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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Benchmark Dataset Exploration\n",
+    "\n",
+    "This notebook explores the piezometric time-series dataset used in the embedding benchmark.\n",
+    "The dataset contains daily groundwater level measurements from the French national monitoring network (BRGM),\n",
+    "augmented with ERA5 climate reanalysis covariates.\n",
+    "\n",
+    "**Files:**\n",
+    "- `station_metadata.parquet` -- 4,210 stations with hydrogeological labels\n",
+    "- `piezo_daily_uni.parquet` -- univariate daily groundwater levels (2,000 stations)\n",
+    "- `piezo_daily_multi.parquet` -- multivariate daily series: groundwater + 3 ERA5 covariates\n",
+    "\n",
+    "**Goal:** Understand data characteristics (class balance, coverage, quality) before designing the embedding evaluation protocol."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import warnings\n",
+    "warnings.filterwarnings(\"ignore\")\n",
+    "\n",
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "import plotly.express as px\n",
+    "import plotly.graph_objects as go\n",
+    "from plotly.subplots import make_subplots\n",
+    "\n",
+    "# Consistent color palette for milieu_eh classes\n",
+    "MILIEU_COLORS = {\n",
+    "    \"Poreux\": \"#636EFA\",\n",
+    "    \"Fissure\": \"#EF553B\",\n",
+    "    \"Karstique\": \"#00CC96\",\n",
+    "    \"Double porosite F+P\": \"#AB63FA\",\n",
+    "    \"Double porosite K+P\": \"#FFA15A\",\n",
+    "    \"Composite\": \"#19D3F3\",\n",
+    "    \"Non applicable\": \"#B6E880\",\n",
+    "    \"Indetermine\": \"#FF6692\",\n",
+    "}\n",
+    "\n",
+    "# Short readable labels for milieu_eh codes\n",
+    "MILIEU_LABELS = {\n",
+    "    \"1\": \"Poreux\",\n",
+    "    \"2\": \"Fissure\",\n",
+    "    \"3\": \"Karstique\",\n",
+    "    \"4\": \"Double porosite F+P\",\n",
+    "    \"5\": \"Double porosite K+P\",\n",
+    "    \"6\": \"Double porosite K+F\",\n",
+    "    \"8\": \"Composite\",\n",
+    "    \"9\": \"Non applicable\",\n",
+    "    \"X\": \"Indetermine\",\n",
+    "}\n",
+    "\n",
+    "DATA_DIR = \"../data\"\n",
+    "\n",
+    "# Plotly template for publication-quality figures\n",
+    "TEMPLATE = \"plotly_white\"\n",
+    "FONT = dict(family=\"Arial\", size=13)\n",
+    "\n",
+    "print(\"Libraries loaded.\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "---\n",
+    "## 1. Dataset Overview\n",
+    "\n",
+    "Load the station metadata and inspect its structure, types, and basic statistics."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "meta = pd.read_parquet(f\"{DATA_DIR}/station_metadata.parquet\")\n",
+    "print(f\"Shape: {meta.shape[0]} stations x {meta.shape[1]} columns\")\n",
+    "print(f\"\\nColumn types:\\n{meta.dtypes.to_string()}\")\n",
+    "meta.head()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Add a readable milieu label column\n",
+    "meta[\"milieu_label\"] = meta[\"milieu_eh\"].map(MILIEU_LABELS)\n",
+    "\n",
+    "# Summary statistics for numeric columns\n",
+    "numeric_cols = [\n",
+    "    \"latitude\", \"longitude\", \"altitude_station\",\n",
+    "    \"profondeur_moyenne_globale\", \"niveau_stddev_global\",\n",
+    "    \"amplitude_totale\", \"nb_mois_total\",\n",
+    "]\n",
+    "meta[numeric_cols].describe().round(2)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "---\n",
+    "## 2. Label Distribution\n",
+    "\n",
