HESSHydrology and Earth System SciencesHESSHydrol. Earth Syst. Sci.1607-7938Copernicus GmbHGöttingen, Germany10.5194/hess-19-4463-2015Evaluating the utility of satellite soil moisture retrievals over
irrigated areas and the ability of land data assimilation methods to correct for unmodeled processesKumarS. V.sujay.v.kumar@nasa.govPeters-LidardC. D.SantanelloJ. A.ReichleR. H.https://orcid.org/0000-0001-5513-0150DraperC. S.KosterR. D.NearingG.https://orcid.org/0000-0001-7031-6770JasinskiM. F.Science Applications International Corporation, Beltsville, MD, USAHydrological Sciences Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD, USAGlobal Modeling and Assimilation Office, NASA Goddard Space Flight Center, Greenbelt, MD, USAUniversities Space Research Association, NASA Goddard Space Flight Center, Greenbelt, MD, USAS. V. Kumar (sujay.v.kumar@nasa.gov)6November20151911446344781May201522June201521September201519October2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://hess.copernicus.org/articles/19/4463/2015/hess-19-4463-2015.htmlThe full text article is available as a PDF file from https://hess.copernicus.org/articles/19/4463/2015/hess-19-4463-2015.pdf
Earth's land surface is characterized by tremendous natural heterogeneity
and human-engineered modifications, both of which are challenging to
represent in land surface models. Satellite remote sensing is often the most
practical and effective method to observe the land surface over large
geographical areas. Agricultural irrigation is an important human-induced
modification to natural land surface processes, as it is pervasive across
the world and because of its significant influence on the regional and global
water budgets. In this article, irrigation is used as an example of a human-engineered,
often unmodeled land surface process, and the utility of satellite soil
moisture retrievals over irrigated areas in the continental US is examined.
Such retrievals are based on passive or active microwave observations from
the Advanced Microwave Scanning Radiometer for the Earth Observing System
(AMSR-E), the Advanced Microwave Scanning Radiometer 2 (AMSR2), the Soil
Moisture Ocean Salinity (SMOS) mission, WindSat and the Advanced
Scatterometer (ASCAT). The analysis suggests that the skill of these
retrievals for representing irrigation effects is mixed, with ASCAT-based
products somewhat more skillful than SMOS and AMSR2 products. The article
then examines the suitability of typical bias correction strategies in
current land data assimilation systems when unmodeled processes dominate the
bias between the model and the observations. Using a suite of synthetic
experiments that includes bias correction strategies such as quantile mapping
and trained forward modeling, it is demonstrated that the bias correction
practices lead to the exclusion of the signals from unmodeled processes, if
these processes are the major source of the biases. It is further shown that
new methods are needed to preserve the observational information about
unmodeled processes during data assimilation.
Introduction
Examples of human-induced land surface changes include urbanization,
deforestation, and agriculture, all of which have significant impacts on
local and regional water and energy budgets and hydrologic and biogeochemical
processes. The expansion of infrastructure and agriculture, necessitated by
increasing societal demands, has led to significant transformation of the
natural features of the land surface, affecting more than 50 % of the land
area . Most current land surface models are not
only severely deficient in representing the impacts of such engineered
artifacts but are also limited in representing features of many natural
systems such as seasonal flood plains and wetlands. Remote sensing
measurements offer a potential alternative for capturing the effects of such
unmodeled processes. Moreover, data assimilation, which is a common approach
to merge the information from observations with model estimates, may provide
a possible mechanism for incorporating the effects of such unmodeled
processes into model estimates.
Irrigation is an important land management practice that has had a
significant impact on the global and regional water budgets. As noted in
, the global increase in water vapor flows from
irrigation is comparable to the decrease caused by deforestation. It has been
estimated that as much as 87 % of the global fresh water withdrawals by
humans have been used for agriculture , which
leads to significant alteration of the global and regional hydrological
cycle. Though recent studies have reported the development of
conceptual representations of irrigation in land surface models
, capturing and representing the
nature of irrigation practices remains a hard problem.
Therefore, in this article we focus on irrigation as an analog of a
human-engineered process that is typically not represented in land surface models.
There is a long legacy of retrieving estimates of surface soil moisture from
satellite microwave radiometry using a variety of sensors
. In the past decade, near-surface
soil moisture retrievals have become available from a number of passive
microwave and scatterometer-based platforms. They include Advanced Microwave
Scanning Radiometer-Earth Observing System (AMSR-E) aboard the Aqua
satellite, WindSat multifrequency polarimetric microwave radiometer aboard
the Coriolis satellite, the Advanced Scatterometer (ASCAT), a C-band active
microwave remote sensing instrument aboard the Meteorological Operational (METOP)
satellites, the Advanced Microwave Scanning Radiometer 2 (AMSR2)
onboard the Global Change Observation Mission-Water (GCOM-W) satellite,
the Soil Moisture Ocean Salinity (SMOS) mission, and the Soil Moisture
Active Passive (SMAP) mission. Except for AMSR-E, which
stopped functioning in October 2011, all these instruments are currently
providing measurements of surface soil moisture. In this article, we first
examine if the satellite soil moisture retrievals are effective in capturing
the effects of irrigation. The comparison is performed through a quantitative
comparison of the probability density functions (PDFs) of remote sensing
data sets against those of land surface model simulations that do not include
formulations of irrigation.
The second focus of the article is to examine whether the current data
assimilation practices are adequate if unmodeled processes such as irrigation
are present in observations. When irrigation practices are employed, they
lead to wetter soil moisture relative to non-irrigated time periods.
Assuming that the physical model used in data assimilation does not have
irrigation formulations in it, the assimilated observations would have a
systematic bias (relative to the model) during irrigation periods. In real
data assimilation systems, biases between model forecasts and observations
are unavoidable, and they typically result from a combination of model
deficiencies, instrument and retrieval errors. Proper treatment of these
biases is important, as the assimilation methods are primarily designed to
work with errors that are strictly random . Here
we evaluate the impact of using common bias correction practices when
unmodeled processes are the primary source of the biases between the model and observations.
