Adaption of the Agricultural Non-point Source Pollution Model to the Morsa Watershed

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Adaptation of the Agricultural Non-point Source Pollution Model to the Morsa Watershed

Niclas Eriksson

Abstract

Eutrophication of sea and lake ecosystems is basically being caused by high discharges of nutrients from terrestrial basins. In order to explore general strategies for reducing such discharge, the spatially distributed Agricultural Non-point Source Pollution Model (AGNPS) was adapted to the Morsa catchment of south-eastern Norway. This catchment was chosen because of the relatively extensive GIS (geographical information system) databases that have been accumulated in previous research projects. They contain highly resolved data on soil types, topography and land-use, together with time series on hydrology, meteorology, and water quality. The data generally holds high enough quality to make (parts of) the Morsa catchment an ideal site for application of the AGNPS model.

AGNPS is a model that simulates nutrient, pesticide and sediment transport through the watershed. It is developed in an extensive collaboration between the US Agricultural Research Service and the US Natural Resources Conservation Service, and includes state-of-the-art technology as well as the features necessary for continuous watershed simulation on a daily basis.

Data requirements for the AGNPS model are:

GIS data Meteorological data

• Digital elevation model (DEM)

• Soils

• Land-use

• Daily precipitation

• Temperature (minimum and maximum)

• Dew point temperature

• Sky cover

• Wind speed (for certain applications) The AGNPS model is adapted to the actual watershed in a number of steps, whereof many utilise separate programmes written in FORTRAN or similar programming languages. The programs are controlled via a GIS (ArcView) interface supplied with the AGNPS model, but may also be run in manual mode. Each program creates an input file for the AGNPS Input Editor, where parameters describing the spatial characteristics of input data are calculated, edited, and saved for the final simulation. The model is capable of handling approximately 400 parameters, although the number in actual use varies with the application.

AGNPS may be used to map the ratio with which individual landscape elements contribute to the total catchment emission of nutrients. It enables for landscape planners to identify areas that allow

exploitation under simultaneous optimisation of the landscape capacity to retain urban pollution. By manipulating model parameters, different scenarios may be explored and compared. As an example, the optimal morphology of landscape wetlands may be explored with respect to the total catchment export of nitrogen. Although requiring generally large amounts of data, the favourable characteristics of the AGNPS model makes it an ideal tool for the landscape planner to utilize in minimising nutrient discharge at the catchment scale.

Key words: Minimisation of catchment nutrient export, AGNPS.

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1 Introduction

Eutrophication¹, which is a growing problem in the worlds seas and lakes today, is mainly caused by high discharges of nutrients like nitrogen and phosphorus from terrestrial basins. Minimization of the discharges is the obvious solution of the problem and we already know that high levels of discharges derive from agricultural fields where fertilizers and pesticides are applied. In order to find solutions to the problem some kind of model has to be applied. The Agricultural Non-Point Source Pollution Model (AGNPS) is such a model.

The AGNPS model is widely used in the US but there are some problems that occur when adapting the model to a non-US watershed. The general aim of this paper is to provide an example of the steps included when adapting a AGNPS model for a watershed outside the US. It is assumed that the reader has some knowledge of statistical terms but possibly none of hydrology. In the glossary on page 45 some terms are explained more in detail.

I wish to thank my supervisors Dag Jonsson (Uppsala University) and Tomas Thierfelder (Swedish University of Agricultural Sciences) for their help and support. I would also like to thank phd student Dilip Roy (Swedish University of Agricultural Sciences ) for giving me useful comments and support.

Other people involved in some way were Anne Søvik (Jordforsk Norway), Helga Gunnarsdottir, Signe Kroken, Stein Turtumoygard, Knut Bjørnskau (Ski municipality), Cecilie Bergmann (Ski

municipality) and Ron Bingner (USDA).

1.1 The Agricultural Non-Point Source Pollution Model

AGNPS is a model that simulates the transport of nutrients, sediments and other chemicals through watersheds. It can be used as a tool for evaluating how different management decisions have impact on a watershed. AGNPS is a joint USDA-Agricultural Research Service and -Natural Resources Conservation Service developed model. In the beginning AGNPS was only able to simulate one single storm event. But in recent years a new version of AGNPS called AnnAGNPS² (annualised) has been developed. Now the simulation is performed on a day by day basis over several years and the model consists of around 400 parameters. The AGNPS model is constructed in a number of steps including different programs written in FORTRAN or similar programming languages. Each program creates different input files and they are all loaded into an input editor before the final step, the simulation.

Data requirements for the AGNPS model are:

GIS³ data Meteorological data

• Digital elevation model (DEM)

• Soils

• Landuse

• Daily precipitation

• Sky cover

• Wind speed (for certain applications)

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Although AGNPS is a program that can be used without any interaction with other programs, an interface making it easier to use has been produced. The interface called the AGNPS/ArcView interface is loaded into the ESRI program called ArcView¹, where different pull down menus will assist in the process of preparing input data for the AGNPS model.

Adapting an AGNPS model requires systematic work. The general succession of data preparation is as follows:

1. Prepare the DEM 2. Prepare digital soil maps

3. Prepare land-use/land-cover maps

4. Use the ArcView interface to generate input parameters for the input editor 5. Prepare weather data

6. Import the files created by the ArcView interface (cell and reach data) and the weather data into the input editor and edit the remaining parameters

7. Run simulations and calibrate the model

1.2 What types of watersheds are appropriate for an AGNPS model?

Applying a distributed model to a real world watershed requires large quantities of data. The densely monitored Morsa catchment of south-eastern Norway is ideal for AGNPS model fitting. The Morsa catchment was chosen because of the extensive GIS databases that have been accumulated in previous research projects. They contain highly resolved data on soil types, topography and land-use, together with time series on hydrology, meteorology, and water quality. The data generally holds high quality enough to make parts of the Morsa catchment an ideal site for the study performed.

When selecting which sub-catchment within the Morsa watershed to fit with the AGNPS model, data availability has to be considered and the watershed is supposed to have only one outlet and no inlets.

In Figure 1.2-2 it can be seen that "Kråkastadelva", "Mörkelva och Veidalselva" and "Saebyvannet och Svinna" are the watersheds that have only outlets. "Kråkstadelva" is a conveniently sized watershed with lots of existing soil data.

Kråkstadelva is a part of the Ski municipality and has been subject for many projects and

investigations. Actions are taken to decrease the discharges from the municipality and Kråkstadelva is a large contributor to the discharges. Today the water quality in Kråkstadelva is classified as very bad, with discharges mainly caused by agriculture. The watershed is strongly affected by erosion resulting in high sediment levels and associated high discharges of phosphorus.

Figure 1.2-1. Contributors to the total reactive phosphorus in the Kråkstadelva watershed.

