7.1 Water Demand Estimation

7.1 Water Demand Estimation

Introduction to Irrigation Water Demand

Efficient water resource management in agriculture hinges on accurately estimating crop water requirements. This process involves quantifying the water needed by crops for optimal growth (crop water requirement), accounting for all losses in the irrigation system (irrigation water requirement), and understanding the dynamic relationship between soil, water, and plants. Precise estimation ensures sustainable water use, prevents waterlogging or salinity, maximizes crop yield, and forms the basis for designing irrigation canals and scheduling deliveries. This unit deconstructs the key concepts, parameters, and relationships used by irrigation engineers to determine the total water demand for an agricultural command area.

---

1. Crop Water and Irrigation Water Requirements

These are fundamental, distinct concepts that form the starting point for all water demand calculations.

1.1 Crop Water Requirement (CWR) / Consumptive Use ($C_u$)

1. Definition: The total depth of water needed by a crop to meet its evapotranspiration (ET) needs for healthy growth over its entire growing period, under given climatic conditions.

2. Components: It is essentially the Evapotranspiration ($ET_c$) of the crop under optimal (non-stressed) conditions.

   • Evaporation (E): Loss of water from the soil surface.

   • Transpiration (T): Loss of water through the plant's leaves.

3. Key Points:

   • Measured in depth units (mm, cm) over a period (day, month, season).

   • Does not include water lost during application (conveyance, field application losses).

   • Varies with crop type (Kc), growth stage, and climate (ETo).

1.2 Irrigation Water Requirement (IWR)

1. Definition: The total depth of water that must be supplied by the irrigation system to the field to meet the crop water requirement, after accounting for contributions from effective rainfall and soil moisture storage.

2. Formula: $IWR = CWR - (P_e + \Delta S)$ Where:

   • $CWR = ET_c$ (Crop Evapotranspiration)

   • $P_e$ = Effective Rainfall

   • $\Delta S$ = Change in Soil Moisture Storage (utilizable water drawn from the root zone).

3. Significance: IWR is the net amount of irrigation water that must reach the root zone. It is the basis for determining the net irrigation depth.

---

2. Water Availability, Command Areas, and Irrigation Intensity

2.1 Water Availability for Irrigation

1. Source Yield: The dependable flow or volume available from a source (river, reservoir, well) during the critical (driest) period of the cropping season.

2. Assessment: Based on hydrology (flow duration curves, reservoir operation studies, groundwater safe yield).

3. Constraint: The available water (Q available) ultimately limits the Irrigable Command Area.

2.2 Command Area

1. Gross Command Area (GCA):

   • The total area that can be economically irrigated by an irrigation system, bounded by natural features (ridges, drains).

   • Includes culturable and non-culturable land (roads, villages, wasteland).

2. Culturable Command Area (CCA):

   • The portion of GCA that is cultivable. $CCA = GCA - \text{(Non-culturable area)}$

   • This is the area targeted for irrigation planning.

3. Irrigable Command Area: The area that can actually be irrigated given the available water supply. It is a subset of CCA.

2.3 Irrigation Intensity (I.I.)

1. Definition: The percentage of the Culturable Command Area (CCA) that is irrigated in a given season (often annually, considering all crop seasons).

2. Formula: $\text{Irrigation Intensity (\%)} = \frac{\text{Total Irrigated Area in a year (ha)}}{\text{CCA (ha)}} \times 100$

   • Total Irrigated Area: Sum of area under each crop in different seasons (e.g., Kharif + Rabi). If the same land grows two crops, it is counted twice.

3. Interpretation:

   • I.I. = 100%: The entire CCA is irrigated once in a year.

   • I.I. = 150%: On average, 1.5 crops are grown per year on the CCA (e.g., 100% area in Kharif + 50% area in Rabi).

4. Significance: Indicates the cropping intensity and intensity of water use in the command.

---

3. Duty (D), Delta (Δ), and Their Fundamental Relationship

These are classical, interrelated measures of irrigation water use.

3.1 Duty of Water (D)

1. Definition: The area of land (in hectares) that can be irrigated to maturity by a continuous supply of 1 cumec (m³/s) of water throughout the base period of the crop.

   • At the head of the watercourse (field channel).