Primarily, there are two approaches to handling biases in data assimilation
systems : (1) “bias-aware” systems which are built
to diagnose and correct the biases in the observations and/or the model
forecasts during data assimilation integration, and (2) “bias-blind” systems
which assume the observations and model forecasts to be unbiased. Ideally,
biases must be estimated by comparing the observations and/or model states to
the true mean states derived, for example, from in situ measurements. However,
as noted in , developing spatially distributed bias
estimates is much harder for the land surface, compared to the atmosphere or
ocean, since point-scale in situ observations are generally not
representative of the spatial scale of remotely sensed or modeled states, due
to the heterogeneity of land. Though there have been a number of studies that rely on online estimation of
biases ,
the common practice in land data assimilation studies is to remove
the bias between the observations and the model and to use a bias-blind
assimilation approach to correct only short-lived model errors. This is
typically achieved by rescaling the observations prior to assimilation, to
have the same statistics as the model, using quantile mapping approaches so
that the observational climatology matches that of the land model. This
approach is easy to implement as a preprocessing step to the data
assimilation system and has been used extensively in many land data
assimilation studies .
A known disadvantage of the approach is that it assumes stationarity in model–observational biases and
cannot easily adjust to dynamic changes in bias characteristics. Common
quantile mapping approaches used for scaling observations into the model's
climatology include the standard normal deviate based scaling
and the CDF (cumulative distribution function)-matching method
(; hereafter referred to as RK04). The standard
normal-deviate-based scaling matches the first and second moments of the
observation and model distributions, whereas the CDF matching approach
corrects all quantile-dependent biases between the model and observations,
regardless of the shape of the distributions.
When observations are rescaled prior to assimilation, standard normal
deviates or percentiles (rather than the raw observations) are assimilated.
This ensures that the model climatology is preserved in data assimilation and
that assimilation only affects temporal patterns of the anomalies. In such
cases, the influence of assimilation is likely to be greater at the shorter
timescales .
In this article, we argue that the approach of rescaling the observations
could be problematic, particularly when the underlying distributions of the
model estimates and the observations are different. Such differences in the
distributions are possible when features from human-induced activities such
as irrigation are present in observations and missing in modeled
estimates. Through a suite of synthetic experiments, we demonstrate the
limitations of the rescaling approaches when the reference climatology is
fundamentally limited in representing unmodeled processes whose effects
nevertheless impact the observations. In such cases, stationarity assumptions
about the climatologies could also lead to spurious, statistical features in
the assimilation results. As a result, the use of rescaling would become
problematic for demonstrating short-term assimilation impacts.
The rescaling approach through CDF-matching for land data assimilation
proposed by RK04 was motivated by the fact that the true climatology of soil
moisture at the global scale remains unknown. The CDF-matching method is
based on similar applications of the method for establishing
rainfall–reflectivity relationships for the calibration of radar or satellite
observations of precipitation
. The
quantile mapping methods are also widely used for correcting biases of
regional climate model simulations relative to observational data
. These studies assume that the
probability density functions of radar reflectivity and in situ rainfall are
equivalent and therefore quantile mapping can be used to translate one into
the other. RK04 extended this approach to soil moisture data assimilation by
transforming the satellite soil moisture retrievals into the model's
climatology for removing the relative biases between the model and
observations. The important difference between the precipitation/climate
downscaling studies and RK04 is that in the former, the remotely sensed
retrievals/climate model data were rescaled to observed data, whereas in
RK04 the satellite retrievals were rescaled to a modeled climatology. In
this article, we demonstrate that rescaling to a model climatology that is
not representative of the observations may distort the scale of the actual
observational features and may lead to loss of valuable signals.
There are a number of alternative strategies for bias correction in
bias-blind data assimilation systems. Instead of employing a single CDF (at
each grid cell) that encapsulates the soil moisture dynamics across all
seasons (called lumped CDFs), temporally stratified (monthly or seasonally)
CDFs can be used. The finer temporal stratification would help to reduce the
impact of statistical artifacts of using lumped CDFs, but would also require
sufficient sample sizes to accurately derive CDFs for each temporal window.
As demonstrated in , the land surface model could be
calibrated against the retrieval products and the calibrated, unbiased model
could then be used in assimilation. Though this strategy eliminates the
biases in the variables being assimilated, the climatologies of other outputs
from the model could be affected, unless additional constraints are included
in calibration. employed a similar strategy for
assimilating SMOS L-band brightness temperatures, by calibrating the forward
radiative transfer model parameters and by keeping the land surface model
parameters unchanged. This strategy preserves the land surface model
climatology but only works when radiance measurements are being assimilated
through a forward model. suggested a similar strategy
for assimilating passive microwave brightness temperatures for snow data
assimilation through the use of an artificial neural network (ANN). The ANN
uses the inputs from the land surface model and is trained to the observed
brightness temperatures to be assimilated. The results of
indicated that the ANN could serve as a
computationally efficient observation operator instead of more complex
radiative transfer models. In the current study, we evaluate the
effectiveness of a number of these strategies for land data assimilation when
the observations include the effects of processes that are not included in
the land surface model.
The article is organized as follows: First, we examine the effectiveness of
satellite soil moisture retrieval products in their ability to capture the
effects of irrigation (Sect. ). The evaluation is
conducted by quantitatively comparing the probability distribution functions
from various remote sensing soil moisture data sets and land surface model
simulations. The article then focuses on the impact of various a priori bias
correction approaches in data assimilation when the distributions of the
model and the observations are significantly different due to unmodeled
irrigation processes (Sect. ). Section
presents a synthetic data assimilation experiment that explores the
limitations of a suite of a priori bias correction strategies in such
scenarios. Finally, Sect. presents a summary and discussion
of major conclusions of the study.
