1 

## Appendix 2

- A . SAM Model Component Conceptualizations

1. Scenario Generator : Conceptualization and Calculations
The Scenario Generator calculates the daily hydrology, erosion, and plant growth stages that are necessary for use in the subsequent Super PRZM Hydro and Pesticide Transport and Water Body Concentration Calculator. Table 1 lists the key input parameters t hat are calculated for each scenario (sub

- watershed) by the Scenario Generator. Table 1. Scenario Generator: parameters and definitions.

Parameter Definition

covmax Maximum areal coverage of crop canopy (%) num_records Total number of days in simulation (d)
numberOfYears Total number of years in simulation (yr)
Runoff Daily runoff calculated from precipitation, where infiltrating water and surface runoff are distinguished according to USDA NRCS Curve Number (CN) method; only stored for days with runoff > 0 (m)

Erosion Daily erosion loss calculated using MUSS, which includes a peak storm runoff calculation based on the Graphical Peak Discharge Method (USDA NRCS, 1986, 2008b) (kg)

Soil water Daily water content of each soil compartment (m) Velocity Daily infiltration velocity in soil compartment (leaching), only stored for days with velocity > 0 (m) Organic carbon Soil organic carbon content (%) Bulk density Soil bulk density (kg/m 3 )
Delta x Vector of incremental depths of each soil compartment (m )

Rain Daily effective rainfall from meteorology file when temperature > 0°C (m)
Plant factor Daily fraction of plant growth, from emergence (plant factor = 0) to maturity (plant factor = 1)2 

### Plant Growth
Plant growth is independen t of any process in the model , and is pre

- calculated and placed into each scenario file. Plant stages must be retained as they can affect pesticide transport, beyond their influence on hydrology. Plants can retain pesticide as a function of their size, and pesticide applic ation timing can also be a function of plant size. The timing of plant stages, which varies spatially, is also critical in defining the pesticide application window.
As Figure 1 shows, plant size (root depth and areal coverage) is a function that increases in direct proportion with time between the date of plant emergence and the date of plant maturity (linear growth), and remains constant from mat urity to harvest. In the test version of the Scenario Generator, Emergence is 7 days after the planting date, which is an approximate time for germination and surface breakthrough. Maturity occurs at the midpoint between the input planting and harvest dates. The following equations determine the fraction of plant growth in the Scenario Generator:

H H M M E E M E E



### T t t G T t T t G T t T T T T

t t G T t t G

> = < < = < <      

− − = < =

0 ) ( 1

) ( ) ( 0

) (

Where G(t) = the fractional growth

T E = time of emergence

T M = time of plant maturity

T H = time of plant harvest In recent refinements, the plant ing , emergence, maturity, and harvest dates have been updated for consistency with state

- level (or crop reporting district

- level) Crop Progress Reports and Growing Degree Days models

. Section 4 describes the methodology for incorporating more detailed plant growth information, which in turn influences application timing. The growth of plants impacts two parameters

— canopy coverage and root depth. Canopy coverage can affect foliar applications of pesticides. The canopy also captures some precipitation. The quantity that it captures is directly proportional to the growth stage. In the model, root depth affects the soil depth that is involved in satisfying the evapotranspiration demand. The maximum root depths and the maximum canopy coverage were estimated ei ther from study information or from typical values for crops. Root depth and canopy coverage as a function of time are described by the following: 

## ) ( ) (
max 

## t G R t D root 

## =

and3 

### ) ( ) (
max , 

### t G C t C p

p 

### =

Where D root (t) = root depth at time t, [L]

R max = maximum root depth, [L]

C p (t) = fractional canopy coverage at a time t, [

— ]

C p , max = maximum fractional canopy coverage, [

— ]



### Meteorological Data Processing

After the Scenario Generat or reads in the daily meteorological data (see Section 3.3 ), precipitation is classified as either snow or rain, based on the air temperature. Snow is assumed to occur for any precipitation event that occurs at temperatures of 0°C (or below) and accumulat es on the ground surface until temperatures rise above 0°C. On a daily basis, snow accumulation melts as a function of temperature according to the following:


