF] Bao | Device for negative group delay[END_REF][START_REF] Ravelo | Demonstration of negative signal delay with short-duration transient pulse[END_REF][START_REF] Lucyszyn | Analog Reflection Topology Building Blocks for Adaptive Microwave Signal Processing Applications[END_REF][START_REF] Lucyszyn | Negative Group Delay Synthesiser[END_REF][START_REF] Eleftheriades | Transmission Line for Negative Refractive Index Media and Associated Implementations without Excess Resonators[END_REF][START_REF] Siddiqui | Periodically Loaded Transmission Line with Effective Negative Refractive Index and Negative Group Velocity[END_REF][START_REF] Siddiqui | Time-Domain Measurement of Negative-Index Transmission-Line Metamaterials[END_REF][START_REF] Kandic | Asymptotic Limits of Negative Group Delay in Active Resonator-Based Distributed Circuits[END_REF][START_REF] Mirzaei | Realizing Non-Foster Reactive Elements Using Negative-Group-Delay Networks[END_REF][START_REF] Wu | Maximally Flat Negative Group-Delay Circuit: A Microwave Transversal Filter Approach[END_REF][START_REF] Barroso | Negative group velocity in resistive lossy lefthanded transmission lines[END_REF][START_REF] Chaudhary | Microstrip Line Negative Group Delay Filters for Microwave Circuits[END_REF][START_REF] Chaudhary | Distributed Transmission Line Negative Group Delay Circuit with Improved Signal Attenuation[END_REF][START_REF] Liu | Compact transmission-type negative group delay circuit with low attenuation[END_REF][START_REF] Ravelo | Negative Group-Delay Phenomenon Analysis with Distributed Parallel Interconnect Line[END_REF][START_REF] Ravelo | Tee power divider and combiner based negative group delay topology[END_REF][START_REF] Ravelo | Theory on Coupled Line Coupler-Based Negative Group Delay Microwave Circuit[END_REF][START_REF] Das | Lossy Coupling Matrix Synthesis Approach for the Realization of Negative Group Delay Response[END_REF], the present work develops an innovative theory and experimentation demonstrating the possibility to generate the NGD phenomenon in function of the SMA cable length and attenuation. Thus, the proposed structure is helpful for understanding the NGD function. It can be experimented easily with simple SMA connectors and cables by nonspecialists.

The paper is organized in four main sections. Section 2 describes the theoretical investigation of the Tee-Cable topology. The proposed topology is designed with only distributed elements without lossy lumped elements. The circuit theory is elaborated from the S-parameter modelling. The NGD analyses will be introduced in Section 3. The NGD existence equations and centre frequencies in function of the cable delay and attenuation are investigated. Section 4 is focused on the practical validations including the NGD experimentation of the tee connector combined with coaxial cables. Proof-of-concept (POC) built with Tee-Cable based structure will be described. Comparisons between the analytically calculated, simulated and experimented results will be discussed. Then, the last Section presents the conclusion of the paper.

NGD GENERAL THEORY ON TEE CONNECTOR AND CABLE STRUCTURE

This section is focused on the NGD theory. The equivalent circuit of the Tee-Cable structure will be introduced. The S-parameter model will be calculated. The group delay expression will be established in order to perform the NGD analysis.

Description of the Tee connector and cable structure

The NGD microwave circuit under study behaves as a two-port passive topology. In difference to work published in [START_REF] Ravelo | Neutralization of LC-and RC-Effects with Left-Handed and NGD Circuits[END_REF][START_REF] Broomfield | Broadband Negative Group Delay Networks for Compensation of Oscillators, Filters and Communication Systems[END_REF][START_REF] Oh | Compensated circuit with characteristics of lossless double negative materials and its application to array antennas[END_REF][START_REF] Abunjaileh | A matched bridged tee network with positive phase derivative[END_REF][START_REF] Choi | Efficiency enhancement of feedforward amplifiers by employing a negative group delay circuit[END_REF][START_REF] Choi | Bandwidth enhancement of an analog feedback amplifier by employing a negative group delay circuit[END_REF][START_REF] Kandic | Bilateral gain-compensated negative group delay circuit[END_REF][START_REF] Bridges | Gain compensated symmetric loaded transmission line exhibiting bidirectional negative group delay[END_REF][START_REF] Meng | A Broadband Switch-Less Bi-Directional Amplifier with Negative-Group-Delay Matching Circuits[END_REF][START_REF] Wu | A Dual-Purpose Reconfigurable Negative Group Delay Circuit Based on Distributed Amplifiers[END_REF][START_REF] Mirzaei | Arbitrary-angle squint-free beamforming in series-fed antenna arrays using non-Foster elements synthesized by negative-group-delay networks[END_REF][START_REF] Wu | A Novel Arbitrary Terminated Unequal Coupler With Bandwidth-Enhanced Positive and Negative Group Delay Characteristics[END_REF][START_REF] Mortazawi | Negative group delay circuit[END_REF][START_REF] Bao | Device for negative group delay[END_REF][START_REF] Ravelo | Demonstration of negative signal delay with short-duration transient pulse[END_REF], the present NGD topology is constituted by interconnected three-port Tee connectors and cables represented by TLs. The connector terminals are referenced by the elements with connection Ports -- and Ports --.