MODIS-based irrigated grid-cell fraction (%) map of
over the continental US. The boxes (outlined in red
color) highlight three known areas with large-scale seasonal irrigation. The
yellow triangle in the inset indicates the location of the grid cell used in
point-scale land surface model simulations.
Surface soil moisture time series for the year 2000 from two
simulations of a land surface model: (1) a free-running model simulation with
the NLDAS-2 forcing (SIM1), and (2) a seasonal irrigation scheme simulated on
top of SIM1 (SIM2).
Evaluation of satellite remote sensing data over irrigated areas
In this section, we examine the utility of modern soil moisture remote
sensing data sets towards the detection of irrigation features. The irrigation
practices over the world differ in the method of irrigation, the trigger used
and the amount of water used in irrigation. A typical irrigation practice in
the US is to apply irrigation throughout the growing season at a level where
the plants are not under transpiration stress. The introduction of irrigation
at the beginning of the growing season would lead to increased surface soil
moisture and a significant dry down would only occur at the end of the
growing season when irrigation controls are removed.
Figure shows the MODIS-based irrigation grid-cell fraction
map (%) derived by and validated against USGS
irrigation data. Some of the known hotspots of irrigation over the
continental US are highlighted in this map, which includes the plains of
Nebraska, lower Mississippi Basin and California's Central Valley.
To demonstrate the impact of irrigation, land surface model simulations are
conducted at a single grid point located in the plains of Nebraska (as shown
in Fig. ). Figure presents the time series of
surface soil moisture (using a 10 cm thick surface layer) for a
representative year from two simulations of the Noah
(version 3.3; ) land surface model (LSM). The simulations
demonstrate the impact of irrigation at this location: (1) model forced with
a given meteorological forcing data (SIM1), and (2) a seasonal irrigation
scheme simulated on top of the SIM1 configuration (SIM2). The simulations use
the modified 20 category MODIS land cover data and
are forced with meteorological boundary conditions from the North American
Land Data Assimilation System Phase 2 (NLDAS-2; ) data.
The initial conditions for the model simulations are generated by spinning up
the LSM from 1979 to 2000. The irrigation scheme employed here simulates a
demand driven, sprinkler irrigation technique, based on
. Irrigation is triggered when the root zone soil
moisture falls below the transpiration stress threshold for a particular grid
cell. The scheme computes the irrigation requirement as an equivalent height
of water, which is then applied as an addition to the precipitation input to
the model. The irrigation scheme is only applied to irrigated land types such
as crops and grasslands and is only enabled during growing seasons (when
40 % of the annual range of green vegetation fraction at a grid cell is
exceeded). In addition, the irrigation requirement is enabled daily between
06:00 and 10:00 LT (local time), similar to the approach used in .
As the seasonal irrigation picks up in April, surface soil moisture in SIM2
gets much wetter compared to the SIM1 integration. Towards the end of the
summer, the imposed irrigation is removed, which then causes the soil
moisture to dry down and approach the SIM1-based estimates. For the purpose
of developing climatologies, the model integrations were conducted for
several years (2000–2012). Similar features are repeated in other years,
leading to a seasonal wet bias in SIM2 compared to SIM1, mainly in the summer months.
A comparison of the soil moisture distributions from the two integrations are
shown in Fig. , which shows a plot of the quantiles of SIM1
data against the quantiles of SIM2 data. For comparison, the figure also
shows a 45∘ reference line. If the two data sets come from similar
distributions, the points in the q–q (quantile–quantile) plot should fall approximately along
this reference line and the departure from the reference line indicates
differences in the distributions of the two data sets. Figure
indicates that there are significant differences in the SIM1 and SIM2
distributions with shifts in location, scale and symmetry. The data points
are systematically above the 45∘ line indicating that the mean of the
distributions are significantly different, with the distribution for SIM2
valued higher than that of SIM1. The q–q plot also shows a bimodal
nature due to the seasonal effect of irrigation. Finally, the slope of the
points on the q–q plot is higher than 1, indicating that there are
differences in the spread or variances of the two distributions as well.
A two-sample Kolmogorov–Smirnov (K–S) test can
be used to quantitatively compare the probability distributions of two
data sets. The K–S statistic quantifies a distance between empirical
distribution functions of two samples (F(x) and G(x) where x is the
sampled variable) and is computed as follows:
Dm,n=maxx|F(x)-G(x)|,
where m and n are the sample sizes of F and G.
The null distribution of the K–S statistic is calculated under the null
hypothesis that samples are drawn from the same distribution. The null
hypothesis is rejected at level α if
Dm,n>c(α)m+nmn,
where c(α) is the inverse of the Kolmogorov distribution at α.
A comparison of the cumulative distribution functions (CDFs) from
SIM1 and SIM2 integrations.
Kolmogorov–Smirnov distance (D) from comparison of soil moisture
distributions from SIM1 and SIM2 integrations.
K–S distance (D) from the comparison of soil moisture
distributions from the land surface model and various satellite remote sensing
data sets. Grid points in white color indicate locations that are omitted
from the K–S comparisons due to insufficient reliable data.
To examine the impact of irrigation on soil moisture distributions over a
larger spatial domain, the SIM1 and the SIM2 experiments are extended to a
larger domain, encapsulating the continental US at 0.125∘ spatial
resolution. The model integrations are conducted during the time period of
2000–2013. The K–S test is then applied to the probability distributions
of the surface soil moisture estimates from the two integrations. The
resulting values for the K–S statistic (D) are shown in
Fig. . Only locations at which the null hypothesis of
the K–S static is rejected are shown in Fig. .
Values of D closer to zero indicate that the soil moisture distributions
from the SIM1 and SIM2 integrations are similar. Conversely, larger D
values indicate locations where the soil moisture distributions from the two
integrations differ. As the difference between the two integrations in this
example is only due to the simulation of seasonal irrigation, the locations
with positive K–S metric values in Fig. indicate
areas where the irrigation artifacts are applied and are consistent with the
input irrigation intensity data used in the simulations. The K–S metrics,
therefore, can be used to detect instances where the distributions of soil
moisture retrievals and the model estimates differ significantly, including
differences due to the treatment of irrigation.
