Hydrological modelling

Describes what exactly Hydrological modelling is and different types of Modelling, Also includes Hydrograph.

1. Hydrological modelling A  hydrologic model  is a simplification of a real-world system (e.g., surface water, soil water, wetland, groundwater, estuary) that aids in understanding, predicting, and managing water resources. Both the flow and quality of water are commonly studied using hydrologic models.

2. Conceptual models Conceptual models  are commonly used to represent the important components (e.g.,  features, events, and processes ) that relate hydrologic inputs to outputs. These components describe the important functions of the  system  of interest, and are often constructed using entities (stores of water) and relationships between these entitites (flows or fluxes between stores). The conceptual model is coupled with scenarios to describe specific events (either input or outcome scenarios)

3. For example, a watershed model could be represented using  tributaries  as boxes with arrows pointing toward a box that represents the main river. The conceptual model would then specify the important watershed features (e.g., land use, land cover, soils, subsoils , geology, wetlands, lakes), atmospheric exchanges (e.g., precipitation, evapotranspiration), human uses (e.g., agricultural, municipal, industrial, navigation, thermo- and hydro-electric power generation), flow processes (e.g., overland, interflow, baseflow , channel flow), transport processes (e.g., sediments, nutrients, pathogens), and events (e.g., low-, flood-, and mean-flow conditions).

4. Model scope and complexity is dependent on modeling objectives, with greater detail required if human or environmental systems are subject to greater risk.  Systems modeling  can be used for building conceptual models that are then populated using mathematical relationships.

5. Analog models Prior to the advent of computer models, hydrologic modeling used  analog models  to simulate flow and transport systems. Unlike  mathematical models  that use equations to describe, predict, and manage hydrologic systems, analog models use non-mathematical approaches to simulate hydrology. Two general categories of analog models are common;  scale analogs  that use miniaturized versions of the physical system and  process analogs  that use comparable physics (e.g., electricity, heat, diffusion) to mimic the system of interest.

6. Statistical models Statistical models  are a type of  mathematical model  that are commonly used in hydrology to describe data, as well as relationships between data .  Using statistical methods, hydrologists develop  empirical relationships  between observed variables ,  find trends in historical data ,  or forecast probable storm or drought events

7. Stochastic models These models based on data are  black box  systems, using mathematical and statistical concepts to link a certain input (for instance  rainfall ) to the model output (for instance  runoff ). Commonly used techniques are  regression ,  transfer functions ,  neural networks  and  system identification . These models are known as stochastic hydrology models. Data based models have been used within hydrology to simulate the rainfall-runoff relationship, represent the impacts of  antecedent moisture  and perform real-time control on systems.

8.  Rational Method The rational method is appropriate for estimating peak discharges for small drainage areas of up to about 200 acres (80 hectares) with no significant flood storage. The method provides the designer with a peak discharge value, but does not provide a time series of flow nor flow volume.

9. Assumptions and Limitations Use of the rational method includes the following assumptions and limitations: The method is applicable if t c  for the drainage area is less than the duration of peak rainfall intensity. The calculated runoff is directly proportional to the rainfall intensity. Rainfall intensity is uniform throughout the duration of the storm.

10. The frequency of occurrence for the peak discharge is the same as the frequency of the rainfall producing that event. Rainfall is distributed uniformly over the drainage area. The minimum duration to be used for computation of rainfall intensity is 10 minutes. If the time of concentration computed for the drainage area is less than 10 minutes, then 10 minutes should be adopted for rainfall intensity computations. The rational method does not account for storage in the drainage area. Available storage is assumed to be filled.

11. Rational Method

12. Procedure for using the Rational Method The rational formula estimates the peak rate of runoff at a specific location in a watershed as a function of the drainage area, runoff coefficient, and mean rainfall intensity for a duration equal to the time of concentration. The rational formula is:

13. Where : Q  = maximum rate of runoff ( cfs or m 3 /sec.) C  = runoff coefficient I  = average rainfall intensity (in./hr. or mm/hr.) A  = drainage area (ac or ha) Z  = conversion factor, 1 for English, 360 for metric

14. Rainfall Intensity The rainfall intensity (I) is the average rainfall rate in in./hr. for a specific rainfall duration and a selected frequency. The duration is assumed to be equal to the time of concentration. For drainage areas in Texas, you may compute the rainfall intensity using Equation 4-21, which is known as a rainfall intensity-duration-frequency (IDF) relationship (power-law model).

15. Runoff Coefficients Urban Watersheds Table 4-10 suggests ranges of C values for urban watersheds for various combinations of land use and soil/surface type. This table is typical of design guides found in civil engineering texts dealing with hydrology.

16. Table 4-10: Runoff Coefficients for Urban Watersheds Type of drainage area Runoff coefficient Business:   Downtown areas 0.70-0.95 Neighborhood areas 0.30-0.70 Residential:   Single-family areas 0.30-0.50 Multi-units, detached 0.40-0.60 Multi-units, attached 0.60-0.75 Suburban 0.35-0.40 Apartment dwelling areas 0.30-0.70 Industrial:   Light areas 0.30-0.80 Heavy areas 0.60-0.90 Parks, cemeteries 0.10-0.25 Playgrounds 0.30-0.40 Railroad yards 0.30-0.40 Unimproved areas:   Sand or sandy loam soil, 0-3% 0.15-0.20 Sand or sandy loam soil, 3-5% 0.20-0.25 Black or loessial soil, 0-3% 0.18-0.25 Black or loessial soil, 3-5% 0.25-0.30 Black or loessial soil, > 5% 0.70-0.80 Deep sand area 0.05-0.15 Steep grassed slopes 0.70 Lawns:   Sandy soil, flat 2% 0.05-0.10 Sandy soil, average 2-7% 0.10-0.15 Sandy soil, steep 7% 0.15-0.20 Heavy soil, flat 2% 0.13-0.17 Heavy soil, average 2-7% 0.18-0.22 Heavy soil, steep 7% 0.25-0.35 Streets:   Asphaltic 0.85-0.95 Concrete 0.90-0.95 Brick 0.70-0.85 Drives and walks 0.75-0.95 Roofs 0.75-0.9

17. Time of concentration Time of concentration  is a concept used in hydrology to measure the response of a watershed to a rain event. It is defined as the  time  needed for water to flow from the most remote point in a watershed to the watershed outlet. It is a function of the topography, geology, and land use within the watershed.

18. Time of concentration is useful in predicting flow rates that would result from hypothetical storms, which are based on statistically derived  return periods  through  IDF curves .  For many (often economic) reasons, it is important for engineers and hydrologists to be able to accurately predict the response of a watershed to a given rain event. This can be important for infrastructure development (design of  bridges ,  culverts , etc.) and management, as well as to  assess flood risk  such as the  ARkStorm -scenario.

19. This image shows the basic principle which leads to determination of the time of concentration. Much like a  topographic map  showing lines of equal elevation, a map with  isolines  can be constructed to show locations with the same travel time to the watershed outlet. In this simplified example, the watershed outlet is located at the bottom of the picture with a stream flowing through it. Moving up the map, we can say that rainfall which lands on all of the places along the first yellow line will reach the watershed outlet at exactly the same time.

20. This is true for every yellow line, with each line further away from the outlet corresponding to a greater travel time for runoff traveling to the outlet. Furthermore, as this image shows, the spatial representation of travel time can be transformed into a cumulative distribution plot detailing how travel times are distributed throughout the area of the watershed.

21. SCS Curve Number Method The SCS curve number method is a simiple , widely used and efficient method for determining the approxient amount of runoff from a rainfall even in a particular area. Although the method is designed for a single storm event, it can be scaled to find average annual runoff values.

22. The stat requirments for this method are very low, rainfall amount and curve number. The curve number is based on the area's hydrologic soil group, land use , treatment and hydrologic condition. The 2 former being of greatest importance.

