Charlotte Merrick
email: c.merrick@lboro.ac.uk

Rochelle Ackerley

Davide Filingeri

Experimental framework and methods for the assessment of skin wetness sensing in humans

Keywords: Wetness, moisture, hygroreception, temperature, thermosensation, touch, mechanosensation, biophysics, psychophysics, skin

The study of the human ability to both detect the presence and estimate the amount of wetness on the skin has grown in scientific interest over the last century, due the implication of wetness in comfort and skin health. In 1900, Bentley demonstrated that skin wetness is detected based on touch and temperature stimuli combining to produce sensations of liquidity, and that wetness perception increases with cold touch. It has since been demonstrated that, in the absence of a skin hygroreceptor (i.e., wetness receptor), the biophysical effects of moisture on the skin -conductive heat transfer and mechanical interaction -excite specific cutaneous mechanoreceptors and thermoreceptors. The resulting afferent signals are centrally integrated to generate our perception of skin wetness. As well as providing a theoretical foundation for the understanding of this aspect of somatosensation, these insights have helped develop a methodological framework for the study of human skin wetness sensing, which relies on assessing the independent and interactive effects of thermo-tactile stimulation of the skin in the presence of a liquid. This chapter will provide an overview of the experimental framework and methods available to evaluate the biophysical and psychophysical responses to controlled dry and wet stimuli applied to skin, and the resulting wetness perception. We will use example scenarios of skin-moisture interactions (e.g., arising from contact with a wet surface or from sweat production), to critically evaluate the methods, noting their accuracy, reliability and efficiency, and discuss their inherent limitations and commonly encountered difficulties. It is hoped that these considerations will guide and further develop research of this relatively littleinvestigated, yet fundamental, aspect of somatosensation.

INTRODUCTION

Humans experience the sensation of wetness every day, for example, when having a shower in the morning, sweating during exercise, or coming into contact with a wet object. The ability to sense wetness enriches our perception, bringing a new depth to sensations, which enhances the way we interpret the world around us. Furthermore, it provides an important signal for behavioural responses, aimed at maintaining both thermoregulatory homeostasis (e.g., sweat-induced skin wetness drives thermal discomfort and triggers coolseeking behaviours) [START_REF] Vargas | Exercise intensity independently modulates thermal behavior during exercise recovery but not during exercise[END_REF] and skin health (e.g., incontinence-associated wetness drives discomfort and triggers drying behaviours) [START_REF] Gray | Moisture-Associated Skin Damage Overview and Pathophysiology[END_REF]. This ability to detect wet stimuli on the skin is termed wetness perception. Wetness is currently believed to be a percept generated in the central nervous system, as humans do not seem to possess hygroreceptors, which are specific receptors for encoding wetness [START_REF] Filingeri | The biology of skin wetness perception and its implications in manual function and for reproducing complex somatosensory signals in neuroprosthetics[END_REF][START_REF] Kim | Hygrosensation: Feeling wet and cold[END_REF]. Such specialised neurons are found in certain insects, and detect and quantify relative humidity. This is in contrast to other sensations, such as touch and temperature, where different types of mechanoreceptor and thermoreceptor encode specific aspects of skin stimulation [START_REF] Ackerley | The role of tactile afference in shaping motor behaviour and implications for prosthetic innovation[END_REF][START_REF] Ackerley | Microneurography as a tool to study the function of individual C-fiber afferents in humans: responses from nociceptors, thermoreceptors, and mechanoreceptors[END_REF]. Given that humans, as well as other animals, frequently come into contact with moisture, and that this interaction is essential in our lives, it is perhaps surprising that hygroreceptors do not appear to exist in mammals [START_REF] Filingeri | Peripheral and central determinants of skin wetness sensing in humans[END_REF]. However, due to the high sensitivity that humans have for detecting wetness, it is of interest to probe how touch and temperature signals convey such a sensation.

History of wetness perception

In 1900, Bentley proposed that the sensation of liquidity was made up of specific components that formed a perception of wetness when combined in specific ways [START_REF] Bentley | The synthetic experiment[END_REF]. To understand how the sensation was formed, Bentley attempted to reconstruct the sensation of liquidity through synthetic experimentation, where he manipulated the substance touched and its temperature to create a wetness illusion. At one point, Bentley writes, "molasses, benzine and even mercury passed under certain thermal conditions for water: an indication of how widely the organism is obliged to draw upon its resources for the completion of so simple a perception as that of a liquid" (1900, p. 415-416). Although the use of dangerous liquids is now not acceptable, this work is still very relevant in modern-day wetness perception research, where we vary specific touch and temperature factors to increase or decrease perceived wetness.

Bentley also demonstrated the difference between passive and active wetness perception, where passively applied liquids were always felt as wet, but with active touch when there was an interaction between liquid on a solid surface and the skin, other percepts such as oiliness appeared. Bentley concluded that actual moisture on the skin is not even sufficient to generate the perception of wetness, as a liquid applied with little change in pressure and/or temperature did not evoke wetness. Further, a wetness illusion could be created where a thin rubber sheath was placed on the finger, which was then lowered into a liquid: the participants truly felt wetness, especially when the water was cold.

A study by [START_REF] Sullivan | The perceptions of liquidity, semi-liquidity and solidity[END_REF] found that, in general, the perception of liquidity was made up of blends of pressure and temperature, while solidity was composed of pressure alone [START_REF] Sullivan | The perceptions of liquidity, semi-liquidity and solidity[END_REF]. Further, the perception of 'semi-liquidity' (viscous liquid) was typically a blend of intense pressure and temperature, whereas liquidity was produced from weak pressure and temperature. In related work in the same period, explorations were made into other concepts associated with liquidity such as stickiness [START_REF] Zigler | An experimental study of the perception of stickiness[END_REF], clamminess [START_REF] Zigler | An experimental study of the perception of clamminess[END_REF], and oiliness [START_REF] Cobbey | An Experimental Study of the Perception of Oiliness[END_REF]. Thesewere linked more to tactile aspects such as the stick-slip phenomenon, in which friction varies during an interaction due to changes in surface tension and adhesive forces, although clamminess was also associated with coolness, and oiliness with warmth. Later work added other related concepts, such as spreadability and viscosity, occurring from specific interactions between wetted surfaces and the skin that are particularly affected by the thermal conductivity of fluids [START_REF] Demartine | Predicting subjective spreadability, viscosity, and stickiness[END_REF].

Work from Gagge et al. in 1967 introduced ideas of thermal comfort, using perceptual scales for both ratings of comfort and temperature sensations. This linked concepts such as sweating, heat transfer, and thermoregulatory physiology together [START_REF] Gagge | Comfort and thermal sensations and associated physiological responses at various ambient temperatures[END_REF]. Sweeney and Branson later took this further by investigating moisture sensation in sensorial comfort, by using both absolute and difference thresholds [START_REF] Sweeney | Sensorial Comfort: Part I: A Psychophysical Method for Assessing Moisture Sensation in Clothing[END_REF] and magnitude estimation to rate moisture sensation [START_REF] Sweeney | Sensorial comfort: Part II: A magnitude estimation approach for assessing moisture sensation[END_REF], including considering comfort in-wear factors. The exploration of wetness has evolved from perceptual descriptions to psychophysical ratings, and these previous studies have allowed us to further develop the investigation of wetness on different levels, such as by accurately manipulating temperature and in the perception of sweating, more of which we cover below.

Directions in wetness perception research

There are many directions in current wetness perception research, which can be discussed most simply when divided according to the source of moisture and underlying research question. For example, one may be interested in investigating the minimum amount of skin wetness that can be detected at the finger pad, as this is relevant to optimise the design of absorbent products that involve individuals touching a wet material to determine its state -consider a parent touching an infant's diaper to check its dryness. In addition, one may be interested in investigating regional differences across the body in the sensitivity to wet fabrics applied on the skin at different moisture saturations. These differences are relevant to optimise the design of sports clothing to maintain comfort during physical activity -consider an individual running and experiencing a sweaty t-shirt sticking to different parts of their torso. Different biophysical and psychophysical assessment methods can therefore be derived depending on whether a detection threshold or magnitude estimation approach is required, that is, whether one aims to determine the intrinsic sensitivity of the skin to moisture, or the participant's ability to differentiate amongst moisture levels and assess their relative salience.

