# Hydrological Model Performance With Different Calibration Approaches Biology Essay

Due to its elaborateness in stand foring a complex-non linear system, hydrological modeling requires some parametric quantities accommodations. Once the theoretical account has been chosen, by and large it is non possible to gauge those parametric quantities by either measuring or observation.

For that ground, it is required some ordinance of the theoretical account parametric quantities values until the theoretical account end product lucifers acceptably to the observed informations. It is done in an indirect manner by an reverse procedure ( standardization ) utilizing historically observed input-output informations.

When implementing a semi distributed hydrological theoretical account over a certain country, the great figure of unknown consequences in a high dimensional parametric quantity hunt infinite, well complicates the optimisation issue. Therefore, when this dimension becomes so big that the terra incognitas can non be unambiguously constrained by the informations, the job is said to be ill conditioned.

In this manner, this survey evaluates some schemes which were applied in order to cut down the dimensionality of the graduated parametric quantities. Two of those schemes focused on a pre-calibration procedure of the slow constituents as the groundwater parametric quantities. At the same clip, other schemes were applied, such as lumped parametric quantity, the execution of one factor for each parametric quantity group and clusterization of the groundwater parametric quantities for sub-catchments with same word picture.

For the intent of this survey, the standardization processes run utilizing PEST, an independent non-linear parametric quantity calculator. The HEC-HMS theoretical account was used to bring forth the fake flow hydrographs in order to compare with the ascertained informations.

The full process was applied to the Leineturm catchment, a southern sub-catchment of the Aller Leine catchment, located North of Germany.

The consequences suggested the theoretical account is non strongly sensitive to spacial parametric quantity variableness, therefore a average value may be represent good particularly on the mercantile establishment. However, the clusterization of the groundwater parametric quantities showed bantam better public presentation.

## Contentss

List of Figures

Three

List of Tables

Four

1. Introduction

1

2. Methodology

3

2.1 Datas

3

2.2 Model

5

2.3 Calibration

8

2.4 Objective map and rating

13

3. Study country and database

16

4. Consequences

19

5. Discussion

27

Mentions

28

Appendix

29

Declaration

32

## List of Figures

Figure 1.1: Hydrological rhythm with planetary one-year mean H2O balance given in units relative to a value of 100 for the rate of precipitation on land

1

Figure 2.1: Sketch of the application of the reverse distance method

3

Figure 2.2: Disaggregating precipitation. ( Left ) Figure shows an illustration in hourly clip stairss. ( Right ) Figure shows the transmutation of the day-to-day clip stairss in hourly

4

Figure 2.3: Outline of the dirt wet accounting

6

Figure 2.4: Simulation ( HEC-HMS ) and standardization ( PEST ) procedure

9

Figure 2.5: Sketch of a catchment with lumped parametric quantity

11

Figure 2.6: Sketch of a catchment with one factor parametric quantity

12

Figure 2.7: Sketch of a catchment with bunch parametric quantity

13

Figure 3.1: Digital Elevation Model ( DEM ) – Location of Leineturm as a sub-catchment of Aller Leine catchment

16

Figure 3.2: ( Left ) Precipitation gages of Leineturm catchment. ( Right ) Net radiation and temperature gages of Leineturm catchment

17

Figure 3.3: Discharge gages of Leineturm catchment

17

Figure 4.1: Observed and simulated flow for the twelvemonth 1998of the Leineturm gage, utilizing the two stairss daily/hourly scheme

19

Figure 4.2: Precipitation event ( left ) , possible evapotranspiration ( in-between ) , existent evapotranspiration ( right )

20

Figure 4.3: Observed and simulated flow for the twelvemonth 2007 utilizing the two stairss traveling mean scheme

21

Figure 4.4: Observed and simulated flow for the twelvemonth 2007 of the Leineturm gage, utilizing the lumped scheme

23

Figure 4.5: Observed and simulated flow for the twelvemonth 2007 of Mariengarten gage, utilizing the lumped scheme

23

Figure 4.6: Nash-Sutcliffe A- Failure volume of Leineturm gage ( left ) and Mariengarten gage

24

Figure 4.7: Fifteen highest independent extremums for the lumped scheme for Leineturm gage

25

Figure 4.8: Fifteen highest independent extremums for the one factor scheme for Leineturm gage

25

Figure 4.9: Fifteen highest independent extremums for the clusterization scheme for Leineturm gage

25

Figure 4.10: Square correlativity coefficient of Leineturm gage for lumped ( left ) , one factor ( in-between ) and clusterization ( right ) schemes

26

## List of Tables

Table 2.1: Applied methods and their classs

10

Table 2.2: Applied methods and their parametric quantity groups

13

Table 2.3: Parameter schemes applied and their clip measure

15

Table 3.1: Leineturm features

16

Table 4.1: Calibration and proof of the different schemes

19

Table 4.2: Failure volume and Nash-Sutcliffe index of every gage and every scheme

22

Table 4.3: Square correlativity coefficient of Leineturm, Reckershausen and Mariengarten gages for lumped, one factor and clusterization schemes

26

## 1. Introduction

Water is the most abundant compound on the Earth, the chief component of every life being and responsible for determining the surface of the Earth. It is the cardinal key for the clime characteristics, giving conditions for the human subsistence and finding the development of the civilisation ( Chow et al. , 1988 ) .

Additionally, H2O is among the few substances that can be found in all three stages within the Earth ‘s clime scope. In this context, harmonizing to Meyer ( 1917 ) , hydrology is the scientific discipline that dainties of the phenomena of H2O in all its provinces, taking into history the distribution and happening of H2O in the Earth ‘s ambiance, surface, dirt and stone strata.