## T F P melt

melt 

## =

Where P melt = daily snowmelt (daily vector), [L]

F melt = snowmelt factor (scalar) [L /°C] 0 0.2 0.4 0.6 0.8

1 1.2

0 200 400 600 800 DaysFractional Growth

emergence emergence maturity maturity harvest harvest

Figure 1. Depiction of the plant growth factor varying over time.4 T = temperature (daily vector) [°C] The snowmelt is treated as water input to the top soil layer via leaching, as described later. The entire precipitation and snowmelt dataset is processed in this manner and stored in an array. Because rain and snowmelt are treated identically, they are added together and stored for later use in the program:

melt rain melt rain 

## P P P + = /
Where P rain = precipitation falling as rain (daily vector) [m]

P rain/m e lt = the sum of rain and snowmel t production (daily vector) [m] Pan evaporation is converted to potential evapotranspiration by use of a pan factor:

pan pan t 

### E F E =

Where F pan = pan factor (scalar)

E t = potential evapotranspiration (daily vector), [m]

E pan = pan evaporation (daily vector), [m] 

### Irrigation
At the start of each simulated day, the Scenario Generator determines whether irrigation is required (if the irrigation flag has been turned on). For irrigation on demand, an irrigation depth is specified, which is the depth beneath the surface to which a water demand is applied. Along with this irrigation depth, an available water fraction below which irrigation is required is also specified by the user. With these inputs along with the soil property inp uts of field capacity and wilting point, a target dryness is determined, which represents the amount of water in the irrigation zone below which irrigation should be applied: 

## ( ) 

# [ ] { } 

# ∑

= 

### ∆ +

− = irr

D

i i i irr i i et t 

### x WP F WP FC W

1 arg

Where W target = the target dryness within the irrigation zone, [m] FC = field capacity WP = wilting point

F irr = fraction of available water below which irrigation is desired

D irr = irrigation depth [m] This irrigation water is applied either overhead in which it can interact with the canopy, or below the
canopy . Both irrigation types are treated in the same way as precipitation. The different effects that the two irrigation methods have on the canopy are considered in the canopy water accounting described later. Irrigation water is added to the P rain/melt vect or:

irrig melt rain irrig melt rain 

### P P P + = / / /5 

### Runoff
The Curve Number (CN) method (USDA NRCS, 2008a) is used to partition precipitation (including irrigation and snowmelt) into runoff or leaching as follows: 

# ( ) ( ) ) ( ) ( / / 2 ) ( ) ( / / ) ( 

### 8

. 0 2

. 0

i i irrig melt rain i i irrig melt rain i R 

### S P S P Q + −
= for 

## ) ( 2

. 0 ) ( / 

## i S i P melt

rain 

## >

0 ) ( 

### = i R 

### Q for 

### ) ( 2

. 0 ) ( / 

### i S i P melt

rain 

### ≤

Where S ( i ) = CN method’s maximum potential retention on day i , [m]
Q R ( i ) = runoff on day i , [m] The amount of water that is held on the canopy is determined after runoff is calculated. Therefore, the

amoun t of water held in the canopy should not affect the amount of calculated runoff. In this canopy calculation (consistent with the CN method), if there is available water from an over

- canopy source and if there is leftover water after considering runoff, th en that remaining water is considered to have been available for canopy holdup. To determine the amount available for holdup, it is assumed that the source of runoff (whether it is snowmelt, rain, or irrigation) is equally effective at producing runoff a nd therefore its contribution to runoff is proportional to its relative volume. With this assumption, the amount of water that is available to the canopy for holdup, which can come only from over

- canopy sources, is: 

# ( )        

− + = ) ( / / ) ( ) ( ) ( ) ( 

### 1 i irrig melt rain i R i

oc i rain i g 

### P Q I P W

Where W g ( i ) = available water for canopy holdup gain, [m]

