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            "1812": {
                "pageid": 1812,
                "ns": 0,
                "title": "Rural Catchments",
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                        "*": "{{BlueM.Sim_nav}}\n{{BlueMTheory_nav}}\n\nThe natural process leading from rain to run-off is divided into three phases. The phases are Belastungsbildung, run-off generation (bzw. Belastungsaufteilung) and run-off concentration. The calculation approach for each of these phases is described in the following sections of this article.\n\n\n==Belastungsbildung==\n\n\nDie Belastungsbildung describes the determination of an areal rainfall for the considered catchment.Rainfall data is imported into BlueM via external time series. Therefore no explicit calculations are necessary for this phase.\n\n\n==Run-off generation==\n\nIn this phase surface run-off, infiltration, evaporation and interflow are determined by calculating the effective rainfall out of the fallen rain. Snow is calculated for temperatures below 0\u00b0C. The Snow-Compaction-Method {{:Literatur:Knauf_1980|Knauf}} is applied.\n\nRainfall (system load) is divided into rainfall which directly generates run-off and run-off diminishing losses (wetting, trough, evaporation and infiltration losses). Therefore this phase is also called the Belastungsaufteilung. The mathematical equation for the momentary Belastungsaufteilung is as follows:\n\n\n:<math>Nw(t) = N(t) - VP(t) - I(t) - \\frac{dO}{dt} - \\frac{dS}{dt}</math>\n\n:mit: \n:NW = run-off generating rainfall\n:N = rainfall\n:VP = potential evaporation\n:I = infiltration into the soil\n:O = surfacce water reservoir content\n:S = snow reservoir content\n\nThe individual elements of the equation and the calculation of these elements is described in the following.\n\n\n===Rainfall N(t)===\n\nBlueM requires rainfall data in form of rain time series. In general is does not matter if a block rain, Regenspektrum or a longtime rainfall time series. Depending on the purpose of the simulation the appropriate load (type) must be chosen. Rainfall time series originate out of the BlueM time series management <span class=\"TALSIM\"> or are created immediately before simulation begin as is the case for short term prediction by supplying a rainfall duration, rainfall height and choosing a model rainfall </span>.\n\n\n===Evaporation VP(t)===\nThere are two possibilities for the [[EZG-Datei|input]] of potential evaporation:\n\n====a) annual evaporation ====\n[[File:Theorie_Abb33.gif|thumb|Abbildung 33: annual pattern of potential evaporation according to {{:Literatur:Brandt_1979}}]]\nA normed annual pattern of potential evaporation according to {{:Literatur:Brandt_1979|Brandt}} is utilized for the calculation of potential evaporation. Through the evaluation of measurements from twenty different stations, whichs mean-values are depicted as a histogram in [[:File:Theorie_Abb33.gif|Abbildung 33]], the following smoothing function was derived (doted line in [[:File:Theorie_Abb33.gif|Abbildung 33]]):\n\n:<math>VP[\\mbox{mm/d}] = \\begin{cases}(0.96 + 0.0033 \\cdot i) \\cdot \\sin(\\frac{2 \\pi}{365})(i - 148) + 1.58, & i <= 300 \\\\ 2.56 - 1.53 / 65. \\cdot (i - 300.), & i > 300 \\end{cases}</math>\n\n:\u00b4with \n:i = ongoing day of the hydrological year \n:i = 1 &rarr; 1. November\n\n\nPotential evaporation according to Brandt refers to  {{:Literatur:DVWK_1996|'''grass reference evaporation'''}} and assumes an annual total evaporation loss of 654,282 mm. If a different annual total evaporation loss is entered, the value determined by Brandt is scaled accordingly. \n\n====b) evaporation time series====\nIf a evaporation time series is supplied the utilized time step is imported. <br/>\n''Attention:'' For time steps  < 1 day the time series value is additionally overprinted with a daily pattern! (Bug 1)\n\n====daily pattern of evaporation====\n[[File:Theorie_Abb34.gif|thumb|Abbildung 34: Daily pattern of potential evaporation as a multiple of mean daily evaporation]]\nIf the chosen time step for the calculation is < 1 day the potential evaporation for each time step is calculated by taking the daily pattern depicted in [[:File:Theorie_Abb34.gif|Abbildung 34]] into consideration. If the chosen time step is &ge; 1 day the daily pattern is disregarded.