Stream Hydrology: Flow Measurement, Rating Curves, and Pulse Analysis

Overview of Stream Hydrology and Data Management

• Hydrology Practical Structure: The hydrology component of the unit consists of two distinct practical sessions:

  • Practical 1: Focuses on the process of measuring stream flow and the initial analysis of hydrological data.

  • Practical 2 (Post-Break): Focuses on further analysis of hydrological data, specifically relating to flow history and regimes.

• Research Project Applicability: While the practical covers field measurement methods (how flow is measured), students focusing on research projects primarily need to understand the analysis of hydrological data to interpret stream-gauge results.

• Data Availability in Australia: Australia maintains an extensive network of hydrological stations and gauges. Some records are exceptionally long, extending over 100 years. This abundance of data necessitates systematic summarization and analysis.

• Data Resolution: While gauges can measure discharge continuously, the practical utilizes daily flow data to maintain a manageable dataset size, which is sufficient for characterizing catchment behavior.

Fundamental Concepts of Stream Discharge

• Definition: Stream discharge is a key output of a catchment system. It is the product of climate inputs (e.g., rainfall) and the specific way the catchment processes those inputs.

• Variability: Discharge varies over time; these variations are illustrated using a hydrograph.

• Hydrograph: A graphical representation of how discharge changes over time.

Hierarchical Scales of Hydrological Analysis

Hydrological data is divided into several scales to characterize different processes and catchment features:

• Hydraulic Behavior (Short Time Scale):

  • Focuses on velocity and how it changes second-to-second.

  • Analyzes flow direction (up-and-down, side-to-side) and turbulence, which is critical for riverine biological and physical processes.

• Flow Pulse:

  • Refers to how a specific rainfall event moves through the catchment system.

• Flow History:

  • Concerns the sequence of events (pulses) over time.

  • Key phenomena include flood frequency and flood probability (e.g., Return Intervals like 1-in-100, 1-in-50, or 1-in-10 year floods).

• Flow Regime:

  • The total population of flows experienced by a system.

  • Characterized by the distribution and variation of flows, including the median, $10^{th}$ percentile, and $90^{th}$ percentile flows.

  • Seasonality: Determining whether high flows occur primarily in summer, winter, or other specific times of the year.

Field Methodologies: The Velocity-Area Method

• Fundamental Formula: Discharge ($Q$) is the product of flow velocity ($V$) and the cross-sectional area ($A$) through which the water moves.

  • $Q = V \times A$

• The Problem of Variability: Velocity is not uniform across a channel; it is highest furthest from the bed and banks and lower near the boundaries due to friction.

• Sub-sectioning: To account for variability, a river cross-section is divided into more homogenous vertical subsections. The discharge for each subsection is calculated and then summed for the total discharge.

• The 0.6 Depth Rule: A standard approximation in hydrology is that the average velocity of a vertical water column is found at 0.6 of the total depth measured from the surface ($0.6 \times D$).

• ISOVELS: These are lines (similar to contour lines on a map) representing areas of equal velocity within a cross-section.

• Practical Calculation Steps (Hypothetical Cross-section):

  1. Divide the cross-section into wedges or rectangles.

  2. Determine the width and depth of each subsection.

  3. Convert measurements from millimeters ($mm$) to meters ($m$) using specific scales:

     • Width Scale: Divide $mm$ by $12.5$ (since $10.0\,mm = 0.8\,m$).

     • Depth Scale: Divide $mm$ by $24.0$.

  4. Calculate the $0.6$ depth point to locate the average velocity meter placement.

  5. Example calculation: A width of $10.0\,mm$ ($0.8\,m$) and a depth of $19.0\,mm$ ($0.79\,m$) with a measured velocity of $3.5\,m/s$ results in approximately $2.2\,m^3/s$ for that subsection.

  • Note: Cubic meters per second is expressed as $\text{m}^3/\text{s}$.

The Rating Curve and Stage-Discharge Relationships

• Definition: A rating curve is a relationship between river stage (height) and discharge.

• Purpose: It allows hydrologists to infer discharge accurately simply by measuring the river's height, avoiding the need for constant, labor-intensive velocity-area measurements.

• The Yakko Gauge Case: Gaugers at Link Crossing on the Yakko River measured height and discharge every two hours over a six-day pulse to establish this relationship.

• Unsteady Rating Curves (The Hysteresis Effect):

  • The relationship between height and discharge is not always a single line. Often, at a given height, there are two possible discharge values.

  • Rising Limb: The river has a higher velocity and higher discharge for a specific height because a "bulge" of water is moving down the system with a steeper water surface slope and less downstream resistance.

