🗺 Map & Footprint
Cumulative Weights
Weight Table
Method
Click anywhere on the map to place the CRNS sensor. Drag the marker to reposition. Footprint contours update live as you change parameters.
Cumulative radial signal fraction
Run the tool to see results.
Cumulative depth signal fraction
Run the tool to see results.
Adjust parameters to populate table.
Radial weighting Wr(r, x, y) — Schron et al. (2017) eq. 4–5, Table A1:
where F1–F4 are functions of absolute air humidity x (g m⁻³) and volumetric soil moisture y (m³ m⁻³). The cumulative ring-area integral
Sensor height correction hs — Schron et al. (2017) eq. A5:
An elevated sensor reduces the near-field weight relative to far-field, expanding the footprint.
Effect: ~1.5 m increase in R₈₆ per 0.5 m of sensor height. D₈₆ is unaffected.
Vertical (depth) weighting Wd(d, r) — Köhli et al. (2015), Schrön et al. (2017), exact formulation as implemented in the neptoon Python package:
D₈₆ depends on radial distance r from the sensor — sensing depth is shallower close to the sensor and deeper further out (Schrön 2017, Fig. 1b). This replaces the distance-independent Franz (2012) formula used in earlier versions of this tool. Since depth sensitivity varies with distance, the depth profile shown here is evaluated at the footprint's characteristic radius (R₈₆ of the horizontal footprint) as a representative single-point summary. D₂₅, D₅₀, D₇₅, D₈₆, D₉₀ are the depths above which 25%, 50%, 75%, 86% and 90% of vertical signal sensitivity accumulates at that radius.
Absolute humidity x is derived from T and RH via the Buck (1981) equation.
Altitude / pressure correction fp (Desilets et al. 2010, Schron 2017 eq. 1):
where M = 0.0289644 kg/mol (molar mass of air), g = 9.8 m/s², R = 8.31432 J/(mol·K), and T_K is air temperature in Kelvin. At altitude, lower air pressure means less atmospheric shielding and more incoming cosmic ray flux. fp is shown for reference but is not directly applied to the radial or depth footprint formulas, which are evaluated at the site's actual humidity and moisture conditions.
Bulk density ρb:
Appears directly in the denominator of the D₈₆(r) formula above — denser soils have a shallower sensing depth at every radius. No separate lattice water correction is applied in this formulation; the effect is absorbed into the calibrated 8.321/0.14249 coefficients.
Map contours are true geodesic circles at R₂₅ (orange), R₅₀ (blue), R₇₅ (teal), R₈₆ (gold, thicker — standard footprint) and R₉₀ (red).
References
· Köhli M. et al. (2015) Water Resour. Res. 51, 5772–5790. doi:10.1002/2015WR017169
· Schron M. et al. (2017) Hydrol. Earth Syst. Sci. 21, 5009–5030. doi:10.5194/hess-21-5009-2017
Wr(r) = F1·exp(−F2·r) + F3·exp(−F4·r)where F1–F4 are functions of absolute air humidity x (g m⁻³) and volumetric soil moisture y (m³ m⁻³). The cumulative ring-area integral
∫₀ᴿ 2πr·Wr(r)dr defines R₂₅, R₅₀, R₇₅, R₉₀ —
the radii enclosing 25%, 50%, 75%, 86% and 90% of total signal. The 86% radius (R₈₆) is the standard CRNS footprint metric and is highlighted throughout.Sensor height correction hs — Schron et al. (2017) eq. A5:
An elevated sensor reduces the near-field weight relative to far-field, expanding the footprint.
Wrh(r) = Wr(r) / (1 + 0.0604 × hs × exp(−0.0182 · r))Effect: ~1.5 m increase in R₈₆ per 0.5 m of sensor height. D₈₆ is unaffected.
Vertical (depth) weighting Wd(d, r) — Köhli et al. (2015), Schrön et al. (2017), exact formulation as implemented in the neptoon Python package:
D₈₆(r) [cm] = (1/ρ_b) × [8.321 + 0.14249×(0.96655+e−0.01r)×(20+θ)/(0.0429+θ)]Wd(d, r) = exp(−2·d / D₈₆(r))D₈₆ depends on radial distance r from the sensor — sensing depth is shallower close to the sensor and deeper further out (Schrön 2017, Fig. 1b). This replaces the distance-independent Franz (2012) formula used in earlier versions of this tool. Since depth sensitivity varies with distance, the depth profile shown here is evaluated at the footprint's characteristic radius (R₈₆ of the horizontal footprint) as a representative single-point summary. D₂₅, D₅₀, D₇₅, D₈₆, D₉₀ are the depths above which 25%, 50%, 75%, 86% and 90% of vertical signal sensitivity accumulates at that radius.
Absolute humidity x is derived from T and RH via the Buck (1981) equation.
Altitude / pressure correction fp (Desilets et al. 2010, Schron 2017 eq. 1):
fp = exp(M·g·alt / (R·T_K))where M = 0.0289644 kg/mol (molar mass of air), g = 9.8 m/s², R = 8.31432 J/(mol·K), and T_K is air temperature in Kelvin. At altitude, lower air pressure means less atmospheric shielding and more incoming cosmic ray flux. fp is shown for reference but is not directly applied to the radial or depth footprint formulas, which are evaluated at the site's actual humidity and moisture conditions.
Bulk density ρb:
Appears directly in the denominator of the D₈₆(r) formula above — denser soils have a shallower sensing depth at every radius. No separate lattice water correction is applied in this formulation; the effect is absorbed into the calibrated 8.321/0.14249 coefficients.
Map contours are true geodesic circles at R₂₅ (orange), R₅₀ (blue), R₇₅ (teal), R₈₆ (gold, thicker — standard footprint) and R₉₀ (red).
References
· Köhli M. et al. (2015) Water Resour. Res. 51, 5772–5790. doi:10.1002/2015WR017169
· Schron M. et al. (2017) Hydrol. Earth Syst. Sci. 21, 5009–5030. doi:10.5194/hess-21-5009-2017