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Figure 1.2-2. Flow scheme over the Morsa catchment.

Langen

Mjaer

Kråkstad -elva

Hoböelva -Övre Hoböelva

-nedre

Mörkelva och Veidalselva

Saebyvannet och Svinna

Vansjö - Storefj.

Vasjö - Vanemfj.

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2 Adapting the GIS data for AGNPS application

2.1 DEM

The DEM (digital elevation model) applied here is a grid (in raster format) with topographical data with a precision of 30x30 metres. The vertical resolution for each cell is optimal if it is 0.1 metres, which is the highest resolution that AGNPS can use, or more precisely for the TopAGNPS program that is a part of the AGNPS package. At resolutions higher then 0.1 metres TopAGNPS truncates the values to 0.1 metres precision.

Figure 2.1-1. The original shape file (vector format) of the topographical data over the whole Morsa area together with a zoomed picture. The range of the area from north to south is 65000 metres and from west to east 34000 metres.

The steps when creating a DEM are

1. Convert the vector data to raster data with 30x30 metres cell size.

2. Interpolate the grid to predict the missing values.

The first step is the easiest one. ArcView has a pull down menu “Theme / Convert to grid”. And here we set the cell size to 30 metres and create our grid. The second step requires a lot of consideration. A method that can be used is the “TIN” interpolation. In TIN interpolation the elevation vectors are tied together with triangles. TIN interpolation works well and you get a surface for the DEM but it does not take the correlation in the data into consideration. It is not difficult to understand that the elevation in a point depends on the surrounding points. A commonly used interpolation method in geostatistics that uses the covariances between the data is called kriging. Kriging is a very computer intensive method which means that you can not interpolate over surfaces that are too extensive. Therefore I choose to interpolate the whole grid of Morsa with the TIN method and Kråkstadelva with kriging (see chapter 4 for kriging).

With TIN interpolation you have to begin with the second step, meaning you first create a tinned surface and then convert the tinned surface into a grid. In Figure 2.1-2 the DEM is shown after

conversion from vector format. The values corresponding to black fields are to be interpolated. Figure 2.1-3 shows a zoomed tinned surface and in Figure 2.1-4 the final DEM is shown.

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Figure 2.1-2. The DEM after step one (left) and a zoomed version ( right).

Figure 2.1-3. A zoomed tinned surface. Figure 2.1-4. The resulting DEM from the TIN interpolation.

"Hillshade" is a function which is available in most GIS programs. Applying this function to the DEM makes it possible to see in more detail what the topography looks like. The Hillshade is presented in Figure 2.1-5.

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Figure 2.1-5. A Hillshade of the tinned DEM showing the effects of the TIN interpolation. In areas of large missing values large triangles are fitted.

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2.2 Soils

Soil type is an important parameter in the AGNPS model. The landscape ability to retain nutrients, as well as runoff ratio, are highly depending on soil parameters. The GIS files of the soil data only contain which type of soil group different areas belong to, the in-depth parameters for each soil has to be manually entered for each soil type in the input editor.

Figure 2.2-1. Soil GIS data. The region marked with red is the watershed Kråkstadelva. This soil data is a combination of two GIS data files.

The soil data were spread over different GIS files that had to be spatially joined with different functions of the ArcView program. The denotations of the soils 101A, 102D etc in Figure 2.2-1 are abbreviations for the original soil names, which are given In Table 2.2-1.

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Table 2.2-1. Soil codes (original names in Norwegian).

Name Code

1 Lettleire 101C

2 Leire 102D

3 Organisk 103U

4 Sand 104A

5 Silt 105B

6 Hav- og fjordavsetning, tykt dekke 106D

7 Bart fjell 107U

8 Forvitringsmateriale, uspesifisert 108U 9 Morenemateriale, tynt dekke 109U 10 Hav-, fjord- og strandavsetn., tynt dekke 110U 11 Lösmasser/berggrunn under vann (uspes.) 111U 12 Elve- og bekkeavsetning, uspesifisert 112U 13 Torv og myr (Organisk materiale) 113U 14 Marin strandavsetning, tykt dekke 114U 15 Morenemateriale, tykt dekke 115U 16 Humusdekke/tynt torvdekke over berggrunn 116U 17 Fyllmasse (antropogent matr.), uspesifisert 117U

18 Breelvavsetning 118U

19 Skredmateriale, tykt dekke 119U

20 Randmorene 120U

21 Innsjöavsetning 121U

2.3 Fields

AGNPS uses five parameters when classifying fields. These are 1. Cropland

2. Pasture 3. Rangeland 4. Forest 5. Urban areas

The field types are later used to specify the operations that take place in them. The most important type of land use is the cropland field type where different agricultural methods have a large impact on the discharges. As mentioned in the introduction, approximately fifty percent of the discharges from Kråkstadelva derive from agricultural fields.

The operations carried out in the fields are later set in the input editor. For agricultural fields the main operations are the following

• Soil surface disturbed

• Current crop residue added to the surface

• Other residue added to the field

• Current residue removed from the field

• Current crop harvested

• Plant crop

These operations can be applied in a succession, where a possible sequence is “soil surface disturbed”

– “plant crop”. All operations have a number of parameters which are illustrated by the operation “soil surface disturbed”, that has to be specified with the percentage area disturbed and percentage

remaining residue.

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Figure 2.3-1. Fields of "Kråkstadelva".

In Figure 2.3-1 the fields are shown with the AGNPS classification. The urban area in the north-west is the Ski town and the urban area in the centre is the Kråkstad village. There is a corresponding picture in the appendix on page 53 over the whole Ski municipality.

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3 Adapting weather data to AGNPS

3.1 Weather data

Weather data that is required by AGNPS (in AnnAGNPS mode) are:

• Daily precipitation (rainfall)

• Sky cover

• Wind speed (not used by AGNPS, currently being implemented into the model)

The climate timeseries were acquired from Agricultural University of Norway, Ås. The time series span between 1990 - 2002 and have daily values.

Table 3.1-1. Meteorological measurements at the Agricultural University of Norway, Ås.