   • Units: hectares per cumec (ha/cumec).

2. Concept: A measure of water-use efficiency. Higher duty means more area is irrigated per unit of water (more efficient use).

3. Factors Affecting Duty:

   • Climate: Hot/dry climates lower duty (more water per hectare).

   • Soil Type: Sandy soils have lower duty (more percolation) than clay soils.

   • Crop Type: Different crops have different water needs.

   • Efficiency of the System: Higher conveyance/application efficiency increases duty.

3.2 Delta of a Crop (Δ)

1. Definition: The total depth of water (in cm or m) required by a crop over its entire base period (growing season) to mature.

   • This is the total net irrigation depth applied to the field.

   • Units: centimeters (cm).

2. Relation to IWR: Delta is the seasonal summation of the Irrigation Water Requirement (IWR). $\Delta = \sum IWR_{\text{over base period}}$

3.3 The Duty-Delta Relationship

1. Derivation: Links the area irrigated (Duty), the water depth needed (Delta), and the water flow rate.

2. Formula: $\Delta = \frac{8.64 \times B}{D}$ Where:

   • $\Delta$ = Delta (in cm)

   • $D$ = Duty (in hectares per cumec, ha/cumec)

   • $B$ = Base period of the crop (in days)

   • 8.64 = Conversion constant.

3. Derivation of Constant:

   • 1 cumec flow for 1 day (86400 seconds) = 1 * 86400 = 86,400 m³.

   • Volume for B days = $86,400 \times B$ m³.

   • This volume irrigates D hectares = $D \times 10,000$ m².

   • Depth of water (Delta, in m) = Volume/Area = $\frac{86,400 B}{D \times 10,000} = \frac{8.64 B}{D}$ m.

   • Converting m to cm (×100): $\Delta = \frac{864 B}{D}$? Wait, check:

     • Depth (m) = (86,400 * B sec) / (D * 10,000 m²). 86,400/10,000 = 8.64.

     • So Depth (m) = (8.64 * B) / D.

     • Depth (cm) = (8.64 * B * 100) / D = (864 * B) / D.

   • The standard formula is: $\Delta (\text{cm}) = \frac{8.64 \times B}{D}$ where D is in ha/cumec and Δ is in meters. OR $\Delta (\text{cm}) = \frac{864 \times B}{D}$.

   • Commonly used: $\Delta (m) = \frac{8.64 B}{D}$ or $\Delta (cm) = \frac{864 B}{D}$.

---

4. Water Losses and Irrigation Efficiencies

Water is lost at every stage from source to root zone. Efficiencies quantify these losses.

4.1 Types of Water Losses

1. Conveyance Losses: Evaporation, seepage, and leakage in canals and watercourses.

2. Application Losses: Deep percolation beyond root zone, surface runoff from the field, and evaporation during application.

4.2 Irrigation Efficiencies

1. Water Conveyance Efficiency ($\eta_c$): $\eta_c = \frac{W_f}{W_r} \times 100\%$

   • $W_f$ = Water delivered to the field (or watercourse head).

   • $W_r$ = Water diverted from the source (reservoir/river).

2. Water Application Efficiency ($\eta_a$): $\eta_a = \frac{W_s}{W_f} \times 100\%$

   • $W_s$ = Water stored in the root zone (net irrigation depth).

   • $W_f$ = Water delivered to the field.

3. Water Use Efficiency ($\eta_u$): $\eta_u = \frac{\text{Yield (kg)}}{\text{Water used (m³ or ha-cm)}}$

   • Measures crop output per unit of water consumed.

4. Overall Project Efficiency ($\eta_o$): $\eta_o = \eta_c \times \eta_a$

   • Represents the fraction of water diverted from the source that is actually stored in the root zone.

   • Crucial for design: The gross irrigation requirement at the source = Net Requirement / $\eta_o$.

---

5. Effective Rainfall ($P_e$)

1. Definition: The portion of total rainfall that is available and useful for meeting the crop water requirement. It excludes runoff and deep percolation losses.

2. Calculation (Simplified USDA SCS Method): $P_e = \frac{P(125 - 0.2P)}{125} \quad \text{for } P \leq 250 \text{ mm/month}$ $P_e = 125 + 0.1P \quad \text{for } P > 250 \text{ mm/month}$ Where P is the average monthly rainfall (mm).

