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.TXT 2 1 72 0 0
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\fonttbl{\f0\fcharset0\fnil Times New Roman;}}\plain\cf1\fs20 \pard {
\cf2\fs28\b B2.  Philip's Two-Term Model (PHILIP2T) }}
.ATT
.ATT_END
.ATT
.LINK file:C:\REVIEW\FRONT.MCD
.ATT_END
.TXT 4 -1 2 0 0
Cg a72.000000,72.000000,16
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;\red64\green0\blue64;}{
\fonttbl{\f0\fcharset0\fnil Times New Roman;}}\plain\cf1\fs20 \pard {
\cf2\b   A. Description}}
.TXT 4 3 208 0 0
Cg a71.000000,71.000000,826
{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;\red64\green0\blue64;}{
\fonttbl{\f0\fcharset0\fnil Times New Roman;}}\plain\cf1\fs20 \pard {
\cf2\b The Philip's two-term model (PHILIP2T) is a truncated form of 
the power series solution of Philip (1957).  During the initial stages 
of infiltration, }{\cf2\b\i i.e.}{\cf2\b , when }{\cf2\b\i t}{\cf2\b  
is very small, the first term of Equation 1 below dominates.  In this 
stage the vertical infiltration proceeds at almost  the same rate as 
absorption or horizontal infiltration, because the gravity component, 
represented by the second terms of Equation 1, is negligible.  As 
infiltration continues, the second term becomes progressively more 
important until it dominates the infiltration process.  Philips (1957) 
suggested the use of the two-term model in applied hydrology when }{
\cf2\b\i t}{\cf2\b  is not too large.   A scenario was chosen to 
simulate the water infiltration into a sandy soil by using the 
PHILIP2T model.  Input parameters and simulation results were given below.}}
.TXT 18 -2 49 0 0
Cg a71.000000,71.000000,27
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\fonttbl{\f0\fcharset0\fnil Times New Roman;}}\plain\cf1\fs20 \pard {
\cf2\b B.  Definition of Variables}}
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{0:t}NAME:1;24
.TXT 0 20 6 0 0
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\cf2\b Duration of infiltration (h)}}
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\fonttbl{\f0\fcharset0\fnil Times New Roman;}{\f1\fcharset2\fnil Symbol;}}
\plain\cf1\fs20 \pard {\cf2\b The sorptivity of a soil defined by}{\cf2
\b\i  S = I/(t)}{\cf2\fs16\b\i\up 1/2}{\cf2\b\i  (cm/h}{\cf2\fs16\b\i
\up 1/2}{\cf2\b\i ) }{\cf2\b for the horizontal infiltration and is a 
function of the boundary and initial water contents }{\cf2\f1\b\i Q}{
\cf2\f1\fs16\b\i\dn 0}{\cf2\b  and saturated water content }{\cf2\f1\b
\i Q}{\cf2\fs16\b\i\dn s}{\cf2\fs16\b\dn  }{\cf2\b (Philip, 1969)  }}
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Cg a50.000000,50.000000,39
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\fonttbl{\f0\fcharset0\fnil Times New Roman;}}\plain\cf1\fs20 \pard {
\cf2\b Saturated hydraulic conductivity (cm/h)}}
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{0:A}NAME:0.363*{0:K.s}NAME
.TXT 0 20 12 0 0
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\cf2\b A constant in Equation 3 (cm/h)}}
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\cf2\b C.  Equations}}
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs20 \pard {\b Infiltration rate}}
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\cf2\b (1)}}
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs20 \pard {\b Cumulative infiltration}}
.TXT 0 54 199 0 0
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\cf2\b (2)}}
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0 1 1 21 15 10 0 2 
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\fonttbl{\f0\fcharset0\fnil Times New Roman;}}\plain\cf1\fs20 \pard {
\cf2\b D.  Results}}
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\cf2\b Figure B2-1.  Surface infiltration as a function of time. }}
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0 1 1 21 15 10 0 2 
.TXT 26 2 75 0 0
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\cf2\b Figure B2-2.  Cumulative Infiltration as a function of time.}}
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;\red64\green0\blue64;}{
\fonttbl{\f0\fcharset0\fnil Times New Roman;}}\plain\cf1\fs20 \pard {
\cf2\b E.  Discussion}}
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;\red64\green0\blue64;}{
\fonttbl{\f0\fcharset0\fnil Times New Roman;}}\plain\cf1\fs20 \pard {
\cf2\b Figure B2-1 shows a typical soil infiltration pattern, with an 
infiltration rate relatively high at the onset of the infiltration, 
then decreasing, and eventually approaching a constant rate}{\cf2\b .   
