Research article

Nonlin. Processes Geophys., 30, 457–479, 2023
https://doi.org/10.5194/npg-30-457-2023© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.

Comparative study of strongly and weakly
coupled data assimilation with a global
land–atmosphere coupled model
Kenta Kurosawa1,2 , Shunji Kotsuki1,3,4,5,6 , and Takemasa Miyoshi1,2,5,6,7
1 Data Assimilation Research Team, RIKEN Center for Computational Science, Kobe, Japan
2 Department of Atmospheric and Oceanic Science, University of Maryland, College Park, Maryland, USA
3 Center for Center for Environmental Remote Sensing, Chiba University, Chiba, Japan
4 PRESTO, Japan Science and Technology Agency, Chiba, Japan
5 RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program, Kobe, Japan
6 Prediction Science Laboratory, RIKEN Cluster for Pioneering Research, Kobe, Japan
7 Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan

Correspondence: Kenta Kurosawa (kkurosaw@umd.edu) and Shunji Kotsuki (shunji.kotsuki@chiba-u.jp)
Received: 5 May 2023 – Discussion started: 15 May 2023
Revised: 22 August 2023 – Accepted: 5 September 2023 – Published: 23 October 2023

Abstract. This study explores coupled land–atmosphere data assimilation (DA) for improving weather andhydrological forecasts by assimilating soil moisture (SM) data. This study integrates a land DA component into
a global atmospheric DA system of the Nonhydrostatic ICosahedral Atmospheric Model and the local ensemble
transform Kalman filter (NICAM-LETKF) and performs both strongly and weakly coupled land–atmosphere DA
experiments. We explore various types of coupled DA experiments by assimilating atmospheric observations
and SM data simultaneously. The results show that analyzing atmospheric variables by assimilating SM data
improves the SM analysis and forecasts and mitigates a warm bias in the lower troposphere where a dry SM bias
exists. On the other hand, updating SM by assimilating atmospheric observations has detrimental impacts due
to spurious error correlations between the atmospheric observations and land model variables. We also find that
assimilating SM by strongly coupled DA is beneficial in the Sahel and equatorial Africa from May to October.
These regions are characterized by seasonal variations in the precipitation patterns and benefit from updates in
the atmospheric variables through SM DA during periods of increased precipitation. Additionally, these regions
coincide with those identified in the previous studies, where a global initialization of SM would enhance theprediction skill of seasonal precipitation.

1

Introduction

The Earth’s natural environment can be considered a unified system in which several subsystems (e.g., atmosphere,hydrosphere, cryosphere, and biosphere) interact with eachother. Coupled models consider at least two of the Earth’s
subsystems and have been developed to emulate such interactions within unified systems. For example, coupled land–
atmosphere models consider land–atmosphere interactions
by passing the output data from the land subsystem to theatmospheric subsystem and vice versa during model time in-tegrations. Coupled models represent more realistic physicalprocesses and provide improved predictions of Earth’s phenomena compared to those models that consist of only a single component.
Data assimilation (DA) plays an important role in numerical weather prediction (NWP) by providing accurate initialconditions. Some studies investigated coupled DA for ocean–
atmosphere interactions (e.g., Zhang et al., 2007; Sugiura etal., 2008; Fujii et al., 2009; Frolov et al., 2016; Laloyaux etal., 2016; Sluka et al., 2016; Browne et al., 2019; Penny and
Hamill, 2017; Penny et al., 2019) and land–atmosphere inter-

Published by Copernicus Publications on behalf of the European Geosciences Union & the American Geophysical Union.

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K. Kurosawa et al.: Comparative study of strongly and weakly coupled data assimilation

actions (e.g., de Rosnay et al., 2012; Lea et al., 2015; Suzuki
et al., 2017; Sawada et al., 2018; Draper and Reichle, 2019;
Fairbairn et al., 2019).
In this study, we focus on experiments to evaluate thepotential benefits of assimilating synthetic soil moisture(SM) data from the Global Land Data Assimilation System(GLDAS; Rodell et al., 2004), within a controlled experimental setup through the effective use of land–atmosphereinteractions via data assimilation. Specifically, this study investigates whether assimilating atmospheric (land) observational data into land (atmospheric) models is beneficial
for their subsequent forecasts. We employ SM data fromGLDAS, a comprehensive and reliable dataset which facilitates simple data handling and is suitable and sufficient forthis study (see Sect. 2.4). SM is particularly important among
land variables because it controls the exchange of water andenergy between the atmosphere and land surface (Bateni and
Entekhabi, 2012). For example, SM has a profound impact
on the evolution of boundary layers and precipitation during the warm season, a time characterized by high incoming radiation and evapotranspiration (Betts, 2009; Dirmeyerand Halder, 2016; Drusch and Viterbo, 2007). Moreover, improving SM data is essential for enhancing seasonal-scale
climate predictions (Dirmeyer, 2000; Douville and Chauvin,2000; Drusch, 2007; Hauser et al., 2017). With a regional
NWP system, Santanello et al. (2019) showed that SM DA
changed surface fluxes, evolution, entrainment of the planetary boundary layer, and ambient weather.
Two well-known coupled DA methods are weakly coupled DA and strongly coupled DA (cf. Sect. 2.2). One argument suggests that strongly coupled DA is preferable forenvironmental prediction, as discussed at the 2012 International Workshop on Coupled Data Assimilation. A follow-up
workshop in Toulouse in 2016 further elaborated on the needfor coupled DA. As for ocean–atmosphere models, Pennyet al. (2019) explored a method to improve the initialization process using a simplified model. They estimated ocean
conditions with atmospheric observations and vice versa andfound strongly coupled DA approaches were generally superior to weakly coupled approaches when using the simple toymodel. As Tang et al. (2021) stated, however, regarding more
complex models, it is unclear whether strongly coupled DA
generally outperforms weakly coupled DA. When it comes toland–atmosphere models, several studies have demonstrated
the benefits of strongly coupled DA approaches for mediumrange NWP (Suzuki et al., 2017; Sawada et al., 2018). In
terms of assimilation of land observations, while weakly coupled land–atmosphere DA is still the mainstream in NWP
systems (e.g., Zhang et al., 2007; Lea et al., 2015; Draperand Reichle, 2019), several studies have already examined
the benefits of strongly coupled DA on land observations.
For example, Lin and Pu (2019, 2020) assimilated surface
SM, 2 m temperature and humidity, and conventional atmospheric observations, showing advantages of strongly coupled DA. They also showed that SM had crucial impacts on
Nonlin. Processes Geophys., 30, 457–479, 2023

the temperature field rather than the other variables. Thus, it
is already known that SM DA is beneficial for the coupledland–atmosphere models, but updates of cross-components
have not yet been explored enough. Therefore, this study
aims at exploring better strategies to assimilate SM data ina strongly coupled land–atmosphere DA system.
This study uses a global atmospheric DA system known
as the NICAM-LETKF (Terasaki et al., 2015), which consists of the Nonhydrostatic ICosahedral Atmospheric Model(NICAM; Satoh et al., 2008, 2014) and the local ensemble transform Kalman filter (LETKF; Hunt et al., 2007).
NICAM incorporates the Minimal Advanced Treatments ofSurface Interaction and RunOff model (MATSIRO; Takata
et al., 2003) as the land surface subsystem. We implement
coupled land–atmosphere DA in NICAM-LETKF to assimilate SM observations using either the weakly or strongly coupled DA methods. Our primary scientific question is whether
the assimilation of synthetic observational data from one
model into another can improve compatibility between thetwo models in the NICAM-LETKF system. In addition toconventional atmospheric observations and AMSU-A radiances in NICAM-LETKF, this study assimilates SM data as
land observations.
This article is organized as follows. Section 2 describes the
newly developed coupled land–atmosphere DA system. The
experimental settings are described in Sect. 3. The results arepresented and discussed in Sect. 4. Finally, a summary is provided in Sect. 5.
2
2.1

Methodology
NICAM and MATSIRO models

NICAM is an icosahedral-grid-based atmospheric model thathas been widely used for NWP (e.g., Kotsuki et al., 2019b,c) and climate-scale predictions (e.g., Kodama et al., 2015;
Kikuchi et al., 2017). We use NICAM with a 112 km horizontal resolution and 38 vertical layers to a height of approximately 40 km. Due to the relatively coarse horizontal resolution, the Arakawa and Schubert scheme (Arakawa and Schubert, 1974) and Berry’s parameterization (Berry, 1967) are
employed for cumulus parameterization and the large-scalecondensation scheme, respectively. See Satoh et al. (2008,2014) for further details about NICAM.
MATSIRO represents all the major processes of waterand energy exchange between land and atmosphere. MATSIRO consists of five vertical layers used for simulating soil
temperature and moisture: 0–0.05, 0.05–0.25, 0.25–0.5, 0.5–
0.75, and 0.75–2 m. Surface energy and water fluxes arecomputed from their budgets at the ground and canopy surfaces in snow-free and snow-covered regions, considering
the subgrid-scale snow distribution (Takata et al., 2003). SM
is calculated in each soil layer and is representative of theentire land component of a model grid area, whether snowcovered or not. Note that, in general, SM in NWP models has
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K. Kurosawa et al.: Comparative study of strongly and weakly coupled data assimilation

been updated using 2 m temperature and humidity observations for decades (e.g., Mahfouf et al., 2000; de Rosnay etal., 2014; Gómez et al., 2020).
2.2

