Hydrologic Losses

Hydrologic Losses

Understanding the processes that reduce the volume of water available for runoff, including Evaporation, Transpiration, and Infiltration.

Introduction

Not all precipitation that falls becomes runoff. A significant portion is lost to Hydrologic Losses (or abstractions). These processes reduce the volume of water available for streamflow and groundwater recharge.

Major Components of Hydrologic Losses

Hydrologic losses include Interception (rain caught by vegetation), Depression Storage (water trapped in small puddles), Evaporation (water vaporizing from surfaces), Transpiration (water released by plants), and Infiltration (water entering the soil).

Initial Abstractions

Interception

Precipitation that is caught by the vegetative canopy and never reaches the ground. It eventually evaporates back into the atmosphere. The volume depends on storm size, vegetation species, and season (e.g., leaf-on vs. leaf-off).

Interception Capacity

Interception initially occurs rapidly at the beginning of a storm until the vegetative surfaces are saturated (the interception capacity). After this, interception loss occurs only at the rate of evaporation from the wet leaves during the storm.

Depression Storage

Water trapped in small puddles, depressions, and uneven surfaces on the ground. Once filled, water spills over to become overland flow. It is eventually lost to evaporation and infiltration after the rain stops.

Reduction of Evaporation

In arid regions, significant volumes of water are lost from reservoirs due to evaporation. Measures are often taken to reduce this loss.

Methods of Reducing Evaporation

Methods include reducing the exposed surface area (deep reservoirs instead of shallow ones), mechanical covers (floating spheres or roofs), and Chemical Films. Chemical films are thin, monomolecular layers of organic compounds spread on the water surface. The most common chemicals are Cetyl Alcohol (Hexadecanol) and Stearyl Alcohol. They are non-toxic, effectively form a barrier to water molecules, and are cheap, though they can be disrupted by wind and wave action.

Evaporation

Evaporation

The process by which water changes from liquid to vapor state, occurring from free water surfaces (lakes, oceans), soil moisture, and vegetation surfaces.

Factors Affecting Evaporation

Solar Radiation

The primary energy source providing latent heat of vaporization.

Temperature

Higher air and water temperatures increase the saturation vapor pressure, accelerating evaporation.

Wind

Removes the saturated air layer directly above the water surface, maintaining a vapor pressure gradient.

Humidity

High relative humidity reduces the vapor pressure deficit

(e_s - e_a)

, slowing evaporation.

Estimation Methods

Pan Evaporation Method

Uses a standard US Weather Bureau Class A Pan (diameter 1.21m, depth 25.5cm).

Lake Evaporation

E_{lake} = C_p \cdot E_{pan}

Variables

$E_{lake}$ : Lake evaporation (mm/day)
$E_{pan}$ : Pan evaporation (mm/day)
$C_p$ : Pan coefficient (typically 0.7 for Class A Pan)

Meyer's Formula (Empirical)

Meyer's Formula

E = C (e_s - e_a) (1 + 0.1 w)

Evaporation Rate Simulator

Adjust the environmental variables to see how they impact the daily evaporation rate.

Mean Daily Temp (°C): 25

Relative Humidity (%): 50

Wind Speed (km/h): 10

Peak Solar Radiation (W/m²): 500

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Variables

$e_s$ : Saturation vapor pressure (mm Hg)
$e_a$ : Actual vapor pressure (mm Hg)
$w$ : Wind speed (mph)
$C$ : Coefficient (approx 0.36 for large deep waters, 0.50 for small shallow waters)

Penman Equation

A more theoretically sound, combination method that calculates potential evaporation based on both the energy balance (net radiation) and aerodynamic (wind and humidity) principles.

Penman Method Principles

The Penman equation estimates the rate of evaporation from an open water surface or transpiration from vegetation (evapotranspiration) using weather data. It combines the mass transfer method (aerodynamic factors) and the energy budget method (solar radiation) to provide a robust estimation.

The most widely accepted and accurate method for estimating reference evapotranspiration (

ET_0

) is the FAO Penman-Monteith equation. It physically combines the energy balance (radiation driving vaporization) with the aerodynamic transport (wind and humidity removing vapor).

FAO Penman-Monteith Equation

ET_0 = \frac{\Delta (R_n - G) + \rho_a c_p \frac{(e_s - e_a)}{r_a}}{\lambda (\Delta + \gamma (1 + \frac{r_s}{r_a}))}

Variables

$ET_0$ : Reference evapotranspiration rate
$R_n$ : Net radiation at the surface
$G$ : Soil heat flux density
$e_s - e_a$ : Vapor pressure deficit (saturation minus actual)
$r_a, r_s$ : Aerodynamic and surface resistances
$\Delta, \gamma, \lambda$ : Thermodynamic constants and psychrometric parameters

Evapotranspiration ( $ET_0$ ) Simulator

Temperature (T): 20°C

Higher temperature increases capacity to hold moisture.