The hydrological rhythm can be considered the cardinal point for the hydrological surveies. It consists in a conceptual signifier of how H2O moves between the Earth and atmosphere in its three different stages ( Davie, 2002 ) . As shown in Figure 1.1, the rhythm has no beginning and no terminal.

Figure 1.1: Hydrological rhythm with planetary one-year mean H2O balance given in units relative to a value of 100 for the rate of precipitation on land ( Chow et al. , 1988 )

Through vaporization of liquid H2O into vapor it becomes portion of the ambiance ; the vapor is moved around until it condenses into a liquid ( or solid ) and fall down on the land or on the ocean ; precipitated H2O may be intercepted by flora, become overland flow, infiltrates into the dirt, turn into subsurface flow, and discharge into watercourses as surface overflow ( Chow et al. , 1988 ) .

Due to the sum of variables and complexness that revolve the hydrological rhythm, it becomes necessary the development of working Equations and hydrological theoretical accounts for a better apprehension of the system.

Furthermore, hydrological modeling becomes indispensable for practical jobs in H2O appraisal as inundation prediction, design of engineered channels, measuring the impacts of wastewaters on H2O quality, foretelling pollution incidents, and many other purposed ( Beven, 2001 ) .

The procedure of hydrological modeling can be defined as an estimate of the existent system utilizing a set of Equations to associate the inputs and end products ( Chow et al. , 1988 ) . In other words, hydrological theoretical account, harmonizing to Penman ( 1961 ) ( Singh et al. , 2002 ) answers the inquiry “ What happens to the rain? “ .

In recent old ages, with the increasing demands on H2O resources, hydrological modeling has become an of import tool. In add-on, particularly with progresss in treating power of computing machines and accordingly the development of improved theoretical accounts, the possibilities to obtain a closer realistic catchment description of the involved constituents are higher.

However, hydrological modeling is still unsure due to its elaborateness in stand foring a complex-non additive system. Once the theoretical account has been chosen, by and large it is non possible to gauge the parametric quantities of a theoretical account by either measuring or observation ( Beven, 2001 ; Cunderlik & A ; Simonovic, 2004 ) .

For that ground, it is required an accommodation of the theoretical account parametric quantities values until the theoretical account end product lucifers acceptably to the observed informations. It is done in an indirect manner by an reverse procedure ( standardization ) utilizing historically observed input-output informations. However, some grade of standardization is usually inevitable in hydrological mold ( Pokhrel & A ; Gupta, 2010 ) .

When implementing a semi distributed hydrological theoretical account over a certain country, the great figure of unknown consequences in a high dimensional parametric quantity hunt infinite, well complicates the optimisation issue. Therefore, when this dimension becomes so big that the terra incognitas can non be unambiguously constrained by the informations, the job is said to be ill conditioned ( Pokhrel & A ; Gupta, 2010 ) .

For the purpose of this survey, some schemes were applied in order to better suit the nonsubjective map with the utilizing of restraints that cut down the dimensionality of the parametric quantity.

Two of those schemes focus on a pre-calibration procedure of the slow constituents as the groundwater parametric quantities. At the same clip, other schemes, such as lumped parametric quantity, the execution of one factor for each parametric quantity group and clusterization of the groundwater parametric quantities, were applied puting the parametric quantities in group in order to cut down their dimension.

## 2. Methodology

## 2.1 Datas

For the probe of this survey, insertion methods were used due to the demand to obtain an aerial variableness of clime variables. Those methods are normally used in appraisal of variables which have an component of random variableness in infinite with a grade of spacial correlativity. For illustration, in instance of rainfall appraisal normally we have a figure of observations informations from few rain gages and we wish to deduce the distribution of rainfall over the catchment country ( Sorooshian et al. , 2008 ) .

In this survey, the insertion methods applied were: reverse distance method ( IDM ) , ordinary kriging ( OK ) and external impetus kriging ( EDK ) .

The IDM is based on the premise that the informations at any given point of the catchment country is influenced by the nearest Stationss, where each one is weighted by the opposite of the power of its distance to the point. To obtain the areal norm, the method is applied by subdividing the country into thousand rectangular subareas ( raster ) , each win an false unvarying value as calculated for the point at the centre, as illustrated in Figure 2.1 ( Brutsaert, 2005 ) .

1

2

3

4

5

6

7

8

9

10

11

12

13

14

d1,7

d2,7

d3,7

Figure 2.1: Sketch of the application of the reverse distance method ( Adapted from Brutsaert, 2005 )

Therefore, utilizing the IDM the consequence is determined by the Equation 2.1 ( Brutsaert, 2005 ) .

( 2.1 )

Where:

Phosphorus: areal precipitation

Aj: surface country of the jth raster cell ;

A: entire surface country of the catchment ;

Ns: entire figure of Stationss ;

dij: distance of the Centre of the jth raster cell from the ith gage ;

B: invariable, largely used as 2.

Interpolation by kriging is normally used in environmental informations. In kriging, the weights are determined on the footing of the spacial variableness of the information. Furthermore, it is based on the double standards that the appraisal mistake and the corresponding mean square mistake are minimum ( Brutsaert, 2005 ) .

The base of kriging uses the same proposal as IDM, where with a giving figure of mensural values zi at a specific location within country A, the value zirconium at a new location can be estimated as a leaden norm of the zi, where I»ir represents the weight attached to the ith observation, see Equation 2.2 ( Sorooshian et al. , 2008 ) .