For the shake of mathematical simplicity, the constituting connectors are represented by ideal three port S-matrix. As depicted in Fig. 1, connector port  and port  represent respectively as the overall NGD topology main input and output.

Fig. 1. Equivalent schematic of the combined tee connectors and cables network under study.

The overall circuit is loaded by R0=50 Ω which is assumed as the reference impedance. Ports  and  are directly connected and ports  and  are interconnected through a lossy cable with characteristic impedance R0 and physical length d. The variables am and bm (m={1,…,6}) represent the input and output wave powers propagating through the structure branches. The proposed topology S-parameter modelling will be described in the next paragraph.

Theoretical modelling of S-matrix

This analytical study is elaborated by supposing that the Tee connector with negligible physical length and the cable is perfectly matched. By hypothesis, the three-port Tee connector S-parameter model is symmetrically expressed as:

  1/ 3 2 / 3 2 / 3 2 / 3 1/ 3 2 / 3 2 / 3 2 / 3 1/ 3 Tee S -   =-   -  . ( 1
)
This Tee connector S-matrix can be operated with the topological parameters of the circuit based on the following the matrix relation:

  11 22 33 Tee ba b S a ba         =             , (2) and:
 

        =             . ( 3
)
In this paper, the interconnect lossy cable characteristic impedance is assumed equal to Zc=R0. By denoting v the wave speed, the cable physical length is expressed as:

d=v•τ0. ( 4
)
The lossy cable is characterized by the parameter:

a=e -αd <1, ( 5
)
with α is the attenuation constant. Under this hypothesis, by denoting the angular frequency variable ω, the interconnect reflection and insertion losses introduced in [39-45] become:

==   = =   , (6) 00 11 22 ( ) ( ) 12 21 ( ) ( ) 0 ( ) ( )
TL TL jj TL TL S j S j S j S j b e a e         - + - + ==   = =     , (7)
with:

τ0=d/v, (8)
and

Δτ=Δd/v, (9)
are the cable delay. These S-parameters are linked to the access port wave powers by the matrix relation:

      =             , (10)
SS        =           . ( 11
)
Consequently, we have the power wave expressions:

      - + - +  =   =   . ( 13
)

Frequency dependent expression of S-parameter coefficients

relation:

1 11 22 1 6 12 21 1 ( ) ( ) ( ) ( ) b S j S j a b S j S j a  ==     ==     . ( 14
)
These coefficients can be expressed in function of the circuit parameters by calculating the output wave powers b1 and b6, and the input wave power a1. First, b1 and b6 can be determined by successive combination of the wave powers propagating through the cable and connector access ports. The analytical expressions obtained from the Smatrices defined previously in equations ( 1), ( 6) and [START_REF] Weinstein | Fundamental limitations in passive time-delay estimation-Part II: Wide-band systems[END_REF] give the simplified formulas:

0 0 0 0 0 0 0 2 (2 ) 2 (
+ + - + ==     + - -                       , ( 15
)
 +- ==     + - -                  . ( 16
)
The associated reflection coefficient magnitude 11

11 ( ) ( ) S S j  =
is written as:

                22 4 2 4 2 0 0 0 0 2 2 2 2 0 0 0 0 11 2 2 0 00 3 3 cos 2 (2 ) cos(2 ) 3 sin 2 (2 ) sin (2 ) 8 cos (2 ) cos 2 ( ) 8 sin (2 ) sin 2 ( ) () 3 cos (2 ) cos
( ) cos( ) a a a a a a a a S aa aa     + +  + - +  + -     +     +  + +  +  + +          =  - +  + +  +  +                                          
    +  -+ +  +  +      +  + +  +                                (17)
The transmission coefficient magnitude 21

21 ( ) ( ) S S j  =
is given by:

              2
=   +  +  +  -   +-       - +  +   -                               2 0 2 2 00 () 3 cos( ) 3 sin( ) sin ( ) sin( ) aa aa a      --       - +  +   -           , (18)
With the presence of sin(.) and cos(.) terms, we can understand that these magnitudes are periodical function.

