From 5a546688f1e3846b54cf06e83011256e550ef249 Mon Sep 17 00:00:00 2001 From: Richard Dern Date: Mon, 17 Nov 2025 14:59:59 +0100 Subject: [PATCH] =?UTF-8?q?Premi=C3=A8res=20analyses=20de=20corr=C3=A9lati?= =?UTF-8?q?on?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- docs/08 - Corrélations.md | 124 +++++++++++++++ figures/correlation_heatmap.png | Bin 0 -> 111789 bytes .../lagcorr_humidity_to_rain_rate.png | Bin 0 -> 53210 bytes .../lagcorr_illuminance_to_temperature.png | Bin 0 -> 51363 bytes .../lagcorr_pressure_to_illuminance.png | Bin 0 -> 52292 bytes .../lagcorr_pressure_to_rain_rate.png | Bin 0 -> 55542 bytes .../lagcorr_pressure_to_wind_speed.png | Bin 0 -> 54878 bytes .../lagcorr_temperature_to_humidity.png | Bin 0 -> 58685 bytes .../lagcorr_temperature_to_rain_rate.png | Bin 0 -> 48912 bytes .../scatter_humidity_vs_illuminance.png | Bin 0 -> 324990 bytes .../scatter_humidity_vs_pressure.png | Bin 0 -> 245373 bytes .../scatter_humidity_vs_rain_rate.png | Bin 0 -> 41909 bytes .../scatter_humidity_vs_wind_direction.png | Bin 0 -> 388778 bytes .../scatter_humidity_vs_wind_speed.png | Bin 0 -> 211660 bytes .../scatter_illuminance_vs_wind_direction.png | Bin 0 -> 351715 bytes .../scatter_illuminance_vs_wind_speed.png | Bin 0 -> 221342 bytes .../scatter_pressure_vs_illuminance.png | Bin 0 -> 243565 bytes .../scatter_pressure_vs_rain_rate.png | Bin 0 -> 50135 bytes .../scatter_pressure_vs_wind_direction.png | Bin 0 -> 310159 bytes .../scatter_pressure_vs_wind_speed.png | Bin 0 -> 184069 bytes .../scatter_rain_rate_vs_illuminance.png | Bin 0 -> 43298 bytes .../scatter_rain_rate_vs_wind_direction.png | Bin 0 -> 56485 bytes .../scatter_rain_rate_vs_wind_speed.png | Bin 0 -> 50384 bytes .../scatter_temperature_vs_humidity.png | Bin 0 -> 285311 bytes .../scatter_temperature_vs_illuminance.png | Bin 0 -> 293214 bytes .../scatter_temperature_vs_pressure.png | Bin 0 -> 227025 bytes .../scatter_temperature_vs_rain_rate.png | Bin 0 -> 46699 bytes .../scatter_temperature_vs_wind_direction.png | Bin 0 -> 386062 bytes .../scatter_temperature_vs_wind_speed.png | Bin 0 -> 201919 bytes .../scatter_wind_speed_vs_wind_direction.png | Bin 0 -> 204899 bytes meteo/analysis.py | 117 ++++++++++++++ meteo/plots.py | 149 ++++++++++++++++++ meteo/variables.py | 82 ++++++++++ scripts/plot_all_pairwise_scatter.py | 45 ++++++ scripts/plot_correlation_heatmap.py | 45 ++++++ scripts/plot_lagged_correlations.py | 69 ++++++++ 36 files changed, 631 insertions(+) create mode 100644 docs/08 - 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Corrélations.md b/docs/08 - Corrélations.md new file mode 100644 index 0000000..80e1a34 --- /dev/null +++ b/docs/08 - Corrélations.md @@ -0,0 +1,124 @@ +# Corrélations + +## Matrice de corrélation + +| | Température | Humidité relative | Pression atm. | Précipitations | Luminance | Vitesse du vent | Direction du vent | +| --------------------- | ----------- | ----------------- | ------------- | -------------- | --------- | --------------- | ----------------- | +| **Température** | — | ✅ | ✅ | ✅ | ✅ | ❌ | ❌ | +| **Humidité relative** | ✅ | — | ✅ | ✅ | ✅ | ❌ | ❌ | +| **Pression atm.** | ✅ | ✅ | — | ✅ | ✅ | ✅ | ✅ | +| **Précipitations** | ✅ | ✅ | ✅ | — | ✅ | ✅ | ✅ | +| **Luminance** | ✅ | ✅ | ✅ | ✅ | — | ❌ | ❌ | +| **Vitesse du vent** | ❌ | ❌ | ✅ | ✅ | ❌ | — | ❌ | +| **Direction du vent** | ❌ | ❌ | ✅ | ✅ | ❌ | ❌ | — | + +## Température ↔ Humidité relative ✅ + +L’humidité relative (HR) est, par définition, le rapport entre la quantité de vapeur d’eau réellement présente dans l’air et la quantité maximale qu’il pourrait contenir à cette température. Cette “quantité maximale” est donnée par la pression de vapeur saturante, qui augmente de façon quasi exponentielle avec la température, selon la relation de Clausius–Clapeyron.