PREDICTING ROOT ZONE SOIL MOISTURE WITH SATELLITE NEAR-SURFACE MOISTURE DATA IN SEMIARID ENVIRONMENTS

Prof. Ing. Salvatore Manfreda, Soil Moisture Monitoring 1/127
PREDICTING ROOT ZONE SOIL MOISTURE WITH
SATELLITE NEAR-SURFACE MOISTURE DATA IN
SEMIARID ENVIRONMENTS
Prof. Salvatore Manfreda
E-mail: salvatore.manfreda@unibas.it
www2.unibas.it/manfreda
www.salvatoremanfreda.it
@Sal_Manfreda
University of Twente, Enschende, August 2019
AMBIENTE

Motivations
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

Soil Moisture Dynamics
• Soil moisture represents a critical component of the hydrological cycle
and is a central factor in climate, soil and vegetation interactions (e.g.,
Albertson and Montaldo, 2003; Porporato et al., 2004). It affects
catchments response and modulates interactions between land surface
and atmosphere influencing climate and weather (e.g., Entekhabi et al.,
1996; Porporato et al., 2000).
• Soil moisture availability represents a critical control on plant growth
dynamics and ecological patterns in semiarid ecosystems (Meron et al.,
2004; Caylor et al., 2005; Scanlon et al., 2005) and its space-time
variability is crucial to formulate accurate predictions of the behavior of
hydrological systems (Western et al., 2002).
0.05
0.15
0.25
150 200 250 300 350
Julian Day
q(%)
interspace
canopy
Sevilleta,
New Mexico
q

Soil moisture patterns obtained by hydrological
simulations
The North American Land Data Assimilation System (NLDAS) [Mitchell et
al., 2004] provides estimates of soil moisture from four different models at
sub-daily intervals across the United States. The NLDAS is a multi-
institution partnership aimed at developing a real-time and retrospective
data set, using available atmospheric and land surface meteorological
observations to compute
the land surface
hydrological budget.
Further information about
the NLDAS project along
with model outputs can be
found at http://
ldas.gsfc.nasa.gov/
Matrix: 80 x 250 pixels

Hydrological Simulation: VIC model
Hydrologic Model (Liang et al., 1994)

Experimental results
The relationship between
soil moisture at different
depths has been
investigated using field
measurements over
three pasture sites in
New Zealand. Wilson et
al. (2003) were unable to
find a clear relationship
between the soil
moisture measurements
over depths of 30 cm and
6 cm.
(Wilson et al., JH, 2003)

Characteristics of relative soil moisture in deep
and shallow layers
0 50 100
0
0.1
0.2
p(S100
|S10
=15%)
0 50 100
0
0.1
0.2
p(S100
|S10
=20%)
0 50 100
0
0.1
0.2
p(S100
|S10
=25%)
0 50 100
0
0.1
0.2
p(S100
|S10
=30%)
0 50 100
0
0.1
0.2
p(S100
|S10
=35%)
0 50 100
0
0.1
0.2
p(S100
|S10
=40%)
0 50 100
0
0.1
0.2
p(S100
|S10
=45%)
0 50 100
0
0.1
0.2
p(S100
|S10
=50%)
0 50 100
0
0.1
0.2
p(S100
|S10
=55%)
0 50 100
0
0.1
0.2
p(S100
|S10
=60%)
0 50 100
0
0.1
0.2
p(S100
|S10
=65%)
0 50 100
0
0.1
0.2
p(S100
|S10
=70%)
0 50 100
0
0.1
0.2
p(S100
|S10
=75%)
0 50 100
0
0.1
0.2
p(S100
|S10
=80%)
0 50 100
0
0.2
0.4
p(S100
|S10
=85%)
0 50 100
0
0.2
0.4
p(S100
|S10
=90%)
0 50 100
0
0.2
0.4
p(S100
|S10
=95%)
0 50 100
0
0.1
0.2
p(S100
|S10
=100%)
S100
S10

Characteristics of relative soil moisture in deep and
shallow layers
Developing a relationship between the relative soil moisture at the
surface to that in deeper layers of soil would be very useful for remote
sensing applications.
This implies that prediction of
soil moisture in the deep layer
given the superficial soil
moisture, has an uncertainty
that increases with a reduced
near surface estimate.
Manfreda et al. (AWR – 2007)

Model performance versus model complexity

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
(1)

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;
s1(t)
s2(t)
First layer
Second layer
(2)
Zr2
Zr1
sc1 [-] is the value of relative
saturation at field capacity.