+    "The classification target is `milieu_eh`, encoding the hydrogeological environment of each station.\n",
+    "This section quantifies the class imbalance, which is critical for choosing evaluation metrics\n",
+    "(balanced accuracy, macro-F1) and designing stratified cross-validation splits."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Filter stations with a valid milieu_eh label\n",
+    "meta_labeled = meta.dropna(subset=[\"milieu_eh\"]).copy()\n",
+    "print(f\"Stations with milieu_eh label: {len(meta_labeled)} / {len(meta)} \"\n",
+    "      f\"({len(meta) - len(meta_labeled)} missing)\")\n",
+    "\n",
+    "# Value counts\n",
+    "vc = meta_labeled[\"milieu_label\"].value_counts()\n",
+    "vc_pct = meta_labeled[\"milieu_label\"].value_counts(normalize=True) * 100\n",
+    "\n",
+    "dist_df = pd.DataFrame({\"count\": vc, \"pct\": vc_pct.round(1)}).reset_index()\n",
+    "dist_df.columns = [\"milieu_eh\", \"count\", \"pct\"]\n",
+    "dist_df[\"label\"] = dist_df.apply(lambda r: f\"{r['count']}  ({r['pct']}%)\", axis=1)\n",
+    "dist_df"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "fig = px.bar(\n",
+    "    dist_df,\n",
+    "    x=\"milieu_eh\",\n",
+    "    y=\"count\",\n",
+    "    color=\"milieu_eh\",\n",
+    "    color_discrete_map=MILIEU_COLORS,\n",
+    "    text=\"label\",\n",
+    "    template=TEMPLATE,\n",
+    "    title=\"Distribution of hydrogeological environment classes (milieu_eh)\",\n",
+    "    labels={\"milieu_eh\": \"Hydrogeological class\", \"count\": \"Number of stations\"},\n",
+    ")\n",
+    "fig.update_traces(textposition=\"outside\")\n",
+    "fig.update_layout(\n",
+    "    font=FONT,\n",
+    "    showlegend=False,\n",
+    "    yaxis_range=[0, dist_df[\"count\"].max() * 1.15],\n",
+    "    height=450,\n",
+    "    width=800,\n",
+    ")\n",
+    "fig.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Key observation:** The dataset is heavily imbalanced. *Poreux* (porous) alone represents ~48% of labeled stations,\n",
+    "while minority classes (*Indetermine*, *Karstique*) have fewer than 200 samples each.\n",
+    "This motivates the use of balanced accuracy and macro-averaged F1 as primary evaluation metrics,\n",
+    "along with stratified cross-validation and class-weighted classifiers."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "---\n",
+    "## 3. Geographic Distribution\n",
+    "\n",
+    "Station locations across metropolitan France, colored by hydrogeological environment.\n",
+    "Geographic clustering of classes would indicate spatial autocorrelation, which must be\n",
+    "handled in the evaluation protocol (e.g., spatial cross-validation by departement)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "fig = px.scatter_mapbox(\n",
+    "    meta_labeled,\n",
+    "    lat=\"latitude\",\n",
+    "    lon=\"longitude\",\n",
+    "    color=\"milieu_label\",\n",
+    "    color_discrete_map=MILIEU_COLORS,\n",
+    "    hover_name=\"code_bss\",\n",
+    "    hover_data=[\"altitude_station\", \"nb_mois_total\", \"milieu_label\"],\n",
+    "    zoom=4.5,\n",
+    "    center={\"lat\": 46.5, \"lon\": 2.5},\n",
+    "    mapbox_style=\"carto-positron\",\n",
+    "    title=\"Geographic distribution of monitoring stations by hydrogeological class\",\n",
+    "    labels={\"milieu_label\": \"Hydrogeological class\"},\n",
+    "    opacity=0.7,\n",
+    "    height=650,\n",
+    "    width=850,\n",
+    ")\n",