For the purpose of devising appropriate testing methodologies, the interaction between the skin and moisture can broadly be divided into two categories: one where the source of moisture is external to the body such as touching a cloth to determine if it is wet, or when wet clothing rubs against the skin; and one where the source of moisture is internal to the body, such as when sweat, urine, teardrops, or other bodily fluids are produced. This initial differentiation is essential, as it determines the specific scenario within which skin-moisture interactions will occur, and the resulting thermo-tactile inputs https://www.springer.com/series/7657 2 that are likely to take place at the skin interface. Ultimately, this initial evaluation will inform the development of specific hypotheses as well as the appropriate experimental methods. In short, thermal factors may be more relevant for externally-generated and mechanical factors than for internallygenerated moisture (Figure 1). When moisture is externally generated (e.g., when touching a wet object), one may expect that thermal factors like moisture temperature and the related heat transfer, may be highly variable, and therefore play a larger role in determining variance in our wetness perception. By contrast, when moisture is internally generated (e.g., when sweat is produced), the thermal conditions are more constrained -sweat temperature is likely equal to skin temperature). Accordingly, the biophysical and psychophysical assessment of thermal cues when moisture is externally generated may take priority over the evaluation of mechanical components.

Conversely, when moisture is internally generated (e.g., incontinence) one may expect that mechanical factors such as the adhesion and friction of wet continence pads to the skin, may play a greater role than thermal factors such as elevated temperature and humidity in the microclimate surrounding the skin and the incontinence pad. In this case, the biophysical and psychophysical assessment of tactile cues when moisture is internally generated may take priority over the evaluation of thermal components.

The methodological framework outlined above is presented schematically in Figure 1, which provides a flow diagram for method selection. In this chapter, we use three examples to highlight potential methodological pathways. These examples are not exhaustive, and we would like to emphasise that, as this field is ever expanding, alternative methodologies and approach could be developed. Yet, we believe that the theoretical foundation of these examples related methods cover a broad spectrum of conditions and could form the basis for further methods development. The first of these examples will focus on evaluating wetness detection thresholds from touch interactions between the index finger pad and externally wet stimuli, and assessing threshold modulations at different moisture temperatures. The second will focus on comparing wetness perception of stimuli applied to various locations across the body and the production of associated body maps. Finally, postexercise skin wetness perception will be examined, considering sweat production and different tactile inputs. The production of a consistently implemented methodology is critical in this research field as it not only allows for a wider comparison of scientific constructs, but also presents possibilities to develop specific informative and diagnostic tests. This is relevant in industrial applications, for example the improvement of moisture management products [START_REF] Merrick | Skin wetness detection thresholds and wetness magnitude estimations of the human index fingerpad and their modulation by moisture temperature[END_REF], within clinical contexts such as the design of early diagnostic tests for individuals with sensory disorders [START_REF] Filingeri | Why wet feels wet? A neurophysiological model of human cutaneous wetness sensitivity[END_REF], and in leisure and performance applications such as the management of sweat patterns in sports clothing [START_REF] Farage | Evaluation of modifications of the traditional patch test in assessing the chemical irritation potential of feminine hygiene products[END_REF].

MATERIALS 2.1. Hardware

The typical hardware that may be used in wetness perception experiments [20] [21] [22] [START_REF] Vargas | Thermal behavior alleviates thermal discomfort during steady-state exercise without affecting whole body heat loss[END_REF] are:

1. Force plate (e.g., 0 to 5 N) 2. Thermal plate and controller (e.g., 10 -45 °C) 3. Thermal probe (consider the size and temperature of the probe, e.g., 10 -45 °C) and controller (e.g. Physitemp Instruments Inc., Clifton, NJ, USA) 4. Water bath(s) to change the temperature of applied liquids (e.g., 15 -45°C) (e.g. Techne FRB2D, Cole-Parmer, Stone, UK) 5. Thermocouples to measure surface temperature (e.g., 0.08 mm wire diameter, 40 Gauge) (e.g. 5SRTC-TT-TI-40-2M, Omega, Manchester, UK) 6. Indoor air quality monitor or combined thermometer and hygrometer to measure air temperature and humidity (e.g. 440dP, Testo, Lenzkirch, Germany) 7. Infrared thermometer to measure surface temperature remotely (e.g. TG56, FLIR Systems, Wilsonville, OR, USA) 8. Items to obscure the stimulation from the participant, depending on the type of perceptual assessment scales used (e.g., screen, glasses, headphones) 9. Scale and stadiometer or tape measure (for measuring weight and height of the participant) 10. Climatic chamber 11. Water perfused suit [START_REF] Filingeri | Why wet feels wet? An investigation into the neurophysiology of human skin wetness perception[END_REF]:

Consumables

1. Skin tape (e.g. 25 mm width Transpore, 3M, Loughborough, UK) 2. Graduated plastic syringes 3. Tissues

Environmental conditions: Depending on the experiment, specific thermal and humidity conditions may be required, but typical, standard, or neutral conditions would be a room between 20 and 25 °C and roughly 50% relative humidity depending on clothing, with atmospheric pressure around 100 kPa.

METHODS

Investigations of wetness perception rely heavily on the use of single-blind psychophysical testing (Notes 4.1 & 4.2) 00 . This is a branch of sensory examination which focuses on the quantification of specific modalities such as haptic touch, thermal inputs and auditory cues. It relies on a stimulus-response paradigm (Note 4.3) 0 , in which a series of specific stimuli are prepared by an experimenter and are introduced to a participant wearing a blindfold or otherwise visually obscured from the stimulus (Note 4.4) 0 . The participant's sensory responses are recorded, and the collation of these responses across various conditions allows the target sensory modality to be further assessed according to the chosen psychophysical test [START_REF] Ehrenstein | Psychophysical methods[END_REF]. Psychophysical testing can be broadly divided into two categories depending on the desired nature of the outcome: threshold determination & magnitude estimation (Notes 4.3-4.5). The first of these is threshold determination, which use a series of stimuli varying across a range of predetermined characteristics. In classical psychophysics, the stimuli can be introduced to the participant in several ways: the method of limits that increases the magnitude of a stimulus until a specific response is reached; the method of constant stimuli in which the stimuli are introduced in a random or balanced order; and the method of adjustment, in which the participant adjusts the stimulus magnitude to a certain detection level, or to match another stimulus. Thresholds can also be estimated using adaptive staircase procedures, in which changes to the stimulus are made according to the participant's previous response(s), thus allowing the progressive and specific testing of a particular threshold [START_REF] Hatzfeld | Human perception measures for product design and development-a tutorial to measurement methods and analysis[END_REF][START_REF] Treutwein | Adaptive Psychophysical Procedures[END_REF]. The establishment of the detection threshold can either be in its absolute state, showing the minimum magnitude of a stimulus required to elicit a positive response, or as a differential threshold, which denotes the minimum difference between stimuli for them to be perceived as different [START_REF] Ehrenstein | Psychophysical methods[END_REF]. The threshold determination methodologies in this chapter will focus on absolute values.

A second form of psychophysical testing is magnitude estimation. This can also be approached in two ways, the most common being the sequential presentation and subsequent rating of a stimulus. This involves, for example, a continuous visual analogue scale on which the participant must mark a point to reflect their perception, an unbounded rating scale where the participant uses their own ratings to quantify a percept that can subsequently be normalised, or a graduated Likert scale forming of a series of descriptors with numerical counterparts. Alternatively, a participant may be presented with a stimulus and be asked to generate one of equal magnitude using the method of adjustment [START_REF] Breedlove | Biological psychology : an introduction to behavioral, cognitive, and clinical neuroscience[END_REF], but this technique is likely to be of less use in wetness perception due to the methods required to create the stimulus.

Participants

Participants are typically screened for inclusion criteria to limit the variance of results and maintain applicability to a healthy population, unless a different population is specifically required. For example, it is preferable to recruit individuals from a specified age range, such that they will understand and comply with testing protocols but not have any degenerative sensory disorders [START_REF] Peters | The Effects of Normal Aging on Nerve Fibers and Neuroglia in the Central Nervous System[END_REF]. For example, participants under 30 years old may be preferred, as both touch and temperature detection sensitivity decrease with age [START_REF] Stevens | Spatial Acuity of the Body Surface over the Life Span[END_REF][START_REF] Stevens | Temperature sensitivity of the body surface over the life span[END_REF]. Lifestyle factors can also be considered, such as the recruitment of nonsmoking individuals. Prolonged smoke exposure can make individuals more susceptible to dermatological diseases and actively contributes to peripheral neuropathy, which would interfere with sensation [START_REF] Ortiz | Smoking and the skin[END_REF].

Body mass can be considered, as participants having a body mass index (BMI) above 30 kg m -2 , may have some degree of peripheral nerve impairment [START_REF] Yadav | Somatic neural alterations in non-diabetic obesity: a cross-sectional study[END_REF]. The same applies to a alcohol consumption above the recommended weekly alcohol intake, as exceeding this limit can result in both physical and psychological interference [START_REF] Schrieks | Influence of moderate alcohol consumption on emotional and physical well-being[END_REF]. It is also preferable for individuals to not be taking any long-term medication, as the somatosensory effects of these may be unknown or hard to quantify. Finally, participants should not have any long-term somatosensory disorder, such as peripheral neuropathy, which may interfere with perceptual ratings.

While exclusion criteria are generally quite uniform and similar between tests, participants may also be recruited for specific characteristics. For example, in clinically-focussed studies there may be a need to recruit target individuals along with matched controls. Participants may also be required for sensory comparison studies, such as identifying perceptual differences between males and females, from different countries or environmental factors, or pre-and post-partum women. Provided all choices have a justifiable scientific basis, this is a fairly flexible component of the methodology.

Where appropriate, prior to the scheduled testing, participants' body mass and height should be recorded with a digital scale and stadiometer in order to determine their BMI and hence confirm eligibility for the study. This also applies to the completion of a health screen questionnaire to highlight any matches with the exclusion criteria. The number of participants required can be established using a sample size calculation based on data from previous or pilot studies.

Experimental Protocol 3.2.1. Example 1: Wetness detection -external moisture and active touch

The investigation aimed to establish the wetness detection threshold of the human index finger pad during active touch, and assess its modulation by moisture temperature [START_REF] Merrick | Skin wetness detection thresholds and wetness magnitude estimations of the human index fingerpad and their modulation by moisture temperature[END_REF]. This was achieved using a single-blind repeated measures design. Stimuli consisted of textile samples varying in the applied liquid content across the range of 0 ml -50 ml, which was determined during pilot studies. Each of the six wetness levels were repeated multiple times and introduced in a balanced order. Each participant attended four experimental sessions, with each session representing a different temperature condition.

At the beginning of each experimental session, participants underwent a familiarisation detailing the protocols and a calibration to show the extremes of the perceptual scales and provide experimental context. During experimental sessions, they touched with the sample using only the index finger pad and provided transient responses using a modified yes/no task, in which they had to select from either 'dry' or 'wet' descriptors on a digital screen. Prior to the start of each experimental session, 1 L of water was placed into a small manually controlled thermal chamber which maintained temperature at either 25.1 °C, 29.2 °C, 33.4 °C or 37.7 °C ± 0.1 °C. These temperatures were established during pilot studies to account for thermal changes which occur during sample preparation, such that the initial participant contact with the substrate would be at 25 °C, 29 °C, 33 °C or 37 °C. Different volumes were applied to individual stimuli to moisten them prior to participant interaction using 0 ml, 10 ml, 20 ml, 30 ml, 40 ml or 50 ml of water applied with a graduated syringe.

When participants arrived at the laboratory, their height was recorded with a stadiometer and weight recorded with a scale to confirm eligibility for the study. Participants were seated for the duration of the experiments. Prior to experimental interactions, participants were familiarised with study protocols and rating scales to ensure they were correctly and consistently used. The protocol involved four different stimulus combinations; cold-wet, warm-wet, cold-dry and warm-dry, which demonstrated the extremes of each possible wetness and thermal combination. Each stimulus was presented under standard test conditions and the most appropriate response on the psychophysical form shown, providing a frame of reference as well as acquainting participants with procedures.

Following the familiarisation, a single thermocouple was affixed to the centre of the index finger pad using surgical skin tape, ensuring the thermocouple tip was in contact with the skin but not covered by tape. Participants then placed their non-dominant hand through an aperture in an Lshaped screen which obscured the experimental set up from sight and hence limited visual cues (Figure 2). The base of the screen included a foam mat to reduce conductive heat transfer and could be inverted to allow for left-or righthand dominance. Participants placed their index finger on a fixed-position thermal plate (Figure 2), which maintained a neutral skin temperature (Tsk) at 33 °C and hence established a thermal baseline. When the stimulus had been prepared, the participant was given the command 'contact' and moved their hand from the thermal plate to contact the stimulus at a static resting pressure. Participants had previously been informed of the commands and the positioning and transfer of the finger has been demonstrated and practiced. The stimulus was always positioned correctly below the finger, and was slightly adjusted before contact if necessary. Upon transient contact participants completed a digital form to record their perceptions, taking no more than 3 s. Both a dichotomous response method (dry/wet) and a 100 mm visual analogue scale (very dry to very wet) were used. The responses associated with the dichotomous method were assigned binary scores for subsequent analyses, with a 'dry' response as 0 and a 'wet' response as 1.

After a contact period of 3 s the participant was prompted to remove their finger from the stimulus using the command 'lift'. Post-contact perceptual assessments, analogous to those used during contact, were completed again within 3 s. When finished, participants used the command 'done', at which point the stimulus would be replaced with a cotton towel. The participant was instructed 'dry', and would statically press their index finger on to the dry towel to collect residual water for 5 s. This was repeated regardless of wetness to prevent any learning effect or bias. Before the next stimulus, the participant's index finger was returned to the thermal plate to maintain Tsk at 33 °C. This also served as a perceptual refractory period with a minimum duration of 20 s, during which time the next stimulus was prepared before cyclically repeating the protocol. All stimuli were repeated and presented in a balanced order. Each participant attended individual experimental sessions for the different temperature conditions.

Overall, detection threshold tests are slightly more time consuming than magnitude estimation tests as they require a large number of repeats, both within and between participants, to provide a high resolution and low noise output. However, they have been shown to be a reliable methodologies that participants readily complete [START_REF] Ehrenstein | Psychophysical methods[END_REF].

Example 2: Wetness magnitude estimation -external moisture and passive touch

The method aimed to establish differences in regional wetness sensitivity across the body, which was achieved using a single-blind psychophysical approach [START_REF] Valenza | Thermosensory mapping of skin wetness sensitivity across the body of young males and females at rest and following maximal incremental running[END_REF]. A series of sites were mapped across the left and medial areas of the body, assuming perceptual symmetry on opposite sides of the body. Participants underwent a brief familiarisation detailing the study protocols and a calibration using the volar, or palm-side, of the forearm. The stimuli consisted of a square thermal probe with a contact surface of 25 cm 2 with attached cotton square, to which 0.8 ml of water was applied. The temperature of the probe was regulated to be either Tsk -5 °C, Tsk, or Tsk + 5°C, as established with an infrared thermometer for a specific site, with each temperature condition representing a different experimental session. The stimuli were contacted sequentially on the mapped sites, during which time participants reported the local wetness sensation on a digital visual analogue scale, from dry to completely wet.