3. Significance: Directly reduces the Irrigation Water Requirement (IWR). Accurate $P_e$ estimation prevents over-irrigation.

---

6. Soil-Moisture-Irrigation Relationship

6.1 Key Soil Moisture States

1. Saturation: All pores filled with water.

2. Field Capacity (FC): Water held after gravity drainage (upper limit of available water).

3. Permanent Wilting Point (PWP): Water content below which plants cannot extract water (lower limit).

4. Available Water Capacity (AWC): $AWC = FC - PWP$

   • Expressed as depth of water per unit depth of soil (cm/cm or mm/m).

6.2 Soil Moisture Depletion

1. Management Allowable Depletion (MAD): The fraction of AWC that is allowed to be depleted before irrigation is scheduled (typically 50-60% for most field crops). $\text{Readily Available Water (RAW)} = AWC \times MAD$

---

7. Depth and Frequency of Irrigation

7.1 Net Irrigation Depth (d)

1. Definition: The depth of water required to be stored in the root zone during one irrigation cycle. It refills the soil moisture from the depletion level back to Field Capacity.

2. Calculation: $d = (FC - \theta_i) \times D_z \times MAD$ Or more simply: $d = RAW = (FC - PWP) \times D_z \times MAD$ Where:

   • $\theta_i$ = Initial soil moisture content before irrigation.

   • $D_z$ = Effective root zone depth (m).

   • Units: d is in meters or cm.

7.2 Irrigation Frequency (F)

1. Definition: The time interval between two consecutive irrigations.

2. Calculation: $F = \frac{d}{ET_c}$ Where:

   • $d$ = Net irrigation depth (mm).

   • $ET_c$ = Peak daily crop evapotranspiration rate (mm/day).

   • Units: F is in days.

3. Significance: Determines the irrigation schedule (how often to irrigate).

---

8. Design Discharge for Canals

The canal must be sized to carry the peak water demand of the command area.

8.1 Peak Irrigation Demand

1. Critical Period: The period when the crop water requirement ($ET_c$) is maximum (often during the hot, dry, flowering/fruiting stage).

2. Design Crop: The crop with the highest peak water requirement in the rotation.

8.2 Calculation of Design Discharge (Q)

1. At the Head of the Watercourse (Field Channel) – for a specific crop: $Q = \frac{A}{D}$ Where:

   • $Q$ = Discharge required (cumec).

   • $A$ = Area under the crop (hectares).

   • $D$ = Duty of water for that crop at the field head (ha/cumec).

2. At the Project Head (Main Canal) – for the entire command:

   • Must account for simultaneous cropping patterns and overall project efficiency.

   • Gross Duty ($D_g$): Duty at the project head, considering conveyance losses. $D_g = D \times \eta_c$.

   • Weighted Average Duty: If multiple crops with different duties are grown simultaneously, calculate an area-weighted duty.

   • Formula: $Q_{\text{design}} = \frac{\sum (A_i / D_i)}{\eta_o}$ Or more practically: $Q_{\text{design}} = \frac{A_{\text{peak}}}{D_g} = \frac{A_{\text{peak}}}{D \times \eta_c}$ Where $A_{\text{peak}}$ is the area to be irrigated during the peak demand period.

3. Considering Kor Period & Kor Depth (for design of canal capacity):

   • Kor Period: The critical short period (2-3 weeks) during the base period when the crop needs the maximum depth of water (Kor Depth).

   • The canal must be designed to supply the Kor Depth over the Kor Period for the entire area under that crop. This often governs the canal's capacity.

8.3 Factors in Final Design Discharge

• Leakage and operational losses.

• Water allocation for other uses (domestic, industrial).

• Flexibility and safety margins.

Conclusion: Water demand estimation synthesizes climatology, agronomy, soil science, and hydraulics. From the basic crop evapotranspiration to the final design discharge in the canal, each step involves accounting for losses, efficiencies, and the variability of natural systems. Mastery of these concepts—Duty-Delta, efficiencies, soil moisture dynamics—enables the irrigation engineer to bridge the gap between the water available and the water needed, designing systems that are both productive and sustainable.