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
(6)
(5)
(4)

Soil Moisture Analytical Relationship (SMAR) beetween
surface and root zone soil moisture
Expanding Eq. 8 and assuming Dt = (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
(7)
(9)
!! !! = !! + (!! !!!! − !!)!!!! !!!!!!!
+ 1 − !! !!! !! !! − !!!!
For practical applications, one may need the discrete form as well:
(8)

Sensitivity of 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).
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

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, s
w
=0.085, s
c1
=0.143
time (days)
relativesaturation(−)
S
10−135cm
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.

Remote sensed data vs field mesurements
(Faridani et al., J. Irr. Drain., 2016)

Use with satellite data: coupling the SMAR with EnKF
(Baldwin et al., J. Hydr., 2016)
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).

US soil moisture network: SCAN
Criteria for choosing 51 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 locations representative of U.S.
ecoregions.

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

Results of SMAR-EnKF with AMSR-E
Satellites consistently over-
predict near-surface soil
moisture in dryer
ecoregions.
(Baldwin et al., J. Hydr., 2017)

Multiple regression equations used for each SMAR model
parameter
Significance levels of coefficients: *** = p < 0.001, ** p < 0.01, * p < 0.05;
AET = Average annual evapotranspiration;
Multivariate regression models to estimate SMAR parameters at 11 other
sites using STATSGO-derived soil properties and EPA Level 1 ecoregion type
as covariates.
DtB = depth to bedrock

Cross validation of 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.

Spatial Heterogeneity in Landscape Patterns
Semiarid ecosystem of Northern Australia

On the spatial organization of soil moisture
Such analysis allow to study the role of different source of
heterogeneity :
i. Different soil types;
ii. Morphology of the river basin;
iii. Spatial organization of vegetation and coexistence of
phisiologically different plat species;
iv. Spatial variability of rainfall fields.
Soil Texture
Vegetation
Dynamics
Morphology
Spatial Soil Moisture
Patterns
Rainfall and solar
Radiation ForcingsPhysical Features

Soil moisture simulation and transpiration
Relative saturation of soil (%) Transpiration (mm)

The variance of soil moisture as a function of the mean
100 cm layer 10 cm layer

Correlogram of two soil moisture fields simulated by
VIC model in a box of 80x250 pixels
Map of 01/10/98 with
mean soil moisture of
50.6%.
Map of 01/02/99 with
mean soil moisture of
67.3%.

Scaling of soil moisture
An element of particular interest is the spatial variability of soil moisture
for downscaling/aggregation of small scale processes to larger scales in
order to prevent systematic biases in modelled water and energy fluxes. A
promising approach towards this task may lie in examining the scaling
behavior of soil moisture fields.
Rodriguez-Iturbe et al. (1995)
recognized that the spatial
variance of the soil moisture
fields follows a power law decay
as a function of area. Such
spatial structure could be
influenced by the scaling of soil
properties or controlled by the
soil moisture state (wet or dry) as
evidenced by changes in the
scaling slopes.
Data from Washita ‘92 Experiment

Scaling of soil moisture
(Manfreda et al., AWR 2006)
Across the range of scales examined
here, the variance of the soil moisture
follows a simple power-law
relationship
where l represents the scale factor
and b is the slope of the scaling
function that ranges between 0.12
and 0.05 for S100 and between 0.32
and 0.12 for S10. Rodrıguez-Iturbe et
al. (1995), using a limited number of
soil moisture maps collected with a
passive microwave sensor during the
Washita ’92 Experiment, found
values of b (between 0.21 and 0.28).

Implications
The scaling of variance imply that the spatial correlation, r(x),
follows a power law for the large distance (Whittle, 1962)
2
)]([ -
µ µ
AASVar
ò
-
=
A
dxxSAAS )()( 1
)2(2
)( -
µ µ
r xx
where
The correlation function will assume the following expression

Slope of the scaling functions of the variance of the
soil moisture averaged over two depths
cyclic behavior due to a persistent pattern

45 50 55 60 65 70
-0.12
-0.11
-0.1
-0.09
-0.08
-0.07
-0.06
-0.05
-0.04
Mean soil moisture (%)
Slope
There is any relationship between the slope of the
scaling exponent and the mean soil moisture?
Hysteresis
Effects
Hysteresis is encountered in many phenomena like: phase transition, plasticity,
ferroelectricity, superconductivity, population dynamics, biological systems (bacterial growth),
etc.