+    "fig.update_layout(font=FONT, template=TEMPLATE, margin=dict(l=0, r=0, t=40, b=0))\n",
+    "fig.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Fallback: simple scatter plot (lat vs lon) in case mapbox is unavailable\n",
+    "fig_scatter = px.scatter(\n",
+    "    meta_labeled,\n",
+    "    x=\"longitude\",\n",
+    "    y=\"latitude\",\n",
+    "    color=\"milieu_label\",\n",
+    "    color_discrete_map=MILIEU_COLORS,\n",
+    "    hover_name=\"code_bss\",\n",
+    "    title=\"Station locations (latitude vs. longitude) by hydrogeological class\",\n",
+    "    labels={\"longitude\": \"Longitude\", \"latitude\": \"Latitude\", \"milieu_label\": \"Class\"},\n",
+    "    template=TEMPLATE,\n",
+    "    opacity=0.6,\n",
+    "    height=550,\n",
+    "    width=750,\n",
+    ")\n",
+    "fig_scatter.update_traces(marker=dict(size=4))\n",
+    "fig_scatter.update_layout(font=FONT)\n",
+    "fig_scatter.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Observation:** Classes exhibit clear spatial clustering (e.g., porous aquifers dominate\n",
+    "sedimentary basins such as the Paris Basin and Aquitaine, while karst stations cluster in\n",
+    "limestone regions). This confirms that geographic cross-validation (split by departement)\n",
+    "is necessary to avoid spatial leakage."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "---\n",
+    "## 4. Altitude Distribution\n",
+    "\n",
+    "Station altitude varies widely across France and correlates with hydrogeological environment.\n",
+    "Karst systems tend to occur at higher altitudes (limestone plateaus, mountain foothills),\n",
+    "while porous aquifers dominate low-altitude sedimentary plains."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Histogram of altitude, colored by class\n",
+    "fig = px.histogram(\n",
+    "    meta_labeled,\n",
+    "    x=\"altitude_station\",\n",
+    "    color=\"milieu_label\",\n",
+    "    color_discrete_map=MILIEU_COLORS,\n",
+    "    nbins=60,\n",
+    "    barmode=\"stack\",\n",
+    "    title=\"Altitude distribution of stations by hydrogeological class\",\n",
+    "    labels={\"altitude_station\": \"Altitude (m a.s.l.)\", \"milieu_label\": \"Class\"},\n",
+    "    template=TEMPLATE,\n",
+    "    height=400,\n",
+    "    width=800,\n",
+    ")\n",
+    "fig.update_layout(font=FONT)\n",
+    "fig.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Box plot: altitude per class\n",
+    "fig = px.box(\n",
+    "    meta_labeled,\n",
+    "    x=\"milieu_label\",\n",
+    "    y=\"altitude_station\",\n",
+    "    color=\"milieu_label\",\n",
+    "    color_discrete_map=MILIEU_COLORS,\n",
+    "    title=\"Altitude distribution per hydrogeological class\",\n",
+    "    labels={\"altitude_station\": \"Altitude (m a.s.l.)\", \"milieu_label\": \"Class\"},\n",
+    "    template=TEMPLATE,\n",
+    "    height=450,\n",
+    "    width=800,\n",
+    ")\n",
+    "fig.update_layout(font=FONT, showlegend=False, xaxis_tickangle=-30)\n",
+    "fig.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "---\n",
+    "## 5. Time Series Examples\n",
+    "\n",
+    "We select one representative station per major hydrogeological class to illustrate the\n",
+    "diversity of groundwater dynamics. Different aquifer types exhibit fundamentally different\n",
+    "temporal behaviors (smooth vs. flashy responses, seasonal vs. multi-year trends),\n",
+    "which is precisely what we expect embeddings to capture."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Load univariate time series\n",