LETKF and coupled data assimilation
implementations

LETKF is a type of ensemble Kalman filter (EnKF; Evensen,
2003) that has been used for atmospheric, hydrological, andoceanic DA. LETKF solves the analysis equations at every
model grid point by assimilating the subset of observations
within its localization influence radius. The analysis equations of LETKF are based on the ensemble transform Kalmanfilter (Bishop et al., 2001):
x a = x f + δXf wa ,T
wa = P̃a HδXf R−1 yo − Hx f ,afaδX = δX W ,hi12
Wa = (m − 1)P̃a ,

(1)
(2)
(3)
(4)

where x is the ensemble-mean model state, δX is the ensemble perturbation matrix, H is the linear observation operator,
R is the observation error covariance matrix, y is the observation data, and P̃a is the model state error covariance matrix in ensemble space, while superscript letters a, f, and odenote analysis (posterior), forecast (prior), and observation,
respectively. Here, P is used for the error covariance in model
space, and P̃ is used for the error covariance in the ensemble
space. m is the ensemble size. w is the (m × 1) ensemble
transform vector for the ensemble mean updates, and W is
the (m × m) ensemble transform matrix for ensemble perturbation updates. The analysis error covariance matrix P̃a isgiven by

−1

T
f
−1
f
P̃ = (m − 1) I + HδX R HδX
,
a

(5)

where I is the identity matrix. In practice, since the error covariance matrix P̃a is often underestimated, and filters eventually become unstable, the introduction of the model error
or variance inflation is necessary for stable filtering. The theoretical explanation of the model error can partially be attributed to the model nonlinearity under the perfect model
assumption. In this study, instead of adding random noise as
the model error, we use a relaxation method at the end of the
DA process, as described in Sect. 3.
The analysis equation of the ensemble mean (Eqs. 1 and 2)
is equivalent to the original analysis equation of the Kalmanfilter:T
x a = x f + δXf P̃a HδXf R−1 yo − Hx f

−1 

= x f + Pf HT HPf HT + R
yo − Hx f .
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459

Here, Pf is the model state error covariance matrix in model
space. The EnKF uses an ensemble-based approximation to
the forecast error covariance:
 T
1
Pf ≈
δXf δXf .
(7)
m−1
For coupled models, Eq. (7) is approximated by
 
Pf

αβ

≈


T
1
δXfα δXfβ ,
m−1

(8)

where α and β are the model variables updated in the coupled DA. Thus, for coupled land–atmosphere models, Pf isrepresented byPf AA Pf AL
Pf =
.
(9)
Pf LA
Pf LL
In Eq. (9), “A” and “L” represent the variables of the atmosphere and land, respectively. In the current study, for example, (Pf )AA represents the covariance between atmosphericvariables, and (Pf )AL represents that between atmosphericvariables and SM. This study employs the ensemble-based
estimation of cross-component error covariance ((Pf )AL and(Pf )LA ) using Eq. (8). Here each ensemble member represents a coupled forecast where the atmospheric and land variables interact each other. Specifically, the MATSHIRO variables are driven by forcing from NICAM, and the upward
flux from MATSHIRO feeds back into NICAM. This coupling captures the essential interactions between the atmosphere and land variable, leading to physically derived crosscomponent error covariance during the forecasts. Note thatthe state variable xf does not include the land component
when the land variables are not updated (cf. Fig. 2a and d).
For such cases, the forecast error covariance matrix also has
the inverse matrix since the land component is also excludedin the background error covariance.
In practice, since some observations have nonlinear observation operators, the following approximation is required:HδXf ≈ H xf 1T + δXf − H xf 1T + δXf 1T ,(10)

where H is the nonlinear observation operator, and 1 denotes
a column vector with all m elements being equal to 1.
For the weakly coupled DA (hereafter WCDA) method, atmospheric observations are used only for updating NICAM
state variables, and land observations are used for thoseof MATSIRO (Fig. 1a). That is, the cross-component error
covariance between atmospheric and land variables is assumed to be 0 in WCDA (i.e., (Pf )AL = 0 and (Pf )LA = 0).
Thus, impacts of atmospheric observations can propagate toland model states, and vice versa, only through interactions
between NICAM and MATSIRO during model forecasts.
For the strongly coupled DA (hereafter SCDA) method, thecross-component covariance is estimated based on ensemble
forecasts (i.e., (Pf )AL 6 = 0, (Pf )LA 6 = 0, or both are nonzero
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K. Kurosawa et al.: Comparative study of strongly and weakly coupled data assimilation

Figure 1. Schematic images of (a) weakly coupled and (b) strongly coupled land–atmosphere data assimilation (DA) methods. Thin blackarrows indicate model state updates through DA. Cyan double-headed arrows indicate land–atmosphere interactions between NICAM and
MATSIRO during subsequent model forecasts. Here, panel (b) shows the fully strongly coupled DA method (cf. Fig. 2g). The image for
NICAM was adapted from Satoh et al. (2014).

matrices). Therefore, atmospheric or land observations areused to update both NICAM and MATSIRO variables basedon the cross-component covariance (Fig. 1b). SCDA extracts
more information than WCDA from the same observations if
an appropriate forecast error covariance (Pf )αβ is applied.
This study considers seven coupled DA experiments(Fig. 2). Referring to Penny and Hamill (2017), we classify these experiments into five categories: quasi-WCDA,
WCDA, quasi-SCDA, SCDA, and fully SCDA. Here we introduce identifiers (IDs) indicating which observation typeis assimilated for each model. This study defines “A” and“L” as representations of the atmospheric and land, respectively. The IDs are defined as follows: “AA× ” represents that
assimilating only atmospheric observations to update the atmospheric model; “AAL ” signifies that assimilating both atmospheric and land observations to update the atmosphericmodel; “LA× ” denotes that assimilating only land observations to update the land model; “L×L ” indicates that assimilating only land observations to update the land model;“LAL ” corresponds to that assimilating both atmosphericand land observations to update the land model; and finally,“L×× ” represents that no observation is assimilated to update
the land model.
For example, “AA× L×× ” indicates that atmospheric observations are used to update the NICAM variables, while
no observations are assimilated for the land model (Fig. 2a).
This experiment is considered quasi-WCDA and is equivalent to the standard NICAM-LETKF system without SM
DA or the control case (hereafter CTRL). “AA× L×L ” stands
for WCDA (Fig. 2b), while “AAL LAL ” signifies fully SCDA
(hereafter full-SCDA; Fig. 2g). The remaining four experiments are treated as quasi-SCDA (Fig. 2c and d) and SCDA
(Fig. 2e and f).
This study designs specific configurations of SCDA and
WCDA to investigate whether updating MATSIRO variables
through assimilating particular atmospheric observations hasa beneficial impact. This investigation aims at finding thebest-performing coupled land–atmosphere DA that consists

Nonlin. Processes Geophys., 30, 457–479, 2023

of updates with a beneficial effect for the experimental setting of the present study. The best-performing approach
might be different if we use different DA configurations orchange the experimental settings, such as resolution and DA
frequency.
2.3

Atmospheric data

The original NICAM-LETKF system assimilates conventional observations from the NCEP operational system (a.k.a.
NCEP PREPBUFR), satellite radiance from Advanced Microwave Sounding Unit-A (AMSU-A), and the near-realtime version of Global Satellite Mapping of Precipitation(GSMaP_NRT). The dataset includes a number of different
types of data: radiosondes, wind profilers, aircraft reports,
surface pressure, atmospheric motion vectors, and surface
winds derived from satellite observations. The channel selections for satellite radiances are 6, 7, and 8 for AMSUA. The stratospheric sensitive channels are not assimilated
in this study, considering the relatively low top level of the
NICAM in this study (40 km). The satellite radiance scans
and air mass biases are adaptively estimated and corrected ateach data assimilation cycle. This experimental setting followed the operationally running NICAM-LETKF system. In
this study, we use these data as atmospheric observations (cf.
Table 1 of Kotsuki et al., 2019a). For further details of theassimilation methods used for these observations, we referreaders to previous studies (Terasaki et al., 2015; Kotsuki etal., 2017a; Terasaki and Miyoshi, 2017).
2.4