Quantity measured Derived quantity Current instrument Time series

start

1 temperature PT100 1874

2 temperature minimum temperature PT100 1874

3 temperature maximum temperature PT100 1874

4 relative humidity hair hygrometer 1874

5 precipitation manual/ITF 1874

6 # sunshine hours / day sunshine recorder 1897-1982

7 global irradiation Eppley Precision Pyranometer 1950

8 diffuse irradiation Eppley Precision Pyranometer 1966

9 global irradiation

down (reflected) irradiation balance (7 -9)

albedo (9 / 7) Eppley Precision Pyranometer 1966 1983 10 radiation energy

balance Radiation Energy Balance System /

Pyranometer 1960

11 PAR photosyntetic active radiation

LI-COR Quantum sensor 1977 12 irradiation RG8

IR (695-2800nm) red (630-695nm)

(13 - 12) Eppley Precision Pyranometer 1977

13 irradiation RG2 green (495-630nm)

(14 - 13) Eppley Precision Pyranometer 1977

14 irradiation GG14 blue (385-495nm)

(7 - 15 - 14) Eppley Precision Pyranometer 1977 15 irradiation UV

(295-385nm) Eppley Ultra-Violet Pyranometer 1977

16 min. temp. grass level minimum temperature Mercury thermometer 1969

17 soil temperature 2cm PT100 1983

21 soil temperature 25cm PT100 1896-1960

23 soil temp. 100cm PT100 1960

24 soil heat flux EKO/CN-81H 1983

25 evaporation Vibrating Wire Gauge/ITF 1961-64, 1996

26 snow # days with snow/snow depth Manual 1874

27 wind speed maximum / minimum Windmaster Ultrasonic Anemometer 1882

28 wind direction Windmaster Ultrasonic Anemometer 1874

29 air pressure Vaisala/Digital Barometers PTA200 1885

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Daily precipitation is the prime driver of the hydrologic circle, temperatures are used to define frozen conditions and the remaining parameters are used to compute potential evapotranspiration.

Furnished with AGNPS is a module called GEM and a program called “complete climate” which both are used to simulate the required meteorological data for use with AGNPS. They are both adapted for US weather, and cannot easily be transformed for Norwegian weather characteristics. The weather data can be actual recorded data, simulated data or a combination of both. A big difference between simulated data and true data is that you can compare the outputs that AGNPS generates with actual recorded values from the watershed. This is a way to check the model for errors.

A disadvantage with the weather data from Ås is that the series contain missing values. The

temperature time series were complete, but all other time series contained missing values that had to be estimated. These missing values are simulated with different methods in the following subchapters, therefore making our weather data a combination of simulated values and actual observations.

Tmax Tmin Tavg January

February March

April May

June July

August

September October

November December -20

-15 -10 -5 0 5 10 15 20 25 30

Figure 3.1-1. Temperature data from 1990. Monthly average temperature and min/max value.

The following subchapters assume that the reader has some knowledge of time series analysis.

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3.2 Preparation of daily precipitation data

The daily precipitation had 667 missing values spread over the 4749 days (14%). Since rain data come from a complicated distribution that depends on a number of parameters, it is quite difficult to

simulate.

Figure 3.2-1. The original daily precipitation time series with a moving average over the years 1990-2002.

In the figure above it can be seen that there is no apparent trend or seasonal component. If there would have been a season, the moving average curve would tend to look like a sinus curve with a white noise added. A re-sampling method was used to fill in the missing data. Assuming the rain data had no season or trend, missing values were re-sampled from the whole data set. Re-sampling is generally carried out as follows. First you load your sample into a array of some sort that has indexes for the position the values are at. Then generate a random value from a U(0,1) distribution. Multiply the random value with N equal to the number of values that you are re-sampling from. Round this value to integer and you have your re-sampled values index. It might be easier to understand when examining the Matlab code that follows.

sample=[0.0 0.0 0.0

. . . . 0.2 1.7 32.0];

for i=1:4749

index=round(rand(1,1,1)*4082);

tal(i,1)=index;

if tal(i,1)==0 tal(i,1)=1;

end

index2=tal(i,1);

resample(i,1)=sample(index2);

end

Matlab code used to resample.

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0 10 20 30 40 50 60 70 80 90 0

500 1000 1500 2000 2500 3000 3500 4000

After the re-sampling has been done it is recommended to check that the re-sampled values tend to look like the original sample and that the random values that were used really were drawn from a uniform distribution. This is shown in Figure 3.2-2 and Figure 3.2-3. In Figure 3.2-3 the histogram of the random uniform values is also shown.

Figure 3.2-2. Histogram of the original rain data. Figure 3.2-3. Histogram of the re-sampled rain data.

The small picture is a histogram of the random values from the U(0,1) distribution.

The re-sampled values were then used to fill in the missing values; this is seen in the following figure.

Figure 3.2-4. Method of filling in the missing values

The operation performed in Figure 3.2-4 is preferably done with a spreadsheet program like Excel or similar.

3.3 Preparation of dew point temperature data

Since dew point temperature was not monitored in the Morsa catchment, it was estimated using a formula that includes temperature and relative humidity. We already know that there are no missing values in the temperature time series but the relative humidity series had 245 missing values.

Original timeseries Resampled timeseries New timeseries orig

orig orig orig missing

orig . . .

res res res res res res . . .

orig orig orig orig res orig

. . .

0 10 20 30 40 50 60 70 80 90

0 500 1000 1500 2000 2500 3000 3500 4000 4500

0 100 200 300 400 500 600

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Figure 3.3-1. The original time series of the relative humidity (%)

The missing values has to be predicted in some way. In contrast to the daily precipitation time series in Figure 3.2-1 that have no seasonal component this time series have an obvious seasonal component.

To this seasonal component a random process is added, a white noise. The key to simulating a time series of this type is to find the distribution of the white noise. If this can be done, random values can be drawn from the distribution.

t t

t

S

X = + ε

,

t = 1 ,.... 4750

, assuming

ε

_t

∈ WN ( 0 , σ

²

)

( 3.1) An estimate of

ε

_t can be calculated using the first difference estimator

t t

t

= X

₋₁

− X

ε ˆ

,

t = 2 ,.... 4750

( 3.2)

This estimator usually removes the trend in the data but in this case it also removes most of the seasonal variation. The reason for this is that we have a time series with daily values, in a small interval of data the values are fairly the same.

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Figure 3.3-2. Time series plot of the white noise estimated in formula ( 3.2). A moving average is also calculated to show that there is no seasonal variation left.

The histogram in Figure 3.3-3 looks as if it could have been generated by some Laplace distribution.

Simulated values from a Laplace distribution shown in Figure 3.3-4 with location parameter 0 and scale 6 give "close enough" estimation of the white noise values. The random values from the Laplace distribution are therefore used to model the white noise

ε ˆ

_t in ( 3.2).

To predict the missing values we also need to estimate the seasonal component St where values are missing. This is done by calculating an average over the previous thirty days when a missing value is found.

Mean = 0, Maximum = 46.4,Minimum = -53.7, Standard deviation = 12.3 Mean = -0.09, Maximum = 50.66, Minimum = -42.03, Standard deviation = 8.50

Figure 3.3-3. Histogram of the white noise Figure 3.3-4. 4749 simulated values from a Laplace distribution with scale parameter 6.

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After the missing values have been estimated the dew point temperature is calculated with the following formula.

)) 7 . 237 /(

) 5 . 7 ((

^ 0 . 10 11 .