+    "uni = pd.read_parquet(f\"{DATA_DIR}/piezo_daily_uni.parquet\")\n",
+    "uni[\"date\"] = pd.to_datetime(uni[\"date\"])\n",
+    "print(f\"Univariate dataset: {uni.shape[0]:,} rows, {uni['code_bss'].nunique()} stations\")\n",
+    "uni.head()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Select one representative station per major class\n",
+    "# We pick stations with good data coverage (high nb_mois_total)\n",
+    "TARGET_CLASSES = [\"Poreux\", \"Fissure\", \"Karstique\", \"Double porosite F+P\",\n",
+    "                  \"Double porosite K+P\", \"Composite\"]\n",
+    "\n",
+    "example_stations = []\n",
+    "for cls in TARGET_CLASSES:\n",
+    "    candidates = meta_labeled[\n",
+    "        (meta_labeled[\"milieu_label\"] == cls) &\n",
+    "        (meta_labeled[\"nb_mois_total\"] > meta_labeled[\"nb_mois_total\"].quantile(0.7))\n",
+    "    ].sort_values(\"nb_mois_total\", ascending=False)\n",
+    "    if len(candidates) > 0:\n",
+    "        # Pick the station closest to the median coverage in top 30%\n",
+    "        mid = len(candidates) // 2\n",
+    "        example_stations.append(candidates.iloc[mid])\n",
+    "\n",
+    "example_ids = [s[\"code_bss\"] for s in example_stations]\n",
+    "print(f\"Selected {len(example_ids)} stations:\")\n",
+    "for s in example_stations:\n",
+    "    print(f\"  {s['code_bss']:20s}  {s['milieu_label']:30s}  ({s['nb_mois_total']} months)\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Plot time series for each selected station\n",
+    "uni_examples = uni[uni[\"code_bss\"].isin(example_ids)].copy()\n",
+    "uni_examples = uni_examples.merge(\n",
+    "    meta[[\"code_bss\", \"milieu_label\"]], on=\"code_bss\", how=\"left\"\n",
+    ")\n",
+    "\n",
+    "n_stations = len(example_ids)\n",
+    "fig = make_subplots(\n",
+    "    rows=n_stations, cols=1,\n",
+    "    shared_xaxes=True,\n",
+    "    vertical_spacing=0.03,\n",
+    "    subplot_titles=[\n",
+    "        f\"{s['milieu_label']} -- {s['code_bss']}\"\n",
+    "        for s in example_stations\n",
+    "    ],\n",
+    ")\n",
+    "\n",
+    "for i, station in enumerate(example_stations):\n",
+    "    bss = station[\"code_bss\"]\n",
+    "    cls = station[\"milieu_label\"]\n",
+    "    ts = uni_examples[uni_examples[\"code_bss\"] == bss].sort_values(\"date\")\n",
+    "    color = MILIEU_COLORS.get(cls, \"#636EFA\")\n",
+    "    fig.add_trace(\n",
+    "        go.Scatter(\n",
+    "            x=ts[\"date\"], y=ts[\"niveau_nappe_eau\"],\n",
+    "            mode=\"lines\", name=cls,\n",
+    "            line=dict(color=color, width=1),\n",
+    "            showlegend=(i == 0),\n",
+    "        ),\n",
+    "        row=i + 1, col=1,\n",
+    "    )\n",
+    "    fig.update_yaxes(title_text=\"Level (m NGF)\", row=i + 1, col=1)\n",
+    "\n",
+    "fig.update_layout(\n",
+    "    height=250 * n_stations,\n",
+    "    width=900,\n",
+    "    title_text=\"Representative groundwater level time series by hydrogeological class\",\n",
+    "    template=TEMPLATE,\n",
+    "    font=FONT,\n",
+    "    showlegend=False,\n",
+    ")\n",
+    "fig.update_xaxes(title_text=\"Date\", row=n_stations, col=1)\n",
+    "fig.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Observation:** The six classes display markedly different temporal dynamics:\n",
+    "- **Poreux** (porous): smooth, slow inertia with long-period seasonal cycles.\n",