Wind Speed (u₂): 2.0 m/s

Higher wind speed removes saturated air from the surface.

Relative Humidity (RH): 60%

Lower humidity increases Vapor Pressure Deficit (VPD).

Net Radiation (Rₙ): 15 MJ/m²/day

Energy available to convert liquid water to vapor.

Estimated Evapotranspiration ( $ET_0$ )

4.25 mm/day

Penman-Monteith Factors:

Energy Term: Radiation drives vaporization.
Aerodynamic Term: Wind and humidity drive transport.
Higher Temp + Wind + Radiation = Higher ET
Higher Humidity = Lower ET

Evapotranspiration (ET)

The combined process of evaporation from soil and plant surfaces, and transpiration from plant leaves. It is often the largest component of water loss from a catchment.

Potential Evapotranspiration (PET)

The maximum possible rate of evapotranspiration from a surface, assuming an unlimited, adequate supply of water is always available. It depends solely on meteorological factors.

Actual Evapotranspiration (AET)

The real rate of evapotranspiration occurring under existing field conditions. It is limited by the actual soil moisture available.

Note

When soil is at field capacity (plenty of water),

\text{AET} = \text{PET}

. As soil dries out and approaches the permanent wilting point, AET drops significantly below PET.

Measurement using Lysimeters

Lysimeter Types

A Lysimeter is a tank filled with soil and vegetation, buried flush with the surrounding field.

Weighing Lysimeter: The most accurate type. It continuously measures the weight of the entire tank. The loss in mass directly corresponds to the water lost via ET.
Drainage Lysimeter: Operates on a water balance principle ( $ET = \text{Input} - \text{Drainage}$ ). It requires saturating the soil and measuring the water that drains out the bottom.

Infiltration and Soil Moisture

Infiltration is deeply linked to the state of moisture already in the soil profile.

Soil Moisture Characteristic Curve

This curve, also known as the Water Retention Curve, relates the soil water content (

\theta

) to the soil water potential (suction or tension,

\psi

). It shows how strongly water is held in the soil pores.

Field Capacity: The amount of water remaining in soil after downward gravity drainage has ceased.
Permanent Wilting Point: The moisture content at which plants can no longer extract water against the soil's capillary suction, causing them to wilt and die.

Infiltration

Infiltration

The passage of water through the soil surface into the soil profile. It replenishes soil moisture and groundwater aquifers.

Infiltration Capacity ( $f_p$ ) is the maximum rate at which a given soil can absorb water. It is high at the beginning of a storm and decays exponentially to a constant rate (

f_c

) as the soil pores fill with water and clay particles swell.

Measurement of Infiltration (Infiltrometers)

Infiltration rates are typically measured in the field using infiltrometers.

Types of Infiltrometers

1. Single Ring Infiltrometer: A metal ring driven into the soil. Water is added, and the rate it drops is measured. Drawback: Lateral flow beneath the ring overestimates the true vertical infiltration rate. 2. Double Ring Infiltrometer: Uses two concentric rings. Both are filled, but measurements are only taken from the inner ring. The outer ring provides a buffer zone that prevents lateral flow from the inner ring, ensuring accurate vertical infiltration measurements.

Horton's Equation

Robert Horton (1933) modeled this decay process:

Horton's Infiltration Equation

f_p(t) = f_c + (f_0 - f_c) e^{-kt}

Variables

$f_p(t)$ : Infiltration capacity at time $t$ (mm/hr)
$f_0$ : Initial infiltration capacity (mm/hr)
$f_c$ : Ultimate (constant) infiltration capacity (mm/hr)
$k$ : Decay constant ( $hr^{-1}$ ), dependent on soil type and cover.

Horton's Infiltration Equation Simulator

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Initial Capacity (f₀)100 mm/hr

Constant Capacity (fc)15 mm/hr

Decay Constant (k)0.5 /hr

Formula: fₚ = 15 + (100 - 15)e^-0.5t

Observe how increasing k causes the infiltration capacity to drop more rapidly to its constant value.

Green-Ampt and Philip's Models

While Horton's equation is strictly empirical, other more physically-based models exist based on Darcy's Law and capillary principles.

Green-Ampt Method

An analytical solution based on Darcy's Law. It assumes a sharp wetting front separating the saturated soil above from the dry soil below. It requires specific soil parameters like hydraulic conductivity (

K

), capillary suction head (

\psi

), and change in moisture content (

\Delta \theta

Philip's Two-Term Model

An analytical approximation to Richards' equation governing unsaturated flow. It models cumulative infiltration (

F

) using two terms: Sorptivity (

S

), dominating early stages due to capillary forces, and Transmissivity/Conductivity (

A

), dominating later stages due to gravity.

Philip's Equation

F(t) = S t^{1/2} + A t

Infiltration Indices

Used to estimate average infiltration over a storm duration, simplifying the varying rate.

