BEGIN Rainfall-Runoff Models
Excess Precipitation or Runoff Volume Models • May be: • Physically Based • Empirical • Descriptive • Conceptual • Generally Lumped • Etc…… • May not only estimate excess precipitation – hence, we will refer to them as rainfall-runoff models…..
The Basic Process…. Necessary for a single basin Focus on Excess Precipitation Excess Precip. Model Excess Precip. Basin “Routing” UHG Methods Runoff Hydrograph Excess Precip. Stream and/or Reservoir “Routing” Downstream Hydrograph Runoff Hydrograph
Goal of Rainfall-Runoff Models • The fate of the falling precipitation is: • …modeled in order to account for the destiny of the precipitation that falls and the potential of the precipitation to affect the the runoff hydrograph. • … losses include interception, evapotranspiration, storage, infiltration, percolation, and finally - runoff. • Let’s look at the fate of the precipitation…..
Interception........... First, the falling precipitation may be intercepted by the vegetation in an area. It is typically either distributed as runoff or evaporated back to the atmosphere. The leafy matter may also be a form of interception.
Leafy Matter also intercepts... Very thick ground litter layers can hold as much as 0.5 inches!
Interception…the point • The point of the interception is that the precipitation is temporarily stored before the next process begins. • The intercepted/stored precipitation may not reach the ground to contribute to runoff. • Interception may be referred to as an abstraction and is accounted for as initial abstraction in some models. • This is also true for snowfall which may sublimate and leave the watershed!
Infiltration........... Precipitation reaching the ground may infiltrate. This is the process of moving from the atmosphere into the soil. Infiltration may be regarded as either a rate or a total. For example: the soil can infiltrate 1.2 inches/hour. Alternatively, we could say the soil has a total infiltration capacity of 3 inches. Note that in both cases the units are Length or length per time!
Infiltration, cont........... Infiltration is nearly impossible to measure directly - as we would disturb the sample in doing so. We can infer infiltration in a variety of ways (to be discussed at a later point). The exact point at which the atmosphere ends and the soil beings is very difficult to define and generally we are not concerned with this fine detail! In other words, we mostly want to know how much of the precipitation actually enters the soil.
Percolation..... Once the water infiltrates into the ground, the downward movement of water through the soil profile may begin.
Percolation..... The percolating water may move as a saturated front - under the influence of gravity…
Percolation..... Or, it may move as unsaturated flow mostly due to capillary forces.
Percolation….the point • The vertical percolation of the water into various levels or zones allows for storage in the subsurface – these zones will be very important in the SAC-SMA model. • This stored subsurface water is held and released as either evaporation, transpiration, or as streamflow eventually reaching the watershed outlet.
Evaporation.... Is the movement of water from the liquid state to the vapor state - allowing transport to the atmosphere. Occurs from any wet surface or open body of water. Soil can have water evaporate from within, as can leafy matter, living leaves and plants, etc.. The water evaporates from a storage location....
Transpiration.... The process of water moving from the soil via the plants internal moisture supply system. This is a type of evaporative process. The water moves through the stomates, tiny openings in the leaves (mostly on the underside), that allow the passage of oxygen, carbon dioxide, water vapor, and other gases.
Evapotranspiration.... The terms transpiration and evaporation are often combined in the form : EVAPOTRANSPIRATION
Storage.... • Storage occurs at several “locations” in the hydrologic cycle and varies in both space and time - spatially and temporally. • Water can be stored in: • The unsaturated portion of the soil • The saturated portion (below the water table) • On the soil or surface - snow/snowpack, puddles, ponds, lakes, wetlands. • Rivers and stream channels - even though they are generally in motion!
Storage.... Water in storage can still be involved in a process. i.e. : Water in a puddle may be evaporating.....
Depression Storage Channel Storage Detention Storage Ground Water Storage Retention Storage Vegetation Storage The hydrologic cycle represented as a series of storage units & processes.... - RO = E P T Surface runoff Is I > f? Storm Flow yes Base Flow no Channel runoff Is retention full? yes Surface runoff no
- RO RO = E P P T Depression Storage Surface runoff Channel Storage Is I > f? Is I > f? Storm Flow yes Base Flow no Detention Storage Channel runoff Is retention full? yes Ground Water Storage Surface runoff no Retention Storage Vegetation Storage Storage.... The thought process.......
Storage.... • Things to consider: • We looked at these as independent processes! • We looked at the processes as discrete time steps! • What were the initial conditions before the storm? What effects would initial conditions have? • These are the issues that a continuous rainfall-runoff model must consider……
The Units • The units are very important… • Storage is a volume (L3) and flow is a volume per time (L3/T) …. • We often think of these volume units in terms of length only! • This implies a uniform depth or value throughout the watershed….