([asclimateservices.org][1]) + +Conséquences directes : + +- si la quantité absolue de vapeur d’eau reste constante et que la température **augmente**, la pression de vapeur saturante augmente encore plus vite → l’air devient proportionnellement **moins humide** (HR diminue) ; +- si la température **baisse** sans changement d’humidité absolue, l’air se rapproche de la saturation → HR **augmente**. + +On s’attend donc à une relation forte et systématique entre température et humidité relative : même sans changement de masse d’air, le simple réchauffement/refroidissement diurne suffit à faire varier l’HR. + +## Pression atmosphérique ↔ Temps sensible, humidité, précipitations ✅ + +En surface, la pression atmosphérique organise la circulation de l’air et la formation des systèmes météo (anticyclones et dépressions). Les centres de **basse pression** sont associés à de l’air qui converge en surface et s’élève, se refroidit, et condense sa vapeur d’eau en nuages et précipitations. À l’inverse, les **hautes pressions** sont associées à de l’air qui descend, se réchauffe et se dessèche, donnant du temps généralement sec et dégagé.([Centre pour l'Éducation Scientifique][2]) + +D’où plusieurs liens attendus : + +- **Pression ↔ Précipitations** ✅ + Dépressions (basse pression) → air ascendant, condensation, nuages, pluies ; anticyclones (haute pression) → air subsident, ciel souvent dégagé et précipitations rares. Des études relient explicitement les quantités de précipitations aux variations de pression au passage de systèmes météo.([ResearchGate][3]) + +- **Pression ↔ Humidité relative** ✅ + Les basses pressions s’accompagnent souvent d’air plus humide (nuages épais, air proche de la saturation), les hautes pressions d’air plus sec, surtout en basses couches. Ce n’est pas une loi exacte point par point, mais climatologiquement très robuste.([Cordulus][4]) + +- **Pression ↔ Luminance** ✅ + Anticyclones → ciel dégagé, ensoleillement fort, grande amplitude thermique jour/nuit ; dépressions → couverture nuageuse, lumière atténuée et plus diffuse, températures lissées.([Wikipédia][5]) + +- **Pression ↔ Température** ✅ + Pression, température et densité de l’air sont reliées par l’équation d’état (air quasi parfait). Dans la pratique, les systèmes de haute pression sont souvent associés à des nuits plus froides (refroidissement radiatif sous ciel dégagé) et des journées plus chaudes, tandis que les basses pressions limitent les contrastes via les nuages et les précipitations.([Wikipédia][5]) + +## Pression ↔ Vent (vitesse & direction) ✅ + +Le vent est essentiellement une réponse de l’air aux **gradients de pression** : l’air tend à se déplacer des zones de haute pression vers les zones de basse pression. La force de ce mouvement dépend de la pente du “relief de pression” (gradient de pression), et sa direction est fortement influencée par la force de Coriolis.([ESS][6]) + +- **Vitesse du vent ↔ Pression** ✅ + Plus les isobares (lignes d’égale pression) sont serrées, plus le gradient de pression est fort, et plus le vent est rapide. Le vent “géostrophique”, solution idéale de l’équilibre entre gradient de pression et Coriolis, donne une bonne approximation de cette relation : vitesse du vent proportionnelle au gradient de pression.