Soil moisture data

Satellite instruments can measure several land variables, including SM, surface skin temperature, and snow depth. Previous studies have found that land surface models tend tooverestimate SM relative to SM data derived from satellite observations (Bindlish et al., 2018). GLDAS also shows
larger SM values than satellite-based data (Bi et al., 2016).
The significant bias between the model-based estimate andhttps://doi.org/10.5194/npg-30-457-2023

K. Kurosawa et al.: Comparative study of strongly and weakly coupled data assimilation

461

Figure 2. Schematic plots of seven DA experiments for (a) AA× L×× (CTRL; quasi-WCDA), (b) AA× L×L (WCDA), (c) AA× LA× (quasi-

SCDA), (d) AAL L×× (quasi-SCDA), (e) AA× LAL (SCDA), (f) AAL L×L (SCDA), and (g) AAL LAL (full-SCDA). The vertical axis represents atmospheric or land variables, and the horizontal axis shows observations. The shading of variables matches that of the observations
used for their updates. White areas with “no” indicate error correlations that are assumed to be zero in DA. Gray areas with “yes” indicate
error correlations that are included in DA.

observation is unfavorable for DA. Prior to DA experiments,
we compare spatial distributions of climatological SM for
NICAM and satellite-based observations from the Soil Moisture and Ocean Salinity (SMOS; https://smos-diss.eo.esa.
int/oads/access/, last access: 14 October 2023) and the Advanced Microwave Scanning Radiometer 2 of Global Change
Observation Mission – Water (GCOMW/AMSR-2; https://lance.nsstc.nasa.gov/amsr2-science/, last access: 14 October2023). We can see that NICAM SM is greatly biased compared to these satellite-based data (Fig. 3a, c, and d). In contrast, the bias of SM in NICAM relative to GLDAS is muchsmaller than that relative to SMOS and GCOMW/AMSR-2.
Hoover and Langland (2017) assimilated pseudoradiosonde observations from an independent atmosphericreanalysis system. They mentioned that assimilating reanalysis data from an advanced system significantly reduced
biases in atmospheric temperature and geopotential height.
As a first step, this study takes a similar approach and assimilates SM from GLDAS to avoid using satellite observation
data which usually contain significant bias.
It is generally known that satellite, remote sensing, andmodel datasets have different mean SM values. Since we do
not know the true mean values in remote sensing or model
outputs, we cannot attribute these differences in these mean
to bias in any specific data source. Satellite retrieval andmodel averages are determined by the parameters used in
the retrieval and surface models, but we also do not know

https://doi.org/10.5194/npg-30-457-2023

what those parameters should be. Therefore, the standard approach in SM data assimilation is to remove the difference
between modeled and observed SM averages and then assimilate only the temporal anomalies in the observed SM
values. Since it is crucial to have unbiased model and observation states to ensure the DA assumption is correct, several processes are proposed (Dee, 2005). For example, Reichle and Koster (2004) suggest a simple method to remove
strong biases between satellite-based and model-based data,in which they match the cumulative distribution functions(CDFs) of the satellite and model data (a.k.a. CDF matchingapproach). On the other hand, several previous studies havesuccessfully performed data assimilation without bias correction (e.g., De Lannoy et al., 2007; Bosilovich et al., 2007;
Reichle et al., 2010; Honda et al., 2018). For example, Honda
et al. (2018) demonstrated that assimilating geostationary
satellite infrared radiance observations without bias correction every 10 min reduced the bias between the forecast andobservations, leading to improved analysis without causinginconsistencies in the model states. Following the successof these previous studies, the present study assimilates SMdata without bias correction. As shown later in Sect. 4a, thebias between the forecast and observation becomes negligible after a 1-month spin-up period when SM from GLDAS
is assimilated every 6 h. Consequently, assimilating SM data
without bias correction yields improvements in prediction
accuracy of atmospheric variables. Since employing bias cor-

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K. Kurosawa et al.: Comparative study of strongly and weakly coupled data assimilation

Figure 3. Spatial patterns of soil moisture (m3 m−3 ) for NICAM, GLDAS, SMOS_L2_NRT_NN, and GCOM_W/AMSR2, averaged overFebruary to June in 2015 (a, b) and 2016 (c, d).

rection techniques and assimilating real satellite-sensed SMdata could potentially lead to further enhancements, such endeavors are important subjects for future studies.
We perform QC using flags provided with the satellite observation data. In addition, as applied for PREPBUFR and
GSMaP_NRT observations, we simply apply a gross error
check for SM in which observations are rejected when theobservation-minus-forecast value is greater than 10 times theobservation error standard deviation (Terasaki et al., 2015).
GLDAS is a research-oriented land surface reanalysis system that produces spatiotemporally continuous global SM
data. The GLDAS system integrates a suite of land surface
models, which include the Noah, Community Land Model,
Variable Infiltration Capacity, Mosaic, and Catchment. Theseland surface models provide physically based simulations ofsurface conditions, and each model has strengths and weaknesses depending on the applications. Among them, thisstudy uses Noah-model-based SM data (GLDAS Noah Land
Surface Model L4 Version 2.1; Chen et al., 1996; Koren etal., 1999). We only assimilate first-layer SM since satellite
measurements cannot observe deep-layer SM. GLDAS provides 3-hourly SM at a spatial resolution of 0.25◦ × 0.25◦ .
As these data are denser than those of NICAM (112 km and6-hourly resolution), we reduce the data density spatiallyand temporally. The original SM data are averaged within
a NICAM model grid so that each observation corresponds
to one model grid point. The original 3-hourly data are also
averaged over 6 h. These spatial and temporal data aggrega-

Nonlin. Processes Geophys., 30, 457–479, 2023

tion processes are carried out simultaneously prior to data
assimilation.
The GLDAS Version 2.1 simulation is forced with
National Oceanic and Atmospheric Administration(NOAA)/Global Data Assimilation System (GDAS)
atmospheric analysis fields (Derber et al., 1991), thedisaggregated Global Precipitation Climatology Project(GPCP) V1.3 Daily Analysis precipitation fields, and the
Air Force Weather Agency’s AGRicultural METeorologicalmodeling system (AGRMET) radiation fields. Because
GLDAS uses observed precipitation of GPCP, SM in
GLDAS is considered better than that of MATSIRO, whichuses precipitation forecasts from NICAM to drive the land
surface model. Since SM in NICAM has a large bias against
the satellite-based product (Fig. 3), this study assimilates
SM from GLDAS as pseudo-observations as Hoover andLangland (2017) and verifies forecasted SM compared to
GLDAS.
3

Experimental settingThis study performs 40-member NICAM-LETKF experiments. NICAM ensemble forecasts are performed for 9 h intervals, and observation data from the last 6 h period are assimilated. The initial ensemble members of the experiments
are obtained from the 1st–40th members of a long-term 128member NICAM-LETKF experiment (Terasaki et al., 2019).
This means the initial ensemble spread of SM relies on initialhttps://doi.org/10.5194/npg-30-457-2023

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conditions perturbed by the ensemble NICAM forecasts. Covariance localization in LETKF is applied to the observation
error covariance R so that distant observations have smaller
impacts on the analysis (Hunt et al., 2007; Miyoshi and Yamane, 2007). Gaussian functions are used for horizontal andvertical localization, given by

o
1n
2
2
,
(11)
f = exp − (dh /σh ) + (dv /σv )2
where f is the localization function, and dh and dv are thehorizontal distance (km) and vertical difference (log(Ps )) between the analysis model grid point and the observation,
respectively. Standard deviations (SDs) of σh and σv are
400 km and 0.4 natural log pressure, as implemented by
Terasaki et al. (2019).
√ The localization function is replacedby zero beyond 2 10/3 · σh,v . Land (atmospheric) observations are assimilated into the atmospheric (land) model using
the same vertical localization scale. For land observations,surface pressure (Ps ) is assigned for the observed height. This
study uses relaxation to prior spread (RTPS; Whitaker and
Hamill, 2012) for covariance inflation. For atmospheric variables, the relaxation parameter is set to 0.90, which is determined through sensitivity tests (Kotsuki et al., 2017b). As
mentioned in Sect. 2.2, the original NICAM-LETKF method,which assimilates only atmospheric observations, is referred
to as the control experiment. These experimental settings
have been widely applied in previous NICAM-LETKF experiments (e.g., Kotsuki et al., 2018, 2019a). In addition toatmospheric observations, this study assimilates SM data ashydrological land observations. The observation error SD of
SM is estimated at 0.05 (m3 m−3 ) based on the innovation
statistics of Desroziers et al. (2005) (cf. Appendix A). We
perform one control experiment and six SM DA experiments,
as shown in the schematic images of Fig. 2.
Maintaining the ensemble spread is important in the EnKF.
We initially expected that ensemble forecasts could sufficiently maintain the ensemble spreads of MATSIRO variables due to physical coupling with NICAM. However, theensemble spread of SM in MATSIRO decreased rapidly after
initiating assimilation of SM from GLDAS in our preliminary experiment (not shown). We were unable to mitigate this
rapid reduction of ensemble spreads even by applying RTPS
with relaxation parameter α = 0.90. This outcome seems to
be related to two fundamental challenges: (1) the land models are typically more dependent on external forcing, rather
than being modeled as a chaotic dynamical system dependent on initial conditions, and (2) the timescales for dynamical changes in land models are much longer than those inatmospheric models. The latter implies that the land model islikely to have a long memory beyond 6 h for SM. In the caseof assimilating SM with atmosphere–land coupled models,
SM observations correspond to the slow mode, and atmospheric variables correspond to the fast mode. Therefore, offline land DA systems usually inflate the ensemble spread by
adding random noise to atmospheric forcing or observational
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463

