1. Sacramento Soil Moisture Accounting Model (SAC-SMA)
Tanya Hoogerwerf

2. Overview Spatially-lumped continuous soil moisture accounting model
Ideal model for the simulation of large-scale (>1000 km2) basins
Takes mean precipitation, evaporation and temperature as input
accounts for all water entering, stored in, and leaving a Drainage Basin. Though many parameters are used in this water balance accounting process, precipitation has the main impact on runoff.

3. Input
Calibrate by adjusting baseflow, tension water capacities and runoff simulation parameters
Point or areal estimates of historical precipitation, temperature, and potential evaporation
a rainfall generation component, (b) a soil water mass balance component, and (c) a kinematic routing component for channel flow propagation and attenuation.

4. Input (2) Topography Soil characteristics
Location of important features such as reservoirs and river junctions

5. How the SAC-SMA Model Works

6. How the SAC-SMA Model Works (2)
Each basin is represented vertically by two zones:
An upper zone (short- term storage capacity)
A lower zone (bulk of the soil moisture and longer groundwater storage)

7. Soil Zones

8. How the SAC-SMA Model Works (3)
Each layer models …
Tension water elements (water bound by adhesion and cohesion, extracted only by evapotranspiration)
Free water elements (free to move under gravitational forces, may be depleted by evapotranspiration, percolation, horizontal flow)
TENSION
Water bound to the soil by adhesion and cohesion
May be extracted only by evapotranspiration
Water entering a zone is stored as tension water until that zone's tension water capacity is reached.
FREE WATER
Free to move under gravitational forces
May be depleted by evapotranspiration, percolation from the upper zone to the lower zone, horizontal channel flow and groundwater flow.

9. Soil Moisture Budget http://www.cpc.ncep.noaa.gov/soilmst/paper.html
W(t) the soil water content at time t 
P(t) the mean precipitation over area A
E(t) the mean evapotranspiration over area A 
R(t) the net streamflow divergence from area A
G(t) the net groundwater loss (through deep percolation) from area A
The water balance expression gives the model state (Z - water stored in soil column) as a function of the water influx (P - precipitation) and outflux (E - evapotranspiration, R - surface runoff, Bf - baseflow, and L - seepage loss to deep aquifers):
dZdt = P - E - R - Bf - L (13)

10. Soil Moisture Budget (2)
The streamflow divergence R(t) consists of a
surface runoff component S(t) and a subsurface (base flow) runoff component B(t):                 R(t) = S(t) + B(t).     
Wmax is a measure of the capacity of soils to hold water in millimeters
m is a parameter with values greater than 1
 is the inverse of the response time of the baseflow
 is a dimensionless parameter that determines the portion of the subsurface flow that becomes baseflow in the channels draining out from the area of interest.

11. Soil Moisture Budget (3)
G(t) is groundwater flow
E(t) is estimated in this model as follows
(Ep = potential evapotranspiration rate in mm per month)
E = Ep ZZo
where Ep is the potential evapotranspiration rate, Zo is the soil water capacity, m is a coefficient for surface runoff generation, g is the baseflow recession rate, and l determines the fraction of baseflow lost to deep aquifers.
G and B are both functions of gravity

12. Soil Moisture Budget (4)
Ep (potential evaporation):
Depends mainly on the net radiative heating on the surface
Can be estimated from pan evaporation
Thornthwaite's method (1948)…based on observed air temperature and duration of sunlight
Ep is a function of the atmospheric forcing (i.e., net radiation, near-surface wind speed, near-surface relative humidity, etc.) and of the vegetation state (e.g., growing season).
In hydrologic simulations, Ep is either estimated from pan evaporation data and then adjusted monthly with empirical coefficients (e.g., Peck, 1976 for the Sacramento model), or it is based on combination energy-aerodynamic formulas which contain free parameters and which are estimated using historical data (e.g., Brutsaert, 1991).
During storm periods with heavy rain (e.g., convective region of storm in Figure 1, Ep is small due to saturated near-surface air with respect to water vapor, and thus, E may be neglected. For inter storm periods or for periods with moderate and light rain, Ep my be significant and cannot be neglected a priori.

13. SAC-SMA Model Parameters
PCTIM - Percent Impervious.
UZTWM - Upper Zone Tension Water Maximum.
Amount of Rain + Melt needed to meet criteria...estimate from hydrographs...use small to moderate summer rise following dry periods of 2+ weeks.
LZPK - Lower Zone Primary K.
From hydrograph, choose flat part of the baseflow recession in late summer after 2+ weeks of dry weather. LZPK = K = (Qs2/Qs1)**1/t...% freewater like LZSK.
LZSK - Lower Zone Supplemental K.
Flow that persists for anywhere from 15 days to 3-4 months...always > LZPK, uses similar equation...% freewater drained to baseflow, per day.
LZFPM - Lower Zone Free Water Primary Maximum capacity.
Compute from hydrographs...extend primary baseflow recession...try to approximate the highest level (Qx) of primary baseflow runoff...LZFPM = Qx/LZPK.
LZFSM - Lower Zone Free Supplemental Maximum capacity.
Consider hydrograph replot with primary subtracted...minimal estimate...LZFCS <> LZFSM...the larger LZSK the smaller LZFCSmax/LZFSM.
LZTWM - Lower Zone Tension Water Maximum capacity.
May have significant effects on simulated runoff volumes...water balance small/medium runoff event after dry period (normally in the fall after a dry summer, so large LZTW deficit)...use short period...LZTWM larger where deep rooted plants exist...LZTWM smallest in shallow root areas.
UZFWM - Upper Zone Free Water Maximum capacity.
Can move into UZTW and interflow...estimates: 10-15mm if run-off (RO) nearly every event; 15-25mm if RO heavy events; 25-40mm if RO only during largest events; > 40mm if never get RO.
PFREE - Percolation that goes into Lower Zone FREE Water storages.
Examine events when UZTWC is full (UZTWC = UZTWM) and LZTWC < LZTWM...look at small event after dry period or moderate event in a sequence of events.
ZPERC (Zone Percolation) & REXP (exponential relation).
Control the increase in lower zone percolation demand as lower zone storages move from saturated conditions to deficit (drier) conditions...clay = ZPERC , REXP silt = ZPERC 20-75, REXP sand = ZPERC 5-20, REXP (REXP always > 1.0).
UZK - Upper Zone freewater withdrawal rate, as interflow, as a fraction of the upper zone freewater content (UZTWC).
Nominal value of change if early part of simulated recessions is flatter or steeper than observed early recessions.
ADIMP - Area in Drainage that is Impervious.
Hard to determine when slow time to peak in UHG...ADIMP = Runoff Volume/Rain+Melt Volume - PCTIM.
RIVA - Percentage of watershed with Riparian Vegetation (Riparian Vegetation Area).
Examine late summer & fall flows...consider irrigation...ground water withdrawals.
PEADJ - Ratio of ET-demand to PE for a water surface.
Depends on climatic regime & vegetation...use monthly average curve.
RSERV - Fraction of Lower Zone Free Water not available for evapotranspiration.
Set to 0.3 initially.
SIDE - Amount of baseflow lost to deep recharge outside the basin.