( 2.2 )

Therefore, the purpose is to find values for I»ir, which give the optimum value for zirconium for any location, taking in into history the ascertained spacial correlativity construction of the informations ( Sorooshian et al. , 2008 ) .

The OK, a non-stationary method, uses the premise that the mean of the variable of involvement is allowed to change from topographic point to put across the country, although it is assumed to be changeless ( Lloyd, 2007 ) .

Finally, the EDK is used when a secondary variable is linearly related to the primary variable. In other words, the secondary informations Acts of the Apostless as a form map, depicting tendencies in the primary informations ( Lloyd, 2007 ) .

In order to obtain a better declaration of the precipitation informations, a disaggregation method was applied. It was made by utilizing the frequence distribution of the hourly clip stairss into the day-to-day clip stairss, as illustrates in the Figure 2.2.

## Precipitation

24h

## Time

## Precipitation

Transformation

## Precipitation

## Time

24h

Hourly

Daily

Figure 2.2: Disaggregating precipitation. ( Left ) Figure shows an illustration in hourly clip stairss. ( Right ) Figure shows the transmutation of the day-to-day clip stairss in hourly

Due to inaccessibility of measured informations, the net radiation, which is defined by the input of radiation at the surface at any blink of an eye and besides the major energy input for vaporization of H2O ( Chow et al. , 1988 ) , was calculated utilizing the undermentioned Equation ( 2.3 ) ( DVWK-Merkblatt, 1996 ) :

( 2.3 )

Where:

Radon: net radiation ( J/cm2 ) ;

I± : reflective power ;

Roentgenium: planetary radiation ;

I? : Stefan-Boltzmann invariable ;

Checks: absolute air temperature ;

Second: the day-to-day sunlight continuance ;

S0: twenty-four hours length harmonizing to the latitude ;

vitamin E: impregnation vapor force per unit area as a map of the air temperature.

For the computation of the harvest coefficient ( Kc ) , its values were based on land usage features. Kc alterations harmonizing to the growing phase of the harvest. Normally, the values of the Kc vary over a scope of 0.2 a‰¤ Kc a‰¤ 1.3 ( Chow et al. , 1988 ) .

## 2.2 Model

For the intent of this survey, the hydrologic modeling system used was HEC-HMS ( version 3.3 ) , developed by U.S. Army Corps of Engineers, which is included in a class of mathematical theoretical accounts or treated here as a conceptual theoretical account. In those theoretical accounts a set of Equations represent the response of a hydrologic system to a alteration in hydrometeorological conditions.

The conceptual theoretical account incorporated into HEC-HMS is physically based and depict how a catchment responds due to the precipitation falling down either straight on it or to upstream H2O fluxing into it ( US Army Corps of Engineers, 2000 ) .

HEC-HMS includes a broad scope of methods in order to imitate the catchment. Those methods can be classified as physical and weather forecasting. Table 2.1 shows the methods which were applied in this survey.

Table 2.1: Applied methods and their classs

## Description

## Class

## Method

Physical

Runoff coevals

Soil wet accounting ( SMA )

Direct-runoff

Clark ‘s unit hydrograph

Baseflow

Linear reservoir

Routing

Muskingum

Meteorology

Evapotranspiration

Priestly-Taylor

Snowmelt

Temperature index

The SMA is defined as a uninterrupted theoretical account, which simulates both wet and dry conditions conditions. The theoretical account works imitating the motion and storage of H2O through flora, dirt surface, dirt profile and groundwater beds. The SMA theoretical account computes the catchment surface overflow, groundwater flow, losingss due to evapotranspiration and deep infiltration over every sub-catchment country with a given precipitation and evapotranspiration, see Figure 2.3 ( US Army Corps of Engineers, 2000 ) .

Figure 2.3: Outline of the dirt wet accounting ( US Army Corps of Engineers, 2000 )

As illustrated in the Figure 2.3, the SMA theoretical account represents the catchment with a series of storage beds. Canopy-interception storage bed represents the portion of the precipitation which is captured by the flora and does non accomplish the dirt surface. Surface-depression storage is the volume of H2O held in shallow surface depression. Soil-profile storage represents H2O stored in the top bed of the dirt. Finally, the groundwater ( GW ) storage bed, which represents the horizontal interflow ( GW1 ) and the base flow ( GW2 ) procedure ( US Army Corps of Engineers, 2000 ) .

In order to cipher the direct overflow with a unit hydrograph, which describes a simple additive theoretical account that can be used to deduce the hydrograph ensuing from any sum of extra rainfall, HEC-HMS uses a distinct representation in which a pulsation of extra precipitation is known for each clip interval ( Chow et al. , 1988 ; US Army Corps of Engineers, 2000 ) .

The Clark unit hydrograph considers that two procedures dominate the motion of flow through a catchment. The first is interlingual rendition, defined by the downgradient motion of flow through the catchment due to gravitation. The other is named fading, which is the frictional forces and channel storage effects that resist the flow ( Straub et al. , 2000 ) .

Furthermore, together with the Clark unit hydrograph, the additive reservoir theoretical account represents the aggregative impacts of all catchment storage. The additive reservoir theoretical account transforms the rainfall surplus to direct surface overflow. This theoretical account is based on the construct that a catchment behaves as a reservoir in which storage is linearly related to outflow ( US Army Corps of Engineers, 1980 ; US Army Corps of Engineers, 2000 ) .