([Wikipédia][7]) + +- **Direction du vent ↔ Pression** ✅ + En régime moyen, le vent souffle approximativement **parallèle aux isobares**, avec les basses pressions à sa gauche dans l’hémisphère Nord (droite dans l’hémisphère Sud), conformément à l’équilibre géostrophique. La direction du vent est donc un reflet direct de la disposition des centres de haute et basse pression autour du point d’observation.([Wikipédia][7]) + +## Précipitations ↔ Humidité & Température ✅ + +Les précipitations sont la manifestation macroscopique de la condensation de vapeur d’eau en gouttes suffisamment grosses pour tomber. Il y a donc un lien très direct avec le contenu en eau de l’atmosphère et la température : + +- **Humidité ↔ Précipitations** ✅ + Pour qu’il pleuve, il faut que l’air atteigne (localement) la saturation : humidité relative proche de 100 %. Lorsque des systèmes dépressionnaires ou des fronts forcent l’ascendance de l’air, celui-ci se refroidit, sa vapeur d’eau condense et la saturation est atteinte → formation de nuages et de pluie.([NCICS][8]) + +- **Température ↔ Précipitations** ✅ + La capacité de l’air à contenir de la vapeur d’eau augmente d’environ 6–7 % par degré de réchauffement, selon la relation de Clausius–Clapeyron.([asclimateservices.org][1]) + À teneur en humidité relative comparable, un air plus chaud peut donc alimenter des précipitations plus intenses. La phase de la précipitation (neige, pluie, pluie verglaçante) dépend aussi directement de la température dans la colonne d’air. + +## Nuages, Luminance & Pluie ✅ + +Le capteur de luminance mesure essentiellement l’éclairement lumineux en surface, lui-même directement lié au rayonnement solaire incident. Ce dernier est contrôlé par la hauteur du Soleil, mais aussi très fortement par la **nébulosité** (nuages) et, dans une moindre mesure, les aérosols. + +- **Luminance ↔ Précipitations** ✅ + Les situations pluvieuses sont presque toujours associées à des nuages épais et/ou profonds (stratiformes, cumulonimbus). Ces nuages réduisent nettement le rayonnement direct et donc la luminance mesurée en surface, même s’il existe des cas particuliers de “silver lining” où le rayonnement diffus peut être localement renforcé.([American Meteorological Society Journals][9]) + +- **Luminance ↔ Humidité / Pression / Température** ✅ + Plus généralement, les jours anticycloniques secs et stables (haute pression) sont caractérisés par une forte luminance en journée ; à l’inverse, les situations dépressionnaires humides (basse pression, air proche de la saturation) se traduisent par une baisse significative de l’éclairement au sol.([Wikipédia][5]) + +## Vent ↔ Précipitations ✅ + +Les épisodes pluvieux marqués (passage de fronts, lignes de grains, orages) sont fréquemment associés à : + +- une augmentation de la **vitesse du vent**, liée au gradient de pression plus fort autour des systèmes dépressionnaires et aux courants descendantes / rafales convectives ; +- des **directions de vent caractéristiques** pour un site donné (par exemple flux d’ouest ou de sud-ouest apportant de l’air maritime humide sur la France). + +Les études climatologiques et les diagnostics synoptiques mettent systématiquement en avant cette co-occurrence entre précipitations, gradients de pression marqués et vents plus forts.