Rainfall-runoff Process

Rainfall-runoff is an influential process as part of the whole hydrological cycle over the land surface since it regulates the surface runoff that is of primary interest of the hydrologist, as well as the main source of flooding that affects the human’s life. In a very simplified language, rainfall-runoff presents a sequence of processes that begins with precipitation over the land surface. Infiltration and baseflow come afterwards and present the dynamic of the water under the land; while surface runoff presents the movement of the excess water over the land once the soil is saturated and infiltrates no more water. Horton (1933 in Beven, 2004) presented a theory that assumes the excess water are collected in the depression storage due to topographic variation and collectively move in a shallow sheet over the land. The surface runoff then accumulates and discharges into the small channels, merges with other channels in the main channel and form the streamflow.

Precipitation presents the falling of the water droplets on the Earth’s surface in the various forms such as water, snow and some other forms (e.g. Chow et al., 1998). The precipitation is quantified through its depth over an area within a certain period and usually recorded regularly by a meteorological station. It is an interesting fact that precipitation varies over time and space; therefore a number of methods are developed to model the spatial distribution of precipitation over a unit of analysis. The simplest model makes use of arithmetic mean to calculate the average of precipitation presented by separated stations. Thiessen (1911 in Kopec, 1963) introduced a method to create unique polygons that separated the influence of one stations from another. The isohyet method involves lines connecting places with equal precipitation rate (i.e. isohyet) and a linear interpolation to represent gradual changes between the meteorological stations, while the hypsometric method takes the elevation difference into account when calculating the weighted average of the precipitation rates (Davie, 2003).

Evapotranspiration is simply a cumulative value of evaporation and transpiration. Both evaporation and transpiration are quantified in the unit of depth over an area within a certain period. Evaporation and evapotranspiration can be measured by simple devices such as the evaporation pan and lysimeter, or complex instruments such as Eddy

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correlation and Bowen ratio, even a Light Detection and Ranging (LIDAR) remote sensing system (Abtew and Melesse, 2013). However, considering that evaporation and evapotranspiration vary significantly with time and space as well as the complexities of setting up the above equipment, the evaporation and evapotranspiration are often estimated by the knowledge of other parameters such as temperature, solar radiation, wind speed, humidity and air pressure. Among the methods developed to estimate evapotranspiration, the Pristley-Taylor method is popular due to its minimum input requirements, while the Penman-Monteith is mostly preferred complex method due to its similarity with the physical evapotranspiration estimation (Abtew and Melesse, 2013).

Infiltration describes the vertical and horizontal movement of water below the land surface; therefore it highly depends on the physical properties of the soil, which mainly represented by the proportion of water, air and pores within the soil structure (Horton, 1933 in Beven, 2004). The actual measure of the infiltration amount (expressed as the “infiltration capacity”) is related exponentially to the period of observation (Horton, 1939 in Beven, 2004):

𝑓(𝑡) = 𝑓𝑐+ (𝑓0− 𝑓𝑐)𝑒−𝐾𝑓𝑡 (2.39)

where

𝑓(𝑡) : Infiltration capacity at time 𝑡 𝐾𝑓 : Constant of decay 𝑓𝑐 : Minimum constant infiltration capacity 𝑡 : Time period (hr) 𝑓0 : Infiltration capacity at time 𝑡 = 0

Another fundamental development in the field of infiltration is presented by Green and Ampt (1911, in Chow et al. 1988), which is an alternative to quantify the infiltration through a set of required parameters, i.e. hydraulic conductivity, porosity and the wetting front soil suction head, which particularly can be estimated by the effective saturation rate. In addition, Phillips (1957) carried on Horton (1939) work and realized such theory into an equation with less restrictive condition (Chow et al. 1988).

Infiltration drowns the water deeper until it stops at the saturated zone. This is the zone where no more infiltration occurred due to the absence of space for the water to move downward. The saturated zone is separated from the unsaturated zone by a water table. Depending on the slope of the water table, the water at the unsaturated zone may still move downward along with the slope of the water table and discharge to the main channel, which is known as the subsurface flow (e.g. Mays, 2012). Further below the water table, the water also moves downward along the slope and comprises the groundwater flow, which eventually discharges to the main channel. The subsurface and groundwater flow contribute and ensure the continuity of the flow in the main channel, in the absence of precipitation, which is called base flow (Bedient and Huber, 2002).

The response of a watershed to the precipitation is comprehensively expressed in a hydrograph, which presents the time-series of the accumulated channel flow that include surface runoff/streamflow, subsurface and groundwater flow and precipitation over the channel on a specific location of the watershed (Chow et al., 1988; Bedient and Huber, 2002). A “normal depletion curve” can be estimated by an exponential relation as

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given in the equation below, and then the curve can be used to analyze the hydrograph and separate the base flow from overall hydrograph (Horton, 1933 in Beven, 2004).

𝑞𝑡= 𝑞0𝑒−𝑘𝑡 with (2.40)

𝑞𝑡 : Discharge at time 𝑡 𝑘 : Recession constant

𝑞0 : Specified initial discharge 𝑡 : Period (hr)

Direct runoff holds the largest portion out of the overall flow quantified in the hydrograph after the subtraction of baseflow. It comprises of the surface runoff generated by excess precipitation, which refers to the amount of precipitated water subtracted by the infiltration, evaporation and surface depression storage. The difference between the total precipitation and the excess precipitation is abstraction or loss (Chow et al., 1988). Determination of the direct runoff and quantification of the abstraction are the keys in the rainfall-runoff analysis in order to study the response of a watershed to the dynamic of precipitation. The simplest approach to determine direct runoff is through the Φ-Index, which is a constant rate of abstraction and the number of rainfall intervals (N) that keep adjusted until the direct runoff and excess precipitation depth are equal (Mays, 2012).

Another essential method in the determination of direct runoff from the excess precipitation is the time-area curve, which assumes the overall hydrograph is generated solely by translation of direct runoff to the main outlet with consistent speed (Bedient and Huber, 2002). This method then imaginarily divide the watershed into sections with similar “runoff travel time” to the main outlet. In the rainfall event, the closest section will contribute its runoff to the main outlet, followed by those with larger “runoff travel time”. This sequence then develops a chronological unit hydrograph that is useful to estimate the flow magnitude. Clark Unit Hydrograph is actually using the time-area curve as one of its parameter.