Examples of Length Units for Storage • The watershed can infiltrate 75mm of water – a length… • The lower zone of the soil can hold 60mm... • The initial abstraction for the watershed is 10mm • The reservoir can hold 2.5 inches of runoff… • These all imply uniformity over the watershed…
The Rainfall-Runoff Modeling Process • … simplistic methods such as a constant loss method may be used. • … A constant loss approach assumes that the soil can constantly infiltrate the same amount of precipitation throughout the storm event. The obvious weaknesses are the neglecting of spatial variability, temporal variability, and recovery potential. • Other methods include exponential decays (the infiltration rate decays exponentially), empirical methods, and physically based methods. • … There are also combinations of these methods.
Initial Abstractions Initial Abstraction - It is generally assumed that the initial abstractions must be satisfied before any direct storm runoff may begin. The initial abstraction is often thought of as a lumped sum (depth). Viessman (1968) found that 0.1 inches was reasonable for small urban watersheds. Would forested & rural watersheds be more or less?
Rural watersheds would probably have a higher initial abstraction. The Soil Conservation Service (SCS) now the NRCS uses a percentage of the ultimate infiltration holding capacity of the soil - i.e. 20% of the maximum soil retention capacity.
Some Rainfall-Runoff Models • Phi-Index • Horton Equation • SCS Curve Number • SAC-SMA
Constant Infiltration Rate A constant infiltration rate is the most simple of the methods. It is often referred to as a phi-index or f-index. In some modeling situations it is used in a conservative mode. The saturated soil conductivity may be used for the infiltration rate. The obvious weakness is the inability to model changes in infiltration rate. The phi-index may also be estimated from individual storm events by looking at the runoff hydrograph.
Separation of Baseflow • ... generally accepted that the inflection point on the recession limb of a hydrograph is the result of a change in the controlling physical processes of the excess precipitation flowing to the basin outlet. • … In this example, baseflow is considered to be a straight line connecting that point at which the hydrograph begins to rise rapidly and the inflection point on the recession side of the hydrograph. • … the inflection point may be found by plotting the hydrograph in semi-log fashion with flow being plotted on the log scale and noting the time at which the recession side fits a straight line.
Sample Calculations • In the present example (hourly time step), the flows are summed and then multiplied by 3600 seconds to determine the volume of runoff in cubic feet. If desired, this value may then be converted to acre-feet by dividing by 43,560 square feet per acre. • The depth of direct runoff in feet is found by dividing the total volume of excess precipitation (now in acre-feet) by the watershed area (450 mi2 converted to 288,000 acres). • In this example, the volume of excess precipitation or direct runoff for storm #1 was determined to be 39,692 acre-feet. • The depth of direct runoff is found to be 0.1378 feet after dividing by the watershed area of 288,000 acres. • Finally, the depth of direct runoff in inches is 0.1378 x 12 = 1.65 inches.
Summing Flows Continuous process represented with discrete time steps
Estimating Excess Precip. 0.8 1.65 inches of excess precipitation 0.7 0.6 0.5 Uniform loss rate of 0.2 inches per hour. Precipitation (inches) 0.4 0.3 0.2 0.1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Time (hrs.)
Phi-Index Summary • The phi-index for this storm was 0.2 inches per hour. • This is a uniform loss rate. • If the precipitation stops for a time period, the infiltration will still be 0.2 inches per hour when the precipitation starts again. • Regardless of this weakness, this is still very powerful information to have regarding the response of a watershed.
Exponential Decay - Horton This is purely a mathematical function - of the following form: fo fi = infiltration capacity at time, t fc = final infiltration capacity fo = initial infiltration capacity fc
Horton Effect of fo or fc
Horton Effect of K
Horton Assumes that precipitation supply is greater than infiltration rate. 2 1 0
Horton There are now 2 parameters to estimate or calibrate for a watershed!! fo & k
Horton – Issues with Continuous Simulation • Again, if it stops raining how does the soil recover in a Horton model? • i.e. Stopped raining for a short period – how does the soil recover?
SCS Curve Number Soil Conservation Service is an empirical method of estimating EXCESS PRECIPITATION We can imply that precipitation minus excess precipitation = infiltration/retention : P - Pe = F
SCS (NRCS) Runoff Curve Number • The basic relationships used to develop the curve number runoff prediction technique are described here as background for subsequent discussion. The technique originates with the assumption that the following relationship describes the water balance of a storm event. • where F is the actual retention on the watershed, Q is the actual direct storm runoff, S is the potential maximum retention, and P is the potential maximum runoff
Modifications Pe = P - Ia Effective precipitation equals total precipitation minus initial abstraction… We will use effective precipitation in place of precipitation…
More Modifications • At this point in the development, SCS redefines S to be the potential maximum retention • SCS also defines Ia in terms of S as : Ia = 0.2S • A little substituting gives the familiar SCS rainfall-runoff equation: