# Presentation: 264639

## Dr. Dennis L. Johnson
Riverside Technology, inc.

- Riverside Technology, inc.

- NWS / WMO
- Hydrologic Forecasting Course
- October 2003

## Instructor Information

- Juniata College
- Associate Professor
- Environmental Science & Studies
- Information Technology
- Director Technology Solutions Center
- RTi
- Senior Hydrologist
- NWS Hydrologic Research Laboratory
- Distributed Hydrologic Models
- Unsteady Flow

## Overview

**Purpose & Definitions**
**Hydrology - Overview & Quantities**
**Models & Modeling Concepts**
**Precipitation as the Input**
**Rainfall-Runoff Models**
**Unit Hydrograph Models**
**Streamflow Routing**
**Calibration**

## Purpose

Increase the participants knowledge and understanding of the interaction between meteorology and hydrology in watersheds:
Increase participants understanding of the functional aspects of watersheds;
Enhance the participants knowledge of the capabilities, limitations, and applications of hydrologic/hydrometeorologic forecasting systems

**Increase the participants knowledge and understanding of the interaction between meteorology and hydrology in watersheds:**
**Increase participants understanding of the functional aspects of watersheds;**
**Enhance the participants knowledge of the capabilities, limitations, and applications of hydrologic/hydrometeorologic forecasting systems**

## In the end, it is intended that participants will understand the basics of the hydrologic forecast process, the assumptions in the process, and the responsibilities associated with interpreting and issuing the forecast.

## Hydrology

**... ****an earth science.  It encompasses the occurrence, distribution, movement, and properties of the waters of the earth and their environmental relationships." (Viessman, Knapp, Lewis, & Harbaugh, 1977 - **_**Introduction to Hydrology**_**, Harper & Row Publishers, New York)**

## Hydrometeorology

**... ****an interdisciplinary science involving the study and analysis of the interrelationships between the atmospheric and land phases of water as it moves through the hydrologic cycle." (Hydrometeorological Service Operations for the 1990's, Office of Hydrology, National Weather Service, NOAA, 1996).**

## HydrometeorologySimplification of the Links

**Hydrology**

**Engineering/Fluid**

**Mechanics**

- 

- In-depth hydrologic

- analysis

- 

- Execution of complex

- hydrologic models.

- Adjustment of

- model parameters, and

- the derivation of

- hydrologic forecasts for

- all

- time scales

- 

- Applied hydrologic

- research

- 

- Development and

- calibration of

- hydrologic models

- 

- Development of

- hydrologic applications

- procedures.

**Meteorology**

**Thermodynamics/atmospheric**

**physics orientation**

- 

- In-depth meteorological

- analysis

- 

- Weather forecast and

- warning operations

- 

- Climatological forecasting

- 

- Applied meteorological

- and climatological

- research.

- 

- Development and calibration

- of meteorological models

- 

- Development of

- meteorological applications

- and procedures.

**Hydrometeorology**

**Interdisciplinary**

**Orientation**

- 

- Assimilation/use of

- radar based

- precip. estimates

- 

- Production and/or

- use of

- QPF's and

- other

- hydromet.

- forecasts

- 

- Use of guidance

- (e.g. flash flood) in

- hydrologic warning

- operations

- 

- Use of soil moisture

- states from

- hydrologic model in

- atmospheric model

- 

- Applied

- hydrometeorological

- research.

## BEGIN

- Hydrologic Overview & Quantities

## The complexity of what we are trying to accomplish....

**Infiltration**

**Evaporation & Condensation**

**The Water Budget**

**Photosynthesis & Respiration**

**Antecedent Moisture Conditions**

**Transpiration & Interception**

**Variable Source Area**

**Time of Concentration**

- The “sphere” concept was *borrowed* from Dr. Peter Black: _Watershed Hydrology_ – 2nd Edition, Peter Black, 1996, Ann Arbor Press (ISBN# 1-5704 027-1)

## History of Hydrology

- Early philosophers speculated on the hydrologic cycle:
- Homer believed that there existed large subterranean reservoirs that fed the rivers, seas, springs, and wells - *was he wrong?*
- Homer did understand the dependence of flow in the Greek aqueducts on conveyance and velocity!

## History, cont....

- In the first century B.C., Marcus Vitruvius in the treatise De Architectura Libri Decem (the engineers chief handbook), Vol. 8 _***hypothesized***_ that rain and snow falling in the mountains infiltrated into the earth’s surface and appeared in the lowlands as springs and streams.....

## Early Success.....

- 4000 B.C. The Egyptians built a dam on the Nile to allow barren lands to again be used for agricultural purposes.
- 1000’s of years later, a canal to carry fresh water from Cairo to Suez was built.
- Towns in Mesopotamia were protected by flooding from high earthen walls.

## Early Disputes and Rules

- The cities of Lagash and Umma of Mesopotamia have documented water disputes.
- The Romans decree:
*Ne quis aquam oletato dolo malo ubi publice saliet si quis oletarit sestertiorum X mila multa esto*
*It is forbidden to pollute the public water supply; any deliberate offender shall be punished by a fine of 10,000 sesterces!*

## Qualitative Understanding

- Near end of 15th century, Leonardo da Vinci and Bernard Palissy independently reached conclusions on the hydrologic cycle - based on a philosophical understanding.
- There was still a lack of _***quantitative***_ understanding of the hydrologic cycle.

