Chapter 1 Environmental Engineering: Sediment and Nutrient

Chapter 1 Environmental Engineering: Sediment and Nutrient#

  1. Introduction: Sediment and Nutrient

  2. Simulation: MUSLE

  3. Self-Assessment

1. Introduction#

💧 Sediment and Nutrient Characterization in Water Systems#

Understanding sediment and nutrient dynamics is essential for protecting water quality, managing ecosystems, and designing effective watershed interventions. Here’s a breakdown of why, how, and what we measure and model. -

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🧭 Why Measure or Model Sediment and Nutrients?#

Purpose

Explanation

🌿 Ecosystem Health

Excess nutrients (N, P) cause eutrophication, algal blooms, and oxygen loss

🚰 Drinking Water Safety

Sediment and nutrients affect filtration, taste, and treatment costs

🏞️ Watershed Management

Helps target pollution sources and prioritize restoration efforts

📈 Regulatory Compliance

Supports TMDLs, nutrient criteria, and Clean Water Act goals

🔬 Scientific Understanding

Reveals biogeochemical cycling and land–water interactions

📉 Climate & Land Use Impact

Tracks changes due to urbanization, agriculture, and climate variability

  • Modeling supports policy, restoration, and climate adaptation

  • Characterization enables targeted interventions like buffer strips, wetland restoration, and nutrient trading

🧪 How Are They Measured?#

Parameter

Measurement Method

Notes

Total Phosphorus (TP)

Digestion + spectrophotometry

Includes dissolved and particulate P

Total Nitrogen (TN)

Kjeldahl method or combustion analysis

Includes organic and inorganic N

Nitrate / Ammonium

Ion chromatography, colorimetry

Key forms of bioavailable nitrogen

Suspended Sediment (TSS)

Filtration + gravimetric analysis

Measures solids in water column

Sediment-bound Nutrients

Core sampling + extraction

Assesses nutrient storage in sediments

🧮 How Are They Modeled?#

Model / Tool

Type

Application Scope

SPARROW

Statistical regression

Regional nutrient and sediment transport

SWAT

Process-based

Watershed-scale hydrology and nutrient cycling

InVEST SDR

Spatial retention

Ecosystem service valuation and BMP targeting

CAST / STEPL

Scenario tools

Load reduction planning and cost estimation

CSTR Equation

Conceptual

Lake nutrient retention and residence time

Models help simulate sources, transport, and fate of nutrients and sediments — especially when direct measurement is limited or costly.

🧮 Sediment and Nutrient Estimation Models – Comparison Table#

Sediment transport and nutrient loading are often estimated using empirical models that relate landscape characteristics and hydrology to erosion and pollutant export. Here’s a comparative summary of key models:

🏞️ Sediment Transport Models#

Model

Equation Formulation

Key Inputs

Notes

RUSLE

\(( A = R \cdot K \cdot L \cdot S \cdot C \cdot P \))

Rainfall (R), soil (K), slope (LS), cover (C), practices (P)

Estimates annual average soil loss (tons/acre/year)

MUSLE

\(( S = 11.8 \cdot (Q \cdot q_p)^{0.56} \cdot K \cdot C \cdot P \cdot LS \))

Runoff volume (Q), peak flow (qₚ), soil, slope, land use

Estimates event-based sediment yield (tons/event)

MUSLE replaces rainfall erosivity (R) with runoff and peak flow, making it more suitable for storm-event modeling and hydrologic simulations.

💧 Nutrient Load Estimation – Runoff-Based Models#

Model Type

Equation Formulation

Inputs

Notes

Log-Linear Nutrient Model

\(( \log(N) = a + b \cdot \log(Q) \))

Nutrient load (N), runoff (Q)

Empirical correlation between runoff and nutrient export

Export Coefficient Model

$( N = \sum (EC_i \cdot A_i) #)

Land use area (A), coefficients (EC)

Simple land-use-based nutrient estimation

SWAT / SPARROW

Process-based or statistical

Climate, land use, soils, hydrology

Used for regional nutrient modeling and scenario analysis

Nutrient loads (especially phosphorus and nitrogen) are often correlated with runoff volume, land use type, and soil characteristics. Log-linear models are useful for quick estimation, while export coefficient and process-based models offer more detail.

🧠 Insight#

  • RUSLE [Renard et al., 1997] is ideal for long-term erosion planning; MUSLE [Williams, 1975] is better for storm-event sediment modeling.

  • Nutrient export is often nonlinear and land-use dependent, requiring calibration or regional coefficients.

  • Combining sediment and nutrient models helps assess water quality impacts, BMP effectiveness, and TMDL compliance.

🔗 Resources#

Foundational literature#

[Renard et al., 1997] (ideal for long-term erosion planning) and [Williams, 1975] (storm-event sediemnt modeling) are widely recognized as fundamental literature for watershed-scale sediment modeling, each serving distinct modeling purposes. [Reckhow et al., 1980] is the foundational source for export coefficient modeling, introducing the Export Coefficient Model (ECM) for estimating nutrient loads from land use. It is widely used in lake and watershed nutrient modeling. The literature provides tabulated coefficients for nitrogen and phosphorus across land uses and is ideal for long-term nutrient planning and TMDL development.