The procedure used to find the fluctuation of flow rate for a inundation moving ridge as it moves through H2O range in clip and infinite is called hydrologic routing ( Das & A ; Saikia, 2009 ) . For that intent it was used the Muskingum inundation routing method, which is based on the constructs of prism and cuneus storage in a river range under premise that those storages can be treated as a additive relationship between the influx and escape. In this manner, the prism storage is the volume defined by a steady-flow H2O surface profile, while the cuneus storage is the excess volume under the profile of the inundation moving ridge. During flood events, the cuneus storage is positive and so it is added to the prism storage. Unlike, during falling events of a inundation, the cuneus storage is negative and it is subtracted from the prism storage ( US Army Corps of Engineers, 2000 ) .

For the weather forecasting description of the catchment were used methods for evapotranspiration and snowmelt.

With the intent to gauge the possible evapotranspiration EP, the Priestley Taylor method was applied. This method uses as instrument the undermentioned Equation ( 2.4 ) ( Gardelin & A ; Lindstrom, 1996 ) :

-S )

( 2.4 )

Where:

I± : Priestley-Taylor coefficient or dryness coefficient ;

s: gradient of the concentrated vapor force per unit area, which is a map of the air temperature ;

I? : psychrometric invariable ;

Rn net radiation, which comes from the planetary radiation ;

Second: dirt heat flux.

After the appraisal of the possible evapotranspiration, the existent evapotranspiration Et is calculated based on canopy and dirt H2O balances ( Chow et al. , 1988 ) .

Finally, the Temperature Index was used to gauge if the precipitation was fallen as a liquid or frozen signifier and as a consequence to cipher the snowmelt. The accretion and thaw of the snowpack is simulated in response to atmospheric conditions ( US Army Corps of Engineers, 2008 ) . The basic Equation ( 2.5 ) for the Temperature Index method is ( US Army Corps of Engineers, 1998 ) :

( 2.5 )

Where:

Multiple sclerosis: snowmelt

Centimeter: thaw rate coefficient ;

Tantalum: air temperature ;

Terbium: base temperature .

## 2.3 Calibration

The standardization procedure attempts to happen out the optimum parametric quantity values that minimizes the nonsubjective map or the goodness of tantrum ( Cunderlik & A ; Simonovic, 2004 ) .

For the intent of this survey, the accommodation of the parametric quantities ( Table 2.2 ) , or merely standardization, was realized automatically utilizing PEST, an independent non-linear parametric quantity calculator. PEST uses an optimisation algorithm until some “ best tantrum ” parametric quantity has been found ( Beven, 2001 ) .

Table 2.2: Applied methods and their parametric quantity groups

## Method

## Parameter group

## SMA

Maximal Infiltration

Soil Storage

Tension Storage

Soil Percolation

Groundwater1 Storage

Groundwater1 Percolation

Groundwater1 Coefficient

Groundwater2 Storage

Groundwater2 Coefficient

## Clark ‘s Unit Hydrograph

Time of Concentration

Storage Coefficient

## Linear Reservoir

Groundwater1 Coefficient

Groundwater2 Coefficient

## Muskingum

Travel Time

Burdening Factor

Plague can set the theoretical account parametric quantity until the disagreements between the consequences generated by the theoretical account and the corresponding measurings are reduced to minimum. It is done by taking control of the theoretical account and running it as many times as is necessary in order to find the optimum set of parametric quantities. The non-linear appraisal technique used for this process is known as Grauss-Marquardt-Levenberg method ( Doherty, 2004 ) .

The Figure 2.4 illustrates the general procedure of a simulation theoretical account and PEST standardization every bit good as the interaction between both.

## SIMULATION MODEL

Model

input

HEC-HMS

Model

end product

Model parametric quantities

Optimization algorithm

Objective map

## PEST ( CALIBRATION )

Observations

New parametric quantities

Figure 2.4: Simulation ( HEC-HMS ) and standardization ( PEST ) procedure

As HEC-HMS is a physically based theoretical account, the initial parametric quantities estimated as a map of dirt type, land usage and digital lift theoretical account ( DEM ) . After that, PEST is provided within the set of parametric quantities and so it is able to rewrite the theoretical account input informations at any phase of the optimisation procedure. Each clip that PEST runs the theoretical account, it is able to read the theoretical account end product until it fits in the best manner to the measured informations. When calculated the mismatch between the two sets of parametric quantities, and measuring the best manner to rectify it, PEST adjusts the theoretical account input informations and runs the theoretical account once more. This procedure is done by comparing parametric quantities alterations and nonsubjective map betterment achieved through the current loop with those achieved in old loops, so PEST can advise whether it is deserving set abouting other optimisation loop ; if so the whole procedure is repeated ( Doherty, 2004 ) .

In a theoretical account with important Numberss of sub-catchments and legion parametric quantity groups in each of them, consequences in a big figure of unknown consequences in a dimensional parametric quantity hunt infinite, which makes complex the optimisation job.

When utilizing a semi distributed theoretical account, like HEC-HMS, the figure of sub-catchments Ns, with a certain sum of parametric quantity group Np, gives a dimension ???“ , as showed in Equation 2.6:

???“ = NsA·Np

( 2.6 )

Therefore, in order to manage this dimensional issue, some different schemes, as showed in Table 2.3, were applied and later an rating was made in each one of them.