I oc ( i ) = over

- canopy irrigation, [m] The amount of water that is actually gained by the canopy is: 

# ( ) 

# [ ] ) 1 ( ) ( ) ( ) (



### , min −



### − = ∆ i

c i
c,max i g i

c 

### W W W W

Where Δ W c ( i ) = the amount of precipitation that is held up in the canopy on day i [m] , and W c ,max ( i ) is the maximum water that the canopy can hold up on day i as defined by:

) (

max ) (

max , i
p i

c 

### C W W =

Where W max is the maximum canopy storage at full canopy coverage, [m]. The daily canopy water content can then be determined from: ( ) ) ( 1 i

c i h i h 

### W W W ∆ + = −6 The amount of water available for input into the top soil layer is:

) ( ) ( ) ( / / ) ( i C i R i irrig melt rain i 

### W Q P L ∆

− − = Where L = leaching, or the amount of water that enters the top soil layer (daily vector) [m].


### Erosion
The MUSS erosion equation (Carousel et al

. , 2005) is used in the Scenario Generator as a method for estimating soil erosion loss on a per field basis, based on the original USDA Universal Soil Loss Equation (USLE). Using MUSS maintains consistency with PRZM5 and previous regulatory assessments . The MUSS erosion model is formulated as:

XX ee = 0

. 79 � VV rr qq pp � 0

. 65 AA 0

. 009 KK ( LLLL ) CCCC

where X e = t he event soil loss (metric ton s day

- 1 )

V

r = volume of event (daily) runoff (mm)

q p = peak storm runoff (mm/h)

A = field size (h A )

K = soil erod i bility factor (dimensionless)

LS = length

- slope factor (dimensionless)

C = soil cover factor (dimensionless)

P = conservation practice factor (dimensionless) The p eak storm runoff value ( q p ) is calculated using the Graphical Peak Discharge Method as described in USDA NR CS (1986 , 2008b ).

qq pp = qq uu AA QQ FF pp where q p = peak storm runoff (ft 3 /s)

q u = unit peak discharge (csm/in) A = drainage area (mi 2 ) Q = runoff (in)

F

p = pond or swamp adjustment factor For areas without swamps or ponds, F p is equal to 1.0 (default in PRZM5 and Scenario Generator). The unit peak discharge is calculated by USDA NRCS (1986 , 2008b ) as follows : log ( qq uu ) = CC 0 + CC 1 log ( TT cc ) + CC 2 [ log ( TT cc ) ] 2

where T c = time of concentration (hr)

C 0 , C 1 , C 2 = coefficients from USDA NRCS (1986 , 2008b ), g iven in Table 2 below7 R ainfall intensity is assumed to occur according to design storm distributions (Type I, IA, II, and III) as given by USDA NRCS (1986).

Table 2. Coefficients for the unit peak discharge equation (NRCS, 1986).

Rainfall Type Ia/P C 0 C 1 C 2

I 0.10 2.30550

- 0.51429

- 0.11750
0.20 2.23537

- 0.50387

- 0.08929
0.25 2.18219

- 0.48488

- 0.06589
0.30 2.10624

- 0.45695

- 0.02835
0.35 2.00303

- 0.40769 0.01983
0.40 1.87733

- 0.32274 0.05754
0.45 1.76312

- 0.15644 0.00453
0.50 1.67889

- 0.06930 0.0

IA 0.10 2.03250

- 0.31583

- 0.13748
0.20 1.91978

- 0.28215

- 0.07020
0.25 1.83842

- 0.25543

- 0.02597
0.30 1.72657

- 0.19826 0.02633
0.50 1.63417

- 0.0910 0.0

II 0.10 2.55323

- 0.61512

- 0.16403
0.30 2.46532

- 0.62257

- 0.11657
0.35 2.41896

- 0.61594

- 0.08820
0.40 2.36409

- 0.59857

- 0.05621
0.45 2.29238

- 0.57005

- 0.02281
0.50 2.20282

- 0.51599

- 0.01259

III 0.10 2.47317

- 0.51848

- 0.17083
0.30 2.39628

- 0.51202

- 0.13245
0.35 2.35477

- 0.49735

- 0.11985
0.40 2.30726

- 0.46541

- 0.11094
0.45 2.24876

- 0.41314

- 0.11508
0.50 2.17772

- 0.36803

- 0.09525

The time of concentration ( T c ) is the time it takes water to flow from the furthest point in the watershed
to a point of interest within the watershed

