Predicting root zone soil moisture with satellite near-surface moisture data in semiarid environments

1Ferdowsi University of Mashhad, Iran, 26-29 February 2016.
Predicting root zone soil moisture with satellite
near-surface moisture data in semiarid
environments
Salvatore Manfreda
DICEM, University of Basilicata, Matera, Italy.
e-mail: salvatore.manfreda@unibas.it
http://www2.unibas.it/manfreda/HydroLab/home.html

University of Basilicata

Actual Network of Collaboration

Research Activities
Modeling of soil-plant-vegetation interactions;
Impact of climate change on water resources;
DEM-based methods for flood prone area detection;
Modeling vegetation patterns;
Use of remote sensing in hydrology;
Rainfall/runoff modelling;
River basin monitoring;

Network Building in Soil Moisture Monitoring
• Farid Faridani, Ferdowsi University
• Alireza Farid, Ferdowsi University
• H. Ansari, Ferdowsi University
• Doug Baldwin, Pennstate University
• Klaus Keller, Pennstate University
• Erica A.H. Smithwick, Pennstate University
• Luca Brocca, CNR-IRPI
• Tommaso Moramarco, CNR-IRPI
• Florisa Melone, CNR-IRPI
• Justin Sheffield, Princeton
• Teodosio Lacava, CNR-IMAA
• Nicola Pergola, CNR-IMAA
• Valerio Tramutoli, University of Basilicata

Soil moisture availability represents a critical control on plant growth
dynamics and ecological patterns in semiarid ecosystems and its
space-time variability is crucial to formulate accurate predictions on the
behavior of hydrologic systems.
Soil moisture represents a key variable in several fields:
• Ecological patterns
• Agriculture and Plant Production
• Numerical Weather Forecasting
• Climate Prediction
• Shallow Landslide Forecasting
• Flood Prediction and Forecasting
Role of Soil Moisture

8Ferdowsi University of Mashhad, Iran, 26 February 2016.
100 km 10 km 1 km
Day
Week
Month
SMAP Radar-Radiometer
Climate Applications
Weather Applications
Carbon Cycle
Applications
Resolved Spatial Scales
ResolvedTemporalScales
Evolution of Microwave Remote Sensing (Land)
GCOM-W
ASCAT
SMOS
ALOS-2
Scale ranges are based on the NRC Decadal Survey
SMAP will support established
climate and carbon cycle
applications and will open up new
applications in weather and
carbon cycle.
Aquarius
SAOCOM

Motivations
New remote sensing missions will provide soil moisture
measurements at high temporal and spatial resolution
(SMAP);
Explore the potential relationship existing between
surface and root-zone soil moisture;
Identify the controlling physical parameters for this
relationship;
Estimate root-zone soil moisture at regionally or globally
distributed locations, using well-known soil physical
properties as predictors;
Define parameterization for remote sensed time-series.

Exponential filter (Wagner et al., RSE 1999)
where W is the volumetric wetness of the reservoir, Ws of the
surface, t is the time, L is the depth of the reservoir layer, and C is
a pseudodiffusivity coefficient that depends on the soil properties.
The solution of equation 1 is
The water balance equation
(1)
(2)
Ws(t)
W(t)
where T=L/C

Use of the exponential filter
Xn
*
= Xn−1
*
+ Kn X(tn )− Xn−1
*"# $%
⎟
⎠
⎞
⎜
⎝
⎛ −
−
−
−
−
+
=
T
tt
n
n
n nn
eK
K
K
1
1
1
X(tn) surface satellite soil moisture data: SWI
X*n profile satellite soil moisture data: SWI*
t time
tn acquisition time of X(tn)
Kn gain
T characteristic time length
(3)
The recursive formulation of the method relies on (Albergel et al.,
2009):
(4)

Manfreda et al. (HESS 2011)
Temporal dynamics of soil moisture and
AMSU SWI*
Time series of daily rainfall (A). Comparison between the soil
moisture (m3 m−3) simulated by DREAM model and the SWI (K)
index as a function of time expressed in days. On y-axes one finds
the SM on the left and SWI on the right side (B).

Soil Moisture Analytical Relationship (SMAR)
The schematization proposed assumes the soil composed of two layers,
the first one at the surface of a few centimeters and the second one
below with a depth that may be assumed coincident with the rooting
depth of vegetation (of the order of 60–150 cm).
The challenge is to define a soil water balance equation where the
infiltration term is not expressed as a function of rainfall, but of the soil
moisture content in the surface soil layer.
This may allow the derivation of a function of the soil moisture in one
layer as a function of the other one.
Manfreda et al. (HESS - 2014)
s1(t)
s2(t)
First layer
Second layer
Zr2
Zr1

Soil water balance
Defining x=(s-sw)/(1-sw) as the “effective” relative soil saturation and
w0=(1-sw)nZr the soil water storage, the soil water balance can be
described by the following expression:
where:
s [–] represents the relative saturation of the soil,
sw [–] is the relative saturation at the wilting point,
n [–] is the soil porosity,
Zr [L] is the soil depth,
V2 [LT-1] is the soil water loss coefficient accounting for both
evapotranspiration and percolation losses,
x2 [–] is the “effective” relative soil saturation of the second soil layer.
1 − !! n!!!!
d!!(!)
d!
= !!!!!y t − !!!! !
Infiltration Losses
(6)

Water flux exchange between the surface and
the lower layer
The water flux from the top layer can be considered significant only
when the soil moisture exceeds field capacity (Laio, WRR 2006).
Assuming that
where n1 [-] is the soil porosity of the first layer, Zr1 [L] is the depth of the
first layer, s1 (θ1/n1) [-] is the relative saturation of the first layer, and sc1 [-]
is the value of relative saturation at field capacity.
s1(t)
s2(t)
First layer
Second layer
(7)
Zr2
Zr1

The equation above can be simplified using normalized coefficients a
and b defined as:
Simplifying the soil water balance equation
! =
!!
1 − !! !!!!!
,!!!
!! =
!!!!!
1 − !! !!!!!
!.
As a consequence, the soil water balance equation becomes:
dimensionless soil water coefficient
ratio of the depths of the two layers
(10)
(9)
(8)

beetween surface and root zone soil moisture
Expanding Eq. 8 and assuming Δt = (tj - ti), one may derive the
following expression for the soil moisture in the second layer based on
the time series of surface soil moisture:
Assuming an initial condition for the relative saturation s2(t) equal to
zero, one may derive an analytical solution to this linear differential
equation that is
(11)
(13)
!! !! = !! + (!! !!!! − !!)!!!! !!!!!!!
+ 1 − !! !!! !! !! − !!!!
For practical applications, one may need the discrete form as well:
(12)

Sensitivity analysis on SMAR’s parameters
The derived root zone soil moisture (SRZ) is plotted changing the soil water
loss coefficient (A), the depth of the second soil layer (B), and the soil textures
(C).
• The increase of soil water loss coefficient produces a shift on SRZ;
• The second layer depth strongly controls the variability of SRZ;
• The soil texture has a critical role influencing the general pattern observed.
Remaining parameters
are:
n1 = n2 = 0.437,
sw2 =0.06,
sc2 =0.14,
V =2cmday−1,
Zr1 =10cm,
Zr2 = 100 cm.
Manfreda et al. (HESS - 2014)

African Monsoon Multidisciplinary Analysis
(AMMA) database
The entire dataset is available on http://www.ipf.tuwien.ac.at/insitu/
The SMAR approach was applied to soil measurements available in West
Africa. These soil moisture measurements form an excellent database that
well describes the soil moisture along the root-zone profile.

CS616
CS616
CS616
CS616
CS616 CS616
-10cm
-40cm
-70cm
-100cm
-105cm
-135cm
0cm
African Monsoon Multidisciplinary Analysis
(AMMA) database
Tondikiboro station provides six
soil moisture measurements
over the soil profile starting from
5 cm of depth down to 135 cm.
The installation is composed by
two horizontal probes at the
depth of 5 cm and 4 vertical
probes that provide a measure
over a layer comparable to the
probe length (about 30 cm).
Example of installation

01/01/06 01/01/08 01/01/10 01/01/12
0
20
40
Station of Tondikiboro
5cm − horizontal
01/01/06 01/01/08 01/01/10 01/01/12
0
20
40
10−40cm − vertical
01/01/06 01/01/08 01/01/10 01/01/12
0
20
40
01/01/06 01/01/08 01/01/10 01/01/12
0
20
40
Time [hours]
01/01/06 01/01/08 01/01/10 01/01/12
0
20
40
SoilMoisture[%]
Hourly soil moisture at different depths at the
station of Tondikiboro in Niger
Data refers to the period 1 January 2006–31 December 2011

Parameter estimation based on physical info
SMAR contains four parameters that have been estimated based on the
physical characteristics of the site under investigation:
• Parameter sw was defined as the intercept between the empirical soil
water loss function and the x-axis.
• The parameter sc1 was assigned using literature values for sandy soil
(Cosby et al., 1984).
• The parameter a = V/(nZr (1-sw)) is computed based on soil texture and
climate. In particular, the value of the soil water losses is set equal to 20
mm day−1 taking into account the high permeability and
evapotranspiration rates of the site.
0 0.1 0.2 0.3 0.4 0.5
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
s
10
(t
j
) [−]
s10
(tj
)−s10
(tj−1
)[−]
(A)
0 0.1 0.2 0.3 0.4 0.5
0
0.005
0.01
0.015
0.02
0.025
0.03
s
10−135
(t
j
) [−]
s
10−135
(t
j
)−s
10−135
(t
j−1
)[−]
(B)
• The parameter b is estimated
assuming the first layer of soil of 10
cm and the second one considered
with a depth of 1250 mm.