data. For example, Reichle et al. (2002) added perturbations
to the ensemble forecasting system, specifically to forcing
and to the model states variables, to account for sources ofmodel error in the land model forecast to generate an ensemble representative of the model forecast uncertainty. In thecurrent study, we use RTPS to maintain the ensemble spreadof SM in MATSIRO to avoid the ensemble becoming too
confident. In addition, land DA experiments with the land–
atmosphere system would represent model errors to someextent since each land model is driven by different forcing.
The relaxation parameter for SM is set to α = 1.00 so that theanalysis ensemble spread is equivalent to the forecast ensemble spread. For further details on creating ensemble spreads
for land models, we encourage readers to review the summary presented in Draper (2021).
Further, since satellite-borne microwave sensors can measure only surface layer SM, we explore better DA strategies that will be applicable to satellite observations. Thus,
we only use SM data in the surface layer (0–0.1 m) provided
by GLDAS. In our experiments, GLDAS SM data are assimilated into the topmost layer of MATSIRO (0–0.05 m). Although analyzing deeper layers of SM is essential to take advantage of land–atmosphere coupling, this study focuses on
the surface layer where feedbacks to the atmosphere would
be more pronounced than in deeper layers. Note that thepresent experimental setting for assimilating GLDAS SM
data may result in more significant impacts than the experiments with actual satellite observation intervals.
We first perform a spin-up NICAM-LETKF experimentfrom June to September 2014 by assimilating only atmospheric observations. The initial NICAM ensemble conditions are taken from the long-term NICAM-LETKF experiment of Terasaki et al. (2019). DA experiments are performed for 13 months, from 00:00 UTC 1 October 2014 to
18:00 UTC 30 November 2015. The first month (October2014) is considered a spin-up period, and the results for thelatter 12 months are used for validation.
In Sect. 4.1, the data are used for validation to check if theassimilation behaves as expected (i.e., the analysis departuresof SM are reduced by the assimilation). In addition, we alsouse SM from ERA5 reanalysis data (Hersbach et al., 2020)
as an independent dataset for validation scores. We evaluate atmospheric variables against the ERA5 reanalysis data
in Sect. 4.2. The analysis of land variables is performed separately from the atmospheric analysis in the ERA5 by assimilating screen-level temperature, dewpoint, and synoptic
observations with the optimal interpolation. While ERA5 assimilates no SM observation, it assimilates many more satellite observations than the NICAM-LETKF, such as from theMicrowave Humidity Sounder and Advanced Technology
Microwave Sounder. Therefore, validating NICAM-LETKF
atmospheric fields relative to the ERA5 is reasonable. Furthermore, as described, SM of GLDAS can be consideredbetter than the NICAM-LETKF because it is derived by observed precipitation. Hence, in the following sections, weNonlin. Processes Geophys., 30, 457–479, 2023

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demonstrate that the assimilation of SM from GLDAS hasa beneficial effect on atmospheric fields in NICAM-LETKF,
as verified by comparison with ERA5.
4

Results and discussion

4.1

Impacts on soil moisture

We first examine the impacts of SM assimilation on MATSIRO. Figure 4 compares the global bias patterns for the priorstate of SM at the near-surface layer (i.e., 0–0.05 m) relative
to GLDAS, averaged over a 12-month period from November 2014 to October 2015. Three panels show the results for
AA× L×× (CTRL; quasi-WCDA), AA× L×L (WCDA), and
AAL LAL (full-SCDA). AA× L×× (CTRL) shows dry biases
relative to GLDAS in general, especially in the continentsof Africa, South America, Australia, and central Eurasia(Fig. 4a). Assimilating SM into MATSIRO successfully mitigates these SM biases (Fig. 4b and c). Furthermore, assimilating SM mitigates the wet SM bias in regions where SM isoverestimated in AA× L×× (CTRL). Therefore, the newly developed coupled land–atmospheric DA system successfully
assimilates SM data into MATSIRO, and we confirm the developed DA system works well. These results are expected
and not surprising because forecasts are validated using thesame data as observations. No notable differences are observed in global bias patterns between AA× L×L (WCDA)
and AAL LAL (full-SCDA) in global bias patterns (Fig. 4b andc).
Figure 5 shows the time series of global-mean root meansquare differences (RMSDs) for SM relative to GLDAS. All
experiments that assimilate SM have smaller errors in SM
than those in AA× L×× (CTRL; Fig. 5a). Although AA× L×L(WCDA; Fig. 5b) and AAL LAL (full-SCDA; Fig. 5g) show
reduced errors, no clear difference is apparent between thetwo experiments. Among the seven experiments, AAL L×L(SCDA; Fig. 5f) results in the smallest SM error. In thisexperiment, SM observations are used for updating both
NICAM and MATSIRO, whereas atmospheric observations
are used only for updating NICAM and not for MATSIRO.
Since AAL L×L (SCDA) results in better SM estimation than
AAL LAL (full-SCDA; Fig. 5g), we can see that updating SM
in MATSIRO through assimilation of atmospheric observations has a detrimental impact on SM in the experimental
settings of this study.
Such detrimental impacts are also found by comparing
other cases, such as AA× L×L (WCDA; Fig. 5b) and AA× LAL(SCDA; Fig. 5e). The larger error in AA× LAL (SCDA) thanin AA× L×L (WCDA) arises from inaccurate covariance estimates between atmospheric observations and land variables
due to insufficient ensemble size. Ensemble-based DA canprovide spurious error correlations when the ensemble size issmall. Assimilating observations based on spurious error covariances generally degrades the analysis results (cf. variablelocalization of Kang et al., 2011). Moreover, the difference
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Figure 4. Global patterns of 6 h forecast bias for soil moisture(SM; m3 m−3 ) relative to GLDAS for (a) AA× L×× (CTRL; quasiWCDA), (b) AA× L×L (WCDA), and (c) AAL LAL (full-SCDA),
averaged over 12 months from November 2014 to October 2015.
The blue and brown colors represent overestimated and underestimated SM values relative to GLDAS, respectively.

in timescale between the atmospheric and terrestrial models
may have a dominant influence, which could be verified byexperiments using a short assimilation window. Such further
investigation of the assimilation window is essential for future studies of land–atmosphere coupled DA.
AA× LA× (quasi-SCDA; Fig. 5c) shows similar RMSDs to
those of AA× L×× (CTRL; quasi-WCDA), which implies that
atmospheric observations have neither beneficial nor detrimental impacts on updating SM. Because many types of atmospheric observations are assimilated in this study, clarifying impacts of individual observation type is complicated.
The results might be changed if we assimilate only one kindof atmospheric observation, such as precipitation data, withthe variable localization. Accurate estimation of (Pf )AL byincreasing the number of ensembles might reduce the RMSD
of AA× LA× (quasi-SCDA). Penny et al. (2019) also faced
this kind of problem when assimilating slower ocean observation data into an atmosphere–ocean model with coupled
DA. Penny et al. (2019) found that it was more difficult to use
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Figure 5. Time series of global-mean forecast root mean square differences (RMSDs) for soil moisture (SM; m3 m−3 ) relative to GLDAS.