6 Tc Tc

Es = ⋅ ⋅ +

100 / ) ( RH Es

E = ⋅

08 . 19 ) ln(

) ln(

7 . 237 22 . 430

+

−

⋅ +

= −

E Td E

( 3.3)

Es is the saturation vapour pressure,

E

is the actual vapour pressure of the air, Td is the dewpoint temperature, Tcstands for temperature and

RH

is the relative humidity.

Figure 3.3-5. The calculated dew point temperatures.

3.4 Preparation of sky cover data

Sky cover was monitored until 1982, when the university of Ås ceased to monitor daily sunshine hours. These observations could have been used to estimate the sky cover, instead it was calculated as 100 - IR (%) where IR is the infrared radiation. This makes sense since a high value of IR is a direct indicator of low sky cover values.

The infrared radiation series had 322 missing values that had to be simulated.

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Figure 3.4-1. Time series plot and a moving average of the IR values.

Figure 3.4-2. Time series plot of year 1990 and 1991 of the IR data.

When time series of IR data are studied on an annual basis, it can be seen that the variance is larger in the first and the last months of the year. Since such time-varying variance is methodologically difficult to handle, it was not modelled. Instead it was based on the characteristics of the series, where one year ahead values were used to estimate missing data. In cases where these values were also missing, the value two years ahead was used (etc.).

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Figure 3.4-3. The new infra red series without the missing values.

The sky cover was then estimated with 100 - the new IR values.

3.5 Creating the daily climate input file DayClim.imp

The climate data is stored in a ordinary text file which can be crated with Notepad or something similar. Excel was used to save the file as a *.prn file (blank-step-formatted). It is important to get the correct sizes of the gaps between the values at each row, otherwise errors will occur.

Table 3.5-1. The daily climate file DayClim.inp

Norge: Morsa

45.75 118.75 1683.00 1 01/01/0001 1.1 12/31/0010

01/01/0001 -4.40 -11.20 0.00 -9.62 39.50 1.00 0.00 01/02/0001 -4.30 -7.10 0.00 -7.33 47.60 1.40 0.00 01/03/0001 -4.90 -7.10 0.00 -8.56 52.30 1.60 0.00 01/04/0001 -0.70 -4.80 0.00 -2.71 60.10 1.80 0.00 01/05/0001 -0.50 -4.40 0.90 -2.67 51.40 1.80 0.00 01/06/0001 2.90 -6.30 9.00 -1.96 42.60 2.10 0.00 01/07/0001 2.80 0.40 7.80 1.59 49.20 3.70 0.00 . . . . . . . . . . . . . . . . . . . . . . . . 12/31/0010 -7.62 -10.49 0.00 -8.96 53.27 28.68 0.00

This file can be imported and edited with the Input Editor. This step also verifies that the format is correct.

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4 Kriging

4.1 About Kriging

The transposition of multiple linear regression into a spatial context is called Kriging. It is a type of moving average with different weights for the surrounding points of the point we wish to estimate.

The method derives from the 1960s and from two men in particular. D.G. Krige, a mining engineer in the South African goldfields, observed that he could improve the estimates of ore blocks if he took the neighbouring blocks into consideration. Later on his method became practice in the gold mines. At the same time a mathematician, G. Matheron, who was a teacher in the French mining schools, was working on a method to provide the best possible estimates of mineral grades from auto-correlated sample data. He derived solutions to the problem from the fundamental theory of random processes.

His doctoral thesis, Tour de force (1965), still remains the theoretical basis of modern day practice although numerous developments have been done to the technique.

There are a several different types of kriging. The method used here is the most common one, called ordinary kriging.

Kriging is generally performed in three steps.

• Estimation of the variogram

• Modelling the variogram with a continuous function in order to calculate the semi-variances at points where the actual value is unknown.

• Solving the kriging equations to estimate the weights

λ

_i

Ordinary kriging is an exact interpolator, meaning when a sample value is available at the position of interest, the kriging solution is unique.

4.2 Estimation of the variogram

The variogram has an important role in geo-statistics and is therefore vital to estimate. The variogram summarizes the spatial relationships in the data. We are interested in fitting a continuous model for the variogram so that we can predict values of

Z

at lags where observations are missing.

To explain what a variogram is, it is necessary to go back to a problem that mathematicians studied in the 1960's. A stationary random process can be represented by the model

Z(x) = µ + ε(x) (4.1)

This means that the value of Z at x is simply the mean plus an random component drawn from a distribution with mean zero and covariance function

)]

( ) ( [ )

( h E x x h

C = ε ε +

(4.2)

The problem lies in the stationarity. The mean appears to change across a region and the variance increases unboundedly as the area of interest increases. Under these circumstances, the covariance cannot be defined. Matheron recognized the problem and found a solution in 1965 that contributed significantly to applied geo-statistics. His view was that although the mean might not be constant over the entire domain, it would be so for small |h| so that the expected differences would be zero,

0 )]

( ) (

[ Z x − Z x + h =

E

(4.3)

Further he replaced the covariances by the variances of differences as measures of spatial relation

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{ ( ) ( ) } ] 2 ( ) [

)]

( ) (

var[ Z x − Z x + h = E Z x − Z x + h

²

= γ h

^(4.4)

Here we have gone around the problem with the second order stationarity, where formerly the assumptions did not hold or were doubtful. The quantity γ(h) in (4.4) is known as the semi-variance, semi because it is actually half the variance. As a function of h the semi-variance is known as the semi-variogram, or simply the variogram.

For a set of data the semi-variance for each pair of points can be computed as

{ ⁽ ⁾ ⁽ ⁾ }

²

2 ) 1 ,

( x

_i

x

_j

= z x

_i

− z x

_j

γ

(4.5)

When these values are plotted against their lag distance (distance between the points) you get a scatter diagram that shows the spatial variation in the data. However a more sensible approach is to average the semi-variances for a few lags and then examine the result. Recall the definition of the semi- variance from (4.4) as

{ }

[ ⁽ ⁾ ⁽ ⁾

²

]

2 ) 1

( h = Ε Z x − Z x + h

γ

(4.6)

Then the estimator of the semi-variance is

{ }

[ ⁽ ⁾ ⁽ ⁾

²

]

2 ) 1

ˆ ( h = mean z x − z x + h

γ

(4.7)

where z(x) and z(x + h) represent actual values of Z separated by h. For a set of data

z ( x

_i

), i = 1 , 2 ...

(4.7) is computed as

{ }

∑

=

+

−

= ⁽ ⁾

1

) 2

( ) ) (

( 2 ) 1 ˆ(

h m

i

i z x h

x h z

h m

γ

(4.8)

where m(h) is the number of pairs of data points in the given interval h. This is the usual computing formula, although it is implemented different as an algorithm depending on the data (number of dimensions etc).