  • Falling Limb: The river level may still be high, but the velocity and discharge are lower because the water is slowing down and being "backed up" by water already downstream.

• Channel Geometry Changes: Large floods can move sediment, eroding the channel or depositing material. This alters the area-height relationship at the gauge, requiring the rating curve to be updated after major events.

Pulse Characterization: Translation and Attenuation

As a flood pulse moves downstream, it undergoes two primary changes:

• Translation: The pulse occurs later in time as it moves from upstream to downstream sites.

• Attenuation: The peak discharge of the pulse decreases, and the duration of the pulse increases as it moves downstream.

• Causes of Attenuation:

  • Water storage in the channel (backwaters).

  • Floodplain Interaction: The most significant attenuation occurs when water flows out of the banks and onto a floodplain or into wetlands.

  • Engineering: Retention ponds and dams are specifically designed to attenuate pulses to prevent flash flooding and reduce downstream intensity.

Case Study Analysis: Kadjigong River Pulse Dynamics

• Location: The Kadjigong River flows through Mudgee in Central West New South Wales.

• Gauges Used:

  1. Upstream site.

  2. Downstream of Windermere Reservoir.

  3. Yamble Bridge (furthest downstream).

• Observed Data (May Event):

  • Upstream: Peak reached $653\,ML/d$ on May 19.

  • Windermere Site: Showed a lower peak but a much longer duration (significant attenuation due to the storage reservoir).

  • Yamble Bridge: Showed a higher peak than the upstream site ($1236\,ML/d$ on May 21). This is due to the increased catchment size; despite attenuation, tributaries downstream of the other sites contributed additional water.

Characterizing Pulses for Research Projects

Students should use the following metrics to summarize pulses in their data:

• Peak Discharge: The maximum flow recorded during the event.

• Total Volume: Calculated by summing the daily discharges for the duration of the pulse ($\sum Q_{daily}$).

• Duration: Number of days from the start of the pulse (acceleration of flow) to the end (return to baseflow).

• Time of Rise: Number of days from the start to the peak.

• Time of Fall: Number of days from the peak to the end of the pulse.

• Rate of Rise/Fall:

  • Calculated as: $\frac{\text{Peak Discharge} - \text{Start Flow}}{\text{Days to Rise}}$.

  • Pulses typically fall more slowly than they rise because of the time required for water to drain from the system.

• Comparative Analysis: Students should compare pulses of different magnitudes (e.g., a 1-in-2 year flood vs. a 1-in-30 year flood) or compare pulses of similar magnitude from different eras (e.g., 1950 vs. 1990) to see if catchment changes (like land clearing or afforestation) have altered the pulse shape.

Statistical Foundations: Flood Frequency Analysis

• Annual Maximum Series: To perform this analysis, hydrologists identify the single maximum flow experienced in each year of record.

• Ranking: Flows are ranked ($m$) from largest ($1$) to smallest.

• Return Interval ($T$):

  • Formula: $T = \frac{n + 1}{m}$

  • Where:

    • $n = \text{number of years in the record}$

    • $m = \text{rank of the specific event}$

• Probability: A 1-in-10 year return interval means there is a $0.1$ (or $10\%\text{ chance}$) of that magnitude flood occurring in any single year.

• Example (Kadjigong Data):

  • Record length: $63\text{ years}$.

  • Rank 1 flood (1952): $55,000\,ML/d$. Return interval: $T = \frac{63 + 1}{1} = 64$, or 1-in-64 years.

  • Rank 32 flood: Return interval: $T = \frac{64}{32} = 2$, or 1-in-2 years.

Questions and Discussion

• Dialogue on Rating Curves:

  • Question: Why are there two heights for a given discharge in the Yakko gauge data?

  • Response: The velocity is different. If the height is higher but the discharge is the same, the velocity must have decreased ($Q = V \times A$). This reflects the difference between the rising and falling limbs of a flood pulse (hysteresis).

• Dialogue on Pulse Comparison:

  • Question: How should we select pulses to plot for our report?

  • Response: Don't plot every pulse. Use the flood frequency analysis to identify a "small" (1-in-2 year), "medium" (1-in-10), and "large" pulse. If possible, find approximations of these sizes in different decades of the record to see if the catchment is processing water differently over time.

• Dialogue on Attenuation:

  • Question: Why did the Yamble Bridge site have a higher peak if attenuation was occurring?

  • Response: Even though the pulse is attenuating (spreading out), the Yamble Bridge site has a significantly larger catchment area. Tributaries joining the river downstream of Windermere add new water to the system, which can result in a higher absolute discharge despite the attenuation of the upstream pulse.