The slope of the scaling
functions
Deep soils show a greater
organization in their spatial patterns
of water content, and displays a
persistence which is maintained
throughout the studied time period.
On the other hand, the top layer of
soil has higher temporal variability
in its spatial scaling characteristics
due to increased fluctuations
resulting from infiltration (wetting)
and evapotranspiration-leakage
(drying) processes.
(Manfreda et al., AWR 2007)

Soil moisture variability
222
0 withinsss ll +=
2
0
2
0
1 l
b
s
l
l
s
÷
÷
ø
ö
ç
ç
è
æ
-÷÷
ø
ö
çç
è
æ
=within
Assuming that the variance follow a power law, it is possible to define the
internal variance of a cell of dimension λ0 known the reference scale λ of
the hydrological processes
In the modelling of soil water balance, the infield variability of soil moisture
assumes a central role fo a correct estimate of hydrological losses such
as evapotranspiration and leakage.
The variance of the process at the scale of ~14 km is the variance of an
aggregated process given by the sum of the variance at the large scale
(support) and the variance within the cell (Journel and Huijbregts, 1978):

10
-2
10
0
10
2
10
4
0.01
0.02
0.03
0.04
0.05
0.06
Area (km2
)
Variance
VIC scale
(~10 km)
{Point scale
predicted variance
0.041 – 0.054 [cm6/cm6]
{VIC scale
variance
0.016 – 0.04 [cm6/cm6]
Hydrological models scale
(~100 m)
Open Question
Within Variance
0.015 – 0.034 [cm6/cm6]
Standard Deviation
0.12 – 0.18 [cm3/cm3]
Scaling

Assuming realistic the extrapolation done and
Assuming a given distribution of soil moisture …
~14 km
It is possible to evaluate
the effects of this
variability on the
transpiration computed in
global circulation models
0 0.2 0.4 0.6 0.8 1
0
0.5
1
1.5
2
2.5
Relative Soil Moisture [cm3
/cm3
]
p(s)
mean=50%; s=0.18
0 0.2 0.4 0.6 0.8 1
0
0.5
1
1.5
2
2.5
3
3.5
Relative Soil Moisture [cm3
/cm3
]
p(s)
mean=65%; s=0.12

Effects due to the incell soil moisture variability
0 0.2 0.4 0.6 0.8 1
0
1
2
3
4
5
6
7
8
Soil Moisture [cm3
/cm3
]
Soillossfunction[mm]
s=0.04
s=0.06
s=0.08
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
Soil Moisture [cm3
/cm3
]
Soillossfunction[mm]
s=0.04
s=0.06
s=0.08
( ) ( ) ( )dssfsEsET sò=
1
0

Relative errors as a function of the relative saturation of the soil
0 0.2 0.4 0.6 0.8 1
-20
0
20
40
60
80
100
Soil Moisture [cm3
/cm3
]
Error[%]
s=0.04
s=0.06
s=0.08

How to detect Soil Water Content at high Spatial resolution?
From Xurxo Gago

Aerial thermography for water stress detection
(Berni et al., 2009)

UAS-based Soil Moisture Monitoring
http://bestdroneforthejob.com/
WG3

Example of Applications:
Orthomosaic Iran Neshabur
RGB Orthomosaic
5 cm resolution

Thermal mosaic
19 cm resolution
Orthomosaic Iran Neshabur

Orthomosaic Murgia Timone (Matera)

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 SMAR-EnKF 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.
UAS may help in understanding the role of spatial heterogeneity in the
description of SM.

Papers related to this research line…
Baldwin D., S. Manfreda, H. Lin, T. Russo, E. Smithwick, Terrain and soil properties enable the spatial
operation of a multi-scale hydrologic data assimilation system driven with satellite data, Remote Sensing,
2019.
Faridani, F., A. Farid, H. Ansari, S. Manfreda, A modified version of the SMAR model for estimating root-
zone soil moisture from time series of surface soil moisture, Water SA, 43(3), (doi: 10.4314/wsa.v43i3.14)
2017. [pdf]
Baldwin, D., Manfreda, S., Keller, K., and Smithwick, E.A.H., Predicting root zone soil moisture with soil
properties and satellite near-surface moisture data at locations across the United States, Journal of
Hydrology, 546, 393-404, (doi: 10.1016/j.jhydrol.2017.01.020), 2017. [pdf]
Faridani, F., A. Farid, H. Ansari, and S. Manfreda, Estimation of the root-zone soil moisture using passive
microwave remote sensing and SMAR model, Journal of Irrigation and Drainage Engineering, 04016070,
1-9, (doi: 10.1061/(ASCE)IR.1943-4774.0001115), 2016. [pdf]
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.
Manfreda, S., M. McCabe, E.F. Wood, M. Fiorentino and I. Rodríguez-Iturbe, Spatial Patterns of Soil
Moisture from Distributed Modeling, Advances in Water Resources, 30(10), 2145-2150, (doi:
10.1016/j.advwatres.2006.07.009), 2007. [pdf]

PREDICTING ROOT ZONE SOIL MOISTURE WITH SATELLITE NEAR-SURFACE MOISTURE DATA IN SEMIARID ENVIRONMENTS

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