Figure shows a quantitative comparison of the differences
in soil moisture distributions using the K–S metrics from six remote sensing
soil moisture retrievals and a land surface model simulation (SIM1
configuration), for the continental US. The remote-sensing-based products are
(1) the blended multi-sensor soil moisture product from the European Space
Agency (ESA) known as the essential climate variable (ECV) product
, (2) soil moisture retrievals from AMSR-E using the
Land Parameter Retrieval Model (LPRM) algorithm ,
(3) soil moisture retrievals from WindSat, (4) soil moisture retrievals from
the backscatter measurements acquired by ASCAT, (5) soil moisture retrievals
from AMSR2, and (6) soil moisture retrievals from the SMOS mission. The
WindSat and ASCAT retrievals are obtained through the Soil Moisture
Operational Products System (SMOPS; ) of NOAA/NESDIS.
The level 3 AMSR2 data from the Japan Aerospace Exploration Agency (JAXA;
) and the level 2 swath-based SMOS products from ESA
are used in these comparisons. The temporal extent of
these data sets varies. The ECV data are available from January 1979 to December 2013,
AMSR-E from June 2002 to October 2011, WindSat from January 2007 to present,
ASCAT from January 2007 to present, AMSR2 from July 2012 to present and
SMOS from April 2012 to present. The CDFs for each data set
are computed using all available data. The available quality control
information in each remote sensing data set is used to exclude data over
regions with dense vegetation, radio frequency interference, precipitation and frozen
ground. The model CDFs are computed using the simulated surface soil moisture
estimates from 2000 to 2013. Differences in the dynamic range between
observed and modeled soil moisture are normally removed prior to assimilation
and here we remove the differences in the mean and variance prior to
calculating the K–S metrics. The data values are normalized first with a
standard score approach ((xit-μi)/σi where xit is the data
value at time t and μi and σi are the mean and standard
deviation of the data at grid point i) before computing the K–S metrics.
Figure shows the D estimates from the K–S test for each
comparison at grid points where the null hypothesis of the K–S static is
not rejected. Not surprisingly, the ECV data comparison shows the lowest D
values, possibly due to the fact that the ECV product was generated by CDF
matching soil moisture estimates from different sensors to a simulation of
the Noah land surface model from the Global Land Data Assimilation System (GLDAS;
). Comparatively, larger differences are seen in
all other comparisons, which are likely caused by a mix of biases resulting
from instrument error, retrieval algorithm errors, unmodeled processes,
and other representativeness differences.
The spatial patterns of these metrics shown in Fig. can
also be potentially used as a first measure of whether a sensor captures
observational features such as irrigation. Specifically, a relatively small
K–S metric at a location known to have irrigation suggests that the remotely
sensed observations did not detect that irrigation. However, the converse is
not necessarily true, in that a large K–S metric does not necessarily
indicate successful detection of irrigation (since it could be caused by
other model/remotely sensed discrepancies). For example, a strong signal of
vegetation density in the eastern US can be noticed in the K–S metric map for
AMSR2. Similarly, in the ASCAT K–S metric map, large differences can be
observed around several major cities such as Dallas, Houston and Atlanta. We
focus on three key hotspots of irrigation in the US shown in
Fig. : the plains of Nebraska, lower Mississippi Basin and
California's Central Valley. Of these three regions, only the lower Mississippi has
relatively higher K–S metric values, and only for AMSR-E, AMSR2 and SMOS.
To examine if the spatial patterns of differences in K–S metrics from
various remote sensing data sets are in fact representative of observational
artifacts such as irrigation, we examine the time series of soil moisture
over these regions. For an equivalent comparison given the possible
differences in the respective dynamic ranges, each data set is normalized
first (using the standard score approach) before comparing them on the same
graph. Figure shows the normalized time series of soil moisture
from the observations (from SMOS, AMSR2 and ASCAT), the Noah LSM driven with
the NLDAS-2 forcing, with and without irrigation for the year 2013. A 5-day
moving average is applied to the SMOS, AMSR2 and ASCAT retrievals to reduce
the noise in the satellite retrieval time series. As the grid-cell averages
for the satellite retrievals reflect averages of the irrigated and
non-irrigated pixels, a similar weighted estimate was produced for the
LSM-based irrigated soil moisture values. The LSM time series representing
irrigation in Fig. is generated by weighting the model soil
moisture estimate with and without irrigation for each grid cell by the
irrigation fraction and (1 - irrigation fraction) of that grid cell,
respectively. Finally, in each region, only grid cells with at least 30 %
irrigation fraction indicated by the MODIS map are employed in computing the
spatial averages.
Figure indicates that the SMOS and AMSR2 retrievals agree more
closely with the LSM estimate without irrigation, in all three regions. In
particular, there are few indicators of systematic differences between the
observations and the model without irrigation in the summer months,
suggesting the limited skill of the SMOS and AMSR2 retrievals for detecting
features of seasonal irrigation. In contrast, ASCAT retrievals show better
agreement with the LSM estimate with irrigation in the summer and fall
months, over the plains of Nebraska and lower Mississippi Basin. In these
regions, the ASCAT moisture signal shows a wetter trend in the late fall
months, which are in agreement with the LSM estimate with irrigation. In
California's Central Valley, however, no such distinct contrast due to
irrigation is observed in all three satellite retrievals. Similar trends are
seen in other years (not shown). From these results, it appears that neither
SMOS nor AMSR2 retrievals capture the effects of irrigation, whereas the
ASCAT retrievals are somewhat effective in detecting irrigation features in
the plains of Nebraska and the lower Mississippi Basin.
Comparison of normalized soil moisture values from Noah OL
simulation, SMOS, AMSR2 and ASCAT retrievals, for three subregions shown in
Fig. .