\n\n\n===Surface water reservoir content(fraction of impervious area) O===\nSnow reservoir content as well as infiltration can be neglected for impervious areas. Therefore the equation of balance is reduced to:\n\n:<math>Nw(t) = N(t) - VP(t) - \\frac{dO}{dt}</math>\n\nin which the change in surface water reservoir content <code>dO/dt</code> represents wetting of the surface as well as filling and depletion of water (through evaporation) in troughs.\n\nThe wetting loss (BV) for impervious areas is set to the following standard value.\n\n:<code>BV = 0.5 mm</code>\n\nTrough loss (MV) is set by the user in the [[ALL-Datei|ALL-File]].\n\nThe trough loss is the mean value for an inclined surface. Due to the fact that troughs are not evenly distributed and experience has shown that run-off occurs before all troughs are completely filled the following assumption is made, that: \n\n[[File:Theorie_Abb35.gif|thumb|Abbildung 35: Schematic of the model approach for wetting and trough losses]]\n\n* 1/3 of the impervious area has a reduced trough loss of 1/3 MV \n* 1/3 of the impervious area has a mean trough loss of 3/3 MV \n* 1/3 of the impervious area has a elevated trough loss of 5/3 MV \n\n. Therefore run-off occurs as soon as the rainfall (reduced by evaporation) is greater than wetting losses and 1/3 of the trough losses (in dry antecedent conditions). In [[:File:Theorie_Abb35.gif|Abbildung 35]] the assumptions are depicted schematically.\n\nThe run-off coefficient of the impervious areas (after overcoming initial losses) is set to &psi; = 1. When determining the fraction of impervious areas for a catchment it needs to be considered that not all paved or impervious areas drain into the canalization.\n\nWetting and trough losses are continuously made available  through the ongoing balancing of these reservoirs and evaporation. \n\n\n===Surface water reservoir content (fraction of pervious areas) O===\n\nSurface water reservoir content is determined through the ongoing balancing of a loss reservoir in dependency of the chosen run-off generation approach.Details can be found in the following sections about calculation of infiltration respectively run-off generating rainfall.\n\n===Infiltration respectively run-off generating rainfall I(t), Nw(t)===\n\nInfiltration into the soil can not be neglected for pervious areas due to the fact that infiltration substantially influences run-off. Three approaches were implemented in the model for the calculation of infiltration: \n\n# constant run-off coefficient &psi; \n# event specific run-off coefficient similar to the method of the Soil-Conservation-Service (SCS) \n# soil moisture simulation \n\n====constant run-off coefficient &psi;====\n\nBy supplying a &psi;<sub>u</sub>-value the remaining rainfall after having covered the initial losses (wetting and trough losses)generates run-off according to the ratio of the run-off coefficient &psi;<sub>u</sub> independent of previous history and the characteristics of the rainfall (height, intensity, duration). If possible this approach should not be used, because it only represents a very rudimentary description of the run-off generation process.\n\n\n====SCS-Method====\n:''refer to [[SCS-Verfahren|SCS-Method]]''\n\n====Soil moisture simulation====\n:''refer to [[Bodenfeuchtesimulation|Soil moisture simulation]]''\n\n==Run-off concentration==\n[[File:Parallelspeicherkaskade_EZG.gif|thumb|400px|Abbildung 44: Calculation of run-off concentration for rural catchments]]\nRun-off concentration determines the delay of discharge out of the catchment. Calculation of Interflow and base flow is dependent on the chosen calculation approach. If [[Bodenfeuchteberechnung|soil moisture simulation]] is chosen, the discharge of both run-off components at the catchment outlet is delayed through a linear reservoir. If the run-off coefficient approach or the SCS-Method is chosen, interflow is neglected and base flow is determined through regarding the given  specific base discharge and a possible consideration of an annual pattern.\n\nA parallel reservoir cascade is utilized with two reservoirs each for the cascade for pervios and the cascade for impervious areas.\nThe reservoir cascades can be calculated as linear or [[Speicherbaustein|non-linear reservoirs]]. If the reservoir cascade parameters are not supplied, they are calculated through using area characteristics according to {{:Literatur:Zai\u00df 1986}}\n\n\n==Literature==\n<references/>\n\n[[Category:BlueM Theorie]]"