## The 17th Century	

- Perrault, Mariotte, and Halley began quantitative measurements and applications
- Perrault measured rainfall and runoff over the Seine River drainage basin for ~ 3 years - he illustrated that rainfall WAS adequate in quantity to account for river flows
- Mariotte gauged the velocity of the flow in the River Seine and estimated flows by also estimating river cross sectional areas.
- Halley was an astronomer!  He estimated evaporation from the Mediterranean Sea and correlated it to river flows into the Med, concluding that river flows were sufficient enough to provide that volume of water.

## The 18th Century

- Bernoulli - famous for hydraulics and fluid mechanics - the piezometer, the pitot tube, and Bernoulli’s theorem.
- The Chezy formula (channel flow)

## The 19th Century

- Hagen-Poiseuille - capillary flow equation.
- Darcy’s - flow in porous media.
- Duptuit-Thien well formula.
- Manning - Open channel flow.
- Systematic stream gaging.
- Mostly empirical in nature.

## The 20th Century

- Government agencies began to develop programs!
- Rational analysis begins
- Sherman - Unit hydrograph theory
- Horton - infiltration theory
- Snyder - Unit Hydrograph
- Clark - Unit Hydrograph
- etc...........

## Relatively Speaking....

- Hydrology
- Hydrometeorology
- Forecasting.......
- still relatively young!

## Modern day

- Very computer and data intensive
- High tech instruments
- Scale issues
- Policy issues
- Forecasting
- Decision Support
- etc.................

## Reasons to Forecast

- Drought Predictions
- Agriculture
- Flooding
- Warnings
- Decision Making

## Units & Properties of Water

## Area

**1 acre = 43,560 ft****2**
**1 mi****2**** = 640 acres**
**1 hectare = 100m x 100m = 2.471 acres = 10,000 m****2**
**1 km****2**** = 0.386 mi****2**

_**Some Common Unit Conversions**_

## Volume

**1 acre-foot = 1 ac-ft = 1 acre of water x 1 foot deep = 43,560 x 1 = 43,560 ft****3**
**1 ac-inch = 1 acre x 1 inch deep = 43,560 x 1/12 = 3,630 ft****3**
**1 ft****3**** = 7.48 gallons**
**1 gallon H****2****O ~ 8.34 lbs.**

## Runoff Volume

**1-inch of runoff over 1 square mile :**
** ****1/12 feet x 1 mi****2**** x 640 acres/mi****2**** x 43,560 ft2/mi****2****  = 2,323,200 ft****3**

## Discharge

**1 cfs = 1 cubic foot per second**
**1 cfs x 7.48 gal/ft****3**** x 3600 sec/hr x 24 hrs/day = 646,272 gpd = 0.646 MGD**
**1 cfs x 3600 sec/hr x 24 hrs/day = 86,400 cfs/day**
**86,400 cfs/day x 1 ac-ft/43,560 ft****3**** = 1.983 ac-ft/day (~ 2 ac-ft/day)**
**1.983 ac-ft/day x 12 inches/ft x 1 day/24 hrs = 0.992 ac-in/hr**
**1 ac-in/hr x 43,560 ft****3****/ac-ft x 1 hr/3600 sec x 1 ft/12 inches = 1.008 cfs**

## Power

**Hp = ********HQ/550**
**1 hp = 550 ft*lb/sec = 0.7547 kilowatts**

****weight of water
**H = **head or elevation difference
**Q = **flow
- Hydropower wants a lot of flow and a full reservoir.....

## END

- Hydrologic Quantities

## BEGIN

- Overview of Models & Modeling Concepts

## Model Classifications

- There are many classification schemes.
- Many models or models routines fall into multiple categories.
- Hydrologic model classifications are generally based on the method of representation of the hydrologic cycle or a component of the hydrologic cycle.
- Many (if not most) hydrologic models and tools fall into multiple model classifications.....

## Forecasting –vs.- Predicting

- Forecasting in the hydrometeoroligical sense, is a prior estimation of future hydromet. phenomena in a real-time mode...
- Prediction is often thought of as a design mode.  For example one would predict the magnitude of a 100-year event for the purposes of designing a bridge or dam.
- A forecast is essentially a prediction!

## Physical –vs.- Mathematical

- A very basic and simplistic classification:
- Physical attempt to simulate the actual physical processes, often by similitude (i.e. – a 1:10 physical model of a stream channel.
- Mathematical models utilize mathematical statements (equations) to represent.
- Mathematical equations may be based on physical characteristics!

## Continuous –vs.- Discrete

- Continuous models are often referred to as “continuous simulation” models because they represent a continuous process in nature – i.e. the runoff process which leads to a streamflow hydrograph.  The forecasting process basically requires a continuous model.
- Discrete models are often referred to as “single-event” models.  These models are most often used in a predictive mode.
- Many continuous models or attempts to model a continuous function are broken into discrete time steps!