. T c is a function of basin shape, topography, and surface

cover. T c is calculated by summing the travel time for various flow segments within the watershed s8 ( USDA NRCS, 1986 , 2008b ). As with previous PRZM versions, there are two flow segments: 1) sheet flow for the first 100 meters , and 2) shallow concentrated flow (unpaved) for the remaining portion of the hydraulic length . Under the sheet flow segment, T c is calculated as:



## TT

cc 

## = aa 0

. 007 ( NNNN ) 0

. 8 ( PP ) 0

. 5 ss 0

. 4 

## + bb
3600 ( 16

. 1345 ss 0

. 5 ) where s = slope (ft/ft)
P = precipitation

N = Manning’s roughness coefficient for the watershed

L = hydraulic flow length (m)

P = daily precipitation (cm)

s = slope of the hydraulic grade line (land slope, m/m)

a , b = unit conversion factors The equation for shallow concentrate d flow is derived from Manning’s equation , assuming a roughness coefficient, N , of 0.05 and a hydraulic radius of 0.2 ( USDA NRCS, 1986 , 2008b ). The a verage velocities for estimating travel time for shallow concentrated flow are as follows : Unpaved v = 16.1345s 0.5

Paved v = 20.3282 s 0.5

w here v = average velocity (ft/s) s = slope of hydraulic grade line (watercourse slope, ft/ft) These two equations are based on the solution of Manning’s equation with different assumptions for N (Manning’s roughness coef ficient) and r (hydraulic radius, ft). For unpaved areas, N is 0.05 and r is 0.4; for paved areas, N is 0.025 and r is 0.2. 

### Evaporation
Prior to application of the leaching water to the soil, the evapotranspiration demand is addressed. The potential evapo transpiration is first satisfied by canopy holdup. If there is remaining potential, then the remaining potential is supplied to the soil. The potential evapotranspiration available to the soil is calculated from:

) ( ) ( ) (

, i h i
t i soil t 

### W E E

− =

Where E t,soil ( i ) = the evapotranspiration available to the soil on day ( i ), [m]

E t (i) = the evapotranspiration on day (i), [m]

W h (i) = the water held by the canopy on day (i), [m]. The available water in the evapotranspiration zone is:9 ( ) ) ( ) : 0 , ) : 0 ( , ) : 0 ( , ) ( ) ( i

x wp x soil x avail 

### W W W i i



### −

=

Where W soil ,(0: x ) = soil water in the spatial range 0:x

W wp ,(0: x ) = wilting point in the spatial range 0:x The evapotranspiration is satisfied preferentially towards the surface in a proportional manner, and it is also satisfied preferentially according to available water in a proportional manner. This is to roughly mimic the natural processes of plant uptake and root structure ( USDA, 1991 ). This function of evapotranspiration with depth and available water is described here and is identical to the means used in PRZ M5:


# ∑ = ) : 0 ( ) : 0 ( ) : 0 ( , x x

x et 

### U U F

Where F et ,(0:x) = the fraction of evapotranspiration, in the spatial range 0:x U is defined by a depth adjustment and moisture adjustment:



###                

−

= 

# ∑ ) : 0 ( , ) : 0 ( ,

max ) : 0 ( max ) : 0 (

max max max

i i i

d avail d avail i d i

x 

### W W
d d d U

Where d max (i) = the depth that evapotranspiration occurs on day i
d

x = the depth at position x. Potential soil water loss through the profile is then determined as a function of the above distribution and is calculated as follows:

) : 0 ( , , ) : 0 ( , x et soil t x loss 

## F E W =

Where W loss , (0: x ) = potential soil water loss at depths 0 to x, [m] 

### Vertical Transport
Next, the capacity concept is implemented to calculate soil moisture and water movement through the soil profile (top 2

- cm layer and twenty 5

- cm layers). This requires another loop beca use of dependencies on previous conditions (i.e., velocities depend on water content of current state, which in turn depends on velocity of previous state). ( ) ( ) ( ) ( ) j i soil j i loss j i j i soil 

### W W v W , 1 , 1 , , − − 

### +

− =

Where v ( i,j ) = velocity of water entering a soil layer at depth j and time i , [m] In the top 2

- cm soil layer, the entering velocity ( v ( i ,0) ) is equal to the leaching ( L ( i ) ). According to the capacity concept, if the soil water is greater than the field capacity, then the excess water moves downward to the next cell as v ( i, j ) and the calculations proceed to either the end of the evaporation zone or to the point where there is no more excess velocity. The calculations stop at the bottom of the10 evaporation zone because if velocity exists at this point then the same velocity wil l exist for the remainder of the profile and thus the calculations are unnecessary. 

### Output delivered
The main outputs from the Scenario Generator are: 1) a vector of days when runoff occurred and accompanying vectors with the runoff and erosion values, 2) a vector of days when vertical transport occurred (velocity > 0) and an accompanying vector with the velocity values, 3) a vector of daily soil moistures, and 4) a vector of plant growth stages. These are placed into unformatted (binary) files with
spec ific names that identify the scenario. The use of unformatted files increases the read speed at which the Super PRZM Hydro and Pesticide Transport and Water Body Concentration Calculator programs can access them.


## 2. Pesticide Transport and Water Body Concen t ration Calculator: Conceptualization

In the Pesticide Transport and Water Body Concentration Calculator , the transport equation (an ordinary differential equation) is solved analytically at each successive daily time step to account for pesticide transport in the soil . This approach is compared to PRZM3 and PRZM5, which implement a finite difference numerical solution (fully implicit, backwards spatial difference scheme) and a tridiagonal matrix for solving the set of simultaneous equations (Young and Fry, 2014) (Figure M2). In the SAM, the transport equation includes the same major components, but is solved analytically instead of numerically, which allows for increased computational speed and efficiency.



### Solution Technique for the Transport Equation

The solution to the transport equation in SAM is defined below. 

# ( ) C mK C V fC Q C Q C mK C V dt d d s w w R L d w 

### μ μ

− − − − = +

Note: The control volume is the top 2 cm soil compartment. The equation currently does not account for the loss/gain of pesticide mass sorbed/desorbed to eroded soil 1

. Where V w = soil pore water volume (m 3 ) C = pesticide concentration (kg/m 3 ) m = mass of soil (kg)

K d = soil partition coefficient (m 3 /kg)

1 An erosion term (

- C K f Q d E E ) may be added to include eroded pesticide mass transport, where Q E = interacting erosion flow (kg/d) and f E = scaling factor (to be determined) to account for potential differences between bulk soil and eroded material. However, relevant monitoring data of sorbing chemicals is necessary to evaluate th is additional transport pathway.11 Q L = flow leached from top 2 cm soil compartment (m 3 /d)
Q R = interacting runoff flow (m 3 /d) f = uniform extraction fac tor (unitless) (Note: below top 2 cm soil compartment, f=0)

μ w = aqueous degradation rate (1/d)

μ s = sorbed degradation rate (1/d)

Note: V w , Q R , and Q L are assumed constant within each d t, and μ w = μ s . 