23. The initial equation (1) is based on trends observed in data from collected sites, therefore it is an emperical equation instead of a physically based equation. After further empirical evaulation of the trends in the data base, the initial abstractions, Ia , could be defined as a percentage of S (2).

24. With this assumption, the equation (3) could be written in a more simplified form with only 3 variables. The parameter CN is a transformation of S, and it is used to make interpolating, averaging, and weighting operations more linear (4).

25. With the following chart, the amount of runoff can be found if the rainfall amount (in inches) and curve number is known. There are two advantages of using L-THIA over a manual method. One, the availablity of the data. L-THIA provides the rainfall data for any area in the United States. Two, L-THIA completes this caluculation for every rainfall event for thirty years and then reports the average annual runoff value.

26. Time area Method Time-area unit hydrograph theory establishes a relationship between the travel time and a portion of a basin that may contribute runoff during that travel time. The area closest to the basin outlet will contribute to the final runoff hydrograph much sooner than the areas on the basin boundary.

27. In applying this method, the watershed is traditionally broken into areas of approximately travel time. These lines of equal travel time are known as  isochrones . Figure 1 illustrates the breaking of a watershed into areas by isochrones. The mean travel time of each sub-area is calculated and the resulting  time-area  curve is produced.

28. Most of the "time-area" methods utilize a common, basic approach in determining the final unit hydrograph. The cumulative time-area curve is formed by summing the incremental areas (6 in Figure 1) and the corresponding travel times.

29. Thus, the total time can be thought of as the time of concentration of the watershed with 100% of the basin area being accounted for at the time of concentration. Each of the partial areas (between isochrones) responds in the time associated with that area.

30. Therefore; the cumulative time-area curve is a summation of the individual areas. The contributions of the individual areas can be illustrated with a histogram. One can visualize a uniform depth of water (1" for a unit hydrograph) on each of the zones within the isochrones.

31. The volume of water of each area reaches the outlet at the travel time associated with that area. This is effectively a volume over a time period, which is a flow. Figure 2 illustrates a  time-discharge histogram  associated with the hypothetical basin of Figure 1. 

32. The time-area histogram is really a  translation  hydrograph because the volume of water on each area within the basin is simply "translated" to the outlet using the associated travel time for the translation time. A this point a unit hydrograph (in discrete form) exists. 

33. This "instantaneous" unit hydrograph is the result of 1-inch of instantaneous excess precipitation being placed on the individual areas and then translated to the outlet of the basin, arriving at the time associated with the travel time of area.

34. STREAM FLOW HYDROGRAPH Streamflow , or  channel runoff , is the flow of  water  in  streams ,  rivers , and other  channels , and is a major element of the  water cycle . It is one component of the  runoff  of water from the land to  waterbodies , the other component being  surface runoff . Water flowing in channels comes from surface runoff from adjacent hillslopes , from  groundwater  flow out of the ground, and from water discharged from pipes

35. The  discharge  of water flowing in a channel is measured using  stream gauges  or can be estimated by the  Manning equation . The record of flow over time is called a  hydrograph .  Flooding  occurs when the volume of water exceeds the capacity of the channel.

36. Sources of streamflow Surface and subsurface sources: Stream discharge is derived from four sources: channel precipitation, overland flow, interflow, and groundwater. Channel precipitation is the moisture falling directly on the water surface, and in most streams, it adds very little to discharge. Groundwater, on the other hand, is a major source of discharge, and in large streams, it accounts for the bulk of the average daily flow.

37. Groundwater  enters the streambed where the channel intersects the water table, providing a steady supply of water, termed baseflow , during both dry and rainy periods.

38. Because of the large supply of groundwater available to the streams and the slowness of the response of groundwater to precipitation events, baseflow changes only gradually over time, and it is rarely the main cause of flooding.

39. However, it does contribute to flooding by providing a stage onto which runoff from other sources is superimposed.

40. Interflow  is water that infiltrates the soil and then moves laterally to the stream channel in the zone above the water table. Much of this water is transmitted within the soil itself, some of it moving within the horizons. Next to baseflow , it is the most important source of discharge for streams in forested lands. Overland flow in heavily forested areas makes negligible contributions to streamflow .