At the start of an experimental session, participants arrived at the laboratory and changed into specified test clothing. Their body mass was recorded using a digital scale and their height using a stadiometer. A washable marker pen was then used to indicate the stimulation sites across the left and medial body. Following preparation, participants sat at rest for 15 minutes to adjust to environmental conditions, during which time they were familiarised with the experimental procedures. Calibration procedures consisted of six stimuli varying in both temperature and wetness (dry, Tsk -5 °C; wet, Tsk -5 °C; dry, Tsk; wet, Tsk; dry, Tsk + 5 °C; wet, Tsk + 5 °C), which were applied to the left volar forearm in a randomised order. Participants were instructed to associate each stimulus with the anchor points on the visual analogue scale.

Participants were instructed to stand throughout experiments. The local Tsk at the first test site was recorded using an infrared thermometer. A square thermal probe (Figure 3) was set at the corresponding test temperature (either Tsk -5 °C, neutral Tsk, or Tsk + 5 °C). A 100% cotton fabric swatch was then applied to the thermal probe and wetted with a pipette using 0.8 ml of water to ensure full saturation. Participants were notified just before stimulus application, at which point the stimulus was applied statically on the skin site for 5 s. During this time the participant completed their perceptual rating, and the stimulus was removed before proceeding to the next skin region. The order of testing was counterbalanced between thermal conditions, and the order of body regions was counterbalanced between and within participants.

Overall, the use of visual analogue scales in magnitude estimation studies is simple and efficient. The basis of the psychophysical rating scales is easy for participants to grasp, potentially due to many similar real-life scenarios in which they are employed, and is a rapid way to collect large data sets. This rapidity can be mostly attributed to the use of digital rating scales, as hard copies require manual measurements that are very time consuming and can easily lead to errors. However, consistent results are highly reliant on the correct explanation and calibration of rating scales, such as giving examples for anchor points, stating if there is a midpoint to the scale, or clarifying whether it is linear.

Example 3: Wetness magnitude estimation -self produced moisture and active interaction

The study aimed to establish if the perception of skin wetness can be significantly altered by manipulating tactile cues, independently from the level of physical skin wetness [START_REF] Filingeri | Tactile cues significantly modulate the perception of sweat-induced skin wetness independently of the level of physical skin wetness[END_REF]. This was achieved using an incremental walking protocol which caused participants to consistently generate physical skin wetness in the form of sweat. Prior to beginning, participants were familiarised with the experimental protocols and allowed to acclimate to the surroundings. The walking protocol was conducted under two conditions, one using a tightfitting shirt and the other using a loose-fitting shirt. In each condition, wetness perception was recorded using verbal responses to a 7-point Likert scale every four minutes (-3 dripping wet; -2 wet; -1 slightly wet; 0 neutral; +1 slightly dry; +2 dry; +3 very dry).

On experimental days, participants were requested to arrive at the laboratory 30 minutes prior to their scheduled start time to allow for preparation of procedures and bodily acclimation. Before beginning, participants were asked to void their bladder and their semi-nude body mass was recorded on a digital scale. Participants then wore the first layer of either tight-or loose-fitting clothing and were asked to rate their wetness in order to establish a baseline of sensation. Participants then put on the second layer of clothing, consisting of an impermeable jacket and trousers to prevent sweat dissipation.

Participants were moved to the treadmill where they began the 45 minutes incremental walking protocol (5 km h -1 ; gradient: +2 to +16 %). During the protocol, participants were instructed to rate their wetness sensations every five minutes. As soon as a slightly wet response was given, participants were requested to detail whether this included chest, back, arms or thighs, and of these which was the wettest. Subsequent to finishing the walking protocol, participants removed their clothing, at which point their semi-nude body mass was again recorded. With a minimum of 48 hours separating the trials, the protocol was repeated, this time using whichever of the tight-or loose-fitting clothing options that was not previously worn.

Like visual analogue scales, the use of Likert scales to collect perceptual data is simple and efficient. It is easy for participants to comprehend and allows them to rate their perceptions while undergoing other continuous uninterrupted tasks, for example during exercise. An issue which can occur in such scenarios is the size and position of the scale, as it needs to be clearly legible for participants. Again, consistent results rely greatly on the correct explanation and calibration of rating scales.

Analysis

Example 1: Wetness detection -external moisture and active touch

In this study, the independent variables were temperature and volume. Wetness perception was the dependent variable. Coding dry and wet responses as 0 and 1 respectively allowed a perceptual response ratio to be calculated for any given volume. For example, 5 dry responses and 7 wet responses would generate a value of 0.42 (5/12). Perceptual ratios and corresponding volumes were plotted against each other and fitted with a sigmoidal curve. The point at which the response exceeded 0.5 (50 %) was considered the threshold for wetness detection. The threshold values were established for every participant by reading the volume at the 0.5 intersection, and means calculated for each participant and each temperature condition (Figure 4).

Example 2: Wetness magnitude estimation -external moisture and passive touch

The dependent variable in the study was wetness perception, while the independent variables were stimulus location and temperature. Changes in perceptual responses can be mapped to show regional variations in wetness perception and show how these perceptions are correlated with stimulus temperature (Figure 5). This gives insights into regional sensitivity at different temperatures as well as intra-and inter-individual variability. Similarly, if sufficient participants are recruited, the information can reflect differences in perception according to sex, age and other demographics, or under different conditions, such as pre and post exercise. Due to the large number of variables, an ANOVA model is typically used to assess changes in the dependent variables.

Example 3: Wetness magnitude estimation -self produced moisture and active interaction

In this study, the independent variables were condition (loose-and tight-fitting clothing) and time (10 levels, in 5-minute intervals). The dependent variable was wetness sensation. The mean wetness sensation at each 5-minute time interval was established across participants in both the loose-and tight-fitting clothing conditions. As wetness sensation was recorded on a Likert scale and constitutes ordinal data, a non-parametric method was used to assess if there were significant differences between the two conditions as a function of time. A graphical representation is shown in Figure 6. Despite that during both tight-fit and loose-fit trials the level of physical skin wetness did not differ at any time point, the overall perception of skin wetness was significantly reduced during the tight-fit trial as opposed to the loose-fit trial. This main effect significantly interacted with time, 20 min after the exercise protocol was initiated (*P < 0.05) [START_REF] Filingeri | Tactile cues significantly modulate the perception of sweat-induced skin wetness independently of the level of physical skin wetness[END_REF]. (pending permission for republication).

NOTES 4.1. Participants' needs

While there are many hypotheses that researchers would like to investigate, all of the psychophysical experiments must account for the needs of participants. It is important that participants fully understand the nature of the task and what is required of them, and this should be explained clearly, concisely, and hopefully with some enthusiasm. The use of consistent commands such as 'lift', 'touch' or 'dry' will also act as signposting points which help to guide participants through stimuli interactions until they become almost rhythmic. Depending on the nature of the methodology, it may be useful for specific interactions to be demonstrated or for participants to practise them to improve technique and consistency as part of a familiarisation process. However, the sufficient learning of protocols needs to be balanced with limiting potential for learning effects or response bias. The need for clarity also applies to the use of rating scales and calibration protocols, such giving examples of anchor points, encouraging participants to rate stimuli independently or simply reassuring them to trust their own judgement.

Experimental duration

There should be an established timescale that participants are aware of. This aims to ensure that they complete the tasks and corresponding perceptual recordings effectively, without either lingering or rushing. Additionally, an optimum length of session needs to be established. The more research data that needs to be collected, the longer an experimental session will take, and may require splitting into smaller sessions. If a single session is too long, participants may lose motivation, become distracted, rush or otherwise disengage with the task. However, it is also important to set boundaries within the experiment and know when to do when participants do not comply with the protocols of the test or fail to attend sessions.

Experimental design

Depending on the specific methodology, different aspects of the experimental design may need to be considered. A common aspect is the repetition of stimuli, which needs to be established based on the desired resolution, accuracy and precision of the resulting data, as well as accounting for time constraints (Note 4.2). The order in which stimuli are presented also needs to be decided, both within and between participants, such as presenting stimuli in a counter balanced as opposed to a random order. If there is long term exposure to wetness, changes in physical skin characteristics such as increased hydration levels or dermal plasticity should also be considered and the study adjusted accordingly.