SMAR’s results obtained with parameter
assigned based on physical information
01/01/06 01/01/08 01/01/10 01/01/12
0
0.1
0.2
0.3
0.4
0.5
time (days)
relativesaturation(−)
Niger at Tondikiboro
S
10cm
01/01/06 01/01/08 01/01/10 01/01/12
0
0.1
0.2
0.3
0.4
R=0.872, RMSE=0.025, a=0.049, b=0.08, sw
=0.085, sc1
=0.143
time (days)
relativesaturation(−)
S10−135cm
S
*
10−135cm
(B)
(A)A) Time series of relative
saturation, at the daily time-
scale, in the first layer of soil
measured at the station of
Tondikiboro in Niger.
B) Averaged relative saturation in
the lower layer of soil measured
(continuous line) and filtered
(dashed line) at the station of
Tondikiboro. Parameters values
used in the present application
are a=0.049, b=0.08, sw=0.085,
and sc1=0.143, respectively.

Use of remote sensed data
C) Mammoth Cave D) Princeton#1 E)SCAN-Enterprise
A) Tondikiboro B) Wankama

Use of remote sensed data
Measured, SMAR-estimated and SMAR-estimated-using-satellite-data
time series of SSM for AMMA database, Niger. (A) Tondikiboro, and (B)
Wankama.

Measured, SMAR-
estimated and
SMAR-estimated-
using-satellite-data
time series of SSM
for SCAN database,
Kentucky, US. (A)
Mammoth Cave,
and (B)
Princeton#1. SCAN-
Enterprise
database, Utah, US.

An application over the Basilicata Region
Soil moisture assimilation based on satellite data

28
January February March
April May June
Water Requirement

29
July August September
October November Dicember
Water Requirement

Use with satellite data: coupling the SMAR
with EnKF
(Baldwin et al., 2015)
Ridler et al (2014) showed how a satellite correction bias could be
calculated within the EnKF to correct the discrepancy between satellite
and in situ near-surface measurements.
Integrating a simple hydrologic model with an EnKF algorithm can
provide RZSM estimates as accurately as those made by complex
process models (Bolten et al, 2010; Crow et al, 2012).
Since the SMAR model’s four parameters (surface field capacity, root
zone wilting level, diffusivity coefficient and water loss coefficients) are
related theoretically to soil properties that are available globally, it
would be possible to effectively run SMAR across space after
uncovering relationships between soil physical variables and SMAR
model parameters (Reichle et al, 2001).

Coupling the SMAR with EnKF
Satellite-based near-surface (0-2cm) soil moisture estimates have
global coverage but must be downscaled to be useful for watershed or
regional-scale hydrologic applications. We designed an ensemble
Kalman filter (EnKF) data assimilation system that downscales satellite
soil moisture data and then estimates root zone soil moisture content at
sites with the physically based Soil Moisture Analytical Relationship
(SMAR) model.
The SMAR-EnKF optimizes soil
moisture predictions for the large scale
monitoring based on the new satellite
near-surface moisture data (SMAP).

SMAR-EnKF model
The EnKF predicts future states by:
!!
!
= ! !!
!
+ !
P! =
1
! − 1
(!!
!
− !) (!!
!
− !)!
where xi
0 is a forecasted state of the ith ensemble member, f(xi
-) is the
SMAR function that accepts the updated SRZ state from the previous
step as SRZt-1 and the surface measurement at time t as SSL, and Q is
the process covariance matrix with respect to each state.
The EnKF computes the predictive error covariance matrix for a set of
states with:
(15)
(14)

SMAR-EnKF model
The Kalman gain is a matrix of weights that modifies predicted states to
be closer to newly gathered measurements during an analysis step:
where xi
+ is the updated state of the ith ensemble member, zt is a vector
of measurements taken at time t that correspond to each state, and x+
is the mean of the updated state ensemble.
!!
!
= !!
!
+ ! !! − !!!
!
,
!! =
1
! − 1
!!
!
(17)
(16)
After a prediction is made and a measurement at time-step t is
available, the Kalman gain is computed:
where H is a function that translates states into measurements, K is the
Kalman gain weight matrix, and R is the measurement covariance vector.
(16)! = P!
!!
(!P!
!!
+ !)

US soil moisture network: SCAN
51 locations have been
selected over a broad
extent of the
conterminous U.S., so
that our modeling dataset
would be representative
of U.S. ecoregions.
Criteria for choosing locations are:
1) Availability of at least 2 years of data that match the AMSR-E
measurement record (2002-2011);
2) laboratory measured soil texture information is available for each
horizon to estimate total porosity;
3) represent a wide spatial spread of test locations over as many
unique ecoregions as possible.