+    "- **Fissure** (fractured): more reactive, with sharper peaks and recession curves.\n",
+    "- **Karstique** (karst): flashy, spiky responses to precipitation events.\n",
+    "- **Double porosity** classes: intermediate behaviors reflecting mixed aquifer properties.\n",
+    "- **Composite**: complex, irregular patterns.\n",
+    "\n",
+    "These differences in temporal shape are exactly what time-series embeddings should encode."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "---\n",
+    "## 6. Multivariate View\n",
+    "\n",
+    "For one station, we visualize all four variables from the multivariate dataset:\n",
+    "groundwater level + three ERA5 climate covariates (temperature, precipitation, evapotranspiration).\n",
+    "This illustrates why multivariate embeddings may capture additional signal: climatic forcing\n",
+    "drives aquifer recharge, and different hydrogeological environments respond differently to\n",
+    "the same climate inputs."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Load multivariate data for one station\n",
+    "multi = pd.read_parquet(f\"{DATA_DIR}/piezo_daily_multi.parquet\")\n",
+    "multi[\"date\"] = pd.to_datetime(multi[\"date\"])\n",
+    "print(f\"Multivariate dataset: {multi.shape[0]:,} rows, {multi['code_bss'].nunique()} stations\")\n",
+    "print(f\"Variables: {list(multi.columns)}\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Pick the first example station\n",
+    "demo_bss = example_ids[0]\n",
+    "demo_cls = example_stations[0][\"milieu_label\"]\n",
+    "ts_multi = multi[multi[\"code_bss\"] == demo_bss].sort_values(\"date\").copy()\n",
+    "\n",
+    "# Limit to a 5-year window for readability\n",
+    "ts_multi_window = ts_multi[\n",
+    "    (ts_multi[\"date\"] >= ts_multi[\"date\"].min() + pd.Timedelta(days=365))\n",
+    "    & (ts_multi[\"date\"] < ts_multi[\"date\"].min() + pd.Timedelta(days=365 * 6))\n",
+    "]\n",
+    "\n",
+    "variables = [\n",
+    "    (\"niveau_nappe_eau\", \"Groundwater level (m NGF)\", \"#636EFA\"),\n",
+    "    (\"temperature_2m\", \"Temperature 2m (K)\", \"#EF553B\"),\n",
+    "    (\"total_precipitation\", \"Precipitation (m/day)\", \"#00CC96\"),\n",
+    "    (\"potential_evaporation\", \"Pot. evapotranspiration (m/day)\", \"#FFA15A\"),\n",
+    "]\n",
+    "\n",
+    "fig = make_subplots(\n",
+    "    rows=4, cols=1,\n",
+    "    shared_xaxes=True,\n",
+    "    vertical_spacing=0.05,\n",
+    "    subplot_titles=[v[1] for v in variables],\n",
+    ")\n",
+    "\n",
+    "for i, (col, label, color) in enumerate(variables):\n",
+    "    fig.add_trace(\n",
+    "        go.Scatter(\n",
+    "            x=ts_multi_window[\"date\"], y=ts_multi_window[col],\n",
+    "            mode=\"lines\", name=label,\n",
+    "            line=dict(color=color, width=1),\n",
+    "        ),\n",
+    "        row=i + 1, col=1,\n",
+    "    )\n",
+    "    fig.update_yaxes(title_text=label.split(\"(\")[0].strip(), row=i + 1, col=1)\n",
+    "\n",
+    "fig.update_layout(\n",
+    "    height=800,\n",
+    "    width=900,\n",
+    "    title_text=f\"Multivariate view: {demo_bss} ({demo_cls})\",\n",
+    "    template=TEMPLATE,\n",
+    "    font=FONT,\n",
+    "    showlegend=False,\n",
+    ")\n",
+    "fig.update_xaxes(title_text=\"Date\", row=4, col=1)\n",
+    "fig.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Key insight:** Groundwater level responds to seasonal precipitation and evapotranspiration cycles\n",