It is important to note here that the apparent inability of SMOS and AMSR2 to
capture the irrigation signal should not be assumed attributable to sensor
deficiency; it may instead reflect their larger spatial footprints. The raw
resolutions of SMOS and AMSR2 products used here are at least of 40 km, much
coarser than the 0.125∘ resolution employed in the LSM simulations.
Thus, because Fig. focuses on 0.125∘ grid cells with at least
30 % irrigation, the SMOS and AMSR2 data (interpolated to that resolution)
will necessarily include some soil moisture information from areas outside
those defined by the 30 % threshold – areas that are, almost by
definition, drier. ASCAT, with a raw resolution of ∼25 km does not seem
as affected by this, perhaps in part due to its finer base resolution.
Another possible reason may be related to the influence of
intercepted water, which has opposite effects on the active and passive sensors.
More analysis is needed, however, to understand the different behaviors of the sensors.
Note that in the model formulations, irrigation is simulated consistently
from the late spring months to early fall months, though these assumptions
about the timing and duration of irrigation in these regions may be imperfect
relative to the actual practices in the field. In the plains of Nebraska, the
agreement between the ASCAT and model with irrigation is consistent
throughout the summer and early fall months (from late June to early
October). In the lower Mississippi, on the other hand, the ASCAT time series
indicates that the application of irrigation occurs in the later months (from
late August onwards). The agreement between the model with irrigation and the
ASCAT time series is lower in the early summer months. Though it is hard to
ascertain the ability of ASCAT data for characterizing the timing of
irrigation, it can be concluded that ASCAT retrievals perform better than the
SMOS and AMSR2 retrievals in terms of capturing the anomalous wet soil
moisture signals from irrigation over these areas known to be irrigated.
Same as Fig. and including the surface soil moisture
time series from rescaling SIM2 to the SIM1 climatology. The red and blue
lines represent the SIM2 integration rescaled to the SIM1 climatology using
lumped and monthly CDF matching, respectively.
Evaluation of bias correction strategies in the presence of unmodeled processes
This section presents an examination of the effectiveness of a number of a
priori bias correction strategies in data assimilation when unmodeled
processes (such as irrigation) are a major source of biases between the model
and the observations. A synthetic experiment setup based on the SIM1 and SIM2
configurations presented in Sect. is used to explore these issues.
If SIM2 represents the observations to be used in assimilation, the typical
procedure in data assimilation systems is to rescale SIM2 estimates to the
model climatology (SIM1 in this example). Figure
illustrates the impact of rescaling SIM2 to SIM1 climatology with CDF
matching (using both lumped and monthly CDFs), for the year 2000. When lumped
CDFs are used, rescaling leads to a wetter soil moisture time series
(compared to SIM1) during the summer months (but significantly lower than
SIM2), whereas during the non-irrigation months, rescaling leads to a much
drier soil moisture time series, relative to SIM1. Lumped CDF matching
attempts to keep the climatology of the rescaled time series to be close to
the overall SIM1 climatology. As a result, higher soil moisture values during
irrigation are compensated by lower soil moisture values during non-irrigated
months to keep the overall climatology the same as that of SIM1. In this
example, the lumped CDF-based rescaling approach introduces spurious
statistical artifacts during non-irrigated periods. The statistical artifacts
of rescaling during the non-irrigated months are greatly reduced if the
CDF matching is performed in a more temporally stratified manner. As
indicated by Fig. , when rescaling uses monthly CDFs, the
resulting time series remain close to SIM1 both during the irrigated and
non-irrigated periods. Note that most data assimilation studies
use the lumped CDF-scaling approach due to sampling density limitations of
using temporally finer-resolved CDFs.
Structure of synthetic data assimilation experiments
The suite of data assimilation experiments employs an identical twin
experiment setup. The model simulations are conducted at the single grid
point shown in Fig. . The Noah LSM simulation forced with
the NLDAS-2 data is termed the open loop (OL) integration. A scheme
designed to mimic seasonal crop irrigation employed on top of the OL
configuration is used as the “Control/Truth” simulation. All model
integrations use the same forcing and parameter data sets as that of the
experiment presented in Sect. . The time period from
2000 to 2012 is used here for various evaluations.
From the truth simulation, observations are generated after incorporating
realistic errors and limitations of passive microwave remote sensing
retrievals. To account for difficulties in retrieving soil moisture products
from microwave sensors, the observations are masked out when the green
vegetation fraction values exceed 0.7 and when snow or precipitation are
present. Random Gaussian noise with an error standard deviation of
0.02 m3 m-3 is added to the truth soil moisture values to mimic
measurement uncertainties, which is an optimistic estimate of the
error levels in the current space-borne L-band radiometers (SMOS and SMAP).
Finally, a data assimilation (DA) integration that
assimilates the simulated observations in the OL configuration is conducted.
The DA and OL integrations are compared against the known truth to evaluate
the impact of observations.
Most synthetic experiment studies use
different inputs and models in the control and OL configurations to simulate
the systematic biases that are often present (between observations and the
model) in real data assimilation scenarios. Here we intentionally use a setup
where the only difference between the control run and OL is a process
(irrigation) that is not modeled in the OL simulation but is included in the
control run. One could envision similar issues in real data assimilation
systems, where features from engineered systems will be present in
observations but not simulated in physical models. In this idealized
scenario, biases between the model and the observations are purely from
observational features that are not modeled.
Four different data assimilation integrations are conducted using the
synthetic observations: (1) DA-NOBC, assimilating observations directly
without any bias correction; (2) DA-CDFL, assimilating a priori-scaled
observations using CDF matching (using lumped CDFs representing all years and
seasons); (3) DA-CDFM, assimilating a priori-scaled observations using
monthly CDF matching (the model and observation CDFs are generated separately
for each calendar month); and (4) DA-ANN, assimilating the simulated
observations directly and using a trained ANN as the observation operator in
the data assimilation system (see Sect. for details). In
experiments DA-NOBC, DA-CDFL and DA-CDFM, the observation operator is the
land surface model itself, whereas the observation operator is represented by
the trained ANN in the DA-ANN experiment.