SMAR-EnKF optimization and prediction
Root mean square errors ranging from 0.014 - 0.049 [cm3 cm-3].
Predictive 95% confidence intervals captures no less than 86% of observations.
Semi-arid Highlands
Temperate Forests
Temperate Forests
North American Deserts
Great PlainsTropical Wet Forests
Forested Mountains Northern Forests

Multiple regression equations used for each
model parameter
Parameter Level Multivariate Linear Regression Function R2
p-value
SFC STATSGO 0.72***
- SandRZ (0.60)***
- ET (0.00022) 0.381 <0.001
a " -0.07 - SiltRZ (0.25)*
+ ρRZ (0.47)*
+ ET (0.00019)**
0.360 0.002
b " 0.12 - SandRZ (0.31) - ClaySL (0.35) - SiltSL(0.12) + ρRZ (0.44) + ET (0.0002)**
0.299 0.042
SWL " 0.36***
- SandRZ (0.45)***
+ ET (0.00019)*
0.363 <0.001
SFC Site 0.27***
+ ClaySL(1.12)***
+ SiltSL (0.28)*
- ET (0.00022)*
0.570 <0.001
a " 0.08*
- SiltRZ (0.19)*
+ ClayRZ (0.03) + ET (0.0002)**
0.342 0.002
b " 0.09*
- ClaySL (0.42)*
+ ClayRZ (0.43)**
+ ET (0.00012) 0.365 0.001
SWL " 0.11**
+ ClayRZ (0.63)***
+ SiltRZ (0.29)**
0.509 <0.001
Significance levels of coefficients: *** = p < 0.001, ** p < 0.01, * p < 0.05; ET =
Average annual evapotranspiration; RZ = root zone; SL = surface layer
Multivariate regression models to estimate SMAR parameters at 11 other
sites using STATSGO-derived soil properties and EPA Level 1 ecoregion
type as covariates.

Cross validation: SMAR-EnKF
The SMAR-EnKF
system predicts SRZ
with R2 between
observed and
predicted ranging
from 0.81-0.97
(average: 0.93) and
RMSE ranging from
0.018-0.056 [-]
(average: 0.032 [-])
The SMAR-EnKF has been validated using parameters based upon the
STATSGO-based regression relationships.

Results of SMAR-EnKF with AMSR-E
Satellites consistently over-
predict near-surface soil
moisture in dryer ecoregions.
Wetter ecoregions are more
likely to have higher errors in
SMAR-EnKF output .

Conclusions
• SMAR represents a feasible mathematical characterization of the
relationship between the surface and the root zone soil moisture.
• The SMAR model showed high reliability when applied over the
AMMA and the SCAN dataset that has been improved with SMAR-
EnKF.
• The coupled model allows to estimate root zone soil moisture at
regionally or globally distributed locations, using well-known soil
physical properties as predictors.
• This approach is a numerically effective strategy for estimating root
zone soil moisture from satellite near-surface observations (e.g., the
SMAP remote sensing platform) and in unmeasured locations, given
basic soil texture information, providing a critical resource for
estimating drought risk at regional to continental scales.

Papers related to this research line…
• Faridani, F., A. Farid, and H. Ansari, S. Manfreda, Estimation of the root-zone soil
moisture using passive microwave remote sensing and SMAR model, (in prep.), 2016.
• Baldwin, D., S. Manfreda, K. Keller, and E.A.H. Smithwick, Predicting root zone soil
moisture with soil properties and satellite near-surface moisture data at locations across
the United States, (in prep.), 2016.
• Baldwin, D., K. Keller, and E.A.H. Smithwick, S. Manfreda, Applying Satellite and
Ground-based Measurements for Catchment-scale Root Zone Soil Moisture Mapping,
(in prep.), 2016.
• Manfreda, S., L. Brocca, T. Moramarco, F. Melone, and J. Sheffield, A physically based
approach for the estimation of root-zone soil moisture from surface measurements,
Hydrology and Earth System Sciences, 18, 1199-1212, 2014.
• Manfreda, S., M. Fiorentino, C. Samela, M. R. Margiotta, L. Brocca, T. Moramarco, A
physically based approach for the estimation of root-zone soil moisture from surface
measurements: application on the AMMA database, Hydrology Days, pp. 47-56, 2013.
• Manfreda, S., T. Lacava, B. Onorati, N. Pergola, M. Di Leo, M. R. Margiotta, and V.
Tramutoli, On the use of AMSU-based products for the description of soil water content
at basin scale, Hydrology and Earth System Sciences, 15, 2839-2852, 2011.

Many Thanks...

Predicting root zone soil moisture with satellite near-surface moisture data in semiarid environments

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