([NCICS][8]) + +Pour autant, la relation n’est pas parfaitement déterministe : on peut avoir du vent sans pluie (front sec, mistral, tramontane…), et des pluies faibles sous vents modestes. On parle donc plutôt de **tendance statistique robuste** que de loi exacte. + +## Pourquoi des ❌ dans la matrice ? + +Les ❌ ne signifient pas “aucune relation possible”, mais : + +> “Il n’existe pas de relation simple, universelle, monotone entre ces deux grandeurs, valable partout et tout le temps.” + +Quelques exemples : + +- **Température ↔ Vitesse / Direction du vent** ❌ + Le vent dépend de gradients horizontaux de pression et de température à grande échelle, pas de la valeur de la température locale à votre station. Vous pouvez avoir une journée très chaude sans vent, ou un refroidissement brutal par intrusion d’air froid très venteux : la relation locale instantanée n’est pas simple. + +- **Luminance ↔ Vent** ❌ + On peut avoir un grand soleil avec un vent soutenu (temps anticyclonique venteux), ou un ciel uniformément gris et quasi sans vent. Lien, encore une fois, via la situation météo d’ensemble, pas directement entre “lumière” et “vitesse de l’air”. + +- **Vent ↔ Humidité / Température ↔ Direction du vent** ❌ (au sens général) + Sur **un site donné**, il est fréquent d’observer que certains secteurs de vent (advections maritimes, continentales, montagne/plaine, etc.) sont associés à des signatures de température ou d’humidité typiques : c’est le “climat local” des masses d’air. + Mais ce pattern dépend énormément de la géographie. Il n’existe pas, par exemple, de règle universelle “vent du nord = air sec” valable partout sur Terre. D’où le ❌ au sens “relation globale, généralisable”. + +--- + +Toutes ces corrélations sont explorées par les scripts `scripts/plot_all_pairwise_scatter.py` et `scripts/plot_lagged_correlations.py`, qui vont produire des graphiques dans `figures/pairwise_scatter` et `figures/lagged_correlations`. Mais, bien qu'intéressantes et instructives, ces images sont encore primitives. + +Néanmoins, un graphique de type "heatmap" permet déjà de quantifier ces corrélations en se basant sur les données concrètes : + +```shell +python -m scripts.plot_correlation_heatmap +``` + +![](../figures/correlation_heatmap.png) + +[1]: https://asclimateservices.org/code-and-equations/clausius-clapeyron/?utm_source=chatgpt.com "Clausius Clapeyron" +[2]: https://scied.ucar.edu/learning-zone/how-weather-works/highs-and-lows-air-pressure?utm_source=chatgpt.com "The Highs and Lows of Air Pressure" +[3]: https://www.researchgate.net/publication/323079756_A_generalized_relationship_between_atmospheric_pressure_and_precipitation_associated_with_a_passing_weather_system?utm_source=chatgpt.com "A generalized relationship between atmospheric pressure ..." +[4]: https://www.cordulus.com/glossary/atmospheric-pressure?utm_source=chatgpt.com "What is Atmospheric pressure?" +[5]: https://en.wikipedia.org/wiki/Pressure_system?utm_source=chatgpt.com "Pressure system" +[6]: https://www.ess.uci.edu/~yu/class/ess55/lecture.4.motion.all.pdf?utm_source=chatgpt.com "Lecture 4: Pressure and Wind" +[7]: https://en.wikipedia.org/wiki/Geostrophic_wind?utm_source=chatgpt.com "Geostrophic wind" +[8]: https://ncics.org/cics-news/quantifying-the-relationship-between-extreme-precipitation-and-atmospheric-water-vapor/?utm_source=chatgpt.com "Quantifying the Relationship Between Extreme ..." +[9]: https://journals.ametsoc.org/view/journals/apme/42/10/1520-0450_2003_042_1421_ccboai_2.0.co_2.xml?utm_source=chatgpt.com "Cloud Coverage Based on All-Sky Imaging and Its Impact on ..." diff --git a/figures/correlation_heatmap.png b/figures/correlation_heatmap.png new file mode 100644 index 0000000000000000000000000000000000000000..552b0eac0ed585130efa21d84466f576b948f92e GIT binary patch literal 111789 zcmeAS@N?(olHy`uVBq!ia0y~yU_QXWz;uCwje&t7zFcw(0|SFqiEBhjaDG}zd16s2 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