2. Simulation#

Methodology: Watershed Runoff, Sediment, and Nutrient Simulation#

This simulation estimates hydrologic and water quality responses of a watershed under different land use scenarios. It integrates rainfall, land use type, slope, area, and drainage density to compute:

  • Surface runoff (mm and m³)

  • Sediment yield (tons)

  • Nutrient loads (Nitrogen and Phosphorus in kg)

  • Change analysis between baseline and future land use

1. 🌧️ Runoff Estimation: NRCS Curve Number Method#

Runoff is calculated using the NRCS-CN method [United States Department of Agriculture, Natural Resources Conservation Service, 2021], which relates land use and soil conditions to rainfall retention:

\[ S = \frac{25400}{CN} - 254 \quad ; \quad I_a = 0.2 \cdot S \quad ; \quad Q = \frac{(P - I_a)^2}{P + 0.8 \cdot S} \]

Where:

  • \(( CN \)): Curve Number (based on land use)

  • \(( P \)): Rainfall (mm)

  • \(( Q \)): Runoff depth (mm)

Runoff volume is then computed as:

\[ Q_{\text{vol}} = Q \cdot \frac{\text{Area}_{\text{ha}} \cdot 10,000}{1000} \]

2. Sediment Yield: Modified Universal Soil Loss Equation (MUSLE)#

Sediment yield is estimated using a simplified form of MUSLE [Williams, 1975]:

\[ S = 11.8 \cdot Q \cdot A \cdot K \cdot C \cdot P \cdot LS \]

Where:

  • \(( Q \)): Runoff (mm)

  • \(( A \)): Area (ha)

  • \(( K \)): Soil erodibility factor (default 0.3)

  • \(( C \)): Cover factor (default 0.2)

  • \(( P \)): Practice factor (default 1.0)

  • \(( LS \)): Slope length and steepness factor (approximated as slope % / 100)

🧪 Nutrient Load Estimation#

Nutrient loads are estimated using **land use-specific export coefficients

# 📌 Run this cell in a Jupyter Notebook
import numpy as np
import matplotlib.pyplot as plt
import ipywidgets as widgets
from IPython.display import display, clear_output

# 📐 Curve Number lookup
def get_curve_number(landuse):
    cn_dict = {
        'Forest': 55,
        'Urban': 85,
        'Agriculture': 75,
        'Wetland': 50,
        'Grassland': 60
    }
    return cn_dict.get(landuse, 70)

# 📐 Nutrient export coefficients (kg/ha/year)
def get_nutrient_coeffs(landuse):
    coeffs = {
        'Forest': {'N': 1.0, 'P': 0.1},
        'Urban': {'N': 5.0, 'P': 1.0},
        'Agriculture': {'N': 15.0, 'P': 2.5},
        'Wetland': {'N': 0.5, 'P': 0.05},
        'Grassland': {'N': 3.0, 'P': 0.5}
    }
    return coeffs.get(landuse, {'N': 5.0, 'P': 1.0})

# 📐 Runoff estimation using NRCS-CN method
def estimate_runoff(rainfall_mm, CN):
    S = (25400 / CN) - 254
    Ia = 0.2 * S
    if rainfall_mm <= Ia:
        return 0
    Q = ((rainfall_mm - Ia)**2) / (rainfall_mm + 0.8 * S)
    return round(Q, 2)

# 📐 Sediment yield using MUSLE (simplified)
def estimate_sediment(Q, area_ha, slope_percent, K=0.3, C=0.2, P=1.0):
    LS = slope_percent / 100
    sediment_tons = 11.8 * Q * area_ha * K * C * P * LS
    return round(sediment_tons, 2)

# 📐 Nutrient loads
def estimate_nutrients(area_ha, landuse):
    coeffs = get_nutrient_coeffs(landuse)
    N_load = coeffs['N'] * area_ha
    P_load = coeffs['P'] * area_ha
    return round(N_load, 2), round(P_load, 2)

# 📊 Simulation function
def watershed_comparison(rainfall_mm, landuse_base, landuse_future, area_km2, slope_percent, drainage_density):
    clear_output(wait=True)

    area_ha = area_km2 * 100

    def simulate(landuse):
        CN = get_curve_number(landuse)
        runoff_mm = estimate_runoff(rainfall_mm, CN)
        runoff_m3 = runoff_mm / 1000 * area_ha * 10000
        sediment = estimate_sediment(runoff_mm, area_ha, slope_percent)
        N_load, P_load = estimate_nutrients(area_ha, landuse)
        return runoff_m3, sediment, N_load, P_load

    base = simulate(landuse_base)
    future = simulate(landuse_future)