The black, blue, cyan, magenta, green, red, and yellow lines indicate (a) AA× L×× (CTRL; quasi-WCDA), (b) AA× L×L (WCDA),(c) AA× LA× (quasi-SCDA), (d) AAL L×× (quasi-SCDA), (e) AA× LAL (SCDA), (f) AAL L×L (SCDA), and (g) AAL LAL (full-SCDA)
experiments, respectively. Experiments (a)–(g) correspond to the DA patterns (a)–(g) shown in Fig. 2.

slow-mode observations (from the ocean) to update the fastmode observations (atmosphere). They overcame this problem by using larger ensembles and increasing the analysis
update and observation frequency. As discussed for maintaining ensemble spreads for SM, SM observations correspond to the slow mode, and atmospheric variables correspond to the fast mode in our experimental settings. Therefore, applying the approach by Penny et al. (2019) may further improve SCDA.
We can say that Fig. 5 represents the error correlation between the SM observations and the atmospheric model variables, showing that it is more reliable than the correlation
between the atmospheric observations and the SM variablefrom the land model. In terms of reducing the errors in SM,
the optimal coupled DA method in our experimental setting
is AAL L×L (SCDA). The errors in SM can be reduced by
updating atmospheric and land variables through the assimilation of SM. Several previous studies have found that it isimportant to correct the “upstream” dynamics in the coupledsystem (e.g., by Sluka et al., 2016). In other words, since theatmosphere strongly drives the land via surface forcing, correcting the atmospheric variables would improve forecasts ofthe coupled land surface model. From the point of view of theland model, the SM can be updated accurately by assimilating the observed SM directly. Attempting to use fast-varying
atmospheric observations for updating SM would lead tosuboptimal analysis because of the non-perfect ensemblebased error covariance estimate between atmospheric observations and modeled SM. In contrast, the detrimental impacts of updating atmospheric variables by (Pf )AL cancel out
the beneficial impacts of updating SM by (Pf )LA . Therefore,

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for our model configuration and DA design, AAL LAL (fullSCDA) is less effective than AAL L×L (SCDA). This problem
might occur because the DA approach degrades the analysis
when assimilating atmospheric data into the land model. The
approaches for atmosphere–ocean coupled DA suggested by
Penny et al. (2019) could solve the problem, which will be
an important future subject to improve SCDA even more.
Figure 6 shows the time series of ensemble spread of SM.
Since RTPS is used with a relaxation parameter of 1.0 forland variables, the ensemble spread does not change during DA. Because no significant difference is observed in
the ensemble spreads among experiments, the difference in
RMSDs relative to GLDAS must originate from the difference in the update strategy. The ensemble spread of AA× LA×(quasi-SCDA; Fig. 6c) is the smallest among these cases,
which means the atmospheric observations have collapsed
the spread more than any other configurations. By assimilating the atmospheric observations into the land model, theimpact of the land observations becomes less, leading to thedetrimental effect observed in those cases. This could also be
related to the balance between the errors on the atmosphericobservations and the spread of the land model variables. This
indicates that the atmospheric observation error should be inflated when applied to the land DA via SCDA. The processfilters out the impact of high variability in the atmosphere,
similar to adding errors of representativeness in the spatial
dimension.
Figure 7 shows the global patterns of differences in analysis RMSDs for SM, averaged over a 12-month period from
November 2014 to October 2015. Here, we discuss threeexperiments: AA× L×L (WCDA), AAL LAL (full-SCDA), andNonlin. Processes Geophys., 30, 457–479, 2023

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Figure 6. Similar to Fig. 5 but showing forecast ensemble spreads of SM (m3 m−3 ).

AAL L×L (SCDA), which are the best three experiments interms of errors in SM, as shown in Fig. 5. First, we compare
AA× L×L (WCDA) and AAL L×L (SCDA). Figure 7a suggeststhat updating atmospheric variables with SM DA generally
has beneficial impacts on SM. In South America, the Arabian Peninsula, and India, beneficial impacts are seen in regions where AA× L×× (CTRL) shows a dry bias in SM in
Fig. 4. Additionally, beneficial impacts are apparent in central Africa, where AA× L×× (CTRL) has a wet bias in SM.
In contrast, SM DA has moderate impacts in North America and Eurasia. In these areas, AAL LAL (full-SCDA) performs worse than AA× L×L (WCDA; Fig. 7b), suggestingthat assimilating atmospheric observations to update SM in
MATSIRO would be detrimental in the experimental settingsof this study. Therefore, eliminating the updates of MATSIRO with atmospheric observations has beneficial impacts
for SCDA (Fig. 7c).
We also investigate the SM correlations between GLDAS
and the results of the experiments (Fig. 8). We can see thatthe correlation to GLDAS is larger in the regions where positive impacts are observed in Fig. 7. Figure 9 shows the results of the two-sample t test. Time series of absolute bias of
SM analysis relative to GLDAS are sampled from November 2014 to October 2015. When the p values at a point
are smaller than 5 %, the null hypothesis at the 95 % confidence level is rejected, implying a significant difference.
By the significance test, we can see the significant differences between the experiments over broad regions. The significant differences between methods AA× L×L (WCDA) andAAL L×L (SCDA) are mainly located in the areas where thebias was relatively substantial in Fig. 4a (Fig. 9a). From
Figs. 8 and 9, we can reconfirm the points described in thecomments about Fig. 7: (1) using SM to update atmosphericvariables has positive effects, especially in areas where there
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are dry biases; (2) areas where there are wet biases are mitigated by SM DA; and (3) updating SM with atmosphericobservations has detrimental effects, leading to the results of
AAL LAL (full-SCDA) experiments.
We also investigate the seasonal differences in the relationship between precipitation and SM. Figure 10 comparesthe difference of SM analysis RMSD relative to GLDAS between AA× L×L (WCDA) and AAL L×L (SCDA; Fig. 10a, c,e, and g), with observed precipitation of GPCP version 1.3(Fig. 10b, d, f, and h). The SCDA experiment shows improvements in the Sahel and equatorial Africa from May
to October (Fig. 10e and g) compared to the period from
November to April (Fig. 10a and c). These regions are known
to be “hotspots” where SM affects precipitation during June–
August (Koster et al., 2004). SM assimilation by SCDA
would benefit from updating atmospheric variables in the
hotspot regions. On the other hand, the distribution of precipitation from November to April tends to shift slightly southwards, resulting in decreased precipitation in previously defined hotspots (Fig. 10b and d). Therefore, the advantages of
updating atmospheric variables using SM data are not as evident in these areas in our experiments (Fig. 10a and c). This
period includes the summer season in the Southern Hemisphere. For instance, we can confirm a notable increase inprecipitation in South America (Fig. 10b and d). Correspondingly, the advantages of using SCDA in that area become
more pronounced. The Arabian Peninsula is another region
where the advantages of SCDA stand out during this season,
despite being an area with scarce rainfall throughout the year
and minimal seasonal differences. Therefore, comparison of
results from November to April (Fig. 10a–d) with those from
May to October (Fig. 10e–h) implies that the locations of the“hotspots” may vary depending on the season.

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Figure 7. Global patterns of soil moisture analysis RMSD

(m3 m−3 ) relative to GLDAS averaged over 12 months from
November 2014 to October 2015: (a) difference between AA× L×L(WCDA) and AAL L×L (SCDA), (b) difference between AA× L×L(WCDA) and AAL LAL (full-SCDA), and (c) difference between
AAL LAL (full-SCDA) and AAL L×L (SCDA). Warm colors indicate that the latter experiments providing smaller scores than theformer experiments, whereas cool colors indicate larger scores ofthe latter methods.

From the above results, it is clear that precipitation and
SM are closely related. Given the seasonal variation in precipitation distribution, the regions that would benefit fromupdating atmospheric variables using SM data shift accordingly.
We also use ERA5 SM as an independent dataset for
the validation scores, although so far, we have been using
GLDAS to verify that the experimental setup works as expected. Figure 11 compares the global patterns of 6 h forecast bias in SM at near-surface layer as in Fig. 4 but relative
to ERA5. We can see that AA× L×× (CTRL) shows large drybiases relative to ERA5 in South America and central Eurasia (Fig. 11a). The dry biases appear mitigated by updating
MATSIRO with the SM of GLDAS. Furthermore, NICAM
has a large dry bias in the center of the African continent
relative to ERA5, which is not the case when compared to
GLDAS in Fig. 4. There is a wet bias at the southern andhttps://doi.org/10.5194/npg-30-457-2023

467

Figure 8. Global patterns of soil moisture analysis correlation rel-

ative to GLDAS sampled over 12 months from November 2014
to October 2015: (a) difference between AA× L×L (WCDA) andAAL L×L (SCDA), (b) difference between AA× L×L (WCDA) andAAL LAL (full-SCDA), and (c) difference between AAL LAL (fullSCDA) and AAL L×L (SCDA). Warm colors indicate that the latter
experiments providing smaller scores than the former experiments,
whereas cool colors indicate larger scores of the latter methods.