Frequency dependent expression of GD

By denoting the transmission phase associated to S21 is defined as:

  21 ( ) arg ( ) Sj =    . ( 19
)
In circuit theory, the NGD phenomenon can be easily understood based on the group delay (GD) analytical definition. To do this, it is worth to recall this definition. The analytical expression of GD was initiated in [START_REF] Bao | Device for negative group delay[END_REF][START_REF] Ravelo | Demonstration of negative signal delay with short-duration transient pulse[END_REF]:

() () - =     . ( 20
)
The proposed cell NGD fundamental properties and characteristics will be deduced from this transmission coefficient expression. The associated transmission phase is:

( ) ( ) ( ) nd       =-, (21)
with:

    2 0 0 2 0 sin (2 ) sin( ) ( ) arctan arctan 1 cos (2 ) 1 cos( ) n a a  +    = - -   - +  +                 , (22) and: 12 ( ) ( ) ( )
d d d       =+, (23)
where:

      00 1 0 0 0 sin( ) sin( ) sin ( ) ( ) arctan 3 cos( ) cos ( ) cos (2 )
d aa aa

 +  + +     =  - + +  + +                    , ( 24
)       00 2 0 0 0 sin( ) sin( ) sin ( ) ( ) arctan cos (2 ) cos( ) cos ( ) 3 d aa aa  +  - +     =  +  - - +  -                   . ( 25
)
It yields the GD defined earlier in [START_REF] Bridges | Gain compensated symmetric loaded transmission line exhibiting bidirectional negative group delay[END_REF] can be formulated as:

12 ( ) ( ) ( ) ( ) n d d         = + + , (26)
with:

      22 00 0 42 0 (2 ) cos (2 ) () 2 1 2 cos (2 ) n aa aa             +  - +   = -+ + - +  , ( 27
)         2 2 2 0 0 0 22 0 0 0 0 1 4 2 2 2 0 0 0 (1 ) (2 ) 3(1 ) (3 ) ) cos ( ) 3( 1
  + +  - - + -  +        + - +  + +   - +       = + + +  - +  + - + +                                 , (28)
and:

        2 2 2 0 0 0 22 0 0 0 0 2 4 2 2 2 0 0 0 (1 )( ) 3(1 ) ( 3
) ) cos ( )

3(1 ) 2 cos( ) (2
+  + + + -  +        + - -  + +   - +       = + + +  - +  + - + +                                     .( 29
)
It can be pointed out that the frequency responses (transmission and reflection coefficients, and the group delay behave as periodical functions depending to the parameters 0  and   . Therefore, we are proposing to conduct the analytical analyses at some particular frequencies in the next paragraph

NGD ANALYSIS AT PARTICULAR FREQUENCIES

This section develops the main physical approach on the NGD analysis.

Identification of particular frequencies

For the preliminary analytical observation, the NGD analysis can be performed at the particular values of angular frequencies. The reference angular frequency is linked to the quarter wavelength of the cable physical length:

0 0 2(2 ) = +    . ( 30
)
The analyses are performed at very low frequencies ω≈0 and the multiple of the particular angular frequency 0

 : ω(m)=mω0, ( 31
)
with the integer m={0,1,2,…}. It can be speculated the behavior of the tee-cable network at the angular frequencies:

0 2  = , ( 32
) 0 3  = , ( 33
) 0 4  = . ( 34
)

Insertion and Reflection Losses and Group Delay at Very Low Frequencies ω≈0

The reflection and insertion losses expressed in [START_REF] Kandic | Bilateral gain-compensated negative group delay circuit[END_REF] and ( 20) are transformed as respectively:

11 2 8 9 a S a = - , (35)
It can be understood from formula [START_REF] Kandic | Asymptotic Limits of Negative Group Delay in Active Resonator-Based Distributed Circuits[END_REF] that the input and output reflection can be matched. The group delay expressed in (26) becomes: 9)

2 0 2 (9 )(2 ) 2(
a a + +  = -   . ( 37
)
This formula enables to predict the influence of the parameters 0  and   . So, the group delay of the Tee-cable topology is unconditionally positive at very low frequencies ω≈0. Therefore, the circuit cannot operate as a low-pass NGD function. Therefore, let us see in the next paragraph the NGD values at the frequencies expressed in ( 31), ( 32), [START_REF] Siddiqui | Periodically Loaded Transmission Line with Effective Negative Refractive Index and Negative Group Velocity[END_REF] and [START_REF] Siddiqui | Time-Domain Measurement of Negative-Index Transmission-Line Metamaterials[END_REF] if there is possibility of bandpass NGD function.

