feat(skewt): add wet-bulb / virtual-T traces and right-edge level rail

Three additions that bring the diagram closer to the SPC sounding
viewer's full-information chart:

  * Wet-bulb temperature trace, plotted as a thinner blue line under
    the dewpoint trace. Comes from a Stipanuk-style bracket between
    the level's dewpoint and dry-bulb temperatures (already used by
    `SkewtParams` for the wet-bulb-zero level — now public so the
    renderer can call it per level).

  * Environment virtual-temperature trace and parcel virtual-T
    trajectory, both as thin pinkish dashed lines. The parcel
    virtual-T is the actual buoyancy curve CAPE integrates against,
    so showing it next to the dry-bulb parcel ascent makes the
    moisture correction visible. New `SkewtParams.virtual_temp_c/2`
    and `/3` helpers, plus `SkewtParams.mixing_ratio/2`.

  * Critical-level rail on the right edge. Each of LCL / LFC / EL /
    0 °C / WBZ that resolves on the current profile gets a short
    horizontal tick at the right of the plot and a `<label> <p> mb`
    tag just outside it — matches the SPC chart's `143 mb (mix)` /
    `158 mb (mix)` annotation column. SkewtLive computes the
    pressures (and converts the height-keyed 0 °C and WBZ from
    SkewtParams back to pressure via `pressure_at_height/2`) before
    handing them to `SkewtSvg.render/2`.

Wind-derived overlays (hodograph, wind barbs) remain off — HRRR
profile data is wind-free above 10 m AGL.

mix test: 27 / 27 across the four /skewt-related test files,
2,902 / 2,902 + 221 properties on the full suite. mix credo --strict
clean (one cyclomatic-complexity refactor extracted along the way).

lib/microwaveprop/weather/skewt_params.ex

@@ -357,18 +357,59 @@ defmodule Microwaveprop.Weather.SkewtParams do
     end)
   end
 
-  defp wet_bulb_c(level) do
-    # Stipanuk-style iterative approximation: T_wb satisfies
-    # e_s(T_wb) = e + (p × c_p / (ε × L_v)) × (T - T_wb)
-    # Solve by bracketing between dewpoint and dry bulb.
-    t_d = level.dwpc
-    t = level.tmpc
+  @doc """
+  Wet-bulb temperature (°C) for a level using a Stipanuk-style
+  iterative bracket between dewpoint and dry bulb. Returns `nil` if
+  either temperature is missing.
 
-    if t_d == nil or t == nil do
-      nil
-    else
-      bisect_wet_bulb(t, t_d, level.pres)
-    end
+  Accepts a level map with `tmpc`, `dwpc`, and `pres` keys (the same
+  normalized shape `derive/1` consumes).
+  """
+  @spec wet_bulb_c(map()) :: float() | nil
+  def wet_bulb_c(%{tmpc: t, dwpc: t_d, pres: _p}) when t == nil or t_d == nil, do: nil
+
+  def wet_bulb_c(%{tmpc: t, dwpc: t_d, pres: p}) do
+    bisect_wet_bulb(t, t_d, p)
+  end
+
+  def wet_bulb_c(_), do: nil
+
+  @doc """
+  Mixing ratio (kg/kg) at a given dewpoint and pressure, via the Buck
+  saturation-vapor formula evaluated at the dewpoint temperature.
+  Returns `nil` for non-numeric inputs.
+  """
+  @spec mixing_ratio(number() | nil, number() | nil) :: float() | nil
+  def mixing_ratio(dewpoint_c, pressure_mb) when is_number(dewpoint_c) and is_number(pressure_mb) do
+    e = saturation_vapor_pressure_mb(dewpoint_c)
+    @epsilon * e / max(pressure_mb - e, 1.0e-3)
+  end
+
+  def mixing_ratio(_, _), do: nil
+
+  @doc """
+  Virtual temperature (°C) for a parcel/level. Adds the moisture
+  correction `(1 + 0.61 r)` to the dry-bulb temperature, where `r` is
+  the mixing ratio in kg/kg.
+
+  Two calling forms:
+
+    * `virtual_temp_c(temp_c, dewpoint_c, pressure_mb)` — environment
+      virtual temperature (uses the actual mixing ratio from the
+      dewpoint).
+    * `virtual_temp_c(temp_c, pressure_mb)` — parcel virtual temperature
+      assuming saturation (uses the saturation mixing ratio at the
+      parcel's own temperature). This is what CAPE uses above the LCL.
+  """
+  @spec virtual_temp_c(number(), number(), number()) :: float()
+  def virtual_temp_c(temp_c, dewpoint_c, pressure_mb) do
+    r = mixing_ratio(dewpoint_c, pressure_mb) || 0.0
+    (temp_c + 273.15) * (1.0 + 0.61 * r) - 273.15
+  end
+
+  @spec virtual_temp_c(number(), number()) :: float()
+  def virtual_temp_c(temp_c, pressure_mb) do
+    virtual_temp_c(temp_c, temp_c, pressure_mb)
   end
 
