VPD + Dew Point
Live VPD (kPa) and dew point (°F) from latest Temp/RH using Tetens + Magnus

Monochrome, print-ready documentation. Emphasis on exact formulas, unit handling, payloads, and drop-in code.

Contents

1. Overview
2. Inputs & Units
3. Formulas (Tetens + Magnus)
4. Target Ranges
5. Network & Endpoint
6. Payload Contract
7. Python Reference Implementation
8. JavaScript Reference Implementation
9. Minimal Front-End Widget
10. Runtime Behavior
11. Troubleshooting
12. Validation Checklist
13. Security & Hardening
14. Extensions & Variations
15. Interpreting VPD & Dew Point
16. Quick Reference

1) Overview

Compute two derived climate metrics for the tent from air temperature and relative humidity:

• VPD (kPa): vapor pressure deficit = saturation vapor pressure at air temp − actual vapor pressure. Higher VPD = drier air.
• Dew point (°F): temperature where air reaches 100% RH if cooled at constant pressure.

Implementation uses Tetens for saturation vapor pressure and Magnus for dew point. Constants match the dashboard implementation.

2) Inputs & Units

3) Formulas (Tetens + Magnus)

// Saturation vapor pressure (kPa)
e_s(Tc) = 0.6108 * exp( (17.27 * Tc) / (Tc + 237.3) )

// Actual vapor pressure (kPa)
e_a = e_s(Tc_air) * (RH / 100.0)

// Vapor Pressure Deficit (kPa)
// Use Tc_leaf if available, else Tc_air
VPD = max(0, e_s(Tc_for_sat) - e_a)

a = 17.62
b = 243.12  // °C
gamma = ln(RH/100) + (a * Tc_air) / (b + Tc_air)
Td_C = (b * gamma) / (a - gamma)
Td_F = Td_C * 9/5 + 32

4) Target Ranges

5) Network & Endpoint

Assume your server exposes the latest air temp and RH, and accepts derived metrics:

6) Payload Contract

{
  "temp": 77.9,           // °F
  "humidity": 58.2,       // % RH
  "light": 123            // lux (example)
}

{
  "sensor_type": "vpd_kpa",  // or "dew_point_f"
  "reading": 1.12,            // numeric value only
  "plant_id": null            // optional
}
// Post one reading per request.
// Example (dew point): {"sensor_type":"dew_point_f","reading":61.7}

Return HTTP 200/201 on success. Log non-2xx with input values.

7) Python Reference Implementation

# Pure functions with explicit units and clamps.
# Matches the dashboard constants (Tetens + Magnus).

import math
from typing import Tuple

A_TETENS = 17.27
B_TETENS = 237.3   # °C
K0 = 0.6108        # kPa

A_MAGNUS = 17.62
B_MAGNUS = 243.12  # °C

def f_to_c(tf: float) -> float:
    return (tf - 32.0) * (5.0/9.0)

def c_to_f(tc: float) -> float:
    return tc * (9.0/5.0) + 32.0

def tetens_es_kpa(tc: float) -> float:
    # Saturation vapor pressure (kPa) at Tc (°C)
    return K0 * math.exp((A_TETENS * tc) / (B_TETENS + tc))

def dew_point_f_from_air(tf_air: float, rh_pct: float) -> float:
    # Clamp RH to [1,100] to avoid log(0) and nonsense
    rh = max(1.0, min(100.0, rh_pct))
    tc = f_to_c(tf_air)
    gamma = math.log(rh / 100.0) + (A_MAGNUS * tc) / (B_MAGNUS + tc)
    td_c = (B_MAGNUS * gamma) / (A_MAGNUS - gamma)
    td_f = c_to_f(td_c)
    return td_f

def vpd_kpa_from_air(tf_air: float, rh_pct: float, tf_leaf: float | None = None) -> float:
    # Use leaf temperature for saturation term if available; else air temp.
    rh = max(0.0, min(100.0, rh_pct))
    tc_air = f_to_c(tf_air)
    tc_sat = f_to_c(tf_leaf) if tf_leaf is not None else tc_air
    es = tetens_es_kpa(tc_sat)              # saturation at leaf/air
    ea = tetens_es_kpa(tc_air) * (rh/100.0) # actual vapor pressure from air
    vpd = max(0.0, es - ea)                 # never negative
    return vpd