Another aspect to consider in the experimental design is the potential of heat transfer, be this between stimuli, participants, or the ambient environment. For example, a solution is prepared at 35 °C and applied to a fabric sample. By the time interaction occurs, heat energy may have been lost to the ambient environment such that the actual temperature is much lower than anticipated.

Merrick, C, Ackerley, R & Filingeri, D (2022). Wetness perception in humans. In: Holmes NP (Ed). Somatosensory Research Methods. Springer Neuromethods, Berlin (in press).

https://www.springer.com/series/7657 6

This can be accounted for by assessing the thermal decay across the range of samples and adjusting temperatures accordingly.

Between-participant variation

Additionally, variation between participants that is not being regulated as part of inclusion criteria needs to be considered. For example, when creating an Lshaped obscuring screen to limit visual cues for participants, both the varying diameter of participant arms, their seated eye level, and hand dominance needs to be accommodated. While this may seem trivial, it may interfere with interactions and subsequent perceptions.

The psychophysical task

A clear distinction between psychophysical approaches needs to be maintained. In the determination of sensory thresholds, both a two alternative forced choice method (2AFC) and a yes/no task basis (Y/N) are used (see also Chapter 1). The 2AFC allows participants to choose which of two stimuli correspond best to a single descriptor, whereas Y/N involves only a single stimulus to which either a positive or negative response must be assigned [START_REF] Green | General Prediction Relating Yes-No and Forced-Choice Results[END_REF][START_REF] Schulman | Operating Characteristics from Yes-No and Forced-Choice Procedures[END_REF]. The latter is often modified such that the single stimulus is assigned to one of two opposing descriptors. Both 2AFC and Y/N can be equally effective in determining different physiological measures, but their success is pivotal on the accompanying methodology.

Temperature manipulation

While approaches to manipulating temperature vary, many are applicable with appropriate justification. For example, when stimuli and the skin are in contact, the stimulus could either have been manipulated in relation to physical skin properties (e.g., Tsk -10°C), or the skin itself can be maintained at a specific baseline condition (e.g., 33 °C) to ensure the same transient magnitude of change between participants. Typically, the former is used in passive touch and the latter in active touch studies.

  Merrick, C,Ackerley, R & Filingeri, D (2022). Wetness perception in humans. In: Holmes NP (Ed). Somatosensory Research Methods. Springer Neuromethods, Berlin (in press).

Figure 1 :

 1 Figure 1: The methodological framework outlined in the chapter presented schematically as a flow diagram. (theoretical framework pending permission for republication).

Figure 2 :

 2 Figure 2: L-shaped obscuring screen used to limit visual cues available to participants with multiple apertures to allow for variations in participant hand dominance (left) and modifiable thermal plate used to maintain skin temperature of participants between stimuli (right).

Figure 3 :

 3 Figure 3: A square thermal probe which was wrapped in wetted cotton fabric and applied to participants' skin.

Figure 4 :

 4 Figure 4: An example of the sigmoidal curves fitted for each respective temperature within a single participant. Each point represents the ratio of responses from repeated stimuli with 95% confidence intervals.

Figure 5 :

 5 Figure 5: Body maps of wetness perceptions in males (n = 10) and females (n = 10) resulting from the application of the cold wet, neutral wet and warm wet stimuli at rest [34]. (pending permission for republication).

Figure 6 :

 6 Figure6: Means ± SD (n = 10) for wetness perception across time throughout the tight-and loose-fitting trials. Despite that during both tight-fit and loose-fit trials the level of physical skin wetness did not differ at any time point, the overall perception of skin wetness was significantly reduced during the tight-fit trial as opposed to the loose-fit trial. This main effect significantly interacted with time, 20 min after the exercise protocol was initiated (*P < 0.05)[START_REF] Filingeri | Tactile cues significantly modulate the perception of sweat-induced skin wetness independently of the level of physical skin wetness[END_REF]. (pending permission for republication).

  Merrick, C,Ackerley, R & Filingeri, D (2022). Wetness perception in humans. In: Holmes NP (Ed). Somatosensory Research Methods. Springer Neuromethods, Berlin (in press).

https://www.springer.com/series/7657 3

Funding: This work is funded by a European Research Council (ERC) Consolidator grant under the European Union's Horizon 2020 research and innovation programme [grant agreement No. 772242 to R. Ackerley] and by an Engineering and Physical Sciences Research Council (EPSRC) iCASE award (Project Reference: 1965689 to C Merrick and D Filingeri).

Conflicts of interest: None.


Dr Sandrine Maljean-Dubois

Climate litigation: The impact of the Paris Agreement in national courts

Keywords: climate change, litigation, Paris Agreement, interpretation, international law

The slowness and lack of ambition of climate policies have led, in recent years, to the development of a new type of litigation: climate litigation. Various States in the North and South have already been ruled against by national courts because of the inadequacy of their action to reduce greenhouse gas emissions, and litigation is multiplying throughout the world. Here, the international climate regime is likely to make a contribution the magnitude of which was somewhat unexpected. Indeed, the Paris Agreement is a relatively flexible treaty, leaving a very wide discretion to States as to its implementation. However, the way it was designed, and even though its provisions have no or little direct effect, the Agreement increases the pressure on States, including, and perhaps most importantly, at the domestic level. In this article, we show that the Paris Agreement, thanks to the involvement of civil society, has provided fuel for climate litigation in a decisive manner and offered national courts the opportunity to position themselves as key players of climate governance.

Climate change is a serious and urgent global threat that calls for profound changes in our societies. It constitutes a challenge for our legal systems, revealing their inadequacy to deal with such a vital issue. Beyond the distinctions between public and private law, between national and international law, climate change exemplifies and accelerates changes in the ways in which the law is made and applied in a globalised context. For all these reasons, climate change undoubtedly constitutes a good "laboratory" for governance, seeing as it requires permanent interaction between States, international organisations, non-state actors, businesses, experts, and citizens. In order to be powerful, these forces must push in the same direction and thus, at the very least, coordinate their actions through vertical and horizontal interactions. 1 On this subject, the slowness and lack of ambition of climate policies have led, in recent years, to the development of a new type of litigation: climate litigation. Around 2,300 climaterelated lawsuits have been tried or are pending, and this number is still growing. 2 Various States in the North and South have already been ruled against by national courts because of the inadequacy of their action to reduce greenhouse gas emissions, and litigation is multiplying throughout the world. Legal action has also been brought by towns, cities, NGOs, groups of citizens (American children from Our Children's Trust, Swiss senior women, a law student from New-Zealand...) against major corporations whose activities are allegedly causing global warming. Globalised and transnational, these proceedings in some respects break down national borders. 3 Faced with what is perceived as a failure on the part of public authorities and companies, the law is increasingly relied on and used as a "weapon" to serve various objectives: to encourage public authorities or companies to take stronger measures to mitigate climate change, to implement more ambitious policies, to obtain compensation for damage suffered, to stop a project that emits large quantities of greenhouse gas, etc.

Here, the international climate regime is likely to make a contribution the magnitude of which was somewhat unexpected. Indeed, the Paris Agreement, which was adopted on 12 December 2015 and quickly entered into force, and which now counts 195 signatories and 191 Parties, is a relatively flexible treaty, leaving a very wide discretion to States as to its implementation. In order to convince (almost) all States to become Parties, the form and substance of the Paris Agreement were adjusted in comparison to its "predecessor", the Kyoto Protocol. The compromise reached in Paris illustrates a certain evolution of the way States commit themselves. In this regard, the form and substance of the Agreement have been carefully crafted to allow for a consensus to be reached, a consensus that seemed unachievable a few months before. However, the way it was designed, and even though its provisions have no or little direct effect, the Agreement increases the pressure on States, including, and perhaps most importantly, at the domestic level. Indeed, in this article we will show that the Paris Agreement, thanks to the involvement of civil society, has provided fuel for climate litigation in a decisive manner and offered national courts the opportunity to position themselves as key players of climate governance.

