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{{ | {{BlueM.Sim_nav}} | ||
'''<big> | {{BlueMTheory_nav}} | ||
'''<big>Event specific run-off coefficient on the basis of the Curve-Number-Method (CN-Method)of the Soil-Conservation-Service (SCS)</big>''' | |||
__TOC__ | __TOC__ | ||
== | ==Theory== | ||
The Method applied in BlueM is a further development of the CN-Method ({{:Literatur:USDA_1964}}) by {{:Literatur:Zaiß_1989}} | |||
[[Bild: | [[Bild:Theorie_Abb36.gif|thumb|Abbildung 36: Dependency of the run-off coefficient on previous history]] | ||
By supplying a soil type and land use dependent CN | |||
(refer to{{:Literatur:DVWK_1991}}) an antecedent dependent initial loss as well as an antecedent dependent relationship of the run-off coefficient on the accumulated amount of rain up to a desired point in time can be determined. This results in an increasing run-off coefficient due to the accumulating rain amount in the course of a rainfall event. | |||
== | A current run-off coefficient can be determined in dependency of the quantified previous history, as described above, by using the area specific and for average ''antecedent moisture conditions (AMC)'' ({{:Literatur:USDA_1964}}) valid CN. | ||
=== | In [[:Bild:Theorie_Abb36.gif|Abbildung 36]] the development of the run-off coefficient depending on previous history is depicted for different CN. | ||
''' | |||
[[Bild:Theorie_Abb37.gif|thumb|left|Abbildung 37: Dependency of the run-off coefficient on the accumulated amount of rain]] | |||
As soil moisture increases during the course of a rainfall event the conditions for run-off development change which is why the run-off coefficient is additionally adjusted during a rainfall event as a function of accumulated rain. | |||
This correlation is depicted for different CN in [[:Bild:Theorie_Abb37.gif|Abbildung 37]]. | |||
;Attention:The CN-Method was developed for the simulation of solitary events on a daily basis. A further development is being undertaken for continuous simulation with smaller time steps.(refer to Bug 23 and [[Talk:SCS-Verfahren#Weiterentwicklung_.28Bug_23.29|Discussion]])<br clear="all"/> | |||
==Calculation== | |||
===one-time calculated parameters=== | |||
'''Input:''' <code>CN<sub>II</sub></code> | |||
<div class="comment"> | <div class="comment"> | ||
Die Umrechnung von <code>CN<sub>II</sub></code> in <code>CN<sub>I</sub></code> bedeutet, dass davon ausgegangen wird, dass das Gebiet zu Beginn der Simulation trocken ist?! | Die Umrechnung von <code>CN<sub>II</sub></code> in <code>CN<sub>I</sub></code> bedeutet, dass davon ausgegangen wird, dass das Gebiet zu Beginn der Simulation trocken ist?! | ||
</div> | </div> | ||
''' | '''Conversion''' of <code>CN<sub>II</sub></code> to <code>CN<sub>I</sub></code>: | ||
:<math>CN_I = \frac{CN_{II}}{(2.3340 - 0.01334 \cdot CN_{II})}</math> | :<math>CN_I = \frac{CN_{II}}{(2.3340 - 0.01334 \cdot CN_{II})}</math> | ||
''' | '''Maximum retention capability of the area''' (storage capacity) <code>S<sub>max</sub></code> [mm]: | ||
:<math>S_{max} = \frac{25400}{CN_I} - 254</math> | :<math>S_{max} = \frac{25400}{CN_I} - 254</math> | ||
''' | '''area specific initial loss''' <code>I<sub>a</sub></code> [mm]: | ||
:<math>I_a = a \cdot S_{max}</math> | :<math>I_a = a \cdot S_{max}</math> | ||
: | :with | ||
:<code>a</code> = | :<code>a</code> = constant, originally set to <code>0,2</code> {{:Literatur:USDA_1964|}}, adjusted to European conditions in BlueM as <code>0,05</code>{{:Literatur:DVWK_1991|}} | ||
'''Krümmungsparameter''' <code>CVW</code>: | '''Krümmungsparameter''' <code>CVW</code>: | ||
| Line 44: | Line 51: | ||
</blockquote> | </blockquote> | ||
=== | ===continuously calculated parameters=== | ||
==== | ====previous history==== | ||
Previous history is quantified through the 21-day-antecedent rain index <code>V<sub>N</sub></code>: | |||
:<math>V_N = \sum_{j=0}^{21} C(j)^j \cdot h_{N,j}</math> | :<math>V_N = \sum_{j=0}^{21} C(j)^j \cdot h_{N,j}</math> | ||
:''Gl. 2.1 in {{:Literatur:Zaiß_1989}}'' | :''Gl. 2.1 in {{:Literatur:Zaiß_1989}}'' | ||
: | :with | ||
:<code>h<sub>N,j</sub></code> = | :<code>h<sub>N,j</sub></code> = rain height of the preceding day j (<code>j = 0</code> is the current day) | ||
:<code>C(j)</code> = | :<code>C(j)</code> = factor, which describes the influence of the preceding day j | ||
Seasonal influence is considered through the annual pattern of factor c. | |||