4.3 Fitting the variogram with a model

We wish to fit the estimated variogram

γ

ˆ(h₁),

γ

ˆ(h₂),...,at lags

h

_i

, i = 1 , 2 ,...,

with a continuous covariance function. The model that we fit can be approximated from the estimated variogram and there are a set of features that the function should represent:

• A monotonic increase with increasing lag distance

• A constant maximum or 'sill'

• A nugget

• Periodic fluctuation

• Anisotropy

In Figure 4.3-1 a variogram is shown – a common rule when fitting a model is to keep it as simple as possible.

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Figure 4.3-1. A variogram of ten lags with the lag distance ≈ 560.

4.4 Anisotropy

The variogram can behave in different ways depending on the directions. This behaviour is called anisotropy.

Figure 4.4-1. Signs of anisotropy. To the left: Surface variogram. To the right: Variogram. Green (v1 + v2) = 129°, Red (v1) = 39°, Black = omni-directional.

When the process Z is anisotropic the dependence between Z(x) and Z(x+h) is a function of both the magnitude and the direction of h. Anisotropy is easily detected when the variogram is calculated for different angles. Figure 4.4-1 displays a behaviour that is called zonal anisotropy. Since variogram models are defined for isotropic models we need to transform the coordinates to obtain anisotropic random functions from isotropic models. There are two main anisotropies in this type of data,

geometric anisotropy and zonal anisotropy. The difference between these two anisotropies is how they behave towards the sill¹. The zonal anisotropy indicates different values of the sill in different angles.

The geometric anisotropy has the same value for the sill but behaves differently towards the sill for different angles. The variogram in Figure 4.4-1 is therefore categorized as a zonal anisotropy.

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4.5 Ordinary Kriging

One aim of Kriging is to estimate the value of a random variable Z at one or more un-sampled points, z(x1), z(x2), ... , z(xN) at x1, x2, ... , xN.. We estimate Z at a point x0 by

∑

=

^N

i i

z x

i

x Z

1

0

) ( )

ˆ ( λ

,

∑

= N

=

i i

1

λ 1

(4.9)

The estimated point in (4.9) is in fact a weighted average with the condition that the weights λ_i sum up to 1 to keep the estimate unbiased. Here Ε[Zˆ(x₀)−Z(x₀)]=0.

The weights λ_i are selected to minimize the estimation variance.

) , ( )

, ( 2

] )}

( ) ˆ( [{

)]

ˆ( var[

1 1

1

0 2

0 0

0 i j

N i

N j

j i N

i

i x x x x

x Z x Z x

Z

∑ λ γ ∑∑ λ λ γ

= =

=

−

=

− Ε

= (4.10)

For each kriged estimate at a point there is a variance

σ

²

( x

₀

)

defined in equation (4.10). Now we wish to minimize the variance in (4.10), thus finding the weights

λ

_i that minimizes the variance. A method of Lagrange is used.

 



 

 −

−

= ∑

= N i

i

Z x Z x

f

1 0

0

) ( )] 2 1

ˆ ( var[

) ,

( λ ψ ψ λ

(4.11)

When minimizing we set the partial derivatives of the function equal to 0.

) 0 , (

∂ =

∂

∂ =

∂

ψ ψ λ

λ ψ λ

i i i

f f

i = 1,2,....,N (4.12)

This leads to a set of N+1 equations with N+1 unknowns.

∑

=

N

+

i

j j

i

x x x x x

1

0

) ( , )

( ) ,

( ψ γ

γ

λ

, for all j (4.13)

This is the ordinary system of Kriging points. After solving the equation the weights are inserted in the formula (4.9) to provide an estimate

Zˆ

at the point

x

₀.

For every new point we wish to estimate a new set of equations which to be solved making Kriging suitable for computer calculation.

The Kriging variance

σ

²

( x

₀

)

is calculated as

∑

=

+

=

^N

i

x x x

x

1

0 0

0

2

( ) λ γ ( , ) ψ ( )

σ

(4.14)

This variance is an important tool when analysing the fit of a model, if the variances of the predicted values tend to be too large there is a possible error in the choice of model for the variogram.

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4.6 Kriging using the IDRISI software

The three steps of Kriging are performed in IDRISI with simple pull down menus and sliders.

Since the area intended for interpolation with Kriging was to large (273*500 = 136500 values) for IDRISI to calculate a surface variogram (Processor XP2000+, 512MB RAM), it was split up into ten pieces that were modelled separately.

First step: The Spatial Dependence Modeler

Figure 4.6-1. Surface variogram (left) and three different variograms for DEM 10 (right). The variograms are calculated for different angles. . Green = 129°, Red = 39°, Black = omnidirectional. In omnidirectional mode Idrisi calculates the mean in every direction at each point in the variogram.

The surface variogram for “DEM 10” shows clear signs of zonal anisotropy. This is something we have to take into consideration when modelling the variogram.

Now we save the variogram and move on to step two.

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Second step: Model Fitting

After loading the variogram in the “Model Fitting” module, a model may be fitted.

Figure 4.6-2. Model fitting in Idrisi.

The continuous variance models available are:

• Spherical

• Exponential

• Gaussian

• Linear with sill

• Linear

• Power

• Logarithmic

• Circular

• Penta-spherical

• Bessel

• Periodic

Three structures may be combined with a nugget.

After fitting a model it is saved and moved to the next step, the Kriging interpolation.

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Step three: Kriging and Simulation

Now the model DEM can be selected together with a “mask” file for the DEM. The mask file is an indicator of which points that are to be Kriged. It simply has the same size as the DEM, but consists of binary one (1) where binary one means that the point is to be included in the Kriging process and zero that it wont.

Figure 4.6-3. Kriging in Idrisi

Pressing “OK” results in the DEM being kriged and the corresponding variances also being stored in a file.

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Figure 4.6-4. The original “DEM 10”, the kriged version and the variances.

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4.7 Model validation

A simple tool when validating the modelled variogram, instead of inspecting the Kriging variances, is the cross validation of sample locations. The cross validation calculates the Kriging estimates at points where the actual value is known. In this way the residuals can be computed as the actual height data minus the predicted.

Figure 4.7-1. Residuals of "DEM 10"

If the residual histogram of Figure 4.7-1 does not symmetrically fit around zero residual, the fitted variogram is biased and probably needs to be changed. Since ordinary Kriging is an exact interpolator, zero residuals are achieved for the values already known.

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4.8 Results

1 2

3 4

5 6

7 8

9 10

Figure 4.8-1. Surface pictures and histogram of the residuals for the ten pieces of the DEM

In Figure 4.8-2 we can see that DEM 1, 3, 7 and 9 hold relatively high Kriging variances. In Figure 4.8-1 the histograms of the residuals show strange behaviours for DEM 3, 7 and 9. This is caused by multiple underlying anisotropy structures (different covariance directions in different parts of the landscape).