# Example usage with prints for debug:
if __name__ == "__main__":
    tf = 77.9
    rh = 58.2
    print(f"[DEBUG] air_temp_f={tf} rh_pct={rh}")
    dp = dew_point_f_from_air(tf, rh)
    vpd = vpd_kpa_from_air(tf, rh)  # no leaf temp
    print(f"[DEBUG] dew_point_f={dp:.2f} vpd_kpa={vpd:.3f}")

8) JavaScript Reference Implementation

<script>
// Minimal, no dependencies. Mirrors the dashboard implementation.

const A_T = 17.27, B_T = 237.3, K0 = 0.6108;     // Tetens (kPa)
const A_M = 17.62, B_M = 243.12;                 // Magnus (dew point)

function fToC(tf){ return (tf - 32) * (5/9); }
function cToF(tc){ return tc * (9/5) + 32; }
function tetensKPa(tc){ return K0 * Math.exp((A_T * tc) / (B_T + tc)); }

function dewPointF(airTempF, rhPct){
  const rh = Math.min(100, Math.max(1, rhPct));
  const Tc = fToC(airTempF);
  const gamma = Math.log(rh/100) + (A_M * Tc) / (B_M + Tc);
  const TdC = (B_M * gamma) / (A_M - gamma);
  const TdF = cToF(TdC);
  console.log("[dp] Tc=%s rh=%s TdF=%s", Tc.toFixed(2), rh.toFixed(1), TdF.toFixed(2));
  return TdF;
}

function vpdKPa(airTempF, rhPct, leafTempF=null){
  const rh = Math.min(100, Math.max(0, rhPct));
  const Tc_air = fToC(airTempF);
  const Tc_sat = leafTempF==null ? Tc_air : fToC(leafTempF);
  const es = tetensKPa(Tc_sat);
  const ea = tetensKPa(Tc_air) * (rh/100);
  const vpd = Math.max(0, es - ea);
  console.log("[vpd] es=%s ea=%s vpd=%s", es.toFixed(4), ea.toFixed(4), vpd.toFixed(4));
  return vpd;
}
</script>

9) Minimal Front-End Widget

<div id="vpdbox" class="card">
  <strong>Live Air:</strong> <span id="air">--</span> °F,
  <strong>RH:</strong> <span id="rh">--</span> %,
  <strong>VPD:</strong> <span id="vpd">--</span> kPa,
  <strong>Dew Pt:</strong> <span id="dp">--</span> °F
</div>

<script>
async function refreshVPD(){
  try{
    const r = await fetch("api/latest.json", { cache:"no-store" });
    if(!r.ok) throw new Error("HTTP " + r.status);
    const j = await r.json();
    const tf = Number(j.temp);
    const rh = Number(j.humidity);
    const v = vpdKPa(tf, rh);
    const dpf = dewPointF(tf, rh);
    document.getElementById("air").textContent = tf.toFixed(1);
    document.getElementById("rh").textContent  = rh.toFixed(1);
    document.getElementById("vpd").textContent = v.toFixed(2);
    document.getElementById("dp").textContent  = dpf.toFixed(1);
    console.log("[widget] tf=%s rh=%s vpd=%s dp=%s", tf, rh, v, dpf);
  }catch(err){
    console.log("[widget] refresh error:", err);
  }
}
refreshVPD();
setInterval(refreshVPD, 60000);
</script>

10) Runtime Behavior

11) Troubleshooting

12) Validation Checklist

• Hand-check one sample with a calculator: expected VPD within ±0.02 kPa.
• Dew point difference air_temp_f − dew_point_f grows when RH drops.
• Constants identical in server and browser code.

13) Security & Hardening

• LAN is fine with HTTP. Use TLS for WAN access.
• Add X-API-Key and verify server-side on write routes.
• Rate-limit POSTs to derived endpoint.

14) Extensions & Variations

• Persist raw inputs. Derive VPD/dew point on read for latest values.
• Store both vpd_kpa_air and vpd_kpa_leaf if you add IR leaf temp.
• Emit an alert when VPD out of bounds for > N minutes.

15) Interpreting VPD & Dew Point

16) Quick Reference

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