To understand more generally the tee-cable behavior, we are proposing to calculate the reflection and transmission coefficients, and the group delay in function of:

0 2 x  =   , ( 38
)
or 0 x  =   . ( 39
)

Insertion and reflection losses at particular frequencies ω(m)

At the particular frequencies () m  , the reflection and insertion losses introduced in ( 17) and ( 18) are transformed as respectively:

    2 4 4 2 2 4 2 1 3 4 1 3 4 2 11 3(1 ) cos( ) cos( ) 2(3 4) cos( ) sin( ) sin( ) 2(3 4)sin( ) () ( , ) a a a a a Sm D x m     - + + + - + + + -     =        ,(40)   2 2 4 2 2 34 2 21 16 cos ( / 2) 1 2 cos ( / 2) () ( , ) a a a Sm D x m    +-  = . ( 41
)
where:

            22
- + - + + - -            , ( 42
)
with:

1 2 3 2 4 2 ( 2) 2( 1) ( 2) 2( 1) ( 2) 2( 1) mx mx x m x x x mx x  =   +  =  +   +  = +   +  =  +          . ( 43
)
However, these general expressions of the reflection and insertion losses, and the group delay in function of m are rather sophisticated. Therefore, we can proceed with the Maclaurin expanding with respect to x for example limited to third order. Consequently, reflection and insertion losses introduced in formulas ( 40) and ( 41) are reduced as respectively:

 

-- =  - + + - +     . ( 45
)

GD expressions at ω =ω(m)

It is established that at the particular frequencies ω(m), the group delay expressed in [START_REF] Yegnanarayana | Significance of group delay functions in signal reconstruction from spectral magnitude or phase[END_REF]

a a a a a a a a x m a x m a a m a x a a

- + + - + - + + - - =  - - + - -       . ( 46
)
This NGD is mathematically negative under the following condition:

+ - + - + + - -     + - -      , (47) or
 - + + - + - + + - -     + - -      . ( 48
)
Knowing that a<1, condition ( 47) is impossible to achieve because the quantity:

2 2 2 2 2 2 2 (9 )(1 ) m a x a a  = + - -   , (49)
is always positive. The existence of condition (47) depends on the following discriminant of the group delay quantity numerator with respect to the variable x:

4 2 2 4 8 6 2 2 2 4
(81

)(1 ) 2 162 81 16( 5 16
)

a a a a a a m a   = - - -+ - + + +   . ( 50
)
It can be discriminated that:

• If 4 8 6 2 2 2 4 0 2 162 81 16(5 16 ) 0 a a a a m a     -+ - + + +    , (51)
the group delay expressed in ( 45) is always negative independently to the variable x,

• Else

the group delay can be negative when x fulfils the condition:

 - - + -+   . ( 53
)
Table I presents the group delays at the frequencies expressed in (31), ( 32), ( 33) and [START_REF] Siddiqui | Time-Domain Measurement of Negative-Index Transmission-Line Metamaterials[END_REF] in function of the parameters a, 0  and   . As predicted by equation ( 46), the NGD level absolute values increases with m. As illustrated in formulas (54), ( 55) and (56), the tee-cable topology may behave as a bandpass NGD function.

As concrete verification, validation results are discussed in the next section. The POC structure will be described.

Comparisons between the modelled, simulated and measured results will be examined.

SIMULATION AND EXPERIMENTAL DEMONSTRATIONS

To verify the effectiveness of the previous theory, validation results are discussed in the present section. First, numerical feasibility analyses in function of the cable parameters is elaborated based on ideal circuit parametric sweeping. The POC of the tee connector combined with cables is described. Then, the simulated and experimental results are compared with the calculated modelled results.

Parametric analyses with ideal structures

To get further insight about the influence of the cable length on the NGD circuit, parametric analyses are conducted.

Discussion on simulated and measured results

The S-parameters of the tested tee-cable network were measured in the frequency band from 1.5 GHz to 3. 7, the NGD presenting optimal level of about -1 ns, -2 ns and -3 ns were observed around these frequencies respectively. However, the NGD bandwidths are particularly narrow band less than 12

MHz.

Fig. 7. Comparison of the modeled, simulated and measured group delay of the tee-cable NGD POC prototypes

shown in Fig. 6.

The measured NGD circuit enables to achieve insertion losses better than 1 dB and reflection loss better than 15 dB at the first NGD centre frequency as illustrated in Fig. 8. The obtained insertion loss is widely better compared to the existing NGD passive circuits. These theoretical, simulation and experimental results confirm the NGD concept feasibility with the tee-cable network-based topology. The discrepancies between the modelled, simulated and measured S-parameters can be caused by the fabrication imperfections, the tee and cable constituting material characteristic dispersions, the cable attenuation, which is assumed theoretically constant, changes with the frequency in function of the conductivity, and numerical inaccuracies of the simulator. • Dispersions on the parameters of the cable substrate material,

• Mismatch induced by the Tee cables/connectors (see Fig. 6),

• Numerical computation drifts of the full wave simulating tool, and of the calculated tool; this includes for instance the dispersion models and simulations constitutive parameters (geometrical, electrical ones).