In the DA-CDFL experiment, the observation and model CDF are first computed
independently for each grid cell using the 13-year (2000–2012) period.
During data assimilation, the observations are rescaled (separately for each
grid cell) using these lumped CDFs. As noted by , the
climatologies between the model and observations may change with season,
which is clearly the case in our synthetic experiment setup due to the
influence of seasonal irrigation. In the DA-CDFM experiment, the observation
and model CDFs are generated separately for each month and for each grid
point. The 13-year record of data ensures that there is enough sampling
density to accurately derive CDFs when the CDF calculation is stratified by
calendar months.
Data assimilation method
The data assimilation integrations are conducted using a one-dimensional
ensemble Kalman filter (EnKF; ) algorithm. An
ensemble size of 12 is used in the simulations with perturbations applied to
both meteorological fields and model prognostic fields to simulate
uncertainty in the model estimates.
The determination of 12 as the ensemble size was based on prior
works
and because the size of the model state vector is small (4 Noah soil moisture state variables).
The EnKF alternates between an ensemble forecast step and a data assimilation step. An ensemble of model states is
propagated forward in time using the land surface model during the forecast
step. In the update step at time k, the model forecast is adjusted toward
the observation based on the relative uncertainties, with appropriate weights
expressed in the “Kalman gain” Kk:
xki+=xki-+Kkyki-Hkxki-,
where xk and yk represent the model state and observation
vectors, respectively. The observation operator Hk relates the
model states to the observed variable. The superscripts i- and i+ refer
to the state estimates of the ith ensemble member (-) before and (+) after
the update, respectively. Equation () indicates that the
analysis increments (xki+-xki-) are computed by
multiplying the Kalman gain Kk with the innovations
(yki-Hkxki-). In “bias-blind” data assimilation systems,
observations (yk) and model forecasts (Hkxki-)
are expected to be unbiased relative to each other, which
presents two choices for bias correction: (1) rescale observations into the
model climatology, so that the innovations are computed in the climatology of
Hkxki- or (2) compute the innovations in the
observation space by having an operator (Hk) that translates the
model states into the observation space. The quantile mapping approaches fall
in the first category, whereas the use of trained forward models as
observation operator represents the second category. We examine the impact of
using both sets of approaches when unmodeled processes dominate the sources of biases.
Use of a trained ANN as a forward observation operator
Artificial neural networks (ANNs) are data processing systems used for
pattern matching applications and consist of a highly interconnected array of
processing elements (called neurons), designed as a mathematical
generalization of human cognition and learning. The basic architecture of an
ANN consists of three layers: input, hidden and output layers. The inputs
processed through the input layer are communicated to the hidden layers and
the results are output through the output layer. The topology of the layers
(defined by “activation functions”) and the weights of the interconnections
are used to develop accurate outputs. During the training phase, the ANN is
presented with a set of inputs and corresponding outputs. The trained ANN can
then be used for generating new predictions when presented with a new set of inputs.
Figure shows the structure of the ANN used in this study. The
input layer consists of six inputs, which are a combination of the
meteorological inputs (rainfall and snowfall), land surface model parameters
(green vegetation fraction) and land surface model estimates (surface soil
temperature, snow water equivalent and surface soil moisture). Note that the
surface soil moisture in the input layer is from the LSM integration without
irrigation. Five neurons were employed in the hidden layer based on a similar
approach used in and . For this
study, a single output node that estimates surface soil moisture values is
used. The ANN is trained to the simulated surface soil moisture observations
at this grid point (generated from the truth integration) during the time
period of 2000–2012. Since the entire observation record is used for
estimating CDFs, we use the whole record for training the ANN as well, so
that the experiments are comparable. Figure shows a
comparison of the simulated observations and the estimates from the trained
ANN for the year 2000. It can be seen that the trained ANN model helps to
capture the wetting of the soil due to seasonal irrigation during the spring
and summer months. Similar patterns are observed in other years (not shown).
The skill in turning on or off irrigation in the ANN is likely due to the
incorporation of the information in the training inputs of soil temperature
and green vegetation fraction. The trained ANN is then used in the DA experiments.
DA experiment results
The evaluation of the four DA experiments is presented in Figs. –.
Figure shows daily averaged soil moisture estimates from
various model integrations for the year 2000 as a representative time series.
The DA-NOBC integration assimilates the raw observations (shown in the
figure) and as a result provides soil moisture estimates closer to the
Control simulation during times when observations are available.
DA-CDFL and DA-CDFM integrations ingest rescaled
observations (not shown), which do not show a systematic increase in the soil
moisture values during the spring and summer months. Similar behavior is seen
for the DA-ANN integration, which assimilates the raw observations, but does
not represent the anomalously wet soil moisture of the Control simulation.
The DA-CDFL, DA-CDFM and DA-ANN integrations do not deviate much from the
open loop integrations as the size of the analysis increments
(Kk[yki-Hkxki-]) in these
integrations is small. In DA-CDFL and DA-CDFM, the rescaling causes the
innovations to be computed in the climatology of the model states whereas in
the DA-ANN experiment, the innovations are computed in the climatology of the
observations. In either case, when these small increments generated by the
assimilation system are applied back to the soil moisture forecast values (in
the open loop climatology), the anomalous wet signals in the observations are
removed as bias artifacts and are never included in the analysis.
Structure of the artificial neural network employed in the synthetic
DA integrations.
Time series of the Control simulation (black line), open loop
(dashed line), simulated observations (filled circles) and estimates from the
trained ANN (triangles) for the year 2000.