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5 Input data preparation and editing the parameters with the input editor

Note: The following versions of the input editor were used: ArcView interface v2.3 and ArcView v3.2k.

5.1 Using the ArcView interface to generate the cell and reach input files

The ArcView interface is a helpful tool when creating the two input files for cell and reach data. It also contains links to tools such as VBFlownet, GEM, Input editor, AnnAGNPS and the output processor.

For a step-wise description of how the interface is used, see Appendix 10.2 Step by step usage of the ArcView interface is illustrated on page 46.

The sub-catchments of the Morsa watershed are calculated with the interface. These sub-catchments are overlaid on the soil and land-use GIS covers, and the dominating type of soil/field is calculated for each sub-catchment.

Figure 5.1-1. The subwatersheds with fields (left) and soils (right) intersected. In the middle the streamgrid between the cells is shown.

The middle picture of Figure 5.1-1 is a product of a program called VBFlownet that is supplied with the AGNPS package, it provides visual output of the parameters that are created with the ArcView interface. This can all be done within ArcView, but VBFlownet offers functions especially dedicated to this task. For instance, it is possible to click on a sub-catchment in order to see the streams within each cell. This is illustrated in Figure 5.1-2.

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Figure 5.1-2. Zooming in on a sub-catchment (from VBFlownet)

5.2 Using the input editor to edit the parameters of the AGNPS input file

The last phase of constructing the AGNPS model is carried out in the Input Editor. The files for reach data (ann_reach.csv), cell data (ann_cell.csv) and daily climate data (DayClim.inp) that were created in earlier steps are imported into the Input Editor. Here parameters for soils, fields, operations, crop types, simulation years etc are edited. In appendix 10.3 on page 49 the parameter groups that were used are briefly presented.

Figure 5.2-1. The Input Editor

At this stage the point sources for nutrient emission available for Kråkstadelva were added to the model. Point sources are, in large, housings with separate waste water drains. In Figure 5.2-2 these point sources are illustrated with red dots distributed across the watershed.

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There are six parameters in AGNPS for point sources.

Table 5.2-1. Input parameter for the point source data.

Parameter Description Point source identifier Point source name Point cell identifier Cell ID from cell data Point flow Flow in m³/ sec Point nitrogen unit ppm Point phosphorus unit ppm Point organic carbon unit ppm

The unit ppm, parts per million, is equal to µg/L for water solutions. The values for each cell were calculated with different spatial overlay functions in ArcView and manually edited into the AGNPS input file. The normal way to add point sources would be directly through the input editor, but in this case, with approximately hundred point sources, 100 dummy point sources were inserted with the input editor and thereafter manually edited with a standard text editor.

Figure 5.2-2. Point sources (housings) with sub- catchments in the background.

Figure 5.2-3. Required inputs for the AGNPS model.

In Figure 5.2-3 a flow chart is shown over the parameters of AGNPS. The orange fields are parameter groups that are required for simulation. At first the parameter groups are quite confusing but after

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6 Running AGNPS and creating the output files

6.1 Executing AGNPS

Note: Prior to this step, the input file was edited with the input editor and saved as “AnnAGNPS.inp”

in the folder “C:\AGNPS_Watershed_Studies\AGNPS_Arcview_Interface\7_AnnAGNPS_DataSets”.

The simulation program is easily executed with the ArcView interface command “PLModel / STEP 11 Execute AnnAgnps”. It works similar to a compiler in generating an error file when something is wrong with the input file. If there are no errors, simulation is performed. The log file of a typical AGNPS execution is added as an appendix on page 51.

6.2 Using the Output processor

The resulting files that are created when running AGNPS has to be processed before they can be read.

This is done with the Output Processor that is executed within the ArcView interface with the command “OutPross / Execute OutPut processing”. When running the output processor you get an option of creating GIS databases for the event outputs. These GIS databases can be merged with the subwatershed shape file in ArcView to show graphically which subwatersheds that contribute with high levels of discharges to the outlet. This is a perfect tool for visually presenting results from simulations. More analysis tools are currently being developed accomplishing the presentation of simulations.

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7 Calibration and simulation results

7.1 Calibration

The calibration of the AGNPS model is not required, but useful when verifying that the model is correctly adapted.

The AGNPS model is ideally calibrated with respect to 1. Hydrologic runoff

2. Sediment export 3. Solvent export

Although the estimated export of water, sediments and chemicals unlikely will be the same as the actual exports, certain statistical properties may be matched.

It was possible to acquire some observations of water quality variables, but only small quantities. On page 53 there is an illustration showing where the measurements were taken, the station "KRB2" is the one closest to the outlet of Kråkstadelva. There were no data available on sediment export.

7.2 Simulation results

0 5 10 15 20 25 30 35 40 45 50

1 2 3 4 5 6 7 8 9 10

Rainfall hm3 Runoff volume hm3

Figure 7.2-1. Total annual rainfall for the watershed and annual runoff volume at the watershed outlet.

The mean runoff from Kråkstadelva 1930-1960 was 24.72 hm³, in comparison with the simulated values of runoff in Figure 7.2-1 the AGNPS output seems correct. Note that the rainfall in the same figure is only summarized for the cells that produce runoff. This is quite obvious in Figure 7.2-2, where the "rainfall" values are lower during the summer. This is probably caused by increased

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evaporation during summer, which is reflected in decreased runoff from contributing cells, and in an increased number of cells that do not produce any runoff.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

January February

March April

May

June July August

September October

Nove mber

Dece mber

-4 -2 0 2 4 6 8 10 12 14 16 18 Runoff volume hm3

Rainfall hm3

Average Temperature

Figure 7.2-2. Monthly averages of rainfall, runoff volume and temperature (not an AGNPS output). Axis on the right is for the temperature time series.

0 500 1000 1500 2000 2500 3000

1 2 3 4 5 6 7 8 9 10

Sediment Total Mton Clay Mton

Silt Mton

Sand Mton

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There are many factors that have impact on the discharges of nutrients. For instance the organic content of Kråkstadelva soils are highly correlated with the discharges of phosphorus from the outlet.

The discharges of nitrogen are dependent on the levels of fertilizers applied in the agricultural fields.

0 50 100 150 200 250

1 2 3 4 5 6 7 8 9 10

Sol N MTon Sol P Mton

Figure 7.2-4. Yearly averages of solved nitrogen and phosphorous at the watershed outlet.

The values of estimated solute phosphorous are extremely high, at a first glance it seems like something is wrong with the model. Without claiming exact model parameters, these extreme values correspond with the hyper-eutrophic waters of Kråkstadelva. Unfortunately most of the reference values taken at various places in the watershed are measurements of total reactive phosphorous TRP, whereas available observations (from the reference point KRB2 on page 54) reflect the content of total phosphorous (with one observation only, from January 2001). The value is 1827 µgP/l, when

compared with the corresponding estimates of phosphorus discharge it can be seen that the average January estimate is two to three times higher then the observed value (Table 7.2-1).