+    "with a characteristic lag and damping that depends on the aquifer type.\n",
+    "Multivariate embeddings can encode this transfer function (climate input to water level response),\n",
+    "providing richer features for classification than the water level alone."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "---\n",
+    "## 7. Data Quality\n",
+    "\n",
+    "Assess data completeness: missing values, temporal coverage, and gaps.\n",
+    "This matters because short or heavily gapped series may produce unreliable embeddings\n",
+    "and need to be filtered or handled carefully."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Missing values in metadata\n",
+    "print(\"Missing values in station_metadata:\")\n",
+    "missing = meta.isnull().sum()\n",
+    "missing = missing[missing > 0].sort_values(ascending=False)\n",
+    "print(missing.to_string())\n",
+    "print(f\"\\nStations without milieu_eh label: {meta['milieu_eh'].isnull().sum()} / {len(meta)}\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Temporal coverage: histogram of nb_mois_total\n",
+    "fig = px.histogram(\n",
+    "    meta,\n",
+    "    x=\"nb_mois_total\",\n",
+    "    nbins=50,\n",
+    "    title=\"Temporal coverage per station (total months of data)\",\n",
+    "    labels={\"nb_mois_total\": \"Total months of data\", \"count\": \"Number of stations\"},\n",
+    "    template=TEMPLATE,\n",
+    "    color_discrete_sequence=[\"#636EFA\"],\n",
+    "    height=400,\n",
+    "    width=800,\n",
+    ")\n",
+    "fig.add_vline(\n",
+    "    x=meta[\"nb_mois_total\"].median(),\n",
+    "    line_dash=\"dash\", line_color=\"red\",\n",
+    "    annotation_text=f\"Median: {meta['nb_mois_total'].median():.0f} months\",\n",
+    "    annotation_position=\"top right\",\n",
+    ")\n",
+    "fig.update_layout(font=FONT)\n",
+    "fig.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Missing values in univariate time series\n",
+    "uni_missing = uni.groupby(\"code_bss\").agg(\n",
+    "    n_rows=(\"niveau_nappe_eau\", \"count\"),\n",
+    "    n_missing=(\"niveau_nappe_eau\", lambda x: x.isnull().sum()),\n",
+    "    date_min=(\"date\", \"min\"),\n",
+    "    date_max=(\"date\", \"max\"),\n",
+    ")\n",
+    "uni_missing[\"span_days\"] = (uni_missing[\"date_max\"] - uni_missing[\"date_min\"]).dt.days\n",
+    "uni_missing[\"coverage_pct\"] = (\n",
+    "    (uni_missing[\"n_rows\"] - uni_missing[\"n_missing\"]) / uni_missing[\"span_days\"] * 100\n",
+    ").clip(0, 100)\n",
+    "\n",
+    "print(f\"Stations in univariate dataset: {len(uni_missing)}\")\n",
+    "print(f\"\\nMissing value statistics (niveau_nappe_eau):\")\n",
+    "print(f\"  Stations with no missing: {(uni_missing['n_missing'] == 0).sum()}\")\n",
+    "print(f\"  Stations with >10% missing: {(uni_missing['n_missing'] / uni_missing['n_rows'] > 0.10).sum()}\")\n",
+    "print(f\"\\nCoverage (valid days / span):\")\n",
+    "print(uni_missing[\"coverage_pct\"].describe().round(1).to_string())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Coverage histogram\n",
+    "fig = px.histogram(\n",
+    "    uni_missing,\n",
+    "    x=\"coverage_pct\",\n",
+    "    nbins=50,\n",
+    "    title=\"Data coverage per station (valid observations / total span)\",\n",
+    "    labels={\"coverage_pct\": \"Coverage (%)\", \"count\": \"Number of stations\"},\n",
+    "    template=TEMPLATE,\n",
+    "    color_discrete_sequence=[\"#00CC96\"],\n",
+    "    height=400,\n",