Time series of simulated observations, Control, open loop and
various DA integrations for the year 2000. DA-NOBC assimilates observations
directly without any bias correction, DA-CDFL assimilates a priori-scaled
observations using CDF matching (using lumped CDFs), DA-CDFM assimilates a
priori-scaled observations using monthly CDF matching and DA-ANN assimilates
the simulated observations directly and using a trained ANN as the
observation operator in the data assimilation system.
Average seasonal cycle of the RMSE for surface soil moisture from the
open loop, and various DA integrations relative to the Control simulation.
Distribution of normalized innovations from various DA integrations
compared against the standard normal distribution.
Figure shows the average seasonal cycle of RMSE (root mean squared error; stratified
monthly across the entire simulation period of 2000–2012) of surface soil
moisture from various model integrations. Similar to the trends in
Fig. , the DA-NOBC integration shows significant
improvements from data assimilation except for August. The peak of vegetation
(determined based on the green vegetation fraction) occurs in August leading
to observations being excluded from the data assimilation system. As a
result, the improvements through assimilation are small during this time
period. The seasonal nature of the RMSE estimates from DA-CDFL, DA-CDFM, and
DA-ANN is similar and is close to the open loop RMSE estimates. The use of
the scaled observations (in DA-CDFL and DA-CDFM) and the use of the trained
forward model (in DA-ANN) causes the dampening and exclusion of the wet
biases from irrigation in these DA integrations.
An important philosophical point, however, is warranted here. Implicit in the
above discussion of Fig. is the assumption that a higher RMSE
reflects a poorer performance. Depending on application, this may not be true
at all. It is a well-established fact that the soil moisture estimate from the model is
essentially an index of wetness and a highly model-dependent quantity
. As a result, care must be exercised when
comparing model soil moisture directly to in situ or satellite measurements.
The whole point of the scaling exercise is to convert a
satellite-based soil moisture value, prior to its assimilation, to a value
consistent with that of the LSM used. This allows the further use of the
assimilated soil moisture value in that LSM, e.g., to initialize a forecast.
If, once the data assimilation process is finished, a soil moisture value is
needed that reflects a more “correct” climatology (e.g., with an
irrigation-influenced seasonal cycle, as in the Control simulation), the data
assimilation product can easily be scaled back to that climatology using the
reverse of the original scaling approach. Viewed in this light, the data
assimilation approach, with scaling, is essentially designed to capture the
year-to-year or short-term variations in soil moisture anomalies rather than
the structure of the seasonal cycle. Also note that, though the seasonal cycle
of RMSE is lowest in the DA-NOBC integration, this configuration is not
really viable in real data assimilation systems where biases are unavoidable.
The DA-NOBC integration is included in the suite of experiments, as we have
the knowledge of the exact sources and magnitudes that contribute to the
biases in this synthetic configuration. For real data assimilation systems,
metrics recommended by , which compute estimates of soil moisture
accuracy while accounting for biases, may be more appropriate.
The EnKF algorithm assumes linear system dynamics. It further assumes model
and observation errors that are Gaussian and mutually and serially
uncorrelated. If these assumptions hold, then the distribution of filter
innovations (observation minus model forecast residuals) normalized by their
expected covariance will follow a standard normal distribution N[0, 1]
. The deviations from the N[0,1] of the normalized
innovation distribution is typically used as a measure of the degree of
suboptimality of the data assimilation system .
Figure compares the distribution of the normalized
innovations from DA-NOBC, DA-CDFL, DA-CDFM and DA-ANN to the N[0, 1]. The
mean and standard deviation of each distribution are also reported in the
figure. Unsurprisingly, the DA-NOBC indicates the largest deviation in the
mean among the experiments, indicating the presence of a bias. The mean
values of the distributions from DA-CDFL, DA-CDFM and DA-ANN are closer to
zero, due to various a priori bias correction strategies employed.
These internal diagnostics are also often used for the estimation of input
error parameters of the data assimilation system. For example, in adaptive
filter implementations , the model and
observation error specifications are continually adjusted to yield
near-optimal behavior of the internal diagnostics (i.e., close to N[0, 1]
response of normalized innovation distribution). The analysis presented above
indicates that if unmodeled processes are present, these biases are reflected
in the innovation diagnostics as deviations from expected optimal measures.
In such cases, the reliance on these assimilation diagnostics may be
misleading if the end goal of the assimilation process is to correct the
modeled seasonal cycle of soil moisture toward that of the observations. As
noted above, though, the goal may instead be to capture, for various
applications, year-to-year anomalies in soil moisture and, for this purpose,
the innovation diagnostics reveal that the scaling approaches do provide
superior behavior. Again, though, it should be pointed out that the synthetic
experiment was designed to isolate the impacts of unmodeled irrigation. In
practice, the effects of unmodeled irrigation will be conflated with bias
issues that result from differences in land surface parameters and
differences in the very meaning (such as layer-depth) of the modeled and
retrieved soil moisture values.
Summary
Due to the heterogeneity of the land surface and the large impact of human
activities, quantifying the variability of water and energy budgets on the
land surface presents unique challenges compared to the atmosphere and ocean
components of the Earth system. Irrigation is one of the pervasive
human-induced land management practices that has a direct impact on the local and
regional water budgets. In this article, we examine the utility of satellite
soil moisture retrievals to detect irrigated areas. In addition, the article also
examines the limitations of current data assimilation practices when the
observations are dominated by processes that are not included in the land model.
Application of seasonal irrigation is likely to introduce systematic
differences in the soil moisture distributions. Therefore, if the remote
sensing data sets are skillful in detecting irrigation features, the resulting
soil moisture distributions would be significantly different compared to a
model simulation that does not simulate irrigation. We use this hypothesis to
examine the effectiveness of modern remote sensing soil moisture products
from ASCAT, AMSR2 and SMOS in their ability to detect irrigation. A two-sample Kolmogorov–Smirnov test is used to quantify the systematic
differences between distributions of model and remote sensing data sets, over
a continental US domain. The analysis reveals systematic differences in
spatial patterns of the distributions of model and remote sensing data.