:<math>C = 0.85 \cdot \sin\left(\frac{2 \pi}{365}\right) (i + 0.75 ) + 0.85</math> | :<math>C = 0.85 \cdot \sin\left(\frac{2 \pi}{365}\right) (i + 0.75 ) + 0.85</math> | ||
:''Quelle? bei Zaiß finden sich nur so ähnliche Formeln (2.2 & 2.3)'' | :''Quelle? bei Zaiß finden sich nur so ähnliche Formeln (2.2 & 2.3)'' | ||
: | :with | ||
:<code>i</code> = | :<code>i</code> = ongoing day of the hydrological year | ||
<code>C</code> will alternate between <code>0,8 < C < 0,9</code>. This allows for different antecedent rain indices due to seasonal differences for same antecedent rain amounts and thereby leads to different conditions for run-off development. | |||
==== | ====Event dependent initial loss==== | ||
:<math>h_{va} = I_a \cdot e^{-\frac{V_N}{CVW}}</math> | :<math>h_{va} = I_a \cdot e^{-\frac{V_N}{CVW}}</math> | ||
:''Gl. 4.5b in {{:Literatur:Zaiß_1989}}'' | :''Gl. 4.5b in {{:Literatur:Zaiß_1989}}'' | ||
==== | ====run-off coefficient==== | ||
[[Bild:SCS PSI.png|thumb| | [[Bild:SCS PSI.png|thumb|Dependency of <code>ψ</code> on <code>h<sub>va</sub></code> and <code>h<sub>NE</sub></code> (with<code>A<sub>v</sub> = 0.05</code>)]] | ||
:<math>\psi = \begin{cases} | :<math>\psi = \begin{cases} | ||
0, & h_{va} \ge h_{NE} \\ | 0, & h_{va} \ge h_{NE} \\ | ||
| Line 77: | Line 84: | ||
:''Gl. 4.4 in {{:Literatur:Zaiß_1989}}'' | :''Gl. 4.4 in {{:Literatur:Zaiß_1989}}'' | ||
: | :with | ||
: <code>A<sub>v</sub></code> = | : <code>A<sub>v</sub></code> = loss ratio = <code>0,05</code> | ||
: <code>h<sub>NE</sub></code> = | : <code>h<sub>NE</sub></code> = event-driven sum of rainfall [mm] | ||
== | ==Literature== | ||
<references/> | <references/> | ||
[[Kategorie:BlueM Theorie]] | [[Kategorie:BlueM Theorie]] | ||
Latest revision as of 07:14, 9 January 2015
BlueM.Sim | Download | Application | Theory | Development
BlueM.Sim theory
Event specific run-off coefficient on the basis of the Curve-Number-Method (CN-Method)of the Soil-Conservation-Service (SCS)
Theory
The Method applied in BlueM is a further development of the CN-Method (USDA (1964)[1]) by Zaiß (1989)[2]
By supplying a soil type and land use dependent CN (refer toDVWK (1991)[3]) an antecedent dependent initial loss as well as an antecedent dependent relationship of the run-off coefficient on the accumulated amount of rain up to a desired point in time can be determined. This results in an increasing run-off coefficient due to the accumulating rain amount in the course of a rainfall event.
A current run-off coefficient can be determined in dependency of the quantified previous history, as described above, by using the area specific and for average antecedent moisture conditions (AMC) (USDA (1964)[1]) valid CN.
In Abbildung 36 the development of the run-off coefficient depending on previous history is depicted for different CN.
As soil moisture increases during the course of a rainfall event the conditions for run-off development change which is why the run-off coefficient is additionally adjusted during a rainfall event as a function of accumulated rain. This correlation is depicted for different CN in Abbildung 37.
- Attention
- The CN-Method was developed for the simulation of solitary events on a daily basis. A further development is being undertaken for continuous simulation with smaller time steps.(refer to Bug 23 and Discussion)
Calculation
one-time calculated parameters
Input: CNII
Conversion of CNII to CNI:
- [math]\displaystyle{ CN_I = \frac{CN_{II}}{(2.3340 - 0.01334 \cdot CN_{II})} }[/math]
Maximum retention capability of the area (storage capacity) Smax [mm]:
- [math]\displaystyle{ S_{max} = \frac{25400}{CN_I} - 254 }[/math]
area specific initial loss Ia [mm]:
- [math]\displaystyle{ I_a = a \cdot S_{max} }[/math]
- with
a= constant, originally set to0,2[1], adjusted to European conditions in BlueM as0,05[3]
Krümmungsparameter CVW:
Laut Sartor[4], der die selbe Gleichung verwendet, stammt dieser Ansatz aus der Dokumentation von SMUSI 3.0
- [math]\displaystyle{ CVW = \frac{-100.}{\ln(\frac{0.5}{I_a})} }[/math]
- entspricht
b1in Gl. 4.5b in Zaiß (1989)[5] - laut Zaiß:
Eine Abhängigkeit des "Krümmungsparameters" b1 von Gebietskenngrößen konnte im Rahmen dieser Arbeit nicht gefunden werden. Sie läßt sich nach den hier aufgeführten Zusammenhängen lediglich über Regressionsanalysen mehrerer N-A-Ereignisse für das jeweils betreffende Einzugsgebiet ermitteln.