41. Mechanisms that cause changes in streamflow Natural mechanisms Runoff from rainfall and snowmelt Evaporation from soil and surface-water bodies Transpiration by vegetation Ground-water discharge from aquifers Ground-water recharge from surface-water bodies Sedimentation of lakes and wetlands Formation or dissipation of glaciers, snowfields, and permafrost

42. Human-induced mechanisms Surface-water withdrawals and transbasin diversions River-flow regulation for hydropower and navigation Construction,removal , and sedimentation of reservoirs and stormwater detention ponds Stream channelization and levee construction Drainage or restoration of wetlands Land-use changes such as urbanization that alter rates of erosion, infiltration, overland flow, or evapotranspiration Wastewater outfalls Irrigation wastewater return flow

43. Measurement Streamflow is measured as an amount of water passing through a specific point over time. The units used in the United States are  cubic feet per second , while in majority of other countries  cubic meters per second  are utilized. One cubic foot is equal to 0.028 cubic meters . There are a variety of ways to measure the discharge of a stream or canal. A stream gauge provides continuous flow over time at one location for water resource and environmental management or other purposes

44. Streamflow values are better indicators than gage height of conditions along the whole river. Measurements of streamflow are made about every six weeks by  United States Geological Survey  (USGS) personnel. They wade into the stream to make the measurement or do so from a boat, bridge, or cableway over the stream.

45. For each streamgaging station, a relation between gage height and streamflow is determined by simultaneous measurements of gage height and streamflow over the natural range of flows (from very low flows to floods).

46.  This relation provides the current condition streamflow data from that station.For purposes that do not require a continuous measurement of stream flow over time, current meters or acoustic Doppler velocity profilers can be used. For small streams — a few meters wide or smaller —  weirs  may be installed.

47. Hydrograph A  hydrograph  is a graph showing the rate of flow ( discharge ) versus time past a specific point in a river, or other channel or conduit carrying flow. The rate of flow is typically expressed in cubic meters or cubic feet per second ( cms or cfs ).

48. It can also refer to a graph showing the volume of water reaching a particular  outfall , or location in a sewerage network. Graphs are commonly used in the design of  sewerage , more specifically, the design of  surface water  sewerage systems and  combined sewers .

49. The discharge is measured at a specific point in a river and is typically time variant. Rising limb:  The rising limb of hydro graph, also known as concentration curve, reflects a prolonged increase in discharge from a catchment area, typically in response to a rainfall event Recession (or falling) limb:  The recession limb extends from the peak flow rate onward. The end of stormflow (a.k.a.  quickflow  or direct runoff) and the return to groundwater-derived flow ( base flow ) is often taken as the point of inflection of the recession limb. The recession limb represents the withdrawal of water from the storage built up in the basin during the earlier phases of the hydrograph. Peak discharge:  the highest point on the hydro graph when the rate of discharge is greatest Lag time:  the time interval from the center of mass of rainfall excess to the peak of the resulting hydrograph Time to peak:  time interval from the start of the resulting hydro graph Discharge:  the rate of flow (volume per unit time) passing a specific location in a river or other channel

50. Unit hydrograph A  unit hydrograph  (UH) is the hypothetical unit response of a watershed (in terms of runoff volume and timing) to a unit input of rainfall. It can be defined as the  direct runoff hydrograph  (DRH) resulting from one unit (e.g., one cm or one inch) of  effective rainfall  occurring uniformly over that watershed at a uniform rate over a unit period of time.

51. As a UH is applicable only to the direct runoff component of a hydrograph (i.e., surface runoff), a separate determination of the baseflow component is required A UH is specific to a particular watershed, and specific to a particular length of time corresponding to the duration of the effective rainfall. That is, the UH is specified as being the 1-hour, 6-hour, or 24-hour UH, or any other length of time up to the  time of concentration  of direct runoff at the watershed outlet. Thus, for a given watershed, there can be many unit hydrographs, each one corresponding to a different duration of effective rainfall.

52. To be Continued in Next class