northern ends of the African continent, which increases withthe assimilation of SM, but the global-averaged scores show
improvements compared to AA× L×× (CTRL; Fig. 11b andc). No notable differences are observed between AA× L×L(WCDA) and AAL LAL (full-SCDA) in global bias patterns(Fig. 11b and c).
Figure 12 shows the time series of global-mean RMSDs
for SM as in Fig. 5 but relative to ERA5. Similar to the results in Fig. 5, we can find the following features: all experiments that assimilate SM have smaller errors in SM than in
AA× L×× (CTRL). AA× LA× (quasi-SCDA; Fig. 12c) shows
larger RMSDs compared to those of AA× L×× (CTRL),
whereas AAL L×× (quasi-SCDA; Fig. 12d) shows smaller
RMSDs than AA× L×× (CTRL). This validation against
ERA5 SM also supports the previously identified findings:
updating atmospheric variables by SM DA is beneficial to
improving SM forecasts, whereas updating the SM variable
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K. Kurosawa et al.: Comparative study of strongly and weakly coupled data assimilation

tioning reasonably well. These findings support the notion that our experiments, which assimilate SM data fromGLDAS without bias correction, can perform satisfactorily
without violating the underlying assumptions of data assimilation. In this section, the results show that the assimilationof atmospheric observations can lead to detrimental effects
on soil moisture analysis. It is crucial to note that this issue stems from the experimental setup rather than statisticalaspects. The primary cause of these adverse effects would
be the weak dynamical relationship between the lower troposphere and SM. We will explore the issues related to thisphysical relationship in the subsequent section.
4.2

Figure 9. Global patterns of soil moisture analysis absolute bias
(m3 m−3 ) relative to GLDAS: (a) difference between AA× L×L(WCDA) and AAL L×L (SCDA), (b) difference between AA× L×L(WCDA) and AAL LAL (full-SCDA), and (c) difference between
AAL LAL (full-SCDA) and AAL L×L (SCDA). Only the areas where
the t test gives significant differences (the p value < 5 %) are colored, sampling with time series of soil moisture analysis from
November 2014 to October 2015. Areas without significant differences are grayed out.

mental impacts. The differences between the other four experiments, in which SM observations update the MATSIRO
variables, are unclear, but they show a significant decrease in
RMSDs compared to AA× L×× (CTRL).
Lastly, Fig. 13 compares the differences in analysis RMSD
of SM relative to ERA5. We can see a meaningful benefit of
having atmospheric model variables updated by SM observations where there was a robust dry bias, e.g., in the SouthAmerican continent (Fig. 13a and b). On the other hand, there
was originally a wet bias against ERA5, i.e., the Arabian
Peninsula and north of the African continent, resulting in a
modification effect. Furthermore, a feature not seen in Fig. 7
is that with ERA5 as reference data, there is no significant
worsening of the MATSIRO variables by updating them withatmospheric observations (Fig. 13c).
The validation results using an independent dataset suggest that the experiments conducted in this study are funcNonlin. Processes Geophys., 30, 457–479, 2023

Impacts on atmospheric field

Here, we investigate the impacts of assimilation of SM on atmospheric variables. Figure 14 shows the global patterns offorecast biases for temperature (K) in the lower troposphere(850 hPa) relative to the ERA5 reanalysis data averaged over
12 months from November 2014 to October 2015. Hereafter,
we discuss the results of AA× L×× (CTRL) and three coupled DA experiments: AA× L×L (WCDA), AAL L×L (SCDA),
and AAL LAL (full-SCDA). Figure 14a shows that AA× L××(CTRL) has a warm temperature bias in regions with dry SM
biases, as illustrated in Fig. 4 (e.g., South America, Africa,and Australia). In these regions, increasing SM values after
assimilation of SM decreases temperature estimates in thelower troposphere (Fig. 14b–d), since more of the incoming
solar and longwave radiation is converted to latent heat flux
and less to sensible heat flux with greater SM. Compared to
AA× L×L (WCDA), however, AAL L×L (SCDA) and AAL LAL(full-SCDA) show an overcooling effect for temperature in
the continents of Africa and Australia (Fig. 14c and d). This
overcooling effect is caused by the assimilation of SM into
atmospheric variables in NICAM. The condition and type ofsoil determine the allocation of energy to latent and sensible
heat flux. In areas with sufficient SM, evaporation is limitedby the amount of available water, even though more evaporation is energetically possible. In such a case, the ratio oflatent heat to sensible heat (i.e., Bowen ratio) will be determined by the surface temperature. In contrast, in a dry area,
the ratio becomes smaller. In addition, the energy balance is
led by the turbulent fluxes of sensible, latent heat, and theground heat flux. The energy transfer from the surface to theatmosphere creates spatial pressure gradients that drive atmospheric circulation at various scales. Due to the factors
above, the most appropriate setting was AA× L×L (WCDA)
in our experiments. There are no remarkable changes in temperature over the ocean among the DA methods.
Table 1 summarizes the global-mean scores for bias,
RMSD, and mean absolute difference (MAD) in temperature. Table 1a and b show these values averaged over theocean and land, respectively. The errors in Table 1a differ lessstrongly than those in Table 1b, showing that assimilation of
SM changes the temperature field mainly over land. The bias
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Figure 10. Global patterns of soil moisture analysis RMSD (m3 m−3 ) relative to GLDAS (a, c, e, g) and spatial patterns of observed

precipitation of GPCP version 1.3 (mm d−1 ; b, d, f, h). Results are averaged over 3 months: (a, b) November 2014 to January 2015,(c, d) February to April 2015, (e, f) May to July 2015, and (g, h) August to October 2015. Panels (a), (c), (e), and (g) show the difference
between AA× L×L (WCDA) and AAL L×L (SCDA). In panels (a), (c), (e), and (g), warm colors indicate that AAL L×L (SCDA) is performing
better than AA× L×L (WCDA), whereas cool colors indicate a worse performance of AAL L×L (SCDA).

Table 1. Averaged scores for bias, mean absolute difference (MAD), and RMSD for temperature at 850 hPa in Fig. 14. The biases and errorsin (a) and (b) are averaged only over the ocean and only over land, respectively. The smallest errors are indicated by the bold font.
(a) Over the ocean
Temperature(K)(i) AA× L××(CTRL)(ii) AA× L×L(WCDA)(iii) AAL L×L(SCDA)(iv) AAL LAL(full-SCDA)–0.3521.366
1.590−0.3821.363
1.583−0.4341.379
1.600−0.443
1.375
1.595(i) AA× L××(CTRL)(ii) AA× L×L(WCDA)(iii) AAL L×L(SCDA)(iv) AAL LAL(full-SCDA)

0.200
1.320
1.564

–0.0601.287
1.510−0.2661.326
1.544−0.268
1.334
1.555

BIAS
MAD
RMSD
(b) Over land
Temperature
(K)
BIAS
MAD
RMSD

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Figure 11. Similar to Fig. 4 but showing 6 h forecast bias for soil

moisture relative to ERA5 (m3 m−3 ).

values in Table 1b show that AA× L×× (CTRL) has a warm
temperature bias over land in general. Assimilating SM leads
to a cooling effect, thereby mitigating the warm temperaturebias. However, AAL L×L (SCDA) and AAL LAL (full-SCDA)
decrease temperature too much, resulting in a cold bias. Consequently, AA× L×L (WCDA) results in the best temperaturefield among the four experiments in terms of temperaturebias at 850 hPa. Assimilating SM with AA× L×L (WCDA)
decreases the average temperature bias by 0.26 K over land.
These changes over land do not propagate significantly to thetemperature bias over the ocean.
We also investigate changes in the precipitation field, focusing on the continent of Africa, where large changes in SM
occur due to SM DA (Fig. 4). Figure 15a–c show the spatial patterns of analysis increments for precipitation amount,averaged over 12 months from November 2014 to October
2015. Note that DA can be used for analyzing not only model
diagnosed variables (i.e., model state variables) but also other
outputs from the model. For example, Kotsuki et al. (2017a)
analyzed precipitation using NICAM-LETKF, where precipitation is not part of the initial condition. Here, we compare
analysis increments of model-like precipitation (cf. Fig. 3 ofNonlin. Processes Geophys., 30, 457–479, 2023