Comparison of NGD specifications with the state-of-the-art

We can understand from the comparative values of Table 2 the basic performances of the parallel cable structure topology under investigation and the existing ones available in the literature (see [START_REF] Wu | Maximally Flat Negative Group-Delay Circuit: A Microwave Transversal Filter Approach[END_REF] and [START_REF] Shao | A compact transmission line self-matched negative group delay microwave circuit[END_REF][START_REF] Wang | A Negative Group Delay Microwave Circuit Based on Signal Interference Techniques[END_REF][START_REF] Chaudhary | Negative group delay phenomenon analysis using finite unloaded quality factor resonators[END_REF][START_REF] Chaudhary | Transmission-type negative group delay networks using coupled line doublet structure[END_REF][START_REF] Wan | O=O Shape Low-Loss Negative Group Delay Microstrip Circuit[END_REF][START_REF] Wan | NGD Analysis of Turtle-Shape Microstrip Circuit[END_REF]). It can be underlined that the parallel cable NGD structure enable to achieve:

• Low signal attenuation in the NGD bandwidth,

• Reflection loss better than -14 dB in the NGD bandwidth,

• And it can be implemented with fully distributed elements without lossy lumped component.

However, the parallel cable drawbacks are:

• The large size of the cable which is not easy to integrate in the printed circuit boards,

• And the imperfections of the cable fabrications may affect undesirably the bandpass NGD function parameters.

CONCLUSION

An NGD analytical and experimental study on outstanding simple tee-cable network is investigated. The S-matrix model of the tee-cable equivalent circuit is developed. The NGD analysis is introduced in function of the cable parameter. The NGD theory validation is confirmed by calculations, simulations and experimentations. Parametric and numerical analyses of S-parameters in function of the cable length and attenuation are discussed. In addition, as POC, a tee-cable network prototype is tested. The theoretical prediction is verified with both simulations and measurements. It is demonstrated that the tested tee-cable generate a multiband NGD effect around GHz. In difference to the existing NGD passive circuits, the tee-cable NGD topology allows to achieve very low insertion loss, better than 2 dB and reflection loss better than 12 dB.

REFERENCE

Fig. 2

 2 Fig. 2 depicts the schematic of the simulated structure. The tee-cable network was simulated in the SPICE schematic environment of the ADS® simulator from Keysight Technologies®. It is composed of ideal coaxial tees and cables. Th two identical connectors are defined by the characteristic impedance R0=50 Ω, physical length dc=4 mm and relative permittivity εr=2. The two cables present the attenuation a=-0.3 dB and different lengths d and d+Δd.

Fig. 2 .

 2 Fig. 2. Schematic of the simulated tee-cable network.

Fig. 3 .Fig. 4 .Fig. 6 .

 346 Fig. 3. Group delay response of the tee-cable network with the influence of Δd.

Fig. 8 . 6 .

 86 Fig. 8. Comparison of the modeled, simulated and measured reflection and transmission coefficients of the teecable NGD POC prototype shown inFig. 6.

Table 1 : Group delays at particular angular frequencies

 1

	

  5 GHz step 10 MHz. Figs. 7 show the comparisons between the theoretical model, simulation and measurement of the group delays. The particular frequency calculated from (30) is f0≈0.79 GHz. The modelled, simulated and measured results are in good agreement. Original tri-band NGD behaviour is observed at around 2f0≈1.58 GHz, 3f0≈2.42 GHz and 4f0≈3.19 GHz. As seen in Fig.

Table 2 : Comparison of the NGD structure specifications and the available ones in the state-of-the-art.

 2

						Extra lumped
	Ref.	f (GHz)	NGD (ns)	S21 (dB)	S11 (dB)	components
						(Y/N)
	[37]	1	-1.5	-33	-25	N
	[46]	1.57	-8.75	-20.5	-32	Y
	[47]	1.016	-2.09	-18.1	-33	Y
	[48]	2.14	-1.03	3.82	-12	Y
	[49]	1	-1.5	33	-25	N
	[50]	1.2	-2.8	-2.2	-15	N
	[51]	1.97	-1	-2.2	-14	N

This research work was supported in part by NSFC under Grant 61601233 and Grant 61750110535, in part by the Defense Research Foundation under Grant 6140209050116ZK53001, in part by NSF of Jiangsu under Grant BK20150918, in part by the Jiangsu Innovation and Enterprise Group Talents Plan 2015 under Grant SRCB201526, and in part by PAPD.

Author Contributions:

-Fayu Wan performed the main writing of the paper and was a part of NUIST, China.

-Xiaoyu Huang performed the test and the data processing and was a Master student of NUIST, China.

Fig. 5. Group delay, transmission and reflection coefficients of the tee-cable network with the influence of d.

The NGD central frequency changes significantly with d as shown in Fig. 5

Description of Tee-cable POC

The photograph of the simple 50 Ω coaxial tee-cable POC prototype is exposed in Fig. 6


text:
Preface

What is a crop mode!? 'Snake o il ' (J>assioura 1996), i.e. an impossible (and moderately honest) challenge to fit the current scicntific knowledge into a single framework? A mechanistic view of plant growth and development which represent causality between component processes and yield (Yin ct a l. 2004)? Robust empirical relations between plant behaviour and the main environmcntal variables (Passioura 1996)? A tool for analysing plant behaviour and its genctic variability which bypasses, but may help to increase the knowledge about underlying mechanisms (Tardieu 2003, Hammer 2006)? Ali these definitions are partly true, ali are potentially misleading.