I. The Paris Agreement, fuel for climate litigation

The Paris Agreement has boosted the explosion of climate litigation, providing an entry point for international law in these proceedings, and contributing to the emergence of a "global judge" figure .   1) The explosion of climate litigation boosted by the adoption of the Paris Agreement The effects of the Paris Agreement have been amplified by more general developments, leading courts in many countries to rely increasingly on international law. After having long played a very marginal role in national courts, international law is now part of their daily routine. 4 Measurable in quantitative as well as qualitative terms, this phenomenon has been confirmed by more general studies that link this development to the normative expansion of international law and to the increasing interdependence of States in the context of globalisation. 5 The increased presence of international law is also the direct consequence of the growing openness of States to international law.6 All this is leading national courts to think "outside the 'Westphalian' box" marked by the lack of permeability between the international and national spheres. 7 There are several reasons why the Paris Agreement has amplified this phenomenon, putting the field of climate change in the vanguard with regard to the use of international law by national courts. First of all, it is a treaty, and national courts are known to refer more readily to treaties than to international custom or court rulings, because of their advantages in terms of clarity and ease of access for those not familiar with public international law.8 Second, the Paris Agreement is a treaty "for internal consumption".9 Its provisions are mainly designed to penetrate national legal systems; their implementation makes it indispensable. This is all the more true given that the Agreement, in its design, combines the international definition of an ambitious collective goal of limiting global warming with an implementation tool, the so-called nationally determined contributions, the content, form and scope of which are almost entirely up to the Parties, to whom a very wide discretion is thus given. What could be analysed as a congenital weakness of the Agreement has actually "boosted" climate litigation and allowed claimants to define effective legal strategies.10 Third, the Paris Agreement was given an international control mechanism that is much less intrusive and much weaker than its predecessor the Kyoto Protocol. Combined with the fact that it is difficult to bring a case before an international court in the event of a violation, the shortcomings of international enforcement mechanisms here too lead to increased pressure on the national level with regard to implementation.11 Lastly, the extensive media coverage of COP21, during which it was adopted, has put the Agreement in the spotlight; it is probably one of the best-known international treaties outside a circle of specialists. The publicity surrounding the IPCC report on 1.5°C, warning of the urgency and of the closing of the window of action has further strengthened the mobilisation of public opinion. The constitution of a real "international" of activist lawyers working for associations and forming, with a committed academic community, an international "epistemic community" at the service of climate did the rest.12

2) The Paris Agreement, an entry point for international law into climate litigation Although the provisions of the Paris Agreement are only one of the elements invoked amongst other rules of international law, the Agreement is generally at the heart of arguments as well as decisions. It is almost always the entry point for other rules of international law. Here as well, this is a more general phenomenon that has already been described elsewhere. In this respect, some have spoken about a clustering of international law references, "as decisions that cite one kind of international legal material are likely to cite other kinds as well". 13 In particular, courts are often led to invoke other international sources -customary rules, soft law instruments -to help them interpret and apply treaty rules. 14 In climate trials, claims are usually based on several sources of international and domestic law. Claimants demonstrate a certain inventiveness, inviting judges to combine sources and norms in a synergistic manner. 15 Interpreting one norm in the light of another can then make these norms say more than if they were applied in isolation (and thus more than they say).

From the point of view of formal international sources, treaty rules are generally combined with customary rules, but sometimes also with soft law decisions of Conferences of the Parties. In terms of substance, the rules of the international climate regime are combined both with general rules (such as customary duties of care) and with other specific rules. The combination of international climate law rules and international human rights law rules is also increasingly invoked. 16 Courts are then asked to read the States' obligations regarding the protection of human rights in the light of their climate obligations, whether in a national court, 17 or before international human rights protection bodies such as the United Nations Committee on the Rights of the Child 18 or the European Court of Human Rights. 19 The Urgenda case demonstrated a particularly synergistic interpretation of a combination of customary norms (the Dutch duty of care or no harm rule), treaty rules under international human rights law, together with the objectives and principles of the United Nations Framework Convention on Climate Change (UNFCCC). 20 This combination can be found in most similar cases, such as in Belgium, with Klimaatzaak, currently pending before the Brussels Court of Appeal, where the Court of First Instance found that there had been violations of Articles 2 and 8 of the European Convention on Human Rights, read in the light of the duty of care of the good family father (or the reasonable man in Common Law), a standard itself informed by the Paris Agreement. 21 Finally, the IPPC reports have been relied on effectively in many cases. Although they have no legal value, as scientific reports, they have the advantage of reflecting the global consensus of scientists on the subject, a sort of "international truth". The summaries for policymakers that accompany the reports -and which are the parts relied on in court -also carry a particular weight since they are co-approved by scientists and representatives of States. In the New-Zealand Thomson case, the court thus noted that "The IPCC reports provide a factual basis on which decisions can be made". 22 Furthermore, it held that the government should review its long-term objective every time the IPCC publishes a new report, viewing it as a "mandatory relevant consideration". 23

3) The Paris Agreement, a cornerstone for a "global" justice In these cases, courts find support in the case law of other domestic courts. This is, here again, a more general phenomenon, 24 but one that shows very clearly in climate cases. The Internet and the publication of foreign decisions facilitate access to foreign legal decisions. This is all the more true in the field of climate change where two very regularly updated databases publish petitions and judgments. 25 Courts have become accustomed to looking at what other judges have written before them. They know the worldwide publicity that climate judgments enjoy. They also know that their decisions will be analysed and commented on well beyond their country, and that they may in turn inspire courts in other countries. This can work in favour of claimants, as it encourages courts not to be the ones to disappoint international public 16 Jackie Peel, Hari Osofsky, "A Rights Turn in Climate Change Litigation?", Transnational Environmental Law, 7(1), 2018, pp. 37 opinion. This pressure has led several courts to issue press releases and/or full or partial translations, sometimes in several languages, on the very day their decision is made public. Finally, as they know that the courts of other countries apply international law in a similar way, national courts are more inclined to restrict their government's margin of action.26 But they are not constrained by anything either, and they generally cherry-pick the judgements and reasonings that serve their own purposes, discarding others, usually without much explanation. [START_REF] Robert | Comparative International Law? The Role of National Courts in Creating and Enforcing International Law[END_REF] Relationships between national courts, which are based on soft power and "jurispersuasion", rather than constraint, are slowly but surely shifting the classical model of territoriality and sovereignty with regard to the way legal rules are formed and applied. [START_REF] Schiff | From International Law to Law and Globalization[END_REF] For now, the movements are at same level, or bottom-up, but it is conceivable that in the future national decisions will influence the outcome of litigation before international courts or bodies, strengthening the interaction between international law and domestic law. Thus, the recent decision of the German Federal Constitutional Court 29 could inspire the European Court of Human Rights in the case brought by Portuguese young people. 30 This emerging global community of courts is thus driven largely by the power of persuasion, personal contacts and claimants acting on a global "market" for justice. [START_REF] Slaughter | A Global Community of Courts[END_REF] The strong mobilisation and the political sensitivity of cases also raise questions around the balance between the judiciary and the executive. As noted by E. Benvenisti, after a period during which national courts developed avoidance strategies in this area, "References to foreign law and international law are being transformed from the shield that protected the government from judicial review to the sword by which the government's (or governments') case is struck down". [START_REF] Benvenisti | Reclaiming Democracy: The Strategic Uses of Foreign and International Law by National Courts[END_REF] At the very least, international law is used as a tool to critically review the legality of a government policy, in a manner quite comparable to the way in which international courts would have approached the same issue. [START_REF] Shany | National Courts as International Actors: Jurisdictional Implications[END_REF] Many courts have found that they lacked jurisdiction on the basis of the political question doctrine and the principle of separation of powers. For example, in a case brought by representatives of indigenous peoples alleging that Canada's climate change policy violated their human rights, a federal court recently found that the issue raised was "beyond the reach of judicial interference". 34 Taken as a whole, these phenomena illustrate how the processes of normative and judicial intertwining, very well described as early as 2013 by Mireille Delmas-Marty, are capable of "creating a movement that makes it possible, under certain conditions, to integrate and reconcile the multiple constraints of systems -national and international -which were initially based on different models". [START_REF] Delmas-Marty | Le pluralisme ordonné. Les forces imaginantes du droit (II)[END_REF] National courts thus become 'organisers of clouds', to use her beautiful metaphor. 36