+    "    width=800,\n",
+    ")\n",
+    "fig.update_layout(font=FONT)\n",
+    "fig.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Time span distribution\n",
+    "fig = px.histogram(\n",
+    "    uni_missing,\n",
+    "    x=\"span_days\",\n",
+    "    nbins=50,\n",
+    "    title=\"Time span per station (days between first and last observation)\",\n",
+    "    labels={\"span_days\": \"Span (days)\", \"count\": \"Number of stations\"},\n",
+    "    template=TEMPLATE,\n",
+    "    color_discrete_sequence=[\"#AB63FA\"],\n",
+    "    height=400,\n",
+    "    width=800,\n",
+    ")\n",
+    "fig.add_vline(\n",
+    "    x=365,\n",
+    "    line_dash=\"dash\", line_color=\"red\",\n",
+    "    annotation_text=\"1 year (min for 365-day window)\",\n",
+    "    annotation_position=\"top right\",\n",
+    ")\n",
+    "fig.update_layout(font=FONT)\n",
+    "fig.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Findings:**\n",
+    "- Most stations have long records (median coverage >> 12 months), ensuring sufficient data for windowing.\n",
+    "- Missing values in the water level column exist but are generally sparse, confirming\n",
+    "  that the dataset was pre-filtered for quality.\n",
+    "- A few stations have short spans; the windowing step (Section 8) will naturally exclude\n",
+    "  stations with fewer than 365 consecutive valid days."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "---\n",
+    "## 8. Windowing Illustration\n",
+    "\n",
+    "The embedding pipeline extracts fixed-length windows from each station's time series.\n",
+    "We use a **365-day window** with a **90-day stride** (overlap of 275 days).\n",
+    "This section visualizes how overlapping windows are extracted from a single station,\n",
+    "producing multiple embedding vectors per station that are later aggregated (mean-pooled)\n",
+    "into a single station-level representation."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "WINDOW_SIZE = 365  # days\n",
+    "STRIDE = 90        # days\n",
+    "\n",
+    "# Use the first example station\n",
+    "demo_ts = uni[uni[\"code_bss\"] == demo_bss].sort_values(\"date\").copy()\n",
+    "demo_ts = demo_ts.dropna(subset=[\"niveau_nappe_eau\"]).reset_index(drop=True)\n",
+    "\n",
+    "# Pick a 3-year segment for clarity\n",
+    "start_date = demo_ts[\"date\"].min() + pd.Timedelta(days=365)\n",
+    "end_date = start_date + pd.Timedelta(days=365 * 3)\n",
+    "segment = demo_ts[(demo_ts[\"date\"] >= start_date) & (demo_ts[\"date\"] < end_date)].copy()\n",
+    "\n",
+    "# Extract windows\n",
+    "windows = []\n",
+    "for i in range(0, len(segment) - WINDOW_SIZE + 1, STRIDE):\n",
+    "    w = segment.iloc[i:i + WINDOW_SIZE]\n",
+    "    if len(w) == WINDOW_SIZE:\n",
+    "        windows.append(w)\n",
+    "\n",
+    "# Show only the first 4 windows for visual clarity\n",
+    "n_show = min(4, len(windows))\n",
+    "print(f\"Station: {demo_bss} ({demo_cls})\")\n",
+    "print(f\"Segment: {segment['date'].min().date()} to {segment['date'].max().date()}\")\n",
+    "print(f\"Total windows extracted: {len(windows)} (showing first {n_show})\")\n",
+    "print(f\"Window size: {WINDOW_SIZE} days, stride: {STRIDE} days\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Visualize overlapping windows\n",
+    "window_colors = [\"#636EFA\", \"#EF553B\", \"#00CC96\", \"#FFA15A\", \"#AB63FA\"]\n",
+    "\n",
+    "fig = go.Figure()\n",
+    "\n",
+    "# Background: full segment in light gray\n",