Considering the achievements of crop modcls is perhaps the best way to understand what they are. STICS and other crop modcls have profoundly changed the vision that the agronomie community had of the soil -plant atmosphere system and of ils interactions with cultivation techniques. Il bas a lso changed the way agronomists design experiments and test hypotheses. Important and legitimate questions such as "which is the best sowing density for a crop?'', "is an early c ultivar better than a late one?", "what is the best fertilisation strategy?" have been the subject of hundrcds of experiments in the 60's and 70's. Nobody would now imagine answering them without a mode! because "try it and see" experiments may weil be the worst method for answcring them. due to experimental errors and to the variability of bebaviou r of each genotype in different environmcnts. Although our current knowledge is often poor for dctailcd processes, the behaviour of soil-plant-atmosphcre systems is surprisingly prcdictablc in relation to what could be expected from the synthesis of ali mechaoisms involved in it (Tardieu 2003). STlCS, like other crop models, can thcrcfore help to answer the abovc questions for a wide range of conditions which could never be tested experimentally. The role of experiments bas changed, and is now to check whether experimental results, obLained in a limited number of environmental conditions, are consistent with those of the mode! in a widc range of situations to verify the credibility of the mode! in the studied range of environments (Lyon et al. 2003. Corre Hellou et al. 2007). Lack of agreement between the model and the experiments may suggest ways for improving some aspects of the model.

XI

Coru:eptual basis.formalisations and parametri::ation of the STICS crop mode/ ls this science or engineering (Passioura, 1996)? This lengthy debate ha been largcly fruitless. The same mode! can be uscd for good or unexciting science. for good or inappropriatc engineering. The important point is that the user is able to be critical with L hc mode!. so thal hislher judgcmcnt or decisions after using snes will be the re ult of sorne persona! input and understanding of the model. This is the objective. hopefully fulfilled, of this book.

Making it clcar. that TICS is a tool for reasoning and not a magic wand for prediction. is one of the main aims of this book. The mode! is by no rneans an exact representation of ali the processe mvolved in a virtual experiment. lt is therefore esscntial that the user has access to its workings. i.e. its architecture. equations and paramcters. and that the robustness of equations is discussed and compared with that of other models. The reader can find every single proccss used in the STICS mode!, with its equations and parameters. and with figures which explain the meaning of equations and their consequences on mode! outputs. This gives severa! possibilities to the user. Most skilled users can go int:o the detail of sorne processes, check the consistency of hypotheses with their own ideas, and intcrprct rcsults according to this information (''1 gel this output with thal hypothesis. would 1 gct a different output with this other hypothesis? "). Less ski lied users wi ll use the book for understanding the reasoning wh ich accompanies the equations of a particulnr module. For instance the observations of Figure 5.2 and 5.3 clearly suggest tbat the objective is not to compare the root systems of rape seed, corn and whcat, which vary widely between fields, but to investi gate what happens if the characteristics of the root system change with the species or with the soi! ("examplcs arc given for 3 specics. What would be the behaviour of my favourite species in my soil?").

STICS is ba~ed on ::.impie proccsses. cssentially the same as in other crop models, but with sorne appreciable differences in mcthod This book clearly present the basis for computing the progre~sion ofphcnological stages from temperature. the light interception by leaves following Monteith •s equation, the transpiration following Pcnman Montcith 's equation, and the watcr and nutrient uptakcs following Gardncr's pioneering work. To my knowledgc. thesc fundamcntals do nor diffcr esscntially from thosc of other modcls (Yin andVan Laar 2005. Kcating ct al. 2003) except that the equations uscd in STJCS have been chosen in a more "physics-oricntcd" way than those of other modcls. ln STICS. as in any othcr mode!, things become !css straightforward for simulations of growth and of distribution of assimilates and responses to environmental stresses. The STJCS group was successful in representing complex networks of interactions without gencrating scores of equations and paramctcrs which can never be checked. Are the methods uscd in STICS bcttcr than thosc of othcr models? Another book cou Id be written lo compare the respective value of the algorithms used in different models. For most users, it is enough to know thal mcthods and algorithms are coarse but useful representations of rcality and that they can vary substantially between models, soit may be useful for sorne purposcs to compare the output of STICS with 1hose of other models.

An important sidc cffect of the work of the STICS group has been to providc a common "meeting place" for scicntists of several agronomie disciplines (plant science, soit science and cropping systems), for social scientists and for people working in extension services. This book should hclp to provide a bridge between scientific communities. lt is a necessary tool for scient iSIS who use the snes mode~ for agronomists who are curious about the different topics which can be covered with crop models, and for modcllers of xn -Preface different disciplines who wish to copy the methods of the STICS group. Will geneticists and molecular physiologists join the community of plant modellers? This is a major challenge for the years to come. Progress has been made (Hammer et al. 2006, Struik et al. 2007, Chenu et al. 2008), but these two groups seem reluctant to employ modelling methods (see e.g. Benfey and Mitchell-Olds 2008).