Table 7.2-1. Values of phosphorous in January each simulation year.

Simulation

Year 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999

µgP/l 12540 6407 98273 21334 4478 6167 7832 10135 19555 5868

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0 5 10 15 20 25 30 35 40 45

1 2 3 4 5 6 7 8 9 10

Sed N MTon Sed P Mton

Figure 7.2-5. Sediment loads of nitrogen and phosphorous.

In Figure 7.2-5 the characteristics of Kråkstadelva again have high levels of phosphorous associated with the sediments. Due to its chemical properties, phosphorous is relatively easily bound to sediment particles as compared with nitrogen, thus the values of nitrogen in the sediments are lower.

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Figure 7.2-6. Ratios of discharges, sediments and runoff compared to the watershed outlet.

The discharges illustrated in Figure 7.2-6 are ratios relative to the watershed outlet (positioned at the most southern point in the pictures). Almost all sub-catchments contribute with fairly high values of runoff, which could be one reason for the high discharges observed in Kråkstadelva. There are few sub-catchments that offer retention for the nutrients carried through the landscape, and few natural lakes or ponds for de-nitrification and similar processes. The cells that contribute with most of the sediments are mainly positioned at higher altitudes. Since the slopes of these fields are steeper, the erosion tends to be higher.

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Figure 7.2-7. Elevation, fields and soils of the sub-catchments.

In Figure 7.2-76 and 7.2-7, where the sub-catchments are merged with GIS data, it is noticeable that croplands contribute with relative low sediment discharges. One factor contributing to the erosion of croplands is the amount annual disturbance. In this simulation, three disturbances have been chosen (crop, fertilize, harvest) which is low when compared with real life agriculture.

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8 Conclusions and general discussion

AGNPS is a splendid tool for watershed analysis. Different scenarios for how to minimize nutrient and sediment discharges may be simulated and analysed. This gives the user the advantage of immediate response as compared with real life experiments where several years must pass before results can be analysed. Risk analysis can be performed where, as an example, precipitation may be altered in order to study the associated effects on hydrologic runoff sizes and nutrient discharge. Researchers that work with minimization of discharges may use AGNPS as an assemblage of commonly used formulas and spatial models when catchment response is studied.

The disadvantage with catchment scale models like the AGNPS is the notorious demand for exclusive data. Although it is operable with rather simple GIS and meteorological data (either simulated or actual observations), it needs detailed knowledge on parameters like crops, soils and agricultural operations in order to behave correctly. The adaptation of the model requires a lot of work and high- level computer skills of the user. The quality of the AGNPS documentation is clearly below average standard, although it varies with the various parts (modules) of the program. Technical documentation only exists for the input editor. Since this (the input editor) is the "brain" of AGNPS, where all the parameters are entered and edited, it would do no harm with some guide for important parameters.

Using observed time series for the meteorological data causes problems. With time series normally being kept in some spreadsheet format like MS Excel, transforming such formats into the climate AGNPS input format (blank-space-separated text file) is very time consuming. One solution to this problem might be the development of an procedure for the input editor in which different common formats of spreadsheet files could be imported and converted to the correct format.

Although requiring generally large amounts of data, the favourable characteristics of the AGNPS model makes it an ideal tool for the landscape planner to utilize in minimising nutrient discharge at the catchment scale.

Advantages of AGNPS:

• Excellent for watershed analysis

Disadvantages of AGNPS:

• Requires large quantities of data

• Time consuming at the initial stages

• Poorly documented Recommendations

• Enhance the documentation for the input editor

• Add an import function to the input editor that simplifies the usage of time series kept in spreadsheet formats.

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9 References

Books

[1] Richard Webster, Margaret A. Oliver (2001). Geostatistics for Environmental Scientists.

John Wiley & Sons, LTD

[2] Hans Wackernagel (1998). Multivariate Geostatistics, 2^nd edition.

Springer

[3] Noel A. C. Cressie (1993). Statistics for spatial data.

John Wiley & sons, INC.

[4] Chris Chatfield (1996). The analysis of time series.

Chapman & Hall/CRC Compendiums

[5] Margaret A. Oliver, The Analysis of Spatial Data.

Reports

[6] Øivind Løvstad, Knut Bjørnskau, Siri Rønnevik (2001). Lokal, tiltaksrettet vannkvalitetsovervåkning i Ski kommune 2001.

Oslo 15.4.2002

[7] Knut Bjørnskau (2002). Kommunedelplan for vannmiljø Ski kommune.

[8] Lyche Solheim, A., Vagstad, N., Jraft, P.,Løvstad Ø., Skoglund S., Turtumøygard, S., Selvik, J.R., (2001). Tiltaksanalyse for Morsa.

NIVA-rapport nr. 4377-2001.

Websites

[9] The AGNPS website.

http://www.sedlab.olemiss.edu/agnps/main.html [10] Calculation of dew point temperature.

http://www.usatoday.com/weather/whumcalc.htm

Manuals that come with the AGNPS package

[11] TR55 (Urban Hydrology for Small Watersheds), Technical release 55, June 1986 [12] AnnAGNPS Version 3.2 Input File Specifications. Revision 17 September 2002.

[13] AH703 (Agriculture handbook number 703) , Predicting soil erosion by water: A guide to conservation planning with the revised universal soil loss equation.

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Briefings

[14] Arkansas - June 9, 1998.

[15] Lincoln, Nebraska - NSSC - January 1, 1999 [16] Maine - East Region STC - January 14, 1999 [17] Louisiana - March 23, 1999

[18] Kansas - April 7, 1999

[19] Pamplona, Spain - September 23, 2002 (File Size - 82MB)

All downloadable from http://www.sedlab.olemiss.edu/agnps/Presentations.html Workshops

[20] Oxford, Mississippi - October 26-30, 1998

[21] Portland, Oregon - February 22-26, 1999 (24 MB) [22] Baton Rouge, Louisiana - June 14-18, 1999 (115 MB) [23] Monterey, California - September 13-17, 1999 [24] Columbus, Ohio - October 21-25, 2002 (48 MB)

All downloadable from http://www.sedlab.olemiss.edu/agnps/Presentations.html

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10 Appendixes

10.1 Glossary

AGNPS (Agricultural Non-Point Source Pollution Model)

A tool for use in evaluating the effect of management decisions impacting a watershed system.

AnnAGNPS

Annualised AGNPS. Simulations are calculated on a day-by-day basis. Commonly referenced as AGNPS.

AGNPS / ArcView interface

Interface developed for usage within ArcView to run AGNPS.