Kotsuki et al., 2017a). Since precipitation is classified as an
atmospheric diagnosed variable, we observe increments inprecipitation during the assimilation of atmospheric observations. The difference in precipitation analysis increments between AA× L×× (CTRL) and AA× L×L (WCDA) is insignificant (Fig. 15a and b). In contrast, precipitation in AAL L×L(SCDA) can be affected by the assimilation of atmosphericand SM observations (Fig. 15c). In central Africa, where precipitation amount changes significantly with SM DA, theanalysis increments shift noticeably. We observe negative
analysis increments where SM in AA× L×× (CTRL) is drier
and positive increments when it is wetter. This suggests that
coupled land–atmospheric DA performs reasonably, as assimilating SM data increases (decreases) precipitation in areas where NICAM has a dry (wet) bias (Fig. 4a).
Spatial patterns of forecast and analysis biases in precipitation relative to GPCP version 1.3 estimates are shown in
Fig. 15d–i. GPCP, which provides global precipitation data
through the merging of various satellite and gauge datasets,is considered to include the best global precipitation estimates in the climate research community (Kotsuki et al.,2019c). First-guess precipitation in AA× L×× (CTRL) has apositive bias relative to GPCP (Fig. 15d; +0.159 mm 6 h−1 ),and this overestimation is intensified in AA× L×L (WCDA;+0.184 mm 6 h−1 ). In contrast, the first-guess precipitation
bias in AAL L×L (SCDA; +0.176 mm 6 h−1 ) is smaller thanthat in AA× L×L (WCDA), although both experiments assimilate SM (Fig. 15e and f). In AA× L×× (CTRL) and AA× L×L(WCDA), atmospheric variables are not updated through
SM DA. Therefore, differences between the precipitation biases of forecasting and analysis occur due to assimilation of
GSMaP_NRT in AA× L×× (CTRL) and AA× L×L (WCDA).
These two experiments result in differing precipitation biases due to biases in their precipitation forecasts (Fig. 15g
and h). Assimilation of GSMaP_NRT slightly reduces thebias in precipitation relative to GPCP (from 0.159 to 0.157
in AA× L×× (CTRL) and from 0.184 to 0.177 in AA× L×L(WCDA)). In contrast, SM DA changes the analysis precipitation in AA× L×L (WCDA). AAL L×L (SCDA) shows
the smallest bias in analysis precipitation. That is, updating atmospheric variables with SM data plays an importantrole in improving the accuracy of precipitation. Compared to
AA× L×× (CTRL), one of the reasons for the larger bias in the
AA× L×L (WCDA) and AAL L×L (SCDA) is due to increased
rainfall in areas where NICAM has the dry bias. Originally,
NICAM overestimates precipitation (Kotsuki et al., 2019b;
Fig. 6). Improvements in soil moisture may have reinforced
the bias, which leads to worse scores in those cases. It canbe said that an improvement of the model bias contained in
NICAM is necessary to solve this problem.
Figure 16 compares the forecast biases in precipitation relative to GPCP averaged over 3 months from June to August
2015. We selected this period to explore SM–atmosphere
coupling, as suggested by Koster et al. (2004). Figure 16ashows that NICAM tends to overestimate precipitation inhttps://doi.org/10.5194/npg-30-457-2023

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Figure 12. Similar to Fig. 5 but showing RMSDs for soil moisture relative to ERA5 (m3 m−3 ).

Figure 13. Similar to Fig. 7 but showing global patterns of soil
moisture analysis RMSD relative to ERA5 (m3 m−3 ).

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convergence regions at low latitudes (0–10◦ N) and underestimate precipitation in South America and Southeast andEast Asia. Figure 16b and c show changes in the precipitation forecasts of AA× L×L (WCDA) and AAL L×L (SCDA).
The assimilation of SM affects precipitation mainly at low
latitudes. As mentioned in Fig. 10, Koster et al. (2004) found“hotspots” where SM affects precipitation during June–
August. Koster et al. (2004) noted that the initial condition of SM was sensitive to rainfall predictability over the
North American Great Plains, equatorial Africa, and India(cf. Fig. 1 of Koster et al., 2004). These areas correspondto the locations where forecast precipitation differed sharply
from SM DA, as shown in Fig. 16b and c, particularly
for the Sahel, equatorial Africa, and India. When comparing AAL L×L (SCDA) with AA× L×L (WCDA), coupled DA
shows stronger impacts in hotspots where the precipitation
field is sensitive to the initial condition of SM.
Figure 17 shows vertical cross-sections of forecast biases for temperature and vapor mixing ratio (Qv ) relative
to ERA5 reanalysis data along 20◦ E over the continent ofAfrica, averaged over 12 months from November 2014 to
October 2015. AA× L×× (CTRL) generally shows a warm
temperature bias and a dry humidity bias near the land surface (1000–800 hPa). With the assimilation of SM, AA× L×L(WCDA) and AAL L×L (SCDA) show decreases in temperature of the lower troposphere at latitudes where AA× L××(CTRL) has a warm bias (Fig. 17b and c). Since the vertical layers of NICAM are almost the same as those of
the ERA5, the cooling impacts would not be attributed tothe difference in vertical resolutions between NICAM and
ERA5. AA× L×L (WCDA) propagates the impacts of SM DA
for atmospheric variables through the interaction between

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Figure 14. Global patterns of forecast bias for temperature (K) at 850 hPa relative to ERA5 reanalysis values for (a) AA× L×× (CTRL),(b) AA× L×L (WCDA), (c) AAL L×L (SCDA), and (d) AAL LAL (full-SCDA), averaged over 12 months from November 2014 to October
2015. Red and blue colors represent warm and cold biases, respectively.

NICAM and MATSIRO during model time integrations. In
addition, AAL L×L (SCDA) updates atmospheric variables directly through SM DA, which means AAL L×L (SCDA) alters
atmospheric variables both directly and indirectly. Therefore,
AAL L×L (SCDA) lowers temperature too much due to thestrong interaction between SM and atmospheric variables(Fig. 17c). Figure 17d shows that most land surface areas
have dry Qv biases relative to the ERA5. This corresponds
to the locations where AA× L×× (CTRL) exhibits a moist
bias against GLDAS (Fig. 4a). As shown in Fig. 4, the coupled DA improves this in those areas, which also leads toan enhancement in the Qv bias in that region. As the moist
bias relative to GLDAS in that area is improved through the
SM DA, the bias in Qv relative to ERA5 in that area is also
improved by coupled assimilation. AA× L×L (WCDA) andAAL L×L (SCDA) correct for the bias caused by increased or
decreased Qv near the surface using SM DA (Fig. 17e andf). The change for Qv in AAL L×L (SCDA) is larger than thatin AA× L×L (WCDA). This is because, as previously mentioned, AAL L×L (SCDA) makes larger adjustments to atmospheric variables compared to AA× L×L (WCDA).
5

Conclusions

This study aims to explore the optimal coupled land–
atmospheric DA method for improving weather forecasts
through the assimilation of hydrological observations. We
implement a coupled land–atmospheric DA into the NICAMMATSIRO model and assimilated SM data from GLDAS.
We perform a series of coupled DA experiments, including
Nonlin. Processes Geophys., 30, 457–479, 2023

weakly and strongly coupled DA, and reach the following
conclusions.
The assimilation of SM successfully mitigates SM biases.
Updating SM by assimilating atmospheric observations canhave detrimental impacts on SM, due to spurious error correlations between atmospheric observations and land model
variables caused by insufficient ensemble size and the difference in timescale between the atmospheric and land models. In contrast, updating the atmospheric model variables
by assimilating SM observations has beneficial impacts on
SM, implying that the error correlation between SM observations and atmospheric model variables is more reliable. Consequently, the optimal coupled DA method in this study is
AAL L×L (SCDA), in which atmospheric and SM data areused to update the atmospheric variables in NICAM, but
only SM data are used to update the SM variable in MATSIRO. The results of this study indicate that AAL LAL (fullSCDA) is less effective than AA× L×L (WCDA), which is
caused by sampling errors and/or insufficient localization of
the ensemble background-error covariance matrix. As Pennyet al. (2019) have shown, experiments with a simple model toexamine several factors in detail, such as the number of ensemble members, the scale of localization, the spread of theensemble of initial members, and the frequency of couplingintervals, would yield very important information. With adequate settings, such as those proposed by Penny et al. (2019),
the experiments with AAL LAL (full-SCDA) might give a superior performance. In addition, the difference in dynamicaltimescales between the atmospheric and land models may
possibly have a dominant influence. Using a shorter DA winhttps://doi.org/10.5194/npg-30-457-2023

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Figure 15. Spatial patterns of analysis increments for precipitation (mm 6 h−1 ; a–c) and precipitation forecast biases (d–f) and analysis

biases (g–i) relative to GPCP version 1.3 (mm 6 h−1 ), averaged over 12 months from November 2014 to October 2015. Magenta and cyancolors in panels (a)–(c) represent increased and decreased precipitation with DA, respectively. The green and brown colors in panels (d)–(i)represent overestimated and underestimated precipitation values, respectively, relative to GPCP. Panels (a), (d), and (g); (b), (e), and (h); and(c), (f), and (i) show the AA× L×× (CTRL), AA× L×L (WCDA), and AAL L×L (SCDA) experiments, respectively.

dow with more linear cross-domain dynamics could be useful to investigate if this would help improve the impact of the
AAL LAL (full-SCDA). This will be an important future study.
Further, one possible reason that AAL LAL (full-SCDA) did
not always show optimal results in the current study could
be due to the poor and complex physical linkages between
the lower troposphere and soil moisture. This problem hasreasonably positive effects on the atmospheric field but often
results in poor soil moisture analysis. The results presented
in this study seem to indicate that this may be the case for
AAL LAL (full-SCDA).