In conclusion, we have to be grateful to the authors, especially Nadine Brisson, for carrying out the huge and difficult task of explaining the detail of ali that is involved in the STICS mode!.

François Tardieu

François Tardieu is a crop scientist and an ecophysiologist who works to fil! the gap between agronomy and genetics. He was involved in projects in which crop mode/ling had an essential role. This. together with his role in scientific management in Inra (France) gives him a wide overview of the uses and concerns of crop modelling.

XIII

The STICS crop model has been developed since 1996 at INRA (French Nationallnstitute for Agronomie Research) in collaboration with ether research and technical institutes.

The model syntheses, illustrates and concretizes an important part of the French agronomie knowledge as a point of view on the field and cropping systems working. The formalisations of the STICS crop model presented in this book can be considered as references used in the framework of crop sciences. They will help professionals and students in the partitioning and understanding of the complex agronomie system. The book arrangement relies on the way the model designs the crop-soil system functioning, each chapter being devoted to a set of important functions such as growth initiation, yield onset, water uptake, t ransformation of organic matter etc. O ne chapter deals with the cropping system and long term simu lat ions and the final chapter is about t he involvement of the user in t erms of option choices and parameterization.

If this book is mainly intended for scientists who use the STICS model, it can also be useful for agronomists, crop modellers, students and technicians looking for elementary formalizations of t he crop-soil system function ing.

Nadine Brisson is a crop scientist, working at INRA She is at the origin of STICS and has a large experience in crop modelling built, for twenty years, from various approaches, issues and crops. She is i nvolved in programs where the model is used in various ways as a heuristic, prospective or experimental tool. She is head of the INRA agrochmatic service.

M arie

  Launay is a crop scientist, wol'king at INRA. She is responsible for STICS agrophysiol09y and is particularly .nvolved in snes adaptation tc new crops. She is 1n charge of tra1ning and communication about the model. She is now at the head of the research proJect on b iotic stress formalizations into the crop model. Bruno Mary is a senior scientist, wori<ing at INRA. He developed the STICS modules devoted to the crop and soil nitrogen balance. For almost thirty years, he has been studying soil C and N cycles by associating experimental • and modelling approaches, either with mechanistic or functional models. He collaborates in several programs concerning C and N storage. N gaseous emissions and N mineralization, in vari ous agro-ecosystems.Nicolas Beaudoin is an agronomist, working at INRA as research engineer. He contrib uted to the soil module concept ion and parameterisation. He uses STICS for predicting nitrate leaching and crop yield at several spatial scales and for studying the long term nitrogen b alance of various cropping systems, including crop devoted to energy p roduction.


All equals in front of inequalities?

Using Strategy Method to observe individuals' reactions in front of inequalities.

(First Draft1 ) Jérémy CELSE2 and Marc WILLINGER 3 Key words: Income Inequality; Decision making process; envy; subjective wellbeing, strategy method. JEL classification: D6, H0, J0.

Mutual comparison is a deep-rooted human behaviour. Living in a society exposes every member to a huge number of comparisons indeed every interaction with another society's member constitutes a source for comparison. Comparing two situations can reveal inequalities and drive necessarily to a status or to a hierarchy: being the well-off if I get more than my opponent (e.g. my neighbour) or on the contrary being the worst-off if I get less than my opponent. A comparison between two individuals is expected to trigger a specific action which depends on the status resulting from this comparison. Indeed, there are some people who only care about their own position and payoff (selfish persons) whereas some individuals are careful about the difference between their situation and the situation of the others (target afterwards), i.e. they do not want to increase or to decrease the existing gap. Not increasing the gap may follow two distinct paths. On the one hand, a subject can wish to invest or to make costly efforts in order to reach the desired and targeted position. On the other hand, a person can be willing to invest in order to reduce the position of the target, even by incurring a cost. While the final result may seem identical, i.e. reduction of the gap, the implications are very different. In the first case, the difference between an individual and his target enhanced individuals to realise constructive efforts which are required to reach the targeted position. In the second case, the action consists in destroying one's efforts to achieve a specific position.

How do people face inequalities? In other words, how do people react against an economic inequality? Can the inequality be a source of emulation, i.e. inducing the individual to make additional and positive efforts which will increase his/her own situation in order to reduce the inequality (i.e. the difference between his/her situation and the other's situation) or on the contrary can the inequality be a source of negative will, i.e. inducing the individual to realise negative efforts in order to reduce the gap by destroying the other's situation? Do people exhibit higher efforts (positive or negative) when the difference is at their advantage or at their disadvantage? Do they care about the difference between their situation and other's situation? Does the absolute difference between one's situation and other's situations exert an influence on individuals' reactions? In other words, do people react differently when the absolute difference is lower than in the case in which the absolute difference is higher? On the contrary, does the relative difference exert a stronger influence on individual behaviour?