II. National courts, major players of climate governance?

National courts contribute, through the decisions handed down in climate trials, to reintroducing a little harmony in a landscape marked by asynchrony (different speeds in different areas) or polychrony (different speeds in a single area), [START_REF] Delmas-Marty | Le pluralisme ordonné. Les forces imaginantes du droit[END_REF] and thus to reinforce the effectiveness both of the Paris Agreement and of national policies implementing it. By applying the Agreement more indirectly than directly, they can work towards the synchronisation of the global objective with national policies, or of the short-term greenhouse gas emission trajectories with longer-term carbon neutrality objectives.

1) An indirect rather than direct reliance on the Paris Agreement In climate trials, international law is rarely applied directly, as a source of positive law, either because the legal system is dualist, or because the obligations in question are not viewed as self-executing and therefore cannot be directly invoked by individuals. However, the Paris Agreement, alone or in combination with other international obligations, has been successfully used in many cases to interpret domestic rules. The court then carries out a systemic interpretation (domestic law "in the light of", including all of the relevant legal elements, but also factual or even moral elements), a teleological interpretation (the aim is to limit temperatures as decided in the Paris Agreement) and/or an extensive interpretation. The court here has more discretion in its assessment of whether it is appropriate to use international law, as well as in the choice of sources relied on, which may include unratified treaties or soft law instruments. Indeed, as an interpretative source, the international norm becomes subsidiary, as it is not the implementation of the Paris Agreement that the claimants are asking for, but that national policies implement the country's international commitments or conform to a consensual standard of conduct. [START_REF] Bouwer | The Unsexy Future of Climate Change Litigation[END_REF] The monist or dualist nature of the legal system thus becomes irrelevant.

When they contribute to ensuring the implementation of a State's international obligations in the domestic legal order, national courts can, even if in a limited and random manner, be seen as a de facto international player fulfilling an international judicial function, in accordance with the role splitting theory, as defined by Georges Scelle. [START_REF] Shany | National Courts as International Actors: Jurisdictional Implications[END_REF] This role is particularly important with regard to erga omnes partes obligations that no longer "stand" on their own simply thanks to the principle of reciprocity. Many academics have called for this, asking national courts to play a much more important role as instruments safeguarding the international legal order, by taking into account "meta-national" considerations, beyond shortterm national interests. [START_REF] Cassese | Remarks Theory of 'Role Splitting' (dédoublement fonctionnel) in International Law[END_REF] 2) Synchronising the global goal with national policies Here, a provision such as Article 2 of the Paris Agreement, which defines in very general terms the global goal of limiting temperatures to well below 2°C and, if possible, 1.5°C, without sharing this burden between States, acquires a significance that many States had probably not anticipated. Although there is no obligation, no creditor, no debtor, the language of Article 2 is indeed clear and unequivocal. [START_REF] Wegener | Can the Paris Agreement Help Climate Change Litigation and Vice Versa?[END_REF] Whatever the legal value of national contributions, whether a legal system is monist or dualist, Article 2 is like a trap that risks closing itself on States, which will be asked by the courts to align their policies with this global objective. As noted by Hunter et al., [START_REF] Hunter | The Paris Agreement and Global Climate Litigation after the Trump Withdrawal[END_REF] the objective of the Paris Agreement becomes the widely accepted benchmark against which to review national climate policies or decisions to authorise a particular project, such as a new coal-fired power plant in South Africa. [START_REF]Minister of Environmental Affairs and Others[END_REF] Other courts, on the contrary, have held that greenhouse gas emissions do not constitute an "automatic and insuperable obstacle" to the approval of infrastructure projects, the decision-maker having discretion as to the weight to be given to such emissions in approval decisions, [START_REF] Clientearth V | Secretary of State[END_REF] or that the executive has considerable freedom of action in responding to the coronavirus crisis. [START_REF]With regard to the rescue plan for the airline KLM: Greenpeace Netherlands v. State of the Netherlands[END_REF] Thus, the case law is divergent. Use for the purpose of interpreting national law is indeed more flexible and discretionary than direct use; it nonetheless provides a real gateway for international law. [START_REF] Jean D'aspremont | The Systemic Integration of International Law by Domestic Courts[END_REF] Courts here are led to operationalise the so-called principle of common but differentiated responsibilities, which is at the heart of international environmental law in general and of the international climate regime in particular. This principle has not been operationalised by the Paris Agreement, which does not define a carbon budget and does not share the effort between States. It leaves it up to the latter to define a fair national contribution, without this being subject to international control. Here as well, national courts have seized the opportunity to remedy this shortcoming by assessing the fairness (or lack thereof) of States' commitments. In the Urgenda case, relying on Articles 2 and 8 of the European Convention on Human Rights, the court found that the Dutch State had to do "its part" even when dealing with a global problem. For the Dutch Supreme court, "this obligation of the State to do 'its part' is based on Articles 2 and 8 ECHR, because there is a grave risk that dangerous climate change will occur that will endanger the lives and welfare of many people in the Netherlands". 47 Similarly, the recent decision by the German Federal Constitutional Court emphasised that the German contribution to the international effort must be determined so as to foster mutual trust between the contracting parties, and not to minimize efforts. The court considered that it could rely on various provisions of the Agreement (such as Articles 2.2 or 4.4) to operationalise the principle of common but differentiated responsibilities. Its decision also relied on the IPCC reports. 48 In the same vein, when examining the complaint filed in September 2019 by 16 children aged 8 to 17 years, including Greta Thunberg, pursuant to the third Optional Protocol to the Convention on the Rights of the Child, the Committee on the Rights of the Child held that "In accordance with the principle of common but differentiated responsibility, as reflected in the Paris Agreement, the Committee finds that the collective nature of the causation of climate change does not absolve the State party of its individual responsibility that may derive from the harm that the emissions originating within its territory may cause to children, whatever their location." 49 3) Synchronising greenhouse gas emissions trajectories with longer-term carbon neutrality objectives