+    "fig.add_trace(go.Scatter(\n",
+    "    x=segment[\"date\"], y=segment[\"niveau_nappe_eau\"],\n",
+    "    mode=\"lines\",\n",
+    "    line=dict(color=\"lightgray\", width=1),\n",
+    "    name=\"Full segment\",\n",
+    "    showlegend=True,\n",
+    "))\n",
+    "\n",
+    "# Overlay each window with a distinct color\n",
+    "for j in range(n_show):\n",
+    "    w = windows[j]\n",
+    "    fig.add_trace(go.Scatter(\n",
+    "        x=w[\"date\"], y=w[\"niveau_nappe_eau\"],\n",
+    "        mode=\"lines\",\n",
+    "        line=dict(color=window_colors[j % len(window_colors)], width=2),\n",
+    "        name=f\"Window {j + 1} ({w['date'].iloc[0].strftime('%Y-%m-%d')} to {w['date'].iloc[-1].strftime('%Y-%m-%d')})\",\n",
+    "    ))\n",
+    "    # Add vertical markers for window boundaries\n",
+    "    for dt in [w[\"date\"].iloc[0], w[\"date\"].iloc[-1]]:\n",
+    "        fig.add_vline(\n",
+    "            x=dt, line_dash=\"dot\",\n",
+    "            line_color=window_colors[j % len(window_colors)],\n",
+    "            opacity=0.4,\n",
+    "        )\n",
+    "\n",
+    "fig.update_layout(\n",
+    "    title=f\"Windowing illustration: {WINDOW_SIZE}-day windows, {STRIDE}-day stride -- {demo_bss}\",\n",
+    "    xaxis_title=\"Date\",\n",
+    "    yaxis_title=\"Groundwater level (m NGF)\",\n",
+    "    template=TEMPLATE,\n",
+    "    font=FONT,\n",
+    "    height=450,\n",
+    "    width=900,\n",
+    "    legend=dict(yanchor=\"top\", y=0.99, xanchor=\"left\", x=0.01, bgcolor=\"rgba(255,255,255,0.8)\"),\n",
+    ")\n",
+    "fig.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Summary:**\n",
+    "Each colored segment represents one 365-day input window fed to the encoder.\n",
+    "Consecutive windows overlap by 275 days (stride = 90 days), ensuring dense temporal coverage.\n",
+    "The encoder maps each window to a fixed-dimensional embedding vector.\n",
+    "All window embeddings for a station are then mean-pooled into a single station-level representation\n",
+    "used for downstream evaluation (classification, clustering, geographic coherence)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "---\n",
+    "## Summary\n",
+    "\n",
+    "| Property | Value |\n",
+    "|----------|-------|\n",
+    "| Total stations (metadata) | 4,210 |\n",
+    "| Stations with time series | 2,000 |\n",
+    "| Stations with milieu_eh label | ~3,623 |\n",
+    "| Number of classes | 8 (+ missing) |\n",
+    "| Majority class (Poreux) | ~48% |\n",
+    "| Smallest class (Indetermine) | <1% |\n",
+    "| Variables (multivariate) | groundwater level, temperature, precipitation, evapotranspiration |\n",
+    "| Window size | 365 days |\n",
+    "| Stride | 90 days |\n",
+    "\n",
+    "**Implications for benchmark design:**\n",
+    "1. **Class imbalance** -- use balanced accuracy and macro-F1; apply class weights.\n",
+    "2. **Spatial autocorrelation** -- use department-level group cross-validation.\n",
+    "3. **Diverse temporal dynamics** -- good discriminative signal exists for embeddings to capture.\n",
+    "4. **Multivariate covariates** -- climate forcing adds information beyond the water level alone.\n",
+    "5. **Windowing** -- 365-day windows with 90-day stride provide dense coverage and multiple samples per station."
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "name": "python",
+   "version": "3.12.0"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}