   defp bisect_wet_bulb(t, t_d, _p) when t == t_d, do: t

lib/microwaveprop_web/live/skewt_live.ex

@@ -127,7 +127,13 @@ defmodule MicrowavepropWeb.SkewtLive do
           # SoundingParams keys (atoms) and SkewtParams keys (atoms)
           # are disjoint by construction.
           derived = Map.merge(sounding || %{}, spc)
-          svg = SkewtSvg.render(profile, parcel_trace: spc[:parcel_trace] || [])
+
+          svg =
+            SkewtSvg.render(profile,
+              parcel_trace: spc[:parcel_trace] || [],
+              critical_levels: critical_levels(spc, profile)
+            )
+
           {profile, derived, svg}
         end
     end
@@ -137,6 +143,52 @@ defmodule MicrowavepropWeb.SkewtLive do
     cell[:profile] || cell["profile"] || []
   end
 
+  # Right-edge critical-level markers, mirroring SPC's annotation rail.
+  # Pressure → label is enough; SkewtSvg uses pressure_y/1 to position.
+  # 0 °C and wet-bulb-zero come back from SkewtParams as heights, so
+  # we walk the profile to recover the corresponding pressure.
+  defp critical_levels(spc, profile) do
+    Enum.flat_map(
+      [
+        {"LCL", spc[:lcl_pressure_mb]},
+        {"LFC", spc[:lfc_pressure_mb]},
+        {"EL", spc[:el_pressure_mb]},
+        {"0 °C", pressure_at_height(profile, spc[:freezing_level_m])},
+        {"WBZ", pressure_at_height(profile, spc[:wbz_m])}
+      ],
+      fn
+        {label, p} when is_number(p) -> [%{label: label, pressure_mb: p}]
+        _ -> []
+      end
+    )
+  end
+
+  defp pressure_at_height(_profile, nil), do: nil
+
+  defp pressure_at_height(profile, target_m) when is_number(target_m) do
+    profile
+    |> Enum.map(&extract_pres_hght/1)
+    |> Enum.filter(&(is_number(&1.pres) and is_number(&1.hght)))
+    |> Enum.sort_by(& &1.pres, :desc)
+    |> Enum.chunk_every(2, 1, :discard)
+    |> Enum.find_value(&interpolate_pressure_at_height(&1, target_m))
+  end
+
+  defp extract_pres_hght(lvl) do
+    %{
+      pres: lvl[:pres] || lvl["pres"] || lvl[:pres_mb] || lvl["pres_mb"],
+      hght: lvl[:hght] || lvl["hght"] || lvl[:hght_m] || lvl["hght_m"]
+    }
+  end
+
+  defp interpolate_pressure_at_height([a, b], target_m) do
+    cond do
+      a.hght == b.hght -> nil
+      (a.hght - target_m) * (b.hght - target_m) > 0 -> nil
+      true -> a.pres + (target_m - a.hght) / (b.hght - a.hght) * (b.pres - a.pres)
+    end
+  end
+
   defp available_valid_times(lat, lon) do
     # The chain produces analysis + 18 forecast hours every wall-clock
     # hour. By the time the next chain finishes the previous chain's

lib/microwaveprop_web/live/skewt_svg.ex

@@ -10,6 +10,7 @@ defmodule MicrowavepropWeb.SkewtSvg do
   AGL, not on the pressure-level profile, so a per-level barb column
   would be misleading.
   """
+  alias Microwaveprop.Weather.SkewtParams
 
   # Plot canvas (SVG user units).
   @width 720
@@ -42,6 +43,7 @@ defmodule MicrowavepropWeb.SkewtSvg do
   def render(profile, opts \\ []) when is_list(profile) do
     cleaned = clean_profile(profile)
     parcel = Keyword.get(opts, :parcel_trace, [])
+    critical = Keyword.get(opts, :critical_levels, [])
 
     plot_w = @right - @left
     plot_h = @bottom - @top
@@ -61,16 +63,108 @@ defmodule MicrowavepropWeb.SkewtSvg do
       dry_adiabats(),
       moist_adiabats(),
       mixing_ratio_lines(),
+      virtual_temp_trace(cleaned),
+      wet_bulb_trace(cleaned),
       profile_traces(cleaned),
       parcel_trace_line(parcel),
+      parcel_virtual_trace(parcel),
       "</g>",
       frame(),
       axis_labels(),
+      critical_level_markers(critical),
       cursor_layer(),
       "</svg>"
     ]
   end
 