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            "2143": {
                "pageid": 2143,
                "ns": 0,
                "title": "SCS-Method",
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                        "*": "{{BlueM.Sim_nav}}\n{{BlueMTheory_nav}}\n'''<big>Event specific run-off coefficient on the basis of the Curve-Number-Method (CN-Method)of the Soil-Conservation-Service (SCS)</big>'''\n__TOC__\n==Theory==\nThe Method applied in BlueM is a further development of the CN-Method ({{:Literatur:USDA_1964}}) by {{:Literatur:Zai\u00df_1989}}\n\n\n\n[[Bild:Theorie_Abb36.gif|thumb|Abbildung 36: Dependency of the run-off coefficient on previous history]]\nBy supplying a soil type and land use dependent CN \n(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.\n\n\nA 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.\nIn [[:Bild:Theorie_Abb36.gif|Abbildung 36]] the development of the run-off coefficient depending on previous history is depicted for different CN.\n\n[[Bild:Theorie_Abb37.gif|thumb|left|Abbildung 37: Dependency of the run-off coefficient on the accumulated amount of rain]]\nAs 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.  \nThis correlation is depicted for different CN in [[:Bild:Theorie_Abb37.gif|Abbildung 37]]. \n\n;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\"/>\n\n==Calculation==\n===one-time calculated parameters===\n'''Input:''' <code>CN<sub>II</sub></code>\n\n<div class=\"comment\">\nDie 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?!\n</div>\n'''Conversion''' of <code>CN<sub>II</sub></code> to <code>CN<sub>I</sub></code>:\n:<math>CN_I = \\frac{CN_{II}}{(2.3340 - 0.01334 \\cdot CN_{II})}</math>\n\n'''Maximum retention capability of the area''' (storage capacity) <code>S<sub>max</sub></code> [mm]:\n:<math>S_{max} = \\frac{25400}{CN_I} - 254</math>\n\n'''area specific initial loss''' <code>I<sub>a</sub></code> [mm]:\n:<math>I_a = a \\cdot S_{max}</math>\n:with\n:<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|}}\n\n'''Kr\u00fcmmungsparameter''' <code>CVW</code>:\n<div class=\"comment\">\nLaut {{:Literatur:Sartor_1999|Sartor}}, der die selbe Gleichung verwendet, stammt dieser Ansatz aus der Dokumentation von SMUSI 3.0\n</div>\n:<math>CVW = \\frac{-100.}{\\ln(\\frac{0.5}{I_a})}</math>\n:''entspricht <code>b<sub>1</sub></code> in Gl. 4.5b in {{:Literatur:Zai\u00df_1989}}''\n:laut Zai\u00df:\n<blockquote>\nEine Abh\u00e4ngigkeit des \"Kr\u00fcmmungsparameters\" b<sub>1</sub> von Gebietskenngr\u00f6\u00dfen konnte im Rahmen dieser Arbeit nicht gefunden werden. Sie l\u00e4\u00dft sich nach den hier aufgef\u00fchrten Zusammenh\u00e4ngen lediglich \u00fcber Regressionsanalysen mehrerer N-A-Ereignisse f\u00fcr das jeweils betreffende Einzugsgebiet ermitteln.\n</blockquote>\n\n===continuously calculated parameters===\n====previous history====\nPrevious history is quantified through the 21-day-antecedent rain index <code>V<sub>N</sub></code>:\n\n:<math>V_N = \\sum_{j=0}^{21} C(j)^j \\cdot h_{N,j}</math>\n:''Gl. 2.1 in {{:Literatur:Zai\u00df_1989}}''\n\n:with\n:<code>h<sub>N,j</sub></code> = rain height of the preceding day j (<code>j = 0</code> is the current day)\n:<code>C(j)</code> = factor, which describes the influence of the preceding day j\n\nSeasonal influence is considered through the annual pattern of factor c. \n\n:<math>C = 0.85 \\cdot \\sin\\left(\\frac{2 \\pi}{365}\\right) (i + 0.75 ) + 0.85</math>\n:''Quelle? bei Zai\u00df finden sich nur so \u00e4hnliche Formeln (2.2 & 2.3)''\n\n:with \n:<code>i</code> = ongoing day of the hydrological year\n\n<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. \n\n====Event dependent initial loss====\n:<math>h_{va} = I_a \\cdot e^{-\\frac{V_N}{CVW}}</math>\n:''Gl. 4.5b in {{:Literatur:Zai\u00df_1989}}''\n\n====run-off coefficient====\n[[Bild:SCS PSI.png|thumb|Dependency of <code>&psi;</code> on <code>h<sub>va</sub></code> and <code>h<sub>NE</sub></code> (with<code>A<sub>v</sub> = 0.05</code>)]]\n:<math>\\psi = \\begin{cases}\n0, & h_{va} \\ge h_{NE} \\\\\n1 - \\left(\\frac{h_{va}}{A_v \\cdot h_{NE} + (1 - A_v) \\cdot h_{va}}\\right)^2, & h_{va} < h_{NE}\n\\end{cases}</math>\n:''Gl. 4.4 in {{:Literatur:Zai\u00df_1989}}''\n\n:with\n: <code>A<sub>v</sub></code> = loss ratio = <code>0,05</code>\n: <code>h<sub>NE</sub></code> = event-driven sum of rainfall [mm]\n\n==Literature==\n<references/>\n\n[[Kategorie:BlueM Theorie]]"
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