ArcView

A commonly used GIS program. (see GIS) Eutrophication

Eutrophication is the enrichment of watercourses with biogenous substances. Water transparency is reduced, the production of organic substances increases, sedimentation increases, oxygen

concentration decreases, composition of species changes (perennial algae are replaced by annuals, such as blue-green algae and green algae, the composition of benthic species is depleted, the food base for fish changes and correspondingly so does the composition of fish species), and rapid choking of water courses with vegetation takes place.

GIS (Geographic information system)

In short terms a GIS combines layers of information to give you a better understanding of that place. A GIS can be used in a wide range of areas.

Interpolation

To estimate missing values.

Kriging

A commonly used interpolation method in geostatistics.

Stationarity

Treating single realizations of random processes as random variables requires assumptions of stationarity. Second order stationarity implies that the mean and variance of the random process are constant and do not depend on position, the covariance exists and depends only on the lag and not the position.

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10.2 Step by step usage of the ArcView interface

Note: The following versions were used, ArcView interface v2.3 and ArcView v3.2k.

Supplied with the AGNPS package is a step by step usage guide to the ArcView interface. In this section these steps are shown and commented.

Step 1: Pre-processing the DEM

The first command that is used is found under the menu ”Dem pre-processing utilities/process dem”.

This estimates a streamgrid of the watershed. The streamgrid is then used to select a watershed outlet in the next step.

There is one option when performing this step, ”Number of cells to initiate a stream” the default value of 10000 works ok.

Step 2: Choose the outlet of the watershed

In this step we select the outlet of our watershed. Command ”dem processing utilities / deliniate watershed”

Figure 10.2-1. Picture of step 2. The watershed outlet selected (Kråkstadelva).

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Figure 10.2-2. Step 2: Before and after.

Step 3: Define which themes that are used for dem, soil and field data

The command is found under the menu ”data prep / assign themes”. The trick in this step was switching from the tinned DEM to the smaller kriged DEM of Kråkstadelva.

Step 4: Cut the DEM

With the bound theme active select the area with the rectangle select tool and then execute ”data prep / Step 1 Clip dem”. A new theme with the default name DEM_SUBSET is created and added to the view.

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Step 5: Choose the desired output of the watershed

With the stream grid active zoom to your desired watershed outlet and the execute the command ”data prep / Step 2 select watershed outlet” and click on the streamgrid at the desired output.

Step 6: Run Steps 3, 4, 5 and 6 under dataprep

Execute "Step 3: Create TopAGNPS input files", "Step 4: Execute TopAGNPS", "Step 5: Execute AGFlow" and "Step 6: Import TopAGNPS *.arc files" under the dataprep menu. In step 3 you get an option to change the values of MSCL and CSL values. Critical Source Area (CSL) is the minimum upstream drainage area below which a source channel is initiated and maintained. Minimum Source Channel Length (MSCL) is the minimum acceptable length for source channels to exist. I used the default values for these parameters.

Figure 10.2-4. The network of streams and the subwatersheds.

Step 7 and 8: Intersect soils and field data with the subwatersheds

The most dominating soils and fields are automatically calculated for each subwatershed.

Step 9: Create the cell and reach input data for the input editor

Execute "Data Prep / Step 9: Extract cell and reach data" and the cell and reach input data are created in the specified folder from "Step 6: Import TopAGNPS *.arc files".

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10.3 The parameter groups of the input editor

In this appendix the parameter groups that I used are briefly commented.

Parameter group: AnnAGNPS Identifier

In this group the input and output unit is selected, in our case this is SI (metric). You also specify the name of the watershed and its coordinates (longitude, latitude).

Parameter group: Cell data

The cell data input parameters were generated with the ArcView interface. The input editor has an option to "import cell data from ArcView".

Parameter group: Daily climate data

The daily climate data file was generated in chapter 3. As with the cell data the daily climate data is imported into the input editor.

Parameter group: Crop Data

In this group the characteristics of the crops used in the fields is specified.

Parameter group: Fertilizer / Fertilizer application data

Here you specify how much fertilizer that is spread in the selected fields. The “fertilizer rate” is specified in kg / hectacre.

Parameter group: Fertilizer / Fertilzier reference data Details about the fertilizer types are specified here.

Parameter group: Field data / Field data

This is where you specify what the fields are used for:

The different types are:

• Cropland

• Pasture

• Rangeland

• Forest

• Urban

Parameter group: Field data / Field management data

Here you specify what operations are carried out in the different fields.

Parameter group: Operations data / Operations data Specifies which operations that are carried out in the fields.

Parameter group: Operations data / Operations reference data In this parameter group the operations are defined in detail.

Parameter group: Output options

Different options for the output processor are specified here. An important setting is the one to calculate the data only for the outlet and not for all reaches. The output text files are much easier to interpret in this way.

Parameter group: Point source data Point sources of any type are entered here.

Adaption of the Agricultural Non-point Source Pollution Model to the Morsa Watershed

Adaptation of the Agricultural Non-point Source Pollution Model to the Morsa Watershed

Abstract

Contents

1 Introduction

1.1 The Agricultural Non-Point Source Pollution Model

1.2 What types of watersheds are appropriate for an AGNPS model?

2 Adapting the GIS data for AGNPS application

2.1 DEM

2.2 Soils

2.3 Fields

3 Adapting weather data to AGNPS

3.1 Weather data

3.2 Preparation of daily precipitation data

3.3 Preparation of dew point temperature data

S

X = + ε

t = 1 ,.... 4750

ε

∈ WN ( 0 , σ

)

ε

= X

− X

ε ˆ

t = 2 ,.... 4750

ε ˆ

)) 7 . 237 /(

) 5 . 7 ((

^ 0 . 10 11 .

6 Tc Tc

Es = ⋅ ⋅ +

100 / ) ( RH Es

E = ⋅

08 . 19 ) ln(

) ln(

7 . 237 22 . 430

+

−

⋅ +

= −

E Td E

E

RH

3.4 Preparation of sky cover data

3.5 Creating the daily climate input file DayClim.imp

4 Kriging

4.1 About Kriging

λ

4.2 Estimation of the variogram

Z

)]

( ) ( [ )

( h E x x h

C = ε ε +

0 )]

( ) (

[ Z x − Z x + h =

E

{ ( ) ( ) } ] 2 ( ) [

)]

( ) (

var[ Z x − Z x + h = E Z x − Z x + h

= γ h

{ ( ) ( ) }

2 ) 1 ,

( x

x

= z x

− z x

γ

{ }

[ ( ) ( )

]

2 ) 1

( h = Ε Z x − Z x + h

γ

{ }

[ ( ) ( )

]

{ ⁽ ⁾ ⁽ ⁾ }

[ ⁽ ⁾ ⁽ ⁾

[ ⁽ ⁾ ⁽ ⁾