## Descriptive –vs.- Conceptual

- Descriptive models account for observed phenomena utilizing empiricism and basic fundamentals, while,
- Conceptual models tend to rely on theory to represent a process rather than to actually represent the physical process – for example a model that is based on probability theory.

## Lumped –vs.- Distributed

- Lumped models do not allow for variation in model states and parameters throughout the system.
- Distributed models allow for or account for behavior variations throughout the system.  Often on point to point basis.
- Subdividing a watershed is an attempt to make a semi-distributed model!

## Deterministic –vs.- Stochastic

- Deterministic models generally use inpputs that are known with a reasonnable degree of certainty, whereas,
- Stochastic models may have input that is generated or synthesized – perhaps from a probability distribution – i.e. ESP...

## Models Overview

- Many models are combinations of the aforementioned types.
- For example: a conceptual or probabilistic model may use the output from a continuous descriptive model to produce a forecast.

## General Goal of Most Models

**Process**

**OUTPUT**

- INPUT

## General Goal of Most Hydrologic Models

**Basin Process Representation**

**Infiltration**
**Excess Precip.**
**Interception**
**Storage**

**Precipitation**

**Hydrologic**
**Phenomena**

**We must begin to think of the basin as a “whole”**

## General Goal of Most Continuous Simulation Hydrologic Models

**Basin Process Representation**

**Infiltration**
**Excess Precip.**
**Interception**
**Storage**

**Precipitation- Time Series**

**Hydrologic Quantities- Time Series**

**While the process is continuous – we often represent it in discrete fashion!**

## Discrete Representations

- A continuous storm represented as discrete intervals.

## The Basic Process....

**Excess Precip. Model**

**Excess Precip.**

**Excess Precip****.**

**Runoff Hydrograph**

**Runoff Hydrograph**

**Stream and/or Reservoir “Routing”**

**Downstream Hydrograph**

**Basin “Routing” UHG Methods**

- Necessary for a single basin

## From A Basin View

**Excess Precip. Model**

**Excess Precip****.**

**Basin “Routing”**
**Unit Hydrograph**

**Stream “Routing”**

**Runoff Hydrograph**

## END

- Overview of Models & Modeling Concepts

## BEGIN

- Precipitation as the Input

##     Precipitation

- ... primary "input" for the hydrologic cycle (or hydrologic budget).
- ... The patterns of the precipitation are affected by large scale global patterns, mesoscale patterns, "regional" patterns, and micro-climates.
- ... In addition to the quantity of precipitation, the spatial and temporal distributions of the precipitation have considerable effects on the hydrologic response.

## The Basic Process....

**Excess Precip. Model**

**Excess Precip****.**

**Excess Precip****.**

**Runoff Hydrograph**

**Runoff Hydrograph**

**Stream and/or Reservoir “Routing”**

**Downstream Hydrograph**

**Basin “Routing” UHG Methods**

- Necessary for a single basin

**Focus on Precipitation**

## Precipitation As Input

- Precipitation is generally “pre-processed”
- Uniform in space and time – never!
- Gages - Recording & non-recording
- Radar
- Satellite Derived
- QPF

## Precipitation

- ... In lumped models, the precipitation is input in the form of average values over the basin.  These average values are often referred to as mean aerial precipitation (MAP) values.
- ... MAP's are estimated either from 1) precipitation gage data or 2) NEXRAD precipitation fields (MAPX).

## Precipitation (cont.)

- ... If precipitation gage data is used, then the MAP's are usually calculated by a weighting scheme.
- ... a gage (or set of gages) has influence over an area and the amount of rain having been recorded at a particular gage (or set of gages) is assigned to an area.
- ... Thiessen, isohyetal, and the inverse-distance squared are some of the more popular methods.

## Thiessen

**Thiessen method** **is a method for areally weighting rainfall through graphical means.**

## Isohyetal

**Isohyetal method** **is a method for areally weighting rainfall using contours of equal rainfall (isohyets).**

## Inverse-Distance Squared

**Inverse-Distance Squared**

- Used to compute average precipitation at any point based on nearby gages.  The weight of the nearby gages is dependant on the distance from the point to each of the nearby gages.

- Gage A

- Gage B

- Gage C

- dA

- dC

- dB

## NEXRAD

**Nexrad** **is a method of areally weighting rainfall using radar based estimates of the intensity/amount of the precipitation during a time period.**

## Temporal Distributions

- Gages record data at intervals - 10 min., 15 min., 1 hour, 24 hour, etc....
- Models use the data at 1-hour, 6-hour, etc...
- Must either aggregate or disaggregate precipitation amounts....
- i.e. Combine 1 hour values into a 6-hour value...  Not a problem!
- Or... Break a 24-hour value into 6 hour values... Much more difficult!