Commitments to carbon neutrality are multiplying, not only from companies, but also from States: by 2030 (Norway), 2035 (Finland), 2040 (Austria, Iceland), 2045 (Sweden), 2050 (EU, South Korea, Japan, Canada, New-Zealand), 2060 (China) or 2070 (India). This unexpected movement shows how far we have come in the five years since COP 21. It is very encouraging, as it could catalyse the action of other States and finally put us on the trajectory set by the Paris Agreement. It should therefore not be underestimated, even if States are struggling to define short-and medium-term trajectories consistent with this neutrality objective, trajectories without which this objective will remain wishful thinking. Here as well, courts have the opportunity to work on synchronising trajectories. In France, the Grande-Synthe case gave rise on 19 November 2020 to an initial ruling by the French Council of State that is very interesting from this point of view. The latter clarified France's climate commitments and their consequences for the administration of the State. In its decision, based on the reports of the French High Council on Climate, the French Council of State underlined the inadequacies of the policies put in place to achieve the set objectives. It regretted a "shift of the trajectory of emissions reduction which leads to the postponement of most of the effort after 2020, according to a trajectory that has never been reached until now", emphasising that "The most recent scientific data, in particular the reports published by the Intergovernmental panel on climate change, point, on the contrary, to a worsening of the climate risks if temperature rise remains constant (…)". 50 Another decision forces, in fine, the government to reconcile long-term objectives with the short-term carbon strategy and budgets. 51 First, the French Council of State quashed the government's implicit refusal to take all useful measures to curb the curve of greenhouse gas emissions produced on national territory in order to ensure its compatibility with the greenhouse gas emission reduction objectives set both by national regulations and European Union law. Secondly, the high court enjoined the Prime Minister to take all necessary measures to curb the curve of greenhouse gas emissions to ensure its compatibility with said greenhouse gas emission reduction objectives. The ruling handed down in the so-called "Case of the Century" by the Paris Administrative Court goes in the same direction, illustrating how the State (or even a company) can find itself trapped by its own promises. [START_REF] Hautereau-Boutonnet | Affaire du siècle' : les promesses climatiques risquent d'engager ceux qui les font[END_REF] The recent German ruling is also very interesting from this point of view, in that it interprets the German Constitution in the light of an imperative of intergenerational justice. German law "must not place disproportionate burdens on the future freedom of the claimants". Furthermore, "It follows from the principle of proportionality that one generation must not be allowed to consume large portions of the CO2 budget while bearing a relatively minor share of the reduction effort, if this would involve leaving subsequent generations with a drastic reduction burden and expose their lives to serious losses of freedom -something the claimants describe as an "emergency stop" . 53 In a way, consuming a large part of the CO2 budget in the coming years unacceptably aggravates the risk of serious losses of freedom for future generations, who will have no choice but to undergo a painful transition. *** Within the limited framework of this research, which has focused solely on the obligations of States, without addressing litigation involving companies, and without in any way claiming to be exhaustive, we have shown how the Paris Agreement, described as a flexible, bottom-up treaty containing only procedural obligations, and whose transparency and international control mechanism lacks "teeth", can today produce a useful effect in national courts, who themselves do have very good "teeth". Vague international law gains legal certainty through the intervention of national courts, who make up for the lack of an international control mechanism. Through their interpretation of States' international commitments, which go well beyond the Paris Agreement, national courts connect, harmonise, bring together and even hybridise international and national norms, with the various courts mutually inspiring each other across borders. National courts, through their cascading decisions, could thus be one of the keys to better combine, on the one hand, international commitments and national regulations and on the other hand, international ambition and State action. The urgency here is clear, as shown by the first part of the IPCC sixth assessment report, published in the summer of 2021. Indeed, this report highlights the reality of climate change: "Human-induced climate change is already affecting many weather and climate extremes in every region across the globe. Evidence of observed changes in extremes such as heatwaves, heavy precipitation, droughts, and tropical cyclones, and, in particular, their attribution to human influence, has strengthened since" the previous report. It also outlines the worst-case scenarios for the future of our planet.

  54

  54 IPCC, AR6 Climate Change 2021: The Physical Science Basis, 2021 [Masson-Delmotte, V., P. Zhai, A. Pirani, S. L. Connors, C. Péan, S. Berger, N. Caud, Y. Chen, L. Goldfarb, M. I. Gomis, M. Huang, K. Leitzell, E. Lonnoy, J.B.R. Matthews, T. K. Maycock, T. Waterfield, O. Yelekçi, R. Yu and B. Zhou (eds.)] https://www.ipcc.ch/report/ar6/wg1/ (last accessed on 15 December 2021).

  -67.17 See the abovementioned Decision of 2019 in the Urgenda case, §5.6.2. 18 Petition before the Committee on the Rights of the Child on 23 September 2019, Chiara Sacchi et al. c. Argentina, Brazil, France, Germany, Turkey. Decision adopted by the Committee on the Rights of the Child under the Optional Protocol to the Convention on the Rights of the Child on a communications procedure in respect of Communication No. 106/2019, 21 September 2021. 19 With pending cases involving Portuguese young people, Swiss elders or an Austrian with temperature-dependent multiple sclerosis. See Christel Cournil, Camila Perruso, "Le climat s'installe à Strasbourg -Les enseignements des premières requêtes portées devant la Cour européenne des droits de l'Homme", L'Observateur de Bruxelles, 2021/2, n° 124, p. 24 ss. 20 Urgenda, Supreme Court of the Netherlands, ECLI:NL:HR:2019:2007, Hoge Raad, 20-12-2019, § 5.7.5. 21 See their main conclusions, http://climatecasechart.com/climate-change-litigation/wp-content/uploads/sites/16/nonus-case-documents/2019/20190628_2660_na.pdf (last accessed on 15 December 2021).

22

Thomson c. Minister for Climate Change Issues [2017] NZHC 733, §134.

23

Ibid., §. 94.

24

Guy Canivet, "Les influences croisées entre juridictions nationales et internationales : Eloge de la 'bénévolence' des juges", RSC 2005, p. 799.

25

The database of the Sabin Center mentioned above (http://climatecasechart.com/climate-change-litigation/) and the database of the Grantham Institute (https://climate-laws.org/litigation_cases).

(*) Aix Marseille Université, CNRS, UMR DICE, CERIC. This article builds on earlier work, in particular L'éloge du flou ? L'Accord de Paris devant les juges nationaux, Contributions aux mélanges en l'honneur de Mireille Delmas-Marty, Mare et Martin, Paris, forthcoming 2022. 1 Mireille Delmas-Marty, Aux quatre vents du monde, Seuil, 2016, p.120. 2 See the Sabin Center Climate Change Litigation databases http://climatecasechart.com/climate-change-litigation/ (last accessed on 15 December 2021).

See for instance "German court paves way for Peruvian farmer's suit against RWE", Reuters, 30 November 2017.

Lord Bingham, "Foreword" in S. Fatima, Using International Law in Domestic Courts, Hart Pub.,Oxford, 2005.

Yuval Shany, "National Courts as International Actors: Jurisdictional Implications", International Law Forum of the Hebrew University of Jerusalem Law Faculty, Research Paper, N°22-08, 25 Oct. 2008, p. 5.

Jean d'Aspremont, "The Systemic Integration of International Law by Domestic Courts", in The Practice of International and National Courts and the (De-)Fragmentation of International Law, Hart Pub., 2014, p. 143.

Stephane Beaulac, "Westphalia, Dualism and Contextual Interpretation: How to Better Engage International Law in Domestic Courts", EUI Working Paper, MWP 2007/03, p. 4.

Wayne Sandholtz, "How Domestic Courts Use International Law", Fordham International Law Journal, Vol. 38(2), 2015, p. 615.

Slim Laghmani, "Droit international et droits internes : vers un renouveau du jus gentium ?", Droit international et droits internes. Développements récents, R. Ben Achour, S. Laghmani (dir.), Pedone, 1999, p. 34 [Our translation].

David Estrin, "Limiting Dangerous Climate Change: The Critical Role of Citizen Suits and Domestic Courts -Despite the Paris Agreement", CIGI Papers, N°101, 2016, p. 5.

11 Sandrine Maljean-Dubois, "Climate Change Litigation", Max Planck Encyclopedia of International Procedural Law (EiPro), 2019 [on line

]. 12 Austin Sarat, Stuart Scheingold, Cause Lawyering and the State in a Global Era, OUP, Oxford, 2001; J. Gupta, "Legal Steps Outside the Climate Convention: Litigation as a Tool to Address Climate Change", Review of Comparative, International and Environmental Law, 2007, 16(1), p

. 78.13 Wayne Sandholtz, "How Domestic Courts Use International Law", op. cit.,

p. 597

.14 Ibid.15 Christel Cournil, "Les droits fondamentaux au service de l'émergence d'un contentieux climatique contre l'État. Des stratégies contentieuses des requérants à l'activisme des juges", in Martha Torre-Schaub, Christel Cournil, Sabine Lavorel, Marianne Moliner-Dubost (eds.), Quel(s) droit(s) pour les changements climatiques, Mare & Martin, 2018, p.199.

Eyal Benvenisti, "Judicial Misgivings Regarding the Application of International Law: an Analysis of the Attitudes of National Courts", European Journal of International Law, 1993(4), p. 175.