We aim at identifying the individuals' reactions to inequalities, measuring the intensity of (re)actions and the influence of both absolute and relative difference between two subject's payoffs, on the individual behaviour. We elaborate an experimental protocol and we use the Strategy Method (Selten, 1967) in order to identify the different forms of (re)actions of people facing a specific economic inequality and to measure their intensity. We are also able to investigate the role and impact of the absolute difference on decision making process. Using Strategy Method we can observe the strategies used by subjects facing different inequalities and their best reply functions.

Relying on previous studies of philosophy, we hypothesize that subjects are more likely to take into account the difference between their situation and the other's situation when the existing gap is low 4 . On the contrary, when the gap between two situations is high, subjects are expected to behave in a selfish way, i.e. maximising their own situation without any regard on the other's situation (e.g. as a PhD student I will not take into account the difference 4 To illustrate our hypothesis we can quote John Rawls who argues that "we tend to compare our circumstances with others in the same or in a similar group as ourselves, or in positions that we regards as relevant to our aspirations." (J. Rawls, A Theory of Justice, 1971, revised edition, Cambridge, Mass., The Belknap Press of Harvard University Press).

(of merit) between my own situation and my PhD advisor's situation, because the gap is too high).

All subjects receive an initial capita. We use four different treatments; the difference between treatments lies in the absolute difference between players' endowments. In the first treatment, the absolute difference between both players is very low and then the absolute difference increases. In all treatments, the relative difference is kept constant; the well-off player receiving an endowment which corresponds to twice the worst-off player's endowment. In the fourth and last treatment, both players receive the same endowment5 . In all treatments, subjects receive information about their own endowment (conditional on the treatment) and about the endowment received by the other member of the pair (opponent afterwards). Then they must choose a specific action among three different actions denoted A, B and C. The first action (labelled action A) consists in investing part of an initial capita in order to decrease the opponent's final payoff. This action is representative of the negative and destructive side of people, the will to destroy one's effort or one's situation in order to decrease the existing gap. Choosing this first action, an individual shows that he is not indifferent to the absolute difference between his/her own endowment and the endowment of his/her opponent. On the contrary, when choosing action B, the subject must decide to invest part of his/her initial capita in order to increase his/her own payoff. Whereas the previous action embodied the negative side of people, this action represents the constructive and positive side of people who care about any existing gap. Choosing this action is a signal sent by the individual indicating that he takes into consideration the gap between his/her endowment and the endowment of the opponent and that he wants to make efforts in order to stand out from the crowd and to achieve a more enjoyable position. In other words; individuals who chose either action A or B take into account the existing difference (although this difference is positive or negative, high or low) in his/her decision making process. The last action (action C) allows the player to win the highest payoff but choosing that action increases the opponent's payoff and as a consequence the present gap.

From first results, we observe that individuals are strongly concerned about the absolute difference between their position and the position of the target individual. Negative actions are very intense (concerning negative actions, subjects chose to invest 82.5% of their initial capita) and only taken by individuals in the worst-off position when the absolute difference is high. By contrast when the absolute difference is low, worst-off players are more likely to choose the last action in order to increase their own payoff; the gap consideration seems to be less important. On the contrary in the same situation, i.e. when the absolute difference is low, well-off individuals act in more selfish way, in other words they maximise their own payoff without decreasing the existing gap and exhibit more intense positive actions (concerning positive actions they chose to invest 86% of their initial capita). Results are different when both players receive the same endowment. Actually players in a situation of equality are more likely to increase their own payoff, the consideration of the existing gap seems to be secondary. Nevertheless players in equal situations exhibit the more intense positive actions (players chose to invest 93.3% of their initial capita in action B).

The absolute difference seems to play a significant role in decision making process, exerting people to take actions in order to reduce the existing gap. Although the Inequity Aversion model (Fëhr & Schmidt, 1999) seems to give accurate predictions of the behaviour of well-off individuals, it fails at predicting the worst-off individuals' behaviour. More treatments still need to be done in order to test the impact of the relative difference on decision making process (using the Equity, Reciprocity and Competition's model developed by Bolton & Ockenfels, 2000).

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Laboratoire Montpelliérain d'Economie Théorique et Appliquée (LAMETA), University of Montpellier. Mail: jeremy.celse@lameta.univ-montp1.fr . Phone: +

04 67 15 83 22. Corresponding author. 3 Laboratoire Montpelliérain d'Economie Théorique et Appliquée (LAMETA), University of Montpellier

Obviously in this last treatment the relative difference is different and equal to 1.


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