## Temporal Disaggregation

**24-hour gage**
**3.6 inches total**

**1 hour gage with 2.2 total inches and the following distribution:**

**Distribute the 3.6 inches using the breakdown of the hourly gage**

## Precipitation Gage Networks

- A system of gages
- Design Issues:
- density
- location
- quality (of data)
- collection & transmission
- processing, filing, managing

## Factors Affecting Density

- Purpose of Network – Desired Quality/Precision/Accuracy
- Finances – Installation and UPKEEP!
- Nature of Precipitation – rain, rain + snow, orographic, convective, etc..
- Accessibility
- to name a few.....

## END

- Precipitation as the Input

## 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....

**Excess Precip. Model**

**Excess Precip.**

**Excess Precip.**

**Runoff Hydrograph**

**Runoff Hydrograph**

**Stream and/or Reservoir “Routing”**

**Downstream Hydrograph**

**Basin “Routing” UHG Methods**

- Necessary for a single basin

**Focus on Excess Precipitation**

## 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.**

## Canopy...(or lack of)

## 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.....**

## The hydrologic cycle represented as a series of storage units & processes....

**RO**

**P**

**T**

**E**

**=**

**-**

**Is I > f?**

**yes**

**no**

**Surface runoff**

**Channel runoff**

**Is retention full?**

**yes**

**no**

**Surface runoff**

**Base Flow**

**Storm Flow**

## 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 ********-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.**

## Hydrograph Breakdown

## Hydrograph Breakdown

## Derive phi-indexsample watershed = 450 mi2

## 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.**

## Semi-log Plot

## Hydrograph & Baseflow

## Separate Baseflow

## 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

- 0.1

- 0.2

- 0.3

- 0.4

- 0.5

- 0.6

- 0.7

- 0.8

- 0

- 1

- 2

- 3

- 4

- 5

- 6

- 7

- 8

- 9

- 10

- 11

- 12

- 13

- 14

- 15

- 16

- 17

- 18

- 19

**Time (hrs.)**

**Precipitation (inches)**

- Uniform loss rate of

- 0.2 inches per hour.

- 1.65 inches of excess precipitation

## 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 

**Exponential Decay - Horton**

**This is purely a mathematical function - of the following form:**

- fi = infiltration capacity at time, t
- fc = final infiltration capacity
- fo = initial infiltration capacity

**f****o**

**f****c**

## Horton 

**Effect of *****f******o *****or *****f******c***

**Horton**

## Horton

- Effect of K

**Horton**

## Horton

**0**

**1**

**2**

**Horton**

- Assumes that precipitation supply is greater than infiltration rate.

## Horton

***f******o****** & k***

**Horton**

## 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 

**We can imply that precipitation minus excess precipitation = infiltration/retention :**
**P - P****e**** = F**

**SCS Curve Number **

## 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 I****a**** in terms of S as : I****a**** = 0.2S**
**A little substituting gives the familiar SCS rainfall-runoff equation:**** **

## Estimating “S”

**The difficult part of applying this method to a watershed is the estimation of the watershed’s potential maximum retention, S.**
**SCS developed the concept of the dimensionless curve number, CN, to aid in the estimation of S.**
**CN is related to S as follows :**

- CN ranges from 1 to 100 (not really!)

## Determine CN

**The Soil Conservation Service has classified over 8,500 soil series into four hydrologic groups according to their infiltration characteristics, and the proper group is determined for the soil series found.  **
**The hydrologic groups have been designated as A, B, C, and D.  **
**Group A is composed of soils considered to have a low runoff potential.  These soils have a high infiltration rate even when thoroughly wetted.  **
**Group B soils have a moderate infiltration rate when thoroughly wetted, **
**while group C soils are those which have slow infiltration rates when thoroughly wetted.  **
**Group D soils are those which are considered to have a high potential for runoff, since they have very slow infiltration rates when thoroughly wetted (SCS, 1972).**

## Determine CN, cont....

**Once the hydrologic soil group has been determined, the curve number of the site is determined by cross-referencing land use and hydrologic condition to the soil group - SAMPLE**

**Land use and treatment****	****	****    Hydrologic soil group**
**         ****or Hydrologic    **_**                                                   **_**  **
**      ****practice****	**** condition****	****A****	****B****	****C****	****D**
**Fallow**
**Straight row****	****----****	****77****	****86****	****91****	****94**
**Row Crops**
**Straight row****	****Poor****	****72****	****81****	****88****	****91**
**Straight row****	****Good****	****67****	****78****	****85****	****89**
**Contoured****	****Poor****	****70****	****79****	****84****	****88**

## Initial Conditions

**5-day antecedent rainfall, inches**
**   ****Antecedent moisture****	**
**	****	****Dormant Season****	****	****Growing Season**
**  ****I****	****	****Less than 0.5****	****	****Less than 1.4**
** ****II****	****	****0.5 to 1.1****	****	****	****1.4 to 2.1**
**III****	****	****Over 1.1****	****	****	****Over 2.1**

## Adjust CN’s

## Sample Application

**The curve number is assumed to be 70. **
** ****The cumulative runoff (c) is calculated from the cumulative precipitation (b), using equation (4).  **
**The potential maximum storage, S, is calculated to be S = (1000/70) - 10 = 4.286 inches.  **
**Using 20% as the initial abstraction percentage yields 0.2 x 4.286 = 0.8572 inches and will require that at least 0.8572 inches of precipitation must accrue before runoff  may begin.**** **

## Computations

## Problems

**The initial abstraction (I****a****) consists of interception, depression storage, and infiltration that occurs prior to runoff.  **
**It is not easy to estimate the initial abstraction for a particular storm event.  **
**SCS felt that there should be a connection between I****a**** versus S, and they attempted to develop the relationship by plotting I****a**** versus S for a large number of events on small experimental watersheds. - Quite a SCATTER - not very successful.**

## These rainfall-runoff models have varied in complexity – but would have difficulty in modeling a continuous event, as they all lack the ability to allow the soil zones to “recover” when the precipitation stops.....  This leads us to model systems that are intended for continuous simulation with “updating” abilities.