1. $\Phi$ - Index (Phi Index)

The average rainfall intensity above which the rainfall volume equals the runoff volume. It assumes a constant loss rate throughout the storm.

Phi Index condition

\text{Total Runoff Volume} = \sum (I - \Phi) \cdot \Delta t

Note

Only sum for time intervals where

I > \Phi

Phi-Index Simulator

\Phi

-Index15 mm/hr

Adjust the $\Phi$ -Index to see how it separates precipitation into direct runoff and infiltration losses.

Storm Summary

Total Rainfall:107 mm

Direct Runoff:35 mm

Infiltration:72 mm

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2. W - Index

The average infiltration rate over the storm duration.

W Index Formula

W = \frac{P - R - S}{t_r}

Note

Where

P

is total rain,

R

is runoff,

S

is depression storage, and

t_r

is the duration of rainfall.

Green-Ampt Infiltration Model

The Green-Ampt model is a physically-based equation derived from Darcy's Law that describes the infiltration of water into the soil as a sharp wetting front.

Green-Ampt Equation

It assumes a sharp boundary (wetting front) dividing soil with initial moisture content from fully saturated soil. As infiltration progresses, the wetting front moves deeper, and the infiltration rate decreases asymptotically to the saturated hydraulic conductivity.

Green-Ampt Infiltration Rate

f(t) = K \left( 1 + \frac{\psi \cdot \Delta \theta}{F(t)} \right)

Variables

$f(t)$ : Infiltration rate at time $t$
$K$ : Saturated hydraulic conductivity
$\psi$ : Suction head at the wetting front
$\Delta \theta$ : Change in volumetric moisture content (porosity minus initial moisture)
$F(t)$ : Cumulative infiltration volume

Key Takeaways

Hydrologic Losses (or abstractions) represent the portion of precipitation that does not contribute to direct surface runoff.
Primary losses include evaporation, transpiration, infiltration, interception, and depression storage.
Initial Abstractions (Interception and Depression Storage) must be satisfied before any significant surface runoff begins.
Evaporation is driven primarily by solar radiation and the vapor pressure deficit between the evaporating surface and the atmosphere.
Evapotranspiration (ET) combines soil evaporation and plant transpiration.
Potential ET (PET) assumes unlimited water, while Actual ET (AET) is constrained by real soil moisture. They are equal only when the soil is wet.
The FAO Penman-Monteith method is the standard physical model for estimating reference evapotranspiration, combining radiation-driven energy balance with wind-driven aerodynamic mass transfer.
Evaporation can be measured directly using a Class A Evaporation Pan ( $C_p \approx 0.7$ ), while ET is physically measured using a Lysimeter.
Evaporation from reservoirs can be reduced using Chemical Films like Cetyl Alcohol.
Infiltration is the process of water entering the soil surface, heavily dependent on soil type, moisture content, and land cover.
Horton's Equation is an empirical model for the exponential decay of infiltration capacity during a storm event.
Physically-based alternatives include the Green-Ampt method (sharp wetting front) and Philip's Equation (sorptivity vs. gravity).
The $\Phi$ -Index is a constant loss rate assumption used to separate rainfall into hydrologic abstractions and direct runoff.
The W-Index represents the average infiltration rate excluding depression storage and interception.

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Introduction

Major Components of Hydrologic Losses

Initial Abstractions

Interception

Interception Capacity

Depression Storage

Reduction of Evaporation

Methods of Reducing Evaporation

Evaporation

Evaporation

Factors Affecting Evaporation

Solar Radiation

Temperature

Wind

Humidity

Estimation Methods

Pan Evaporation Method

Lake Evaporation

Variables

Meyer's Formula (Empirical)

Meyer's Formula

Evaporation Rate Simulator

Variables

Penman Equation

Penman Method Principles

FAO Penman-Monteith Equation

Variables

Evapotranspiration (ET0ET_0ET0​) Simulator

Estimated Evapotranspiration (ET0ET_0ET0​)

Evapotranspiration (ET)

Potential Evapotranspiration (PET)

Actual Evapotranspiration (AET)

Note

Measurement using Lysimeters

Lysimeter Types

Infiltration and Soil Moisture

Soil Moisture Characteristic Curve

Infiltration

Infiltration

Measurement of Infiltration (Infiltrometers)

Types of Infiltrometers

Horton's Equation

Horton's Infiltration Equation

Variables

Horton's Infiltration Equation Simulator

Green-Ampt and Philip's Models

Green-Ampt Method

Philip's Two-Term Model

Philip's Equation

Infiltration Indices

1. Φ\PhiΦ - Index (Phi Index)

Phi Index condition

Note

Phi-Index Simulator

Storm Summary

2. W - Index

W Index Formula

Note

Green-Ampt Infiltration Model

Green-Ampt Equation

Green-Ampt Infiltration Rate

Variables

Evapotranspiration ( $ET_0$ ) Simulator

Estimated Evapotranspiration ( $ET_0$ )

1. $\Phi$ - Index (Phi Index)