6. Base flow separation

Hydrograph analysis, often referred to interchangeably with base flow separation, is the technique of examining a streamflow hydrograph to distinguish between surface runoff and base flow (groundwater runoff). This analysis is fundamental for understanding how a watershed responds to rainfall events, estimating infiltration capacity, and developing models for flood forecasting and water resources management.

Components of a Hydrograph

To accurately analyze a hydrograph, it is essential to understand its three primary segments, which represent different phases of the runoff process:

• Rising Limb (Concentration Curve): This portion represents the rapid increase in discharge due to the gradual building up of storage in channels and over the catchment surface in response to rainfall.
• Crest Segment: This section contains the peak flow, which occurs when runoff from various parts of the catchment simultaneously contributes the maximum amount of flow at the basin outlet. For large catchments, this peak typically occurs after the rainfall has ceased.
• Recession Limb (Depletion Curve): This segment represents the gradual withdrawal of water from the storage built up in the basin during the earlier phases. Because this phase is driven by the depletion of storage after rainfall ends, its shape depends entirely on the physical characteristics of the basin rather than the storm itself.

Base Flow Separation Methods

A major objective of hydrograph analysis is to separate the total storm hydrograph into its quick-response component (direct surface runoff) and its slow-response component (base flow). Isolating the base flow allows hydrologists to calculate the volume of direct runoff, which in turn yields the volume of effective rainfall (the rainfall remaining after abstractions like infiltration and initial losses).

Three methods for base flow separation:

1. Straight-Line Method: A straight line is drawn from the beginning of the surface runoff to a point on the recession limb that marks the end of direct runoff. The time interval N (in days) from the peak to this end point is often estimated using the empirical formula N = 0.83A^{0.2}, where A is the drainage area in km².
2. Extending the Base Flow Curve: The pre-storm base flow curve is extended forward until it intersects the vertical ordinate drawn at the hydrograph's peak. This intersection is then joined by a straight line to the point marking the end of the direct runoff.
3. Extending the Recession Curve Backward: The base flow recession curve that occurs after the flood water has depleted is extended backward until it intersects the ordinate at the point of inflection. This point is then joined to the start of the hydrograph with an arbitrary smooth curve.

Applications

• Estimating Infiltration: By analyzing measured runoff hydrographs alongside their corresponding rainfall records, engineers can apply the water budget equation to estimate the amount of water lost to infiltration in a watershed.
• Unit Hydrograph Development: Hydrograph analysis is the critical first step in deriving a Unit Hydrograph, which represents the direct runoff resulting from 1 cm of effective rainfall uniformly distributed over a specific duration. Once base flow is separated and the direct runoff hydrograph is established, it can be used to construct unit hydrographs. These are heavily relied upon to predict extreme flood magnitudes for the design of hydraulic structures.
• Decomposing Complex Storms: When ideal, simple, isolated storms are not available for analysis, hydrograph analysis principles are used to decompose a composite flood hydrograph—resulting from successive bursts of rainfall—into its individual direct runoff and base flow components.
  

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Procedure for Base Flow Separation

Base flow separation (or hydrograph analysis) is the process of dividing a total storm hydrograph into two components: the quick-response direct surface runoff and the slow-response base flow (groundwater runoff). While the exact boundary between these flows is difficult to determine, hydrologists commonly use three procedures to separate them:

1. Straight-Line Method (Method 1): This is the simplest method. A straight line is drawn from the start of the surface runoff (Point A on the rising limb) to a point on the recession limb that marks the end of the direct runoff (Point B). The time interval N (in days) from the peak of the hydrograph to Point B is empirically estimated using the formula: N = 0.83A^0.2 Where N is the time in days and A is the drainage-basin area in km².
2. Extending the Base Flow Curve (Method 2): The pre-storm base flow curve is extended forward until it intersects the vertical line (ordinate) drawn down from the hydrograph's peak. From this intersection, a straight line is drawn to Point B on the recession limb. This is considered one of the most widely used procedures.
3. Extending the Recession Curve Backward (Method 3): The base flow recession curve after the flood water has depleted is extended backward until it intersects the ordinate at the point of inflection. This intersection point is then joined to the start of the hydrograph (Point A) using an arbitrary smooth curve.

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Numerical Example and Stepwise Solution

Problem Statement: Following are the ordinates of a storm hydrograph of a river draining a catchment area of 423 km² due to an isolated storm. Separate the base flow using the straight-line method and determine the ordinates of the Direct Runoff Hydrograph (DRH).

Time from start (h)	0	6	12	18	24	30	36	42	48	54	60	66	72	78	84	90
Total Discharge (m³/s)	10.0	30.0	87.5	111.5	102.5	85.0	71.0	59.0	47.5	39.0	31.5	26.0	21.5	17.5	15.0	12.5

Stepwise Solution:

Step 1: Identify the Start of Direct Runoff (Point A) and the Peak (P_m) By inspecting the given data, the hydrograph starts rising at t = 0 h, where the discharge is 10.0 m³/s. This is Point A. The peak discharge occurs around t = 18 h to t = 24 h. Based on the hydrograph curve, the absolute peak (P_m) is estimated to occur at t = 20 h.

Step 2: Calculate the Time Base of Direct Runoff (N) Using the empirical formula for the time interval N from the peak to the end of the direct runoff:

• A = 423  km^2
• N = 0.83 \times (423)^0.2 = \mathbf2.78  days

Step 3: Determine the End of Direct Runoff (Point B) Convert N from days to hours: 2.78  days \times 24  h/day = 66.72  h. The end of the direct runoff will be at t = 20  h (peak) + 66.72  h = 86.72  h. For convenience in calculations matching the recorded time intervals, N is slightly adjusted to 2.91  days (70  h), making the end of the DRH exactly at t = 90 h. The discharge at this Point B is 12.5 m³/s.

Step 4: Establish the Base Flow A straight line is drawn joining Point A (t = 0 h, Q = 10.0 m³/s) and Point B (t = 90 h, Q = 12.5 m³/s). The base flow is linearly interpolated between these two points over the 90-hour duration.

Step 5: Calculate the Ordinates of the Direct Runoff Hydrograph (DRH) The DRH is obtained by subtracting the interpolated base flow from the total storm hydrograph ordinates at each time step (DRH = Total Discharge - Base Flow).

Time (h)	Total Hydrograph (m³/s)	Base Flow (m³/s)	DRH Ordinate (m³/s)
0	10.0	10.0	0.0
6	30.0	10.0	20.0
12	87.5	10.5	77.0
18	111.5	10.5	101.0
24	102.5	10.5	92.0
30	85.0	11.0	74.0
36	71.0	11.0	60.0
42	59.0	11.0	48.0
48	47.5	11.5	36.0
54	39.0	11.5	27.5
60	31.5	11.5	20.0
66	26.0	12.0	14.0
72	21.5	12.0	9.5
78	17.5	12.0	5.5
84	15.0	12.5	2.5
90	12.5	12.5	0.0

(Note: The base flow values are linearly approximated between 10.0 and 12.5 m³/s to match the straight-line method,.)