## SAC-SMA

- ... The Sacramento Soil Moisture Accounting Model (SAC-SMA) is a conceptual model of soil moisture accounting that uses empiricism and lumped coefficients to attempt to mimic the physical constraints of water movement in a natural system.

## Sacramento Soil Moisture Accounting Model

## Sacramento Model Structure

## Hydrograph Decomposition

## Sacramento Soil Moisture Components

## Initial Soil-moisture ParameterEstimates By Hydrograph Analysis

- Initial Soil-moisture ParameterEstimates By Hydrograph Analysis

## Sacramento Soil Moisture Accounting Model

## Sacramento Model Structure

## Hydrograph Decomposition

## Sacramento Soil Moisture Components

## Initial Soil-moisture ParameterEstimates By Hydrograph Analysis

- Initial Soil-moisture ParameterEstimates By Hydrograph Analysis

## Initial Soil-moisture Parameter Estimates By Hydrograph Analysis (continued)

- Initial Soil-moisture Parameter Estimates By Hydrograph Analysis (continued)

- 		         LZSK - Supplemental baseflow recession (always > LZPK)
- 		 Flow that typically persists anywhere from 15 days to 3 or 4 months

## Initial Soil Moisture Parameters Estimates by Hydrograph Analysis (continued)

- Initial Soil Moisture Parameters Estimates by Hydrograph Analysis (continued)

## Initial Soil Moisture Estimates by Hydrograph Analysis (continued)

## Multiyear Statistical Output

## Multiyear Statistical Output (continued)

## Slide 136

## Slide 137

## Slide 138

## Slide 139

## Slide 140

## Slide 141

## Slide 142

## Slide 143

## Slide 144

## Slide 145

## Slide 146

## Slide 147

## Slide 148

## Slide 149

## Slide 150

## Slide 151

## Slide 152

## Slide 153

## Slide 154

## Slide 155

## Slide 156

## Slide 157

## Slide 158

## Slide 159

## Slide 160

## END

- Rainfall-Runoff Models

## BEGIN

- UHG Theory

## Unit Hydrograph Theory

- Moving water off of the watershed...
- A mathematical concept
- Linear in nature
- Uses convolution to transform the excess precipitation to streamflow....

## The Basic Process....

**Excess Precip. Model**

**Excess Precip.**

**Excess Precip.**

**Runoff Hydrograph**

**Runoff Hydrograph**

**Stream and/or Reservoir “Routing”**

**Downstream Hydrograph**

**Basin “Routing” UHG Methods**

- Necessary for a single basin

**Unit Hydrographs**

## Unit Hydrograph Theory

- Sherman - 1932
- Horton - 1933
- Wisler & Brater - 1949 - “the hydrograph of surface runoff resulting from a relatively short, intense rain, called a unit storm.”
- The runoff hydrograph may be “made up” of runoff that is generated as flow through the soil (Black, 1990).

## Unit Hydrograph “Lingo”

- Duration
- Lag Time
- Time of Concentration
- Rising Limb
- Recession Limb (falling limb)
- Peak Flow
- Time to Peak (rise time)
- Recession Curve
- Separation
- Base flow

## Graphical Representation

- Lag time

- Time of concentration

- Duration of excess precip.

- Base flow

## Methods of Developing UHG’s

- From Streamflow Data
- Synthetically
- Snyder
- SCS
- Time-Area (Clark, 1945)
- “Fitted” Distributions

## Unit Hydrograph

***The hydrograph that results from 1-inch of excess precipitation (or runoff) spread uniformly in space and time over a watershed for a given duration.***
- The key points :
- 1-inch of EXCESS precipitation
- Spread uniformly over space - evenly over the watershed
- Uniformly in time - the excess rate is constant over the time interval
- There is a given duration

## Derived Unit Hydrograph

## Derived Unit Hydrograph

## Derived Unit Hydrograph

_**Rules of Thumb :**_
- ... the storm should be fairly uniform in nature and the excess precipitation should be equally as uniform throughout the basin.  This may require the initial conditions throughout the basin to be spatially similar.
- ... Second, the storm should be relatively constant in time, meaning that there should be no breaks or periods of no precipitation.
- ... Finally, the storm should produce at least an inch of excess precipitation (the area under the hydrograph after correcting for baseflow).