Table 2.3: Parameter schemes applied and their clip measure

## Scheme

## Time Step

Two stairss – daily/hourly

Daily and hourly

Two stairss – MAVG

Hourly

Lumped parametric quantity

Hourly

One factor parametric quantity

Clusterization

## a ) Two stairss – daily/hourly

In the two clip stairss scheme foremost the slow constituents ( groundwater 2 ) are calibrated. As the slow constituents produce base flow, which has a drum sander form, the graduated groundwater 2 parametric quantities were hold on and so all fast constituents were calibrated in a 2nd standardization measure.

The standardization utilizing the two clip stairss scheme was realized foremost in day-to-day clip stairss, due to longer handiness of the informations. After that, it was applied to the faster constituents in hourly clip measure. Due to the standardization in 2 stairss the dimension of each standardization gets lupus erythematosuss.

## B ) Two stairss – traveling norm

The moving norm ( MAVG ) was applied with the purpose of cut downing the dimension by utilizing the norm of the parametric quantities. The two stairss traveling mean consists foremost to acquire the mean of the parametric quantities utilizing the MAVG and so stars the standardization procedure.

The MAVG is based on the rule that the constituents of a clip series show autocorrelation while the random fluctuations are non autocorrelated. Therefore, the norm of the adjacent measurings will extinguish the random fluctuations, with the staying fluctuation meeting to a description of the system ( McCuen, 1941 ) . In other words, conveying it to a hydrological position, all fast constituents will be eliminated so that the parametric quantities which have influence will be all from the slower constituents. The Equation 2.7 shows how the MAVG plants.

( 2.7 )

Where:

m: figure of observations

wj: weight applied to value J of the series.

The smooth interval is usually an uneven whole number, with 0.5 ( ma?’1 ) values of Y before the observation I and 0.5 ( ma?’1 ) values of Y after observation I used to gauge the smoothened value. In add-on, the simplest weighting strategy would be the arithmetic mean ( McCuen, 1941 ) .

## degree Celsius ) Lumped Parameter

The lumped parametric quantity lies on the thought of a class of theoretical accounts denominated as lumped theoretical account. Those theoretical accounts make the premise that the full country of the catchment has the same belongingss or in other words, there is no spacial parametric quantity fluctuation ( Hangos & A ; Cameron, 2001 ) .

In this manner, the whole survey country is treated as merely one catchment ( without sub-catchments ) . For this ground, a new dimension becomes in a function ; see Equation 2.8:

???“ = NsA·Np a†’ ???“ = Np

( 2.8 )

For the standardization procedure, each parametric quantity group has the same value for the entire country of the catchment. In order to exemplify the scheme, allow ‘s see I¦i, J for the parametric quantity value of a specific parametric quantity group ( one bases for the parametric quantity group ) and for a specific sub-catchment ( J for the sub-catchment ) , Figure 2.5 shows a study of the lumped scheme.

I¦1,3

I¦1,2

I¦1,4

I¦1,1

I¦1,1 = I¦1,2= I¦1,3= I¦1,4

Sub-catchment boundary line

Figure 2.5: Sketch of a catchment with lumped parametric quantity

In order to see the uniformity across the catchment and as a consequence a big decrease of the figure of parametric quantity, the values for the physically based initial parametric quantities were averaged for each parametric quantity group. Therefore, for the standardization procedure, merely one value for each parametric quantity group is now available.

## vitamin D ) One Factor

Harmonizing to Davison ( 2003 ) , due to the spacial averaging necessary for the parametric quantities, the hypothesis of a lumped catchment brings some restriction in the ability to depict the catchment. In this manner, a spacial distributed parametric quantity premise was adopted utilizing one factor I for each parametric quantity group.

This scheme is done in a manner that the parametric quantity values I¦i, J of every parametric quantity group is multiplied by one common factor I ( Pokhrel & A ; Gupta, 2010 ) , bring forthing new parametric quantity values I¦’i, j see Equation 2.9.

( 2.9 )

The factor I makes the premise that the initial parametric quantity set describes the spacial form. However, it must be taken into history the accommodation of the magnitudes of every parametric quantity to accomplish a better simulation of the theoretical account ( Pokhrel & A ; Gupta, 2010 ) . In this instance, for the factor I, depending on the parametric quantity, was adopted a certain scope

Therefore, the acceptance of the factor for each parametric quantity group brings precisely the same dimension as in the lumped scheme ; see antecedently the Equation 2.8. However, as mentioned before, the spacial variableness is kept. Figure 2.6 illustrate how the one factor scheme works.

I¦1,3

I¦1,2

I¦1,4

I¦1,1

Sub-catchment boundary line

A·I¦1,1 ; A·I¦1,2 ; A·I¦1,3 ; A·I¦1,4

Figure 2.6: Sketch of a catchment with one factor parametric quantity

## vitamin E ) Clusterization

The last scheme of cut downing the parametric quantities dimension and at the same clip to give spacial variableness to the catchment was realized by clusterization of the groundwater1 parametric quantities group I¦gw1, J and groundwater2 parametric quantities group I¦gw2, J.

For the groundwater1, the bunchs Ci were generated harmonizing to the physical features of the sub-catchments. Whereas, for the groundwater2 parametric quantities group a similar process was made. In this instance, alternatively of utilizing the physical features of the sub-catchments to bring forth bunchs, it was made by the place in infinite.

Bellow, Figure 2.7 demonstrates an illustration of the groundwater1 clusterization.

I¦gw1,3

I¦gw1,4,4

C1: I¦gw1,1 and I¦gw1,2

C2: I¦gw1,3 and I¦gw1,4

I¦gw1,1

I¦gw1,2

Sub-catchment boundary line

Figure 2.7: Sketch of a catchment with bunch parametric quantity

Therefore, harmonizing to Figure 2.7, the dimension ???“ is well reduced. In this manner, the new dimension becomes ; see equation ( 2.10 ) .

