Agronomy & Precision Irrigation Engineering
FAO Crop Coefficient Kc & Leaching Fraction Formula
Calculate FAO-56 Crop Evapotranspiration ET_c = K_c * ET_0, Ayers-Westcot Salinity Leaching Requirement LR = EC_w / (5 * EC_e - EC_w), Net Leaching-Adjusted Depth, and Gross Pumped Irrigation.
Prevent root-zone salt accumulation while scheduling FAO-56 drip irrigation!
Under UN FAO Irrigation & Drainage Paper 56 (Allen et al., 1998) and Paper 29 (Ayers & Westcot, 1985), crop water demand starts with Crop Evapotranspiration ET_c = K_c * ET_0 (multiplying Reference Grass Evapotranspiration ET_0 by growth-stage Crop Coefficient K_c) minus Effective Rainfall P_eff! Yet applying only MAX(0, ET_c - P_eff) with brackish well water of Electrical Conductivity EC_w (dS/m) concentrates dissolved salts in the root zone! To keep saturated-paste soil salinity at or below Crop Yield-Loss Threshold EC_e (dS/m), irrigators add Ayers & Westcot’s Leaching Requirement fraction LR = EC_w / (5 * EC_e - EC_w), raising Net Required Soil Infiltration to MAX(0, ET_c - P_eff) / (1 - LR) and Gross Pumped Depth to Net_Depth / eta_irr!
Verify on Reference_ET_0 = 6.00 mm/day (B2), Mid_Season_Kc = 1.15 (B3 -> ET_c = 6.90 mm/day in E2), Effective_Rainfall P_eff = 0.90 mm/day (Net ET Deficit = 6.00 mm/day, B4), Well_Water_Salinity EC_w = 1.50 dS/m (B5), Crop_Salt_Threshold EC_e = 1.80 dS/m (sensitive vegetable/orchard crop, B6), and Drip_System_Efficiency eta_irr = 0.90 (90.0%, B7): Leaching Requirement is 1.50 / (5 * 1.80 - 1.50) = 1.50 / 7.50 = 0.2000 (20.00% in E3); Leaching-Adjusted Net Depth is 6.00 / (1 - 0.20) = 7.50 mm/day (E4); and Gross Pumped Irrigation Depth is 7.50 / 0.90 = 8.33 mm/day (E5)! Test ultrapure rainwater/canal water EC_w = 0.00 dS/m: LR drops to 0.0000 and Gross Depth drops to 6.00 / 0.90 = 6.67 mm/day!
| FAO-56 / Ayers-Westcot Metric (ET0=6.0, Kc=1.15, Peff=0.9, ECw=1.5, ECe=1.8, Eff=90%) | Formula | Verified Output |
|---|---|---|
| Crop Evapotranspiration ET_c | K_c * ET_0 | 6.90 mm/day |
| Salinity Leaching Requirement LR | EC_w / (5 * EC_e - EC_w) | 0.2000 (20.00% Flush) |
| Leaching-Adjusted Net Depth | MAX(0, ET_c - P_eff) / (1 - LR) | 7.50 mm/day |
| Gross Pumped Irrigation Depth | Net_Leached_Depth / eta_irr | 8.33 mm/day (83.3 m^3/ha/d) |
Salinity-Guarded Gross Irrigation Requirement Formula
Check 5 * EC_e - EC_w > EC_w (i.e. EC_w < 2.5 * EC_e so LR < 1): if EC_w >= 2.5 * EC_e, even continuous flushing cannot hold soil salinity down to EC_e ("Water Too Saline (LR >= 1)")!
=LET(et_0, B2, k_cp, B3, p_ef, B4, ec_w, B5, ec_e, B6, et_i, B7, IF(OR(et_0 < 0, k_cp <= 0, p_ef < 0, ec_w < 0, ec_e <= 0, et_i <= 0, et_i > 1), "Invalid Irrigation Input", IF(ec_w >= 2.5 * ec_e, "Water Too Saline (LR >= 1)", LET(lr_f, ec_w / (5 * ec_e - ec_w), nt_d, MAX(0, k_cp * et_0 - p_ef) / (1 - lr_f), ROUND(nt_d / et_i, 2)))))Ayers-Westcot Leaching Requirement Fraction Formula
Monitor LR <= 0.25 in poorly drained clay profiles so salt flushing does not waterlog anaerobic roots!
=IF(OR(B2 < 0, B3 <= 0, B4 < 0, B5 < 0, B6 <= 0, B7 <= 0, B7 > 1), "Invalid Irrigation Input", IF(B5 >= 2.5 * B6, "Water Too Saline (LR >= 1)", ROUND(B5 / (5 * B6 - B5), 4)))Try the example
Use the original values or change them to test your understanding.