## Deriving a UHG from a Stormsample watershed = 450 mi2

**Deriving a UHG from a Storm****sample watershed = 450 mi2**

## 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.

## Semi-log Plot

## Hydrograph & Baseflow

## Separate Baseflow

**Separate Baseflow**

## 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.

## Again - Summing Flows

**Continuous process represented with discrete time steps**

## Obtain UHG Ordinates

- The ordinates of the unit hydrograph are obtained by dividing each flow in the direct runoff hydrograph by the depth of excess precipitation.
- In this example, the units of the unit hydrograph would be cfs/inch (of excess precipitation).

## Final UHG

**Final UHG**

## Determine Duration of UHG

- The duration of the derived unit hydrograph is found by examining the precipitation for the event and determining that precipitation which is in excess.
- This is generally accomplished by plotting the precipitation in hyetograph form and drawing a horizontal line such that the precipitation above this line is equal to the depth of excess precipitation as previously determined.
- This horizontal line is generally referred to as the -index and is based on the assumption of a constant or uniform infiltration rate.
- The uniform infiltration necessary to cause 1.65 inches of excess precipitation was determined to be approximately 0.2 inches per hour.

## Estimating Excess Precip.

**Estimating Excess Precip.**

- 0

- 0.1

- 0.2

- 0.3

- 0.4

- 0.5

- 0.6

- 0.7

- 0.8

- 0

- 1

- 2

- 3

- 4

- 5

- 6

- 7

- 8

- 9

- 10

- 11

- 12

- 13

- 14

- 15

- 16

- 17

- 18

- 19

**Time (hrs.)**

**Precipitation (inches)**

- Uniform loss rate of

- 0.2 inches per hour.

## Excess Precipitation

**Excess Precipitation**

## Changing the Duration

- Very often, it will be necessary to change the duration of the unit hydrograph.
- If unit hydrographs are to be averaged, then they must be of the same duration.
- Also, convolution of the unit hydrograph with a precipitation event requires that the duration of the unit hydrograph be equal to the time step of the incremental precipitation.
- The most common method of altering the duration of a unit hydrograph is by the S-curve method.
- The S-curve method involves continually lagging a unit hydrograph by its duration and adding the ordinates.
- For the present example, the 6-hour unit hydrograph is continually lagged by 6 hours and the ordinates are added.

## Develop S-Curve

**Develop S-Curve**

- Continuous 6-hour bursts

## Convert to 1-Hour Duration

- To arrive at a 1-hour unit hydrograph, the S-curve is lagged by 1 hour and the difference between the two lagged S-curves is found to be a 1 hour unit hydrograph.
- However, because the S-curve was formulated from unit hydrographs having a 6 hour duration of uniformly distributed precipitation, the hydrograph resulting from the subtracting the two S-curves will be the result of 1/6 of an inch of precipitation.
- Thus the ordinates of the newly created 1-hour unit hydrograph must be multiplied by 6 in order to be a true unit hydrograph.
- The 1-hour unit hydrograph should have a higher peak which occurs earlier than the 6-hour unit hydrograph.

## Final 1-hour UHG

**Final 1-hour UHG**

## Average Several UHG’s

- It is recommend that several unit hydrographs be derived and averaged.
- The unit hydrographs must be of the same duration in order to be properly averaged.
- It is often not sufficient to simply average the ordinates of the unit hydrographs in order to obtain the final unit hydrograph.  A numerical average of several unit hydrographs which are different “shapes” may result in an “unrepresentative” unit hydrograph.
- It is often recommended to plot the unit hydrographs that are to be averaged.  Then an average or representative unit hydrograph should be sketched or fitted to the plotted unit hydrographs.
- Finally, the average unit hydrograph must have a volume of 1 inch of runoff for the basin.

## Synthetic UHG’s

- Snyder
- SCS
- Time-area

## Snyder

- Since peak flow and time of peak flow are two of the most important parameters characterizing a unit hydrograph, the Snyder method employs factors defining these parameters, which are then used in the synthesis of the unit graph (Snyder, 1938).
- The parameters are Cp, the peak flow factor, and Ct, the lag factor.
- The basic assumption in this method is that basins which have similar physiographic characteristics are located in the same area will have similar values of Ct and Cp.
- _Therefore, for ungaged basins, it is preferred that the basin be near or similar to gaged basins for which these coefficients can be determined._

## Basic Relationships

## Final Shape

- The final shape of the Snyder unit hydrograph is controlled by the equations for width at 50% and 75% of the peak of the UHG:

## SCS

## Dimensionless Ratios

**Dimensionless Ratios**

## Triangular Representation

## Triangular Representation

- The 645.33 is the conversion used for delivering 1-inch of runoff (the area under the unit hydrograph) from 1-square mile in 1-hour (3600 seconds).

## 484 ?

- Comes from the initial assumption that 3/8 of the volume under the UHG is under the rising limb and the remaining 5/8 is under the recession limb.