( 2.10 )

Where:

: entire figure of parametric quantities,

: figure of groundwater parametric quantities which are in bunchs ;

: figure of bunchs groundwater parametric quantities.

In this manner, comparing to the lumped scheme, for illustration, the parametric quantity dimension utilizing clusterization becomes larger, due to the fact that one factor is used for each bunch. However, if compared to the initial conditions ( see Equation 2.6 ) it becomes much more decreased.

Furthermore, the values of the parametric quantities of each bunch Ci were calculated multiplying the initial parametric quantity values by one factor, like in the old scheme.

After the standardization process, the proof procedure took topographic point. The intent of proof, which can be defined as an extension of the standardization, is to do certain that the graduated theoretical account suitably assesses all the parametric quantities and conditions which can impact the theoretical account ( Donigian, 2002 ) . Furthermore, it proves that the theoretical account parametric quantities are robust plenty outside the standardization clip series.

## 2.4 Objective map and rating

Once interfaced with the theoretical account, PEST aims to minimise the leaden amount of the square differences between the informations generated by the theoretical account and the mensural 1s. This theoretical account and measurement disagreements is referred to as the “ nonsubjective map ” , see Equation 2.11 ( Doherty, 2004 ) .

( 2.11 )

Where:

: aim map ;

: ith remainder ;

: weight refering to observation I.

The pick of a suited step is critical in a robust standardization procedure. The Nash-Sutcliffe efficiency index NSC is a widely used and potentially consistent statistic for measuring the goodness of tantrum of hydrological methods. This index measures the mean of the square mistake to the ascertained discrepancy ; see Equation 2.12 ( McCuen et al. , 2006 ) .

( 2.12 )

Where:

Myocardial infarction: theoretical account end product,

Oi: ascertained values ;

: mean observed value.

If the mistake is zero ( NSC = 1 ) , the theoretical account represents a perfect tantrum. However, if the mistake has the same magnitude as the ascertained discrepancy ( NSC = 0 ) , the ascertained average value is every bit good as a representation of the theoretical account, in this instance the theoretical account represents ill the world ( Wainwright & A ; Mulligan, 2004 ) .

In order to measure the consistence of the fitted theoretical account, the failure volume FV was analyzed. It is nil else than the ratio between the ascertained and the fake values, as shown in Equation 2.13.

( 2.13 )

Where:

Myocardial infarction: theoretical account end product,

Oi: ascertained values.

A positive FV indicates that the theoretical account systematically overestimate the mensural value, while the negative means a consistent underestimate.

Finally, with the purpose to compare the different adoptive schemes, the focal point was relied on the extremums of fake and ascertained discharge utilizing partial series. The extremums were selected due to a bound discharge Qs, which is a map the old ages of the series ; see Equation 2.14 ( Maniak, 2005 ) :

## )

( 2.14 )

Where:

Q: bound ;

Nitrogen: figure of old ages of the series.

In this manner, all independent extremums above Qs were analyzed in order to compare the informations between observed and simulated.

The comparing between the tantrum of the fake and ascertained extremums was made by utilizing the square of the correlativity coefficient R2, which shows the grade of additive arrested development between two random variables ( McCuen, 1941 ) .

## 3. Study country and database

For the intent of this undertaking, the survey country investigated was the Leineturm catchment, a southern sub-catchment of the Aller Leine catchment, located North of Germany. The Figure 3.1 shows the location of the Leineturm catchment in a digital lift theoretical account ( DEM ) with declaration of 10 m x 10 m.

## Hannovera-?

## Leineturm

Figure 3.1: Digital Elevation Model ( DEM ) – Location of Leineturm as a sub-catchment of Aller Leine catchment

The general features of the Leineturm catchment are presented in the Table 3.1.

Table 3.1: Leineturm features

## Characteristic

## Value

Entire country

990 km2

Latitude

51.5A°

Longitude

10.0A°

Average temperature

8.5 A°C

Average precipitation

667 mm/a

The information as air temperature, precipitation and humidness, used for the development of this survey, were acquired from Niedersachsischer Landesbetrieb fur Wasserwirtschaft, Kusten- und Naturschutz – NLWKN ( Lower Saxony Water Management, Coastal Defence and Nature Conservation Agency ) . The location of precipitation, net radiation and temperature gages are illustrated in Figure 3.2. However, for precipitation, non all gages were used in this survey due to little clip series.

Figure 3.2: ( Left ) Precipitation gages of Leineturm catchment. ( Right ) Net radiation and temperature gages of Leineturm catchment

For the purpose to measure the public presentation of the full procedure described antecedently in methodological analysis, the Figure 3.3 shows the location of the discharge gages ( besides from NLWKN ) used for that intent.

Figure 3.3: Discharge gages of Leineturm catchment

For information about dirt type it was obtained from BUK 1000, a dirt map of Germany in scale 1:1,000,000 produced by Bundesanstalt fur Geowissenschaften und Rohstoffe – BGR ( Federal Institute for Geosciences and Natural Resources ) .

The information of land usage was acquired from the undertaking CORINE Land Cover ( CLC ) 2006, a information set of land screen for Europe. In Germany the CLC was performed by the Deutschen Fernerkundungsdatenzentrum ( German Remote Sensing Data Center ) , on behalf of the Auftrag des Umweltbundesamtes ( Federal Environment Agency ) .