The infiltration rate decreased by about 4% within the first 5 hours, 
then the infiltration rate decreased by 1.4% }{\cf2\b from from  5 to 
20 hours,}{\cf2\b  and finally decreased to  0.1% from 20 to 24 hours.   
Figure B2-2 illustrates that the cumulative infiltration increased 
with time.    This occurred because more water accumulated in the soil 
as the time increase.}}
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;\red64\green0\blue64;}{
\fonttbl{\f0\fcharset0\fnil Times New Roman;}}\plain\cf1\fs20 \pard {
\cf2\b F.  Sensitivity and Relative Sensitivity of Infiltration Rate 
to the Sorptivity of Soil}}
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;}{\fonttbl{\f0\fcharset0
\fnil Times New Roman;}}\plain\cf1\fs20 \pard {\b   A sensitivity 
analysis is an estimation for how important an input parameter is to 
affecting the simulation results.   Mathematically the sensitivity 
coefficient, }{\b\i S}{\b\i\dn s}{\b , is defined as:\par \par                
                  S}{\b\dn s}{\b  =df/dx                                      
                                            \tab \tab \tab (3)                
                                                            \tab \tab 
\tab                    \par   where }{\b\i f}{\b  represents the 
output of interest and}{\b\i  x }{\b represents the input parameter 
(McCuen, 1973).  The value of }{\b\i S}{\b\i\dn s}{\b        
calculated from this equation has units associated with it.  This make 
it difficult to compare sensitivities for              different input 
parameters.  This problem can be overcome by using the relative 
sensitivity, }{\b  }{\b\i S}{\b\i\dn r}{\b , given by\par \par                
                     S}{\b\dn r}{\b  = S (x/f)                                
                                             \tab \tab \tab (4)\par 
\par   The relative sensitivity }{\b\i  S}{\b\i\dn r}{\b  gives the 
percentage change in response for each one percent change in the input        
      parameter.  If the absolute value of }{\b\i  S}{\b\i\dn r}{\b  
is greater than}{\b\i  1}{\b , the absolute value of the relative 
change in model output       will be greater than the absolute value 
of the relative change in input parameter.  If the absolute value of }{
\b\i  S}{\b\i\dn r}{\b  is less   than }{\b\i 1}{\b , the absolute 
value of the relative change in model output will be less than the 
absolute value of the relative     change in input (Nofziger }{\b\i et al.,}{
\b  1994).\par }}
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\fonttbl{\f0\fcharset0\fnil Times New Roman;}}\plain\cf1\fs20 \pard {
\cf2\b This section shows the sensitivity, }{\cf2\b\i S}{\cf2\fs16\b\i
\dn s}{\cf2\b , and the relative sensitivity, }{\cf2\b S}{\cf2\fs16\b
\dn r}{\cf2\b , of the surface infiltration rate,}{\cf2\b\i  q}{\cf2\b 
, to the sorptivity of a soil, }{\cf2\b\i S}{\cf2\b .  The expressions 
were obtained by applying Equations 3 and 4  to Equation 1 .}}
.TXT 10 -1 268 0 0
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\fonttbl{\f0\fcharset0\fnil Times New Roman;}}\plain\cf1\fs20 \pard {