## Duration & Timing?

- L = Lag time

- For estimation purposes :

- Again from the triangle

## Time of Concentration

- Regression Eqs.
- Segmental Approach

## A Regression Equation

- where :	Tlag = lag time in hours
- 	L = Length of the longest drainage path in feet
- 	S = (1000/CN) - 10  (CN=curve number)
- 	%Slope = The average watershed slope in %

## Segmental Approach

- More “hydraulic” in nature
- The parameter being estimated is essentially the time of concentration or longest travel time within the basin.
- In general, the longest travel time corresponds to the longest drainage path
- The flow path is broken into segments with the flow in each segment being represented by some type of flow regime.
- The most common flow representations are overland, sheet, rill and gully, and channel flow.

## A Basic Approach

- McCuen (1989) and SCS (1972) provide values of k for several flow situations (slope in %)

- Sorell & Hamilton, 1991

## Triangular Shape

- In general, it can be said that the triangular version will not cause or introduce noticeable differences in the simulation of a storm event, particularly when one is concerned with the peak flow.
-  For long term simulations, the triangular unit hydrograph does have a potential impact, due to the shape of the recession limb.
- The U.S. Army Corps of Engineers (HEC 1990) fits a Clark unit hydrograph to match the peak flows estimated by the Snyder unit hydrograph procedure.
- It is also possible to fit a synthetic or mathematical function to the peak flow and timing parameters of the desired unit hydrograph.
- Aron and White (1982) fitted a gamma probability distribution using peak flow and time to peak data.

## Fitting a Gamma Distribution

## Time-Area

**Time-Area**

## Time-Area

## Time-Area

## Hypothetical Example

- A 190 mi2 watershed is divided into 8 isochrones of travel time.
- The linear reservoir routing coefficient, R, estimated as 5.5 hours.
- A time interval of 2.0 hours will be used for the computations.

## Rule of Thumb

- R - The linear reservoir routing coefficient can be estimated as approximately 0.75 times the time of concentration.

## Basin Breakdown

## Incremental Area

## Cumulative Time-Area Curve

## Trouble Getting a Time-Area Curve?

***Synthetic time-area curve -  The U.S. Army Corps of Engineers (HEC 1990)***

## Instantaneous UHG

******t = the time step used n the calculation of the translation unit hydrograph**
**The final unit hydrograph may be found by averaging 2 instantaneous unit hydrographs that are a ********t time step apart.**

## Computations

## Incremental Areas

## Incremental Flows

## Instantaneous UHG

## Lag & Average

## END

- UHG Theory

## BEGIN

- Putting It All Together

## The Basic Process....

**Excess Precip. Model**

**Excess Precip.**

**Excess Precip.**

**Runoff Hydrograph**

**Runoff Hydrograph**

**Stream and/or Reservoir “Routing”**

**Downstream Hydrograph**

**Basin “Routing” UHG Methods**

- Necessary for a single basin

## Convolution

## Individual Responses

## Overall Response

## END

- Putting It All Together

## BEGIN

- Calibration

## Calibration

- Calibration process
- Estimation of parameter values which will minimize differences between observed and simulated streamflows
- Calibration problems
- Parameter interaction
- Non-unique solutions
- Time-consuming
- Inaccuracies
- Non-linearities
- Lack of understanding

## Calibration System

- Parameter estimation/optimization and watershed simulation
- Input
- Point or areal estimates of historical precipitation, temperature, and potential evaporation
- Initial hydrologic conditions
- Output
- Basin areal averages for point value inputs
- Simulated hydrographs for historical analysis or use in ESP
- Parameter values for models in operational forecast and ESP systems

## Calibration System (continued)

- Characteristics
- Performs computations for few forecast points for many time steps
- Uses operations table
- Compatible with operational system and ESP
- Produces graphical output for manual calibration
- Includes algorithms for automatic optimization
- Applications
- Historical watershed simulation
- Model calibration

## Model Calibration

- Strategy
- Select river system
- Prepare data
- MAP - Mean Areal Precipitation
- MAT - Mean Areal Temperature
- PE - Potential Evaporation
- QME - Mean Daily Discharge
- QIN - Instantaneous Discharge

## Model Calibration (continued)

- Calibrate least complicated headwater basins
- Select calibration period
- Estimate initial parameter - observed Qs
- Trial and error using MCP
- Statistics, observed versus simulated plots
- Proper approach to parameter adjustment
- Automatic parameter optimization - OPT
- Fine tuning - MCP
- Calibrate other headwater areas
- Calibrate local areas

## Model Calibration (continued)

- Important considerations
- Model structure, simulation processes
- Effects of parameter changes
- Use of the forecast information

## Data Preparation

- MAP Algorithms - Mean Areal Precipitation
- 	Techniques for converting point precipitation measurements into areal measurements and distributing them properly in time
- 	Daily and hourly data
- 	Grid point algorithm
- Estimating precipitation at a point (1/D2)
- Estimate: >least, <greatest
- 100-150 points within basin
- Normalize at each grid point, then renormalize
- 	Thiessen weights
- 	Grid point versus Thiessen
- 	Two-pass algorithm - distribute daily, then estimate missing
- 	Consistency plots
- MAT Algorithms - Mean Areal Temperature
- 	Max - min data
- 	Grid point algorithm (1/D)
- 	Elevation weighting factor
- 	Centroid (1/DP)
- 	Conversion to mean temperatures
- 	Consistency plots
- MAPE - Mean Areal Potential Evaporation
- 	Evaporation pan data
- MAPE vs. Mean seasonal curve
- QME
- QIN