Additional analysis, however, suggests that these differences are not always
related to the detection of irrigation artifacts. Generally, ASCAT retrievals
were found to be somewhat more skillful than the SMOS and AMSR2 retrievals in
their ability to capture features of irrigation on the land surface.
Overall, the analysis presented in the paper assumes a demand-driven
irrigation scheme maintained throughout a growing season at a level where the
plants are not under transpiration stress. In reality, however, the type and
level of irrigation may not be seasonally persistent and therefore the nature
of the expected biases in the soil moisture signal due to irrigation may not
be systematic throughout a season. Further comparisons with in situ soil
moisture data at irrigated locations will be required to confirm and isolate
the limitations of the remote sensing data over these areas. A major source
of the biases between the satellite retrievals and the LSM estimates is the
differences in the land surface parameters used in the respective models. The
biases from these parameter differences are likely to dominate the more
subtle effects of irrigation. In addition, the scale mismatches between the
model and the observations are also likely to have an influence in the
comparisons presented here. The spatial resolution of the model
(0.125∘) and the observations (∼ 25–40 km) can be considered
relatively coarse for detecting uniformly and simultaneously irrigated areas.
The second focus of the article is on the limitations of various a priori
bias correction strategies in land data assimilation towards representing
unmodeled processes. This issue is explored through a suite of synthetic data
assimilation experiments. A simulation of seasonal irrigation is used as
analog for an engineered process that is typically not included in
large-scale land surface model simulations. The data assimilation
integrations merge the observations generated from the irrigation simulation
into a model in which irrigation is absent and features a free-running land
surface model. The data assimilation integrations include simulations that
employ no bias correction, a lumped CDF-matching correction, a seasonally
varying CDF-matching correction or ANN as a forward observation operator. As
the a priori bias correction approaches make no distinction of the source of
the biases (unmodeled or from other sources), they treat all systematic
differences between the model and observations as biases. As a result, all a
priori bias correction strategies considered above cause the signal from
seasonal irrigation (or other unmodeled processes) to be excluded in the DA
results, though the analysis of the DA internal diagnostics indicate
near-optimal performance for such configurations.
The challenge in data assimilation systems is to separate the biases that are
due to instrument error and retrieval algorithm errors from the biases
induced by unmodeled processes so that the true observational features are
not excluded during data assimilation. Detecting spatial patterns of such
differences could be useful in the utilization of soil moisture data sets in
data assimilation systems. For example, even if a particular retrieval
data set is not skillful in detecting irrigation in a given region, it could
still perform adequately over other regions. If knowledge of such limitations
are known a priori, at the very least the assimilation system could simply
exclude the use of the retrievals over known irrigated areas. Ancillary
information from other remote sensing platforms could be useful in such
scenarios. For example, estimates of land surface temperature and
evapotranspiration measurements can be obtained from thermal remote sensing
platforms, which can also be used as an analog for detecting the effects of
irrigation. Similar to the wetting effect irrigation has on surface soil
moisture, it also has a cooling effect on the surface temperature. Increased
water availability from irrigation also leads to increased evaporation.
Finally, irrigated time periods also correlate with an increase in vegetation
indices such as leaf area index (LAI) and normalized vegetation difference
index (NDVI). Expected trends of anomalies in these data sets from irrigation
could be used as added constraints in data assimilation to mask the known
limitations of passive microwave soil moisture retrievals.
It is obviously difficult to attribute bias to unmodeled processes or other
factors. Calibrating the land surface model parameters can be an effective a
priori correction approach in this scenario. Land surface model calibration
would incorporate the observational signals by altering the default model
behavior. When the calibrated model is subsequently used in data
assimilation, the observational signal is preserved. In contrast, calibrating
a forward radiative transfer model (or using a trained ANN) has a different
impact in terms of representing unmodeled processes. Calibration of forward
observation operators would attribute the bias to its parameters; however, since
the default land model behavior is unchanged, the unmodeled process is
ultimately not represented. The land surface model parameter estimation in
this context also has a number of disadvantages. The physical realism of the
estimated parameters may be violated given that the calibration would
attribute the error from all unmodeled processes to model parameters. If data
from multiple sensors are being concurrently assimilated into such a
“calibrated” model, the calibration approach would not be viable because a
new set of calibrated model parameters would be needed for each sensor,
leading to differing model climatologies and behaviors.
Another possible alternative may be to examine the characteristics of the
differences between the model and observations over a larger domain and infer
a general estimate of the relative biases. For example, instead of computing
CDFs at each grid point, they can be computed by grouping and stratifying
model and observation estimates based on the vegetation type across a larger
domain. The grid points where the soil moisture PDFs differ significantly
(based on the K–S metrics, for example) can be excluded in the computation of
the CDFs. The model and observation CDFs computed for each vegetation type
can then be used in the data assimilation system. The goal behind such an
approach would be to develop an overall estimate of the true biases between
the model and observations (i.e., an estimate that excludes biases due to
unmodeled processes). The downside of such approaches is that they obviously
disregard the importance of geographic specificity in bias correction
strategies. The synthetic experiment that we have used above is not an ideal
setup to examine this approach. Since the only difference between the
observations and the open loop in this setup is the effect of irrigation, the
use of the above mentioned approach would produce identical CDFs for the
model and observations and therefore the assimilation approach would be
equivalent to that of DA-NOBC. We therefore leave the evaluation of such
alternate approaches to future work.
Acknowledgements
Funding for this work was provided by the NASA Science Mission Directorate's
Earth Science Division through the National Climate Assessment (NCA) project
and NOAA's climate program office (MAPP program). Computing was supported by
the resources at the NASA Center for Climate Simulation. The NLDAS-2 forcing
data used in this effort were acquired as part of the activities of NASA's
Science Mission Directorate, and are archived and distributed by the Goddard
Earth Sciences (GES) Data and Information Services Center (DISC).
Edited by: H.-J. Hendricks Franssen
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