\cf2\b F.1.  Input Data}}
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.TXT 4 -18 241 0 0
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\fonttbl{\f0\fcharset0\fnil Times New Roman;}}\plain\cf1\fs20 \pard {
\cf2\b F.2. Sensitivity}}
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\fonttbl{\f0\fcharset0\fnil Times New Roman;}}\plain\cf1\fs20 \pard {
\cf2\b (5)}}
.TXT 7 -69 244 0 0
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\fonttbl{\f0\fcharset0\fnil Times New Roman;}}\plain\cf1\fs20 \pard {
\cf2\b F.3. Relative Sensitivity}}
.TXT 5 69 249 0 0
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\cf2\b (6)}}
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{0:S.r}NAME({0:S}NAME):({0:S}NAME*({0:t}NAME)^(-((1)/(2))))/(({0:S}NAME*(({0:t}NAME)^(-((1)/(2))))+2*{0:A}NAME))
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0 0 1 1 1 0 0 1 1 Sorptivity 
0 0 1 1 1 0 0 1 1 Sensitivity of infiltration rate
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
0 2 5 0 1 1 NO-TRACE-STRING
0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
0 4 1 0 1 1 NO-TRACE-STRING
0 1 1 21 15 10 0 2 
.TXT 1 -36 247 0 0
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\cf2\b F.4. Results}}
.EQN 5 3 251 0 0
{0:S}NAME=
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\cf2\b Figure B2-3. Sensitivity of infiltration rate for different 
values of sorptivity of the soil at }{\cf2\b\i t = 5 h}{\cf2\b .}}
.EQN 6 0 255 0 0
&&(_n_u_l_l_&_n_u_l_l_)&{0:S.r}NAME({0:S}NAME)@&&(_n_u_l_l_&_n_u_l_l_)&{0:S}NAME
0 0 1 1 1 0 0 1 1 Soprtivity 
0 0 1 1 1 0 0 1 1 Relative sensitivity of infiltr. rate
0 1 0 0 1 1 NO-TRACE-STRING
0 2 1 0 1 1 NO-TRACE-STRING
0 3 2 0 1 1 NO-TRACE-STRING
0 4 3 0 1 1 NO-TRACE-STRING
0 1 4 0 1 1 NO-TRACE-STRING
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0 3 6 0 1 1 NO-TRACE-STRING
0 4 0 0 1 1 NO-TRACE-STRING
0 1 1 0 1 1 NO-TRACE-STRING
0 2 2 0 1 1 NO-TRACE-STRING
0 3 3 0 1 1 NO-TRACE-STRING
0 4 4 0 1 1 NO-TRACE-STRING
0 1 5 0 1 1 NO-TRACE-STRING
0 2 6 0 1 1 NO-TRACE-STRING
0 3 0 0 1 1 NO-TRACE-STRING
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0 1 1 21 15 10 0 2 
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\cf2\b Figure B2-4.  Relative sensitivity of infiltration rate for 
different values of sorptivity of the soil at }{\cf2\b\i t = 5 h}{\cf2
\b .}}
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\cf2\b F.5. Discussion}}
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{\rtf\ansi \deff0{\colortbl;\red0\green0\blue0;\red64\green0\blue64;}{
\fonttbl{\f0\fcharset0\fnil Times New Roman;}}\plain\cf1\fs20 \pard {
\cf2\b Figure B2-3 shows a sensitivity of the infiltration rate for 
different values of sorptivity of a soil,  which has a constant value 
of }{\cf2\b\i 0.224}{\cf2\b  for all sorptivities of the soil at }{\cf2
\b\i t = 5 h}{\cf2\b .  This implies that a 10-fold increase in 
sorptivity will have a 2.24-fold increase in infiltration rate.   
Figure B2-4 shows the relative sensitivity of infiltration rate for 
different values of sorptivity of the soil.  The relative sensitivity 
increased as the sorptivity of the soil increased. }}