## Historical Data Analysis

- General Information Needed
-    Station data on Calibration files
-    Station history infro - obs times, changes, location, moves

-    Topog map of basin

- MAP Specific Information
- Non- Mountainous         Mountains
-    --basin boundary         --isohyetal map
-                                         --station weights

- MAT Specific Information
- --mean max/min temperatures
- Non-Mountainous      Mountains
-   --basin boundary     --areal-elev curve

- MAPE Specific
-  Information
- --Evaporation maps
- --mean monthly  evap
- --station weights

- MAP3
-   (re)check consistency
-   generate time series
-    of MAP

- PXPP
-   check consistency
-   compute normals

- MAT3
-   generate time
-    series of MAT

-          MAT3
-   check consistency

- TAPLOT3
-   get mean max/min for
-    mean zone elevation

- MAPE
-   check consistency
-   generate daily time
-    series of MAPE

- Precipitation

- Temperature

- Evaporation

## END

- Calibration

## BEGIN

- Troubleshooting

## END

- Troubleshooting

## BEGIN

- Future Directions

## END

- Future Directions

## Begin

- GIS Applications

## Introduction to GIS

## What is GIS?

- Geographic Information System
- Geographic implies of or pertaining to the surface of the earth
- Information implies knowledge of or collection of some form of data
- and finally, a system implies some form of organization, arrangement, etc..  Perhaps a framework?

## ........ A computer system for capturing, managing, integrating, manipulating, analyzing and displaying data which is spatially referenced to the Earth." (R McDonnell & K Kemp. 1995. International GIS Dictionary. Cambridge: GeoInformation International)

## The Watershed

- A watershed is an area of land that drains to a single outlet and is separated from other watersheds by a divide.
- Hydrologic analysis and synthesis focus on the watershed.

## The Watershed

- Every watershed has a drainage area.
-   Related terms:  drainage basin, sub-basin, sub-area.

## Defining a Watershed

- Defining a watershed is generally referred to as delineating the watershed.
- The process involves determining that area within which water would drain to a common point.
- It is often easier to visualize the concept by pretending the ground surface is impermeable like cement.

## Defining a Watershed

- Contours are lines of constant elevation.
- Contours “point” or “curve” uphill at stream crossings.
- Contours (generally) have constant spacing.

## Defining a Watershed

- At right, the watershed has been delineated, using the contours, for the indicated watershed outlet.
- The streams/channel sections have also been highlighted within the watershed.

- Outlet

## Defining a Watershed

- The most common form of mapping used for delineation are the USGS topographical maps.
- The most common map scale is the 7.5 minute 1:24,000 scale.

## Defining a Watershed

- The use of electronic or digital data and mapping has become rather common place in the field of hydrology.
- GIS or Geographical Information Systems are used to manage, manipulate, and analyze digital data.
- One of the most common GIS data sets is a Digital Elevation Models or DEM’s.

## Defining a Watershed

- This section is dedicated to providing a basic understanding of the methods used by a Geographical Information System (GIS) programs to delineate a watershed.

## Defining a Watershed

- A GIS uses electronic data sets.  The electronic data sets or coverages represent some property of the earth’s surface.  One of the most common data sets is a Digital Elevation Model or DEM.

## Defining a Watershed

- A DEM is used to represent the elevations of a section or area of land.  The DEM is generally a gridded or raster data set.  A raster data set means a series of rows and columns with each grid cell representing a property such as elevation.

## Defining a Watershed

- Shown below (in 3-D) is a simple DEM, which is comprised of 12 rows and 12 columns.

## Defining a Watershed

- In a plan view, the same DEM looks like :

## Defining a Watershed

- The same DEM shown in an “interpolated” format:

## Defining a Watershed

- The actual values of the grid cells in the rows and columns are illustrated in the table below:

## Defining a Watershed

- In the DEM, each grid cell must be assigned a “flow direction”.  It is the direction that the water would run or flow.  One of the most common methods is the D8 algorithm.  The D8 algorithm looks at 3x3 windows and assigns a flow direction to the cell in the center by considering the direction of the largest drop in elevation.

## Defining a Watershed

- Consider the 3x3 group of cells below.  The center cell flows or points in the direction indicated because that is the direction of the greatest elevation drop.

## Defining a Watershed

- The flow direction is then assigned and recorded.  In this example, the flow directions are simply 0 to 7 as shown below:

## Defining a Watershed

- Each grid cell is assigned a flow direction.  The resulting image of flow directions for the small 12x12 example is illustrated below:

## Defining a Watershed

- Note that each grid cell flows into another grid cell and so forth.  One could tally or keep track of the total number of grid cells that flow into each “downstream” grid cell.  This is generally know as a flow accumulation data set.  The flow accumulation data set for the 12x12 example is illustrated on the next page:

## Defining a Watershed

- Flow accumulation data set

## END

- GIS Applications