# ( ) ( )      

+ + + + + + + − = d w d s d w w w d w R
d w L 

### mK V mK mK V V mK V f Q mK V Q C dt dC μ μ ) ( ) (

We define the retardation factor, R =

w d w 

### V mK V + (for no sorption: K d =0, R=1; otherwise, R increases as

K d increases)


###       + + +

− =
w d s w w R

w L 

### V mK V f Q V Q R C dt dC μ μ

t V mK V f Q V Q R
o w d s w w R

w L o w d s w w R

w L

w d s w
w R

w L



### e C C t V mK V f Q V Q R C C dt V mK V f Q V Q R C dC

        + + +

−



### =       + + +

− = −       + + +

− =

μ μ 

### μ μ μ μ

1 

### 1 ln ln 1

Let 

###       + + + =
w d s w w R

w L 

### V mK V f Q V Q R μ μ κ 1

t

o 

## e C C κ

− 

## =
The initial concentration (C o ) is the total pesticide mass in the top soil compartment at the beginning of a time step (t, day), taking into account any pesticide applied on that day, as well as any pesticide remaining from the previous day. C is the concentration at an indefinite t ime later, calculated as a function of the total first

- order dissipation rate ( κ , or the sum of leaching, runoff, aqueous degradation, and sorbed degradation) and based on C o . C also may be expressed in terms of total mass ( M total ) in the compartment as follows:

w total 

## CRV t M = ) (12 The daily mean concentration for each time step (C avg ) and the associated loss of mass due to leaching, runoff, and degradation are estimated by integrating the above first

- order expression:

avg Bio Degraded avg Runoff Runoff avg Leach Leach t o avg



### C k M C k M C k M e C C

* * * ) 1 (

deg 

### = = = − = − κ


### κ

Where C avg = Daily mean concentration from the top soil compartment (kg/m 3 )

κ

= total first

- order dissipation rate ( Σ leaching, runoff, aqueous degradation, sorbed degradation [1/d])

k Leach = first

- order leaching rate (1/d)

k Runoff = first

- order runoff rate (1/d)

k Biodeg = first

- order biodegradation rate (1/d)

M Leach = daily mass loss due to leaching (kg)

M Runoff = daily mass loss due to runoff (kg)

M Degraded = daily mass loss due to degradation (kg) The loss of mass to each of these processes can be expressed as a function of C avg , given the similarity between the (C o - C) and C avg expressions, under first

- order dissipation:

avg Bio avg Runoff avg Leach avg t o t o o o


### C k C k C k dt dC or C e C e C C C C

deg 

### ) 1 ( ) (

+ + = = − = − = − − − 

### κ κ κ



### Water body concentration calculation
Using the daily pesticide runoff mass flux from the top soil compartment (e.g. M Runoff ), the daily concentration in the receiving water body is calculated next. The washout dissipation rate constant (k) in the water body is derived from the water body volume (V wb ) and calculated total flow (Q) as follows:

kk ( tt ) = QQ ( tt ) VV

ww The initia l water body concentration (C o,wb ) is then the sum of the total runoff mass entering at time t (M Runoff (t)) and the mass remaining (e.g., after washout) from the previous time step (M remaining (t

- 1)), divided by V wb :

CC oo , ww ( tt ) = MM RR RR RRRR ( tt ) + MM rr rr aaaa aa aa ( tt

− 1 ) VV

ww Assuming first

- order dissipation, the water body concentration (C wb ) at time t is estimated as :13 CC

ww ( tt ) = CC oo , ww ( tt ) ee − kk tt
The average concentration in the water body during the 24

- hour time step (C avg,wb ), starting at C o , is then calculated by integrating the concentration vs. time curve over the interval, yielding:

CC aaaaaa , ww = CC oo , ww kk ( 1

− ee − kk )

First

- order washout alone is found to be adequate for flowing water bodies with short residence times. Reservoirs, however, h ave longer residence times, permitting mass to degrade (e.g. via hydrolysis) or partition to the benthic zone. As a result , for reservoirs an additional first

- order degradation rate (k deg ) is added to the first

- order washout rate constant (k) , to account for degradation of the pesticide within the reservoir.