## 4. Consequences

In order to hold an overview about the different schemes, Table 4.1 shows the periods which were used for standardization and proof procedures.

Table 4.1: Calibration and proof of the different schemes

## Scheme

## Calibration period

## Validation period

Two clip stairss

no consequences

no consequences

Two stairss MAVG

no consequences

no consequences

Lumped

2004, 2007, 2008

2005, 2006

One factor

2004, 2007, 2008

2005, 2006

Clusterization

2004, 2007, 2008

2005, 2006

Subsequent, the presentation of the consequences will follow the same order as presented in methodological analysis.

## a ) Two stairss – daily/hourly

As a consequence, the comparing between the ascertained and fake day-to-day flow for the period January 1970 to December 1999 shows clearly a important overestimate of the fake information. For the twelvemonth 1998 for the Leineturm gage, placed in the mercantile establishment of the catchment, this behaviour is pointed out in the Figure 4.1.

Figure 4.1: Observed and simulated flow for the twelvemonth 1998of the Leineturm gage, utilizing the two stairss daily/hourly scheme

The overestimate of the fake information is explained due to a non-accounting of the existent evapotranspiration. As the existent evapotranspiration has non been considerate, this excess finally reflected in the flow.

For an unknown ground, this inaccuracy about the existent evapotranspiration has happened on occasions when there was rainfall. In a manner to show that state of affairs, the period from 5th of June, 1980 until 11th of June, 1980 was investigated.

At this clip, it was observed an event of rainfall from 6th of June until 10th of June. Consequently, for the whole period investigated, the possible evapotranspiration was calculated. However, in the sequence of Figure 4.2 is clearly noted that for periods with rainfall, no evapotranspiration was taken into history.

Figure 4.2: Precipitation event ( left ) , possible evapotranspiration ( in-between ) , existent evapotranspiration ( right )

As mentioned before, this job refering the evapotranspiration has unknown causes. It may be a misreckoning of the theoretical account or some trouble related to handling of the theoretical account. However, this issue is beyond the range of this survey.

Furthermore, refering this job, if the theoretical account is run in hourly clip measure, a twenty-four hours with rainfall does non needfully means that each hr of the twenty-four hours was raining. Due to that, it would be accounted evapotranspiration in hourly clip stairss when there was no evapotranspiration in day-to-day clip stairss. Therefore, it is clear that the appraisal parametric quantities in day-to-day clip measure can non be transfer into a simulation in hourly clip measure, because the H2O balance is non described in the same manner.

## B ) Two stairss – MAVG

The MAVG showed good consequence for the H2O balance over a specific clip period. However, a job was obtained refering that the fluctuations with higher frequence were miss calibrated and portion wise over and underestimated ; see Figure 4.3.

Furthermore, the inaccuracy of the baseflow is clear. Therefore, this state of affairs has a direct native impact on the standardization of the groundwater2 parametric quantities.

Figure 4.3: Observed and simulated flow for the twelvemonth 2007 utilizing the two stairss traveling mean scheme

For this ground, the effort to graduate foremost the slow constituents, without looking at the fluctuation, and so in a 2nd measure to reassign it to the fast constituents, did non take to a satisfactory consequence.

## degree Celsius ) Lumped, one factor and clusterization

Subsequently, the public presentation of the different schemes as lumped, one factor and clusterization, were compared to each other. Furthermore, the schemes were compared without standardization ( initial parametric quantities )

Table 4.2 ( on follow page ) shows the Nash-Sutcliffe index NSC and the failure volume FV for every gage and each parametric quantity scheme every bit good as the indexes of the initial parametric quantities ( without standardization ) .

Table 4.2: Failure volume and Nash-Sutcliffe index of every gage and every scheme

## Gauge

## Area

## Calibration

## Validation

## FV

## National security council

## FV

## National security council

## Lumped

Leineturm

990

1.20

0.82

-1.65

0.61

Gottingen

633

1.86

0.77

5.71

0.60

Reckershausen

321

3.81

0.64

8.36

0.52

Gartemuhle

86.3

-21.65

0.59

-27.77

0.39

Mariengarten

45.2

37.41

-0.23

42.41

-1.04

## 1 Factor

Leineturm

990

3.81

0.83

-11.54

0.76

Gottingen

633

3.03

0.83

-5.11

0.74

Reckershausen

321

1.30

0.62

-4.21

0.62

Gartemuhle

86.3

-32.36

0.38

-68.58

0.20

Mariengarten

45.2

51.57

-2.52

51.23

-3.98

## Clusterization

Leineturm

990

2.21

0.87

-7.22

0.75

Gottingen

633

0.35

0.82

1.53

0.63

Reckershausen

321

-2.05

0.57

3.04

0.48

Gartemuhle

86.3

-48.81

0.04

-56.28

0.11

Mariengarten

45.2

55.63

-4.96

53.85

-8.59

## Without standardization

Leineturm

990

5.37

0.51

-4.45

0.51

Gottingen

633

4.95

0.40

0.91

0.44

Reckershausen

321

1.97

-0.03

-0.41

0.26

Gartemuhle

86.3

-28.37

0.26

-49.10

0.27

Mariengarten

45.2

5.11

-5.57

53.38

-8.54

First of all, all schemes obtained a clear betterment in theoretical account standardization if compared without standardization ( uncalibrated theoretical account ) .

The Mariengarten gage has showed really hapless public presentation degree for every scheme, showing unreasonable NSC values. In contrast, the Gottingen and Leineturm gages showed good public presentations.

