Study on scaling property of Topindex anStudy on scaling property of Topindex and the aquifer rating-curve d the aquifer rating-curve in Illinois with tin Illinois with t

he application of TopModelhe application of TopModel

CE394K Term Project PresentationCE394K Term Project Presentation

Hua SuHua Su

Outline:Outline: IntroductionIntroduction Basic concept of Topmodel and physical inBasic concept of Topmodel and physical in

terpretation of relationship between Topindeterpretation of relationship between Topindex and groundwater discharge and water tablx and groundwater discharge and water table;e;

Scaling property of Topindex in Illinois region;Scaling property of Topindex in Illinois region; The observational groundwater rating curve The observational groundwater rating curve

and exponential function fitting in Illinoisand exponential function fitting in Illinois Examine the Topmodel’s assumption on veExamine the Topmodel’s assumption on ve

rtical variation of soil hydraulic transmissivitrtical variation of soil hydraulic transmissivity y

DiscussionDiscussion

Introduction Introduction Water cycle is an integraWater cycle is an integra

ted system based on Hydted system based on Hydrology-Geomorphology-rology-Geomorphology-Climatology;Climatology;

Topmodel describes the iTopmodel describes the interaction between Topnteraction between Topography and hydrologic ography and hydrologic process and the Topindeprocess and the Topindex is a Key variable when ax is a Key variable when applying Topmodel; pplying Topmodel;

Analyzing spatial pattern Analyzing spatial pattern of Topindex and the perfof Topindex and the performance of Topmdel basormance of Topmdel based on examing its assumed on examing its assumption are objective in this ption are objective in this project project

Upslope contributing

area a

Stream line

Contour line

Water balance and Darcy function in subsurface

q=a*r=T0*exp(-fZ)*tanB(Beven,1978; Sivapalan,1990)

r a

tgB

r

q=a*r

Definition of Topindex ——Ln[a/tg(B)]Variable determined only by Topography

Basic Concept of TopmodelBasic Concept of Topmodel

For given recharge rate r and soil hydraulic For given recharge rate r and soil hydraulic conductivity, in equation (1) the Topindex hconductivity, in equation (1) the Topindex has a linear relationship with the water table as a linear relationship with the water table depth; That means the topography becomedepth; That means the topography becomes a major factor controlling the groundwates a major factor controlling the groundwater storage at local scale when aquifer is wet;r storage at local scale when aquifer is wet;

Local water table depth as a function of TopindexLocal water table depth as a function of Topindex

Z=-1/f*[Ln(r/T0)+Ln(a/tg(B))] (1)Z=-1/f*[Ln(r/T0)+Ln(a/tg(B))] (1)

Scaling property of Topindex in Illinois

The Log-Log relationship between the spatial Variance of Topindex and the spatial resolution (the area of grid scale) of the Topindex in Illinois;

The figure shows the Topindex is not scaling invariant. When the spatial scale increase, the variance of Topindex increase.

The Topmodel provide a scheme to estiThe Topmodel provide a scheme to estimate the aquifer groundwater dischargmate the aquifer groundwater discharge based on the spatial mean value of we based on the spatial mean value of water table. ater table.

Q=Qo*exp[-f*Z(mean)] (2)

——Aquifer rating curve

T=T0*exp(-f*Z)

Here f is assumed to be the parameter to describe the exponential relationship between soil transmissivity and soil depth.

Test this assumption of Topmodel

Use observation data to fit the exponential style of aquifer rating-curve and estimate f1;

Using soil data to fit the exponential style of the soil transmissivity and estimate f2

Compare f1 and f2

Champaignf=2.468

Fayettef=2.611

Greenef=1.08

Henryf=0.808

Randolphf=0.338

Using monthly streamflow data and water table data in the 5 locations in Illinois to fit the exponential function of the rating curve;

Streamflow data is from USGS and the water table data is from Illinois State Water Survey

Randol ph

y = 15. 905e- 0. 3381x

R = 0. 561

0

5

10

15

20

25

30

35

0 0. 5 1 1. 5 2 2. 5 3 3. 5 4Water Tabl e

Stre

amfl

ow(m

m/mo

nth)

Greene

y = 252. 69e- 1. 0841x

R = 0. 832

0

50

100

150

200

250

0 1 2 3 4 5 6 7Water Tabl e

Stre

amfl

ow(m

m/mo

nth)

  Fitted f value in aquifer rating curve(f1) Correlation R

Champaign 2.46 0.618

Fayette 2.61 0.660

Greene 1.08 0.832

Henry 0.80 0.832

Randolph 0.33 0.561

The exponential style of vertical variation for soil hydraulic transmissivity is fitted by soil data from STATSGO.

• STATSGO is the short name for “Soil maps for the State Soil Geographic (STATSGO)” database.

• It provides comprehensive soil information including the SSC percent, soil hydraulic conductivity and soil layer thickness in each state with polygon format and dbf format which are readable by GIS.

• The spatial resolution of STATSGO is limited so we can only get the soil hydraulic transmissivity in an area which is around or include the test location and get an approximate parameter in the exponential curve estimation on that location.

T(Zi)=T0*exp(-f*Zi) (3)

Method

Zi: The thickness of soil in each soil layer

T(Zi): The total transmissivity from Zi to the immpermiable rock

Zi and T(Zi) can be derived from STATSGO dataset

Using nonlinear optimization to get f and T0 in equation(3)

  Fitted f value from STATSGO soil data f2

Champaign 0.16

Fayette 2.76

Greene 0.98

Henry 0.21

Randolph 0.027

 

Fitted f value from aquifer rating curve(f1)

from STATSGO soil data f2

Champaign 2.56 0.16

Fayette 2.61 2.76

Greene 1.08 0.98

Henry 0.80 0.21

Randolph 0.33 0.027

1. The aquifer rating curve in the test Illinois can be estimated 1. The aquifer rating curve in the test Illinois can be estimated by exponential function, which is widely used in Topmodel by exponential function, which is widely used in Topmodel and other model to simulate the groundwater discharge; and other model to simulate the groundwater discharge;

2. Topmodel assume that the exponential factor f in the ratin2. Topmodel assume that the exponential factor f in the rating curve is caused by the soil hydraulic transmissivity has exg curve is caused by the soil hydraulic transmissivity has exponential relationship with the soil thickness; while our tesponential relationship with the soil thickness; while our test shows that this assumption seems not to be reasonable at shows that this assumption seems not to be reasonable at some locations of Illinois. t some locations of Illinois.

3. The exponential factor f2 computed with STATSGO data ne3. The exponential factor f2 computed with STATSGO data need improved since the STATSGO data has limited resolutioed improved since the STATSGO data has limited resolution. n.

Conclusion and Discussion