continuously calculated parameters
previous history
Previous history is quantified through the 21-day-antecedent rain index VN:
- [math]\displaystyle{ V_N = \sum_{j=0}^{21} C(j)^j \cdot h_{N,j} }[/math]
- Gl. 2.1 in Zaiß (1989)[6]
- with
hN,j= rain height of the preceding day j (j = 0is the current day)C(j)= factor, which describes the influence of the preceding day j
Seasonal influence is considered through the annual pattern of factor c.
- [math]\displaystyle{ C = 0.85 \cdot \sin\left(\frac{2 \pi}{365}\right) (i + 0.75 ) + 0.85 }[/math]
- Quelle? bei Zaiß finden sich nur so ähnliche Formeln (2.2 & 2.3)
- with
i= ongoing day of the hydrological year
C will alternate between 0,8 < C < 0,9. This allows for different antecedent rain indices due to seasonal differences for same antecedent rain amounts and thereby leads to different conditions for run-off development.
Event dependent initial loss
- [math]\displaystyle{ h_{va} = I_a \cdot e^{-\frac{V_N}{CVW}} }[/math]
- Gl. 4.5b in Zaiß (1989)[7]
run-off coefficient
- [math]\displaystyle{ \psi = \begin{cases} 0, & h_{va} \ge h_{NE} \\ 1 - \left(\frac{h_{va}}{A_v \cdot h_{NE} + (1 - A_v) \cdot h_{va}}\right)^2, & h_{va} \lt h_{NE} \end{cases} }[/math]
- Gl. 4.4 in Zaiß (1989)[8]
- with
Av= loss ratio =0,05hNE= event-driven sum of rainfall [mm]
Literature
- ↑ 1.0 1.1 1.2 U.S. Department of Agriculture, Soil Conservation Service (1964): National Engineering Handbook, Section 4 Hydrology, Washington
(überarbeitete Fassung von 2004: NEH Part 630 Ch. 10) - ↑ Zaiß, H. (1989): Simulation ereignisspezifischer Einflüsse des Niederschlag-Abfluß-Prozesses von Hochwasserereignissen kleiner Einzugsgebiete mit N-A-Modellen. Technischer Bericht des Instituts für Ingenieurhydrologie und Hydraulik, TH Darmstadt, Nr. 42
- ↑ 3.0 3.1 DVWK (1991): Beitrag zur Bestimmung des effektiven Niederschlags für Bemessungshochwasser aus Gebietskenngrößen. Ergebnis einer vergleichenden Untersuchung durch den DVWK-Fachausschuß "Niederschlag-Abfluß-Modelle", Materialien, Heft 2
- ↑ Sartor, J. (1999): Einsatz der Langzeit-Seriensimulation für kleine Einzugsgebiete, In: Berichte des Fachgebietes Wasserbau und Wasserwirtschaft der Universität Kaiserslautern, Heft 9 (PDF)
- ↑ Zaiß, H. (1989): Simulation ereignisspezifischer Einflüsse des Niederschlag-Abfluß-Prozesses von Hochwasserereignissen kleiner Einzugsgebiete mit N-A-Modellen. Technischer Bericht des Instituts für Ingenieurhydrologie und Hydraulik, TH Darmstadt, Nr. 42
- ↑ Zaiß, H. (1989): Simulation ereignisspezifischer Einflüsse des Niederschlag-Abfluß-Prozesses von Hochwasserereignissen kleiner Einzugsgebiete mit N-A-Modellen. Technischer Bericht des Instituts für Ingenieurhydrologie und Hydraulik, TH Darmstadt, Nr. 42
- ↑ Zaiß, H. (1989): Simulation ereignisspezifischer Einflüsse des Niederschlag-Abfluß-Prozesses von Hochwasserereignissen kleiner Einzugsgebiete mit N-A-Modellen. Technischer Bericht des Instituts für Ingenieurhydrologie und Hydraulik, TH Darmstadt, Nr. 42
- ↑ Zaiß, H. (1989): Simulation ereignisspezifischer Einflüsse des Niederschlag-Abfluß-Prozesses von Hochwasserereignissen kleiner Einzugsgebiete mit N-A-Modellen. Technischer Bericht des Instituts für Ingenieurhydrologie und Hydraulik, TH Darmstadt, Nr. 42
Die Umrechnung von
CNIIinCNIbedeutet, dass davon ausgegangen wird, dass das Gebiet zu Beginn der Simulation trocken ist?!