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 that 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/m3)

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 independent 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 application 

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 maturity 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

M H

E M

M E

E

E

G t t T

G t T t T

T t T

T T

t T G t

G t t T

= >

= < <

 < <



 





−

− =

= <

( ) 0

( ) 1

( )

( ) 0

Where G(t) = the fractional growth

TE = time of emergence

TM = time of plant maturity

TH = time of plant harvest

In recent refinements, the planting, 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 either 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 D t R G t root =

and
3

( ) ( ) ,max C t C G t p = p

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

Rmax = maximum root depth, [L]

Cp(t) = fractional canopy coverage at a time t, [—]

Cp,max = maximum fractional canopy coverage, [—]

Meteorological Data Processing

After the Scenario Generator 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 accumulates 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:

Pmelt = FmeltT

Where Pmelt = daily snowmelt (daily vector), [L]

Fmelt = snowmelt factor (scalar) [L /°C]

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800

Days

Fractional Growth

emergence emergence

maturity harvest maturity 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:

Prain melt Prain Pmelt = + /

Where Prain = precipitation falling as rain (daily vector) [m]

Prain/melt= the sum of rain and snowmelt production (daily vector) [m]

Pan evaporation is converted to potential evapotranspiration by use of a pan factor:

Et = FpanE pan

Where Fpan = pan factor (scalar) 

Et = potential evapotranspiration (daily vector), [m]

Epan = 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 inputs 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: 

∑{[( ) ] } =

= − + ∆

Dirr

i

t et i i irr i i W FC WP F WP x

1

arg

Where Wtarget = the target dryness within the irrigation zone, [m]

FC = field capacity

WP = wilting point

Firr = fraction of available water below which irrigation is desired

Dirr = 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 Prain/melt vector:

Prain / melt /irrig = Prain / melt + Pirrig
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 ( ) ( )

( ) / /

0.8

0.2

i i

rain melt irrig

i i

i rain melt irrig

R

P S

P S

Q

+

− = for ( ) 0.2 ( ) / P i S i rain melt >

0 ( )=i QR for ( ) 0.2 ( ) / P melt i S i rain ≤

Where S(i) = CN method’s maximum potential retention on day i, [m]

QR

(i) = runoff on day i, [m]

The amount of water that is held on the canopy is determined after runoff is calculated. Therefore, the 

amount 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, then 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 and 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

rain melt irrig

i

i R

oc

i

rain

i

g

P

Q W P I

Where Wg

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

Ioc(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 Wc W W W

Where ΔWc

(i) = the amount of precipitation that is held up in the canopy on day i [m], and Wc,max(i) is the 

maximum water that the canopy can hold up on day i as defined by:

( )

max

( )

,max

i

p

i Wc =W C

Where Wmax 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 Wh =W + ∆W −
6

The amount of water available for input into the top soil layer is: 

( ) ( ) ( )

/ /

( ) i

C

i

R

i

rain melt irrig

i L = P −Q − ∆W

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:

XXee = 0.79�VVrrqqpp�

0.65AA0.009KK(LLLL)CCCC

where Xe = the event soil loss (metric tons day-1

)

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

qp = peak storm runoff (mm/h)

A = field size (hA)

K = soil erodibility factor (dimensionless)

LS = length-slope factor (dimensionless)

C = soil cover factor (dimensionless)

P = conservation practice factor (dimensionless)

The peak storm runoff value (qp) is calculated using the Graphical Peak Discharge Method as described 

in USDA NRCS (1986, 2008b).

qqpp = qquuAAQQFFpp

where qp = peak storm runoff (ft3/s)

qu = unit peak discharge (csm/in) 

A = drainage area (mi2

)

Q = runoff (in)

Fp = pond or swamp adjustment factor

For areas without swamps or ponds, Fp 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(qquu) = CC0 + CC1 log(TTcc) + CC2[log(TTcc)]2

where Tc = time of concentration (hr)

C0, C1, C2 = coefficients from USDA NRCS (1986, 2008b), given in Table 2 below
7

Rainfall 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 C0 C1 C2

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 (Tc) is the time it takes water to flow from the furthest point in the watershed 

to a point of interest within the watershed. Tc is a function of basin shape, topography, and surface 

cover. Tc is calculated by summing the travel time for various flow segments within the watersheds
8

(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, Tc is calculated as:

TTcc = aa

0.007(NNNN)0.8

(PP)0.5ss0.4 + bb

3600 (16.1345ss0.5)

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 concentrated 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 average velocities 

for estimating travel time for shallow concentrated flow are as follows:

Unpaved v = 16.1345s0.5

Paved v = 20.3282 s0.5

where 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 coefficient) 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 evapotranspiration 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 Et soil = E −W

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

Et

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

Wh

(i) = the water held by the canopy on day (i), [m].

The available water in the evapotranspiration zone is: 
9

( )

( )

,(0: ) ,(0: ) , 0: )

( ) ( ) i Wavail x Wsoil x Wwp x

i i = −

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

Wwp,(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 PRZM5:

∑

=

(0: )

(0: )

,(0: )

x

x

et x U

U

F

Where Fet,(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

max (0: )

(0: )

max

max max

i

i i

avail d

avail d

i

d

i

x W

W

d

d d

U

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

dx = 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:

Wloss,(0:x) = Et,soilFet,(0:x)

Where Wloss,(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 because of 

dependencies on previous conditions (i.e., velocities depend on water content of current state, which in 

turn depends on velocity of previous state).