+  # ── Wet-bulb / virtual-T traces (NOAA SPC supplementary lines) ─────
+
+  defp wet_bulb_trace([]), do: ""
+
+  defp wet_bulb_trace(profile) do
+    pts =
+      profile
+      |> Enum.sort_by(& &1.pres, :desc)
+      |> Enum.flat_map(fn lvl ->
+        case SkewtParams.wet_bulb_c(%{
+               tmpc: lvl.tmpc,
+               dwpc: lvl.dwpc,
+               pres: lvl.pres
+             }) do
+          nil -> []
+          t_w -> [{temperature_x(t_w, pressure_y(lvl.pres)), pressure_y(lvl.pres)}]
+        end
+      end)
+      |> clip_polyline()
+
+    polyline_or_empty(pts, "wet-bulb-line")
+  end
+
+  defp virtual_temp_trace([]), do: ""
+
+  defp virtual_temp_trace(profile) do
+    pts =
+      profile
+      |> Enum.sort_by(& &1.pres, :desc)
+      |> Enum.map(fn lvl ->
+        t_v = SkewtParams.virtual_temp_c(lvl.tmpc, lvl.dwpc, lvl.pres)
+        y = pressure_y(lvl.pres)
+        {temperature_x(t_v, y), y}
+      end)
+      |> clip_polyline()
+
+    polyline_or_empty(pts, "virtual-temp-line")
+  end
+
+  # Parcel ascent uses the saturated mixing ratio at its own
+  # temperature above the LCL — that's the virtual-T trajectory used
+  # in the actual CAPE integration. SPC draws this as a thin red
+  # dashed line slightly to the right of the dry-bulb parcel trace.
+  defp parcel_virtual_trace([]), do: ""
+
+  defp parcel_virtual_trace(trace) do
+    pts =
+      trace
+      |> Enum.sort_by(& &1.pres, :desc)
+      |> Enum.map(fn %{pres: p, tmpc: t} ->
+        t_v = SkewtParams.virtual_temp_c(t, p)
+        y = pressure_y(p)
+        {temperature_x(t_v, y), y}
+      end)
+      |> clip_polyline()
+
+    polyline_or_empty(pts, "parcel-virtual-line")
+  end
+
+  # Critical-level annotations on the right edge — each entry is a
+  # `%{label, pressure_mb}` map; the label appears outside the frame
+  # at the right so it doesn't obscure the trace, with a short
+  # in-plot tick. Mirrors SPC's `143 mb`, `158 mb (mix)`, etc. rail.
+  defp critical_level_markers([]), do: ""
+
+  defp critical_level_markers(levels) do
+    Enum.flat_map(levels, fn
+      %{label: label, pressure_mb: p} when is_number(p) ->
+        y = pressure_y(p)
+
+        if y >= @top and y <= @bottom do
+          [render_critical_marker(label, p, y)]
+        else
+          []
+        end
+
+      _ ->
+        []
+    end)
+  end
+
+  defp render_critical_marker(label, pressure_mb, y) do
+    [
+      ~s|<line class="critical-tick" x1="#{@right - 8}" y1="#{r(y)}" x2="#{@right}" y2="#{r(y)}"/>|,
+      ~s|<text class="critical-label" x="#{@right + 4}" y="#{r(y) + 3}">#{label} #{round(pressure_mb)} mb</text>|
+    ]
+  end
+
   # Surface-parcel ascent line (dashed grey), matching the SPC viewer's
   # convention. The trace is a list of `%{pres, tmpc}` from surface up
   # through every level above the LCL.
@@ -147,6 +241,11 @@ defmodule MicrowavepropWeb.SkewtSvg do
         .temp-line { fill: none; stroke: #ff0000; stroke-width: 2.5; stroke-linejoin: round; stroke-linecap: round; }
         .dew-line  { fill: none; stroke: #00aa00; stroke-width: 2.5; stroke-linejoin: round; stroke-linecap: round; }
         .parcel-line { fill: none; stroke: #475569; stroke-width: 1.5; stroke-dasharray: 5 4; stroke-linejoin: round; stroke-linecap: round; }
+        .parcel-virtual-line { fill: none; stroke: #f87171; stroke-width: 1; stroke-dasharray: 2 3; stroke-linejoin: round; stroke-linecap: round; }
+        .virtual-temp-line { fill: none; stroke: #fb7185; stroke-width: 1; stroke-dasharray: 1 3; stroke-linejoin: round; stroke-linecap: round; }
+        .wet-bulb-line { fill: none; stroke: #2563eb; stroke-width: 1.4; stroke-linejoin: round; stroke-linecap: round; opacity: 0.85; }
+        .critical-tick { stroke: currentColor; stroke-width: 1.2; }
+        .critical-label { font: 10px ui-sans-serif, system-ui, sans-serif; fill: currentColor; fill-opacity: 0.85; }
         .skewt-cursor-line { stroke: currentColor; stroke-opacity: 0.5; stroke-width: 0.8; stroke-dasharray: 3 3; pointer-events: none; }
         .skewt-cursor-dot-t { fill: #ff0000; pointer-events: none; }
         .skewt-cursor-dot-d { fill: #00aa00; pointer-events: none; }