The Figure 4.4 and Figure 4.5 show clearly the difference in public presentation between the Leineturm and Mariengarten gages. It is apparent the best tantrum of Leineturm gage comparing the ascertained and fake informations.

Figure 4.4: Observed and simulated flow for the twelvemonth 2007 of the Leineturm gage, utilizing the lumped scheme

Figure 4.5: Observed and simulated flow for the twelvemonth 2007 of Mariengarten gage, utilizing the lumped scheme

However, the disagreement degree becomes smaller when the gage receives a higher volume of overflow part. This might be a dependance of the construction of the theoretical account or on the standardization the gage with the biggest country besides received the biggest weight.

For a better apprehension, one time more a comparing between a all right performed gage, as Leineturm, and the poorest performed, Mariengarten, following Figure 4.6 shows in one axis the FV and the NSC index in the other axis.

## Validation

## Calibration

Figure 4.6: Nash-Sutcliffe A- Failure volume of Leineturm ( left ) and Mariengarten ( right ) gages

Harmonizing to Figure 4.6, is apparent the better fulfilment of Leineturm comparing to Mariengarten.

For the gage Leineturm, sing the standardization procedure, the NSC index got values higher than 0.8 for all standardization schemes. In add-on, the failure volume shows a modest overestimate for the standardization and an underestimate for the proof measure.

On the other manus, for the gage Mariengarten, about for all schemes, both for standardization and proof, the NSC index was less than zero, which means that the norm of the mensural values represents better than the fake series. For the failure volume, the grounds is strong that there was a high overestimate, with values around 48 % , for both proof and standardization.

Still, on the Mariengarten gage can be observed for the clusterization scheme for the proof procedure, the FV and NSC index obtained a consequence which does non suit the others 1s. However, this surly is by opportunity.

In order to compare the public presentation of the different schemes for high discharges, a choice of the 15 highest independent extremum was made. For case, the gage Leineturm was selected for that intent ( for the gages Reckershausen and Mariengarten see Appendix II ) . Bellow, the sequence of Figures ( Figure 4.7, Figure 4.8 and Figure 4.9 ) shows for every scheme the observed and the fake extremums for discharge. However, it is of import to see that the period of five old ages is slightly short for deeper statistical analysis.

Figure 4.7: Fifteen highest independent extremums for the lumped scheme for Leineturm gage

Figure 4.8: Fifteen highest independent extremums for the one factor scheme for Leineturm gage

Figure 4.9: Fifteen highest independent extremums for the clusterization scheme for Leineturm gage

When comparing the above artworks the first three lowest extremums have fundamentally the same behaviour, with a good tantrum between observed and simulated values. However, when the highest extremum is compared, the lumped scheme showed the best consequence.

Despite the difference of the highest extremum comparing the three schemes, the other extremums about have the same form. In this manner, in order to compare the tantrum of the schemes, the square correlativity coefficient R2 was used, as showed bellow in Figure 4.10.

Figure 4.10: Square correlativity coefficient of Leineturm gage for lumped ( left ) , one factor ( in-between ) and clusterization ( right ) schemes

Due to the low figure of sample, the difference among the R2 for all schemes was slightly little. However, the lumped and clusterization schemes obtained a better coefficient.

In order to do a comparing between the selected gages as Leineturm, Reckershausen and Mariengarten, the Table 4.3, shows the R2 coefficient for all schemes.

Table 4.3: Square correlativity coefficient of Leineturm, Reckershausen and Mariengarten gages for lumped, one factor and clusterization schemes

## Scheme

## Gauges

## Leineturm

## Reckershausen

## Mariengarten

Lumped

0.987

0.868

0.988

One factor

0.991

0.940

0.905

Clusterization

0.988

0.955

0.978

Sing the norm of R2 the clusterization scheme obtained the best consequence. However, the difference among them is non that apparent.

Furthermore, the Mariengarten gage, which earlier obtained bad public presentation for the full series, at this clip the public presentation was externally good. It means if the aim of analyze is for illustration inundations, where the high extremums are the focal point, the Mariengarten gage could be used for that intent.

## 5. Discussion

First of all, before making any remark refering the consequences, it is of import to stress one time more that the five old ages period used for the intent of this probe it is non sufficient to give an expressed decision about the parametric quantity schemes, when extremes values are focused. However, it is obvious that every bit longer the clip series as more robust the rating is.

Anyhow, except for the two stairss – daily/hourly and the two stairss – traveling mean schemes, where the consequences were non satisfactory in one instance and non to use in the other instance, the other parametric quantity schemes obtained a regular betterment in theoretical account standardization in comparison to the uncalibrated theoretical account.

Although the difference between the schemes is non so apparent, the clusterization of the groundwater parametric quantity groups obtained a bantam better public presentation comparing to the others. It might be due to the given parametric quantity flexibleness, one time the appraisal of the initial groundwater parametric quantities are non that certain.

Furthermore, the consequences suggest that standardization utilizing parametric quantities with or without spacial variableness gave about tantamount public presentation.

Despite pretermiting the spacial variableness of the parametric quantities, the lumped scheme obtained consequences clearly comparable to the others.

In add-on, this response showed that the theoretical account is non strongly sensitive to spacial parametric quantity variableness, therefore well a average parametric quantity value performs good.

However, with those consequences we can non confirm that the spacial parametric quantity variableness is non important.

Finally, this survey explored different techniques with the intent to cut down the parametric quantity dimensions when covering with standardization. However, more ways need to be investigated in order to accomplish good public presentations of parametric quantity standardization.