( ) ( ) ( ) (i j)

soil

i j

loss

i j i j Wsoil v W 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 the 
10

evaporation zone because if velocity exists at this point then the same velocity will 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 

specific 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 Concentration 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.

(V C mK C) Q C Q fC V C mK C

dt

d

w + d = − L − R − μ w w − μ s d

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 soil1

.

Where Vw = soil pore water volume (m3

)

C = pesticide concentration (kg/m3

)

m = mass of soil (kg)

Kd = soil partition coefficient (m3

/kg)

 1 An erosion term (- QE fEKdC ) may be added to include eroded pesticide mass transport, where QE = interacting 

erosion flow (kg/d) and fE = 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 this 

additional transport pathway.
11

QL = flow leached from top 2 cm soil compartment (m3

/d)

QR = interacting runoff flow (m3

/d)

f = uniform extraction factor (unitless) (Note: below top 2 cm soil compartment, f=0)

μw = aqueous degradation rate (1/d)

μs = sorbed degradation rate (1/d)

Note: Vw, QR, and QL are assumed constant within each dt, and μw = μs.

( ) ( )





 





+

+

+

+

+

+

+ = −

w d

d

s

w d

w

w

w d

R

w d

L

V mK

mK

V mK

V

V mK

Q f

V mK

Q C

dt

dC

μ μ ( ) ( )

We define the retardation factor, R = 

w

w d

V

V + mK

(for no sorption: Kd =0, R=1; otherwise, R increases as 

Kd increases)





 



 = − + + +

w

s d

w

w

R

w

L

V

mK

V

Q f

V

Q

R

C

dt

dC μ

μ

t

V

mK

V

Q f

V

Q

R

o

w

s d

w

w

R

w

L

o

w

s d

w

w

R

w

L

w

s d w

w

R

w

L

C C e

t

V

mK

V

Q f

V

Q

R

C C

dt

V

mK

V

Q f

V

Q

C R

dC















 − + + +

=





 



 − = − + + +





 



 = − + + +

μ μ

μ

μ

μ

μ

1

1 ln ln

1

Let 



 



 = + + +

w

s d

w

w

R

w

L

V

mK

V

Q f

V

Q

R

μ κ μ

1

t

o C C e−κ =

The initial concentration (Co) 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 time 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 Co. C also may be expressed in terms of total mass (Mtotal) in the 

compartment as follows:

total CRVw M (t) =
12

The daily mean concentration for each time step (Cavg) and the associated loss of mass due to leaching, 

runoff, and degradation are estimated by integrating the above first-order expression:

Degraded Bio avg

Runoff Runoff avg

Leach Leach avg

o t

avg

M k C

M k C

M k C

e

C

C

*

*

*

(1 )

= deg

=

=

= − −κ

κ

Where Cavg = Daily mean concentration from the top soil compartment (kg/m3

)

κ = total first-order dissipation rate (Σ leaching, runoff, aqueous degradation, sorbed 

degradation [1/d])

kLeach = first-order leaching rate (1/d)

kRunoff = first-order runoff rate (1/d)

kBiodeg = first-order biodegradation rate (1/d)

MLeach = daily mass loss due to leaching (kg) 

MRunoff = daily mass loss due to runoff (kg)

MDegraded = daily mass loss due to degradation (kg)

The loss of mass to each of these processes can be expressed as a function of Cavg, given the similarity 

between the (Co - C) and Cavg expressions, under first-order dissipation:

Leach avg Runoff avg Bio avg

avg

t

o

t

o o o

k C k C k C

dt

dC

or

C C C C e C e C

deg

( ) (1 )

= + +

− = − = − = − − κ κ κ

Water body concentration calculation

Using the daily pesticide runoff mass flux from the top soil compartment (e.g. MRunoff), 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 (Vwb) and calculated total flow (Q) as follows:

kk(tt) = QQ(tt)

VVww

The initial water body concentration (Co,wb) is then the sum of the total runoff mass entering at time t 

(MRunoff(t)) and the mass remaining (e.g., after washout) from the previous time step (Mremaining(t-1)), 

divided by Vwb:

CCoo,ww (tt) = MMRR RR RRRR (tt) + MMrr rraaaa aa aa(tt − 1)

VVww

Assuming first-order dissipation, the water body concentration (Cwb) at time t is estimated as:
13

CCww (tt) = CCoo,ww (tt) ee−kk tt

The average concentration in the water body during the 24-hour time step (Cavg,wb), starting at Co, is then 

calculated by integrating the concentration vs. time curve over the interval, yielding:

CCaaaaaa,ww = CCoo,ww

kk (1 − ee−kk )

First-order washout alone is found to be adequate for flowing water bodies with short residence times. 

Reservoirs, however, have 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 (kdeg) 

is added to the first-order washout rate constant (k), to account for degradation of the pesticide within 

the reservoir.