    # 📋 Output summary
    print(f"🌧️ Rainfall: {rainfall_mm:.1f} mm")
    print(f"📐 Area: {area_km2:.2f} km² | Slope: {slope_percent:.1f}% | Drainage Density: {drainage_density:.2f} km/km²\n")

    print(f"🔄 Baseline Land Use: {landuse_base}")
    print(f"💧 Runoff: {base[0]:,.0f} m³ | Sediment: {base[1]:.2f} tons | N: {base[2]:.2f} kg | P: {base[3]:.2f} kg")

    print(f"\n🔁 Future Land Use: {landuse_future}")
    print(f"💧 Runoff: {future[0]:,.0f} m³ | Sediment: {future[1]:.2f} tons | N: {future[2]:.2f} kg | P: {future[3]:.2f} kg")

    print("\n📊 Change Summary:")
    labels = ['Runoff (m³)', 'Sediment (tons)', 'Nitrogen (kg)', 'Phosphorus (kg)']
    for i, label in enumerate(labels):
        delta = future[i] - base[i]
        pct = (delta / base[i] * 100) if base[i] != 0 else 0
        print(f" - {label}: Δ = {delta:.2f} ({pct:+.1f}%)")

    # 📈 Visualization
    x = np.arange(len(labels))
    width = 0.35
    fig, ax = plt.subplots(figsize=(10, 5))
    ax.bar(x - width/2, base, width, label='Baseline', color='lightblue', edgecolor='black')
    ax.bar(x + width/2, future, width, label='Future', color='salmon', edgecolor='black')
    ax.set_xticks(x)
    ax.set_xticklabels(labels)
    ax.set_title('Watershed Output Comparison')
    ax.set_ylabel('Magnitude')
    ax.legend()
    ax.grid(True, axis='y')
    plt.tight_layout()
    plt.show()

# 🎚️ Interactive controls
rainfall_slider = widgets.FloatSlider(value=50.0, min=10.0, max=200.0, step=5.0, description='Rainfall (mm)')
landuse_base_dropdown = widgets.Dropdown(options=['Forest', 'Urban', 'Agriculture', 'Wetland', 'Grassland'], value='Agriculture', description='Baseline Land Use')
landuse_future_dropdown = widgets.Dropdown(options=['Forest', 'Urban', 'Agriculture', 'Wetland', 'Grassland'], value='Urban', description='Future Land Use')
area_slider = widgets.FloatSlider(value=2.0, min=0.1, max=50.0, step=0.1, description='Area (km²)')
slope_slider = widgets.FloatSlider(value=5.0, min=0.1, max=30.0, step=0.5, description='Slope (%)')
drainage_slider = widgets.FloatSlider(value=1.5, min=0.5, max=5.0, step=0.1, description='Drainage Density')

interactive_plot = widgets.interactive(
    watershed_comparison,
    rainfall_mm=rainfall_slider,
    landuse_base=landuse_base_dropdown,
    landuse_future=landuse_future_dropdown,
    area_km2=area_slider,
    slope_percent=slope_slider,
    drainage_density=drainage_slider
)

display(interactive_plot)

Watershed Simulation: Quiz, Conceptual & Reflective Questions#

This module reinforces understanding of watershed runoff, sediment yield, and nutrient loading using NRCS-CN, MUSLE, and export coefficient methods. It supports learning through multiple-choice questions, conceptual prompts, and reflective challenges.

Conceptual Questions#

  1. What does the Curve Number (CN) primarily represent?

    • A. Soil erosion potential

    • B. Land use and soil infiltration characteristics

    • C. Nutrient export rate

    • D. Slope steepness

  2. Which factor most directly increases sediment yield in the MUSLE equation?

    • A. Rainfall intensity

    • B. Slope percentage

    • C. Drainage density

    • D. Phosphorus coefficient

  3. What is the role of the initial abstraction ( I_a ) in the NRCS-CN method?

    • A. It represents the maximum runoff

    • B. It accounts for infiltration and surface storage before runoff begins

    • C. It adjusts nutrient loading

    • D. It scales sediment transport

  4. Which land use type typically has the highest nitrogen export coefficient?

    • A. Forest

    • B. Urban

    • C. Agriculture

    • D. Wetland

  5. What does the LS factor in MUSLE represent?

    • A. Land use and slope

    • B. Length and steepness of slope

    • C. Load and sediment transport

    • D. Land surface roughness

Interpretation#

  1. Why is runoff volume converted from mm to cubic meters using area and unit conversions?

  2. How does changing slope percentage affect sediment yield in the MUSLE calculation?

  3. Why are nutrient loads estimated using static coefficients rather than dynamic concentration models?

  4. What assumptions are made when comparing baseline and future land use scenarios?

  5. How could drainage density be incorporated more directly into sediment or runoff estimation?

Reflective Questions#

  1. How do land use changes influence both water quantity and quality in a watershed?

  2. Why is it important to simulate both runoff and sediment/nutrient loads when planning restoration?

  3. What are the limitations of using empirical coefficients for nutrient export?

  4. How could this model be adapted to include BMPs (e.g., buffer strips, retention ponds)?

  5. What insights can be gained by visualizing the percent change between baseline and future scenarios?

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