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We demonstrate that precipitation and SM are closely related. Given the seasonal variation in precipitation distribution, the regions that would benefit from updating atmospheric variables using SM data shift accordingly. Assimilating SM provides a proper temperature estimation for the
lower troposphere in areas with a dry SM bias and a warm
atmospheric bias. This effect occurs because more incoming
solar and longwave radiation was converted to latent heat flux
and less converted to sensible heat flux with increased SM.
However, assimilating SM into atmospheric model variables
leads to overcooling effects in regions such as the continentsof Africa and Australia. Furthermore, estimating precipita-

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Figure 16. Spatial patterns of changes in precipitation (mm 6 h−1 )averaged over 3 months from June to August 2014. Panels (a), (b),and (c) show the difference between AA× L×× (CTRL) and GPCP,
AA× L×× (CTRL) and AA× L×L (WCDA), and AA× L×× (CTRL)
and AAL L×L (SCDA), respectively. The green and brown colors inpanel (a) represent overestimated and underestimated precipitation
values relative to GPCP, and the red and blue colors in panels (b)and (c) represent increased and decreased precipitation values withSM DA, respectively.

vations. The issue is thought to be caused by experimental
settings, rather than statistical aspects, due to the poor physical relationships between the lower troposphere and SM. SM
behavior is often highly localized due to spatial differencessuch as soil texture, topography, and vegetation. Therefore,
most NWP centers use a point-wise analysis of SM, without considering the horizontal background error covariance
between grid points. The 40 ensemble members used in thisstudy are close to the number used in operational NWP centers, but using a larger number of ensembles could lead touseful conclusions by evaluating the differences in performance between WCDA and SCDA. Furthermore, using alarge ensemble could be beneficial for understanding variable localization more accurately by improving covarianceestimation between components. In this study, land observations are assimilated into the atmospheric model using thesame vertical localization scale as the assimilation of atmospheric observations. Using a smaller localization scale in alimited ensemble size could help update atmospheric variables with SM assimilation by reducing errors in the error covariance estimates. Furthermore, while this study uses
SM data based on GLDAS, assimilating satellite-derived SMdata is an important direction for future research. When actual GCOMW/AMSR-2 satellite observation data are assimilated, the atmospheric field deteriorates significantly due tothe assimilation of SM (not shown). This suggests that limitations exist in the data assimilation method used in thisstudy and that technical measures, such as CDF matching
preprocessing, may be necessary to assimilate actual observation data successfully. Finally, it is found that a resolutionof about 100 km is very coarse to simulate SM accurately.
Note that the assimilation of GLDAS pseudo soil moisturedata is not a realistic operational setting, as it is likely to havemuch better spatial and temporal coverage than real satellite
observations. When actual observation data are assimilated
at this resolution, the representation error becomes large andcan cause a problem. In addition to using actual satellite observation data, using higher-resolution models is an important future direction.

tion based on SCDA is beneficial in Africa. Coupled DA has
stronger impacts on precipitation forecasts in hotspots where
the precipitation field is sensitive to the initial condition ofSM.
This study demonstrates the potential for improving SM
prediction using the NICAM-LETKF system by assimilating
SM in strong coupled DA. SM is an important variable inland surface models, and its improvement can lead to betterhydrological predictions such as droughts and floods. However, it is still unclear what atmospheric variables should
be updated using each land observation. Therefore, futurestudies will further investigate the effect of variable localization for other land observations. When updating SM in
MATSIRO with atmospheric observations, we obtain unfavorable results due to errors in estimating the error covariance between land model variables and atmospheric obserNonlin. Processes Geophys., 30, 457–479, 2023

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475

Figure 17. Vertical cross-sectional plots of differences in (a–c) temperature (K) and (d–f) water vapor mixing ratio (g kg−1 ) averaged over
12 months from November 2014 to October 2015 along 20◦ E over the continent of Africa. Panels (a) and (d), (b) and (e), and (c) and(f) show the differences between AA× L×× (CTRL) and the ERA5 reanalysis, AA× L×× (CTRL) and AA× L×L (WCDA), and AA× L××(CTRL) and AAL L×L (SCDA), respectively. The vertical and horizontal axes show the pressure level from 1000 to 100 hPa and the latitude,
respectively.

Appendix A

This study diagnoses the observation error SD of SM by using innovation statistics (Desroziers et al., 2005). The innovation statistics is given byE
2 D ooσestimation= y − Hx a yo − Hx f ,(A1)
where σ o is the observation error SD. Subscript estimation means the estimation by the innovation statistics. The
bracket h·i denotes the statistical expectation. Here, we assumed the observation error SD is globally constant andtime independent for SM (Rodríguez-Fernández et al., 2019).
With NICAM-LETKF, we performed preliminary WCDAand SCDA experiments over 2 months from October toNovember 2014 and later used 1-month period data for the
innovation statistics. Here we introduce a measure factor,
given byoofactor = σestimation/σprescribed,(A2)

where the subscript prescribed denotes the prescribed observation error SD of SM used in the preliminary experiments.
If the prescribed SD is optimal, then the diagnosed factor approaches 1.0. Table A1 summarizes the prescribed observation error SD and factor values for five different observation
https://doi.org/10.5194/npg-30-457-2023

SDs with assimilation of GLDAS SM. As noted by Ménard
et al. (2009), when the prescribed observation error SD is
too small, the estimated observation error SD is underestimated, whereas large SDs can lead to overestimation. Basedon these preliminary experiments, this study set the SM observation error SD at 0.05 (m3 m−3 ), which gave the factor
value closest to 1.0 among the preliminary experiments.
Table A1. Observation error SD diagnosed using innovative statis-

tics. “Factor” is the ratio of estimated error SD to the prescribed−value (Eq. A2). The diagnostic values from A×− L× (WCDA) and× ×
A× L× (SCDA) averaged over 2 months are shown.
Prescribed obs.
Error SD(m3 m−3 )
0.01
0.03
0.05
0.07
0.09

Factor−A×− L×(WCDA)×A×
× L×(SCDA)

9.263
1.881
0.898
0.543
0.373

5.716
1.515
0.775
0.509
0.359

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Code and data availability. All of the data used in this study are

Review statement. This paper was edited by Wansuo Duan andstored for 5 years in Chiba University. Due to the large volume ofdata and limited disk space, data will be shared online upon request(shunji.kotsuki@chiba-u.jp; http://www.data-assimilation.riken.jp/
index_e.html, last access: 14 October 2023).

reviewed by Zheqi Shen and one anonymous referee.

Author contributions. KK and SK developed the experimental

system for the parameter estimation, conducted the experiments,
and analyzed the results. TM is the PI and directed the researchwith substantial contribution to the development of this paper.

Competing interests. At least one of the (co-)authors is a mem-ber of the editorial board of Nonlinear Processes in Geophysics.
The peer-review process was guided by an independent editor, andthe authors also have no other competing interests to declare.

Disclaimer. Publisher’s note: Copernicus Publications remains

neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibilitylies with the authors.

Acknowledgements. The authors thank the members of theData Assimilation Research Team, RIKEN Center for Computational Science (R-CCS), and JAXA’s Precipitation Measuring Mission (PMM) project. This study was partly supported by JAXA
(PMM); the Advancement of meteorological and global environmental predictions utilizing observational “Big Data” (Theme 4)
to be tackled using the post-K supercomputer of the FLAGSHIP
2020 Project of the Ministry of Education, Culture, Sports, Scienceand Technology Japan (MEXT); the Initiative for Excellent Young
Researchers of MEXT; JST AIP grant number JPMJCR19U2;
the Japan Society for the Promotion of Science (JSPS) KAKENHI grant nos. JP18H01549, JP21H04571, JP21H05002, andJP22K18821; JST PRESTO MJPR1924; and IAAR Research Support Program of Chiba University. The study used the Supercomputer for earth Observation, Rockets, and Aeronautics (SORA) at
JAXA and the K computer provided by the RIKEN R-CCS (project
IDs: ra000015, hp150289, hp160229, hp170246, and hp180062).

Financial support. This research has been supported by JAXA

(PMM); the Advancement of meteorological and global environmental predictions utilizing observational “Big Data” (Theme 4) to
be tackled using the post-K supercomputer of the FLAGSHIP 2020
Project of the Ministry of Education, Culture, Sports, Science andTechnology Japan (MEXT); the Initiative for Excellent Young Researchers of MEXT; JST AIP (grant no. JPMJCR19U2); the Japan
Society for the Promotion of Science (JSPS) KAKENHI (grantnos. JP18H01549, JP21H04571, JP21H05002, and JP22K18821);
JST PRESTO (grant no. MJPR1924); and IAAR Research Support
Program of Chiba University.

Nonlin. Processes Geophys., 30, 457–479, 2023

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