<figure><img src="image_1.png" /></figure>

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# ESA Climate Change Initiative Root Zone Soil Moisture Product

Piet Emanuel Buechi, Gabriëlle J M de Lannoy, Zdenko Heyvaert, Jean-Christophe Calvet, Yiwen Xu, Wouter Dorigo

► To cite this version:

Piet Emanuel Buechi, Gabriëlle J M de Lannoy, Zdenko Heyvaert, Jean-Christophe Calvet, Yiwen Xu, et al.. ESA Climate Change Initiative Root Zone Soil Moisture Product: Deliverable D7.1 Study Report. Vienna University of Technology. 2022. meteo-03885242

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Submitted on 5 Dec 2022

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ESA Climate Change Initiative Plus - Soil Moisture

CCN 1 Scientific Evolution

Deliverable D7.1 Study Report

Task 1: Root Zone Soil Moisture
Product (RZSM)

Version 2.0 Issue 1.5

12th July 2022

Prepared by:
This document forms the deliverable D7.1, version 2.0, ESA CCI R&D CCN 1; Study Report, Task 1 Root Zone Soil Moisture Product (RZSM) and was compiled for the ESA Climate Change Initiative Plus Soil Moisture Project (ESRIN Contract No: 4000126684/19/I-NB: "ESA CCI+ Phase 1 New R&D on CCI ECVS Soil Moisture") under Contract Change Notice 1 (CCN 1).

For more information on the CCI programme of the European Space Agency (ESA) see
https://climate.esa.int/en/.

Number of pages: 41 (including cover, preface and references).

<table><tr><td>Authors:</td><td colspan="3">E. Büechi, G. De Lannoy, Z. Heyvaert, J.C. Calvet, Y. Xu, W. Dorigo</td></tr><tr><td>Circulation (Internal):</td><td colspan="3">Project consortium and science partners</td></tr><tr><td>External:</td><td colspan="3">ESA CCI Soil Moisture data users, ESA</td></tr><tr><th>Issue</th><th>Date</th><th>Details</th><th>Editor</th></tr><tr><td>i0.1</td><td>16-03-2021</td><td>Template to team</td><td>R. Kidd</td></tr><tr><td>i0.2</td><td>29-03-2021</td><td>Drafted version 1.0 of deliverable. Completion of Sections 0, 2 and 3. Outlined Sections 0 to 6. Compiled Section 7 (references).</td><td>E. Büechi</td></tr><tr><td>i0.3</td><td>07-04-2021</td><td>Reviewed. Inclusion of document scope. Formatted header, footer, updated ToC and document meta data. To ESA for Review.</td><td>R. Kidd</td></tr><tr><td>i1.0</td><td>16-04-2021</td><td>Finalisation.</td><td>R. Kidd</td></tr><tr><td>i1.1</td><td>20-04-2022</td><td>Updated draft for final deliverable</td><td>E. Büechi</td></tr><tr><td>i1.2</td><td>29-04-2022</td><td>Final adjustments for delivery</td><td>E. Büechi</td></tr><tr><td>i1.3</td><td>25-05-2022</td><td>Created track changed document for ESA review</td><td>R. Kidd</td></tr><tr><td>i1.4</td><td>16-06-2022</td><td>Adjusted based on feedback from CA</td><td>E. Büechi</td></tr><tr><td>i1.5</td><td>12-07-2022</td><td>Approved by ESA. Finalised</td><td>R. Kidd</td></tr></table>

**Document Change Record:** For any clarifications, please contact Wouter Dorigo
wouter.dorigo@geo.tuwien.ac.at.
Table of Contents

<table><tr><td>LIST OF FIGURES</td><td>I</td></tr><tr><td>LIST OF TABLES</td><td>III</td></tr><tr><td>ACRONYMS</td><td>V</td></tr><tr><td>SCOPE OF DOCUMENT</td><td>1</td></tr><tr><td>1 INTRODUCTION</td><td>1</td></tr><tr><td>2 STUDY METHODOLOGY</td><td>3</td></tr><tr><td>2.1 LAND SURFACE MODEL</td><td>3</td></tr><tr><td>2.1.1 Noah-MP</td><td>3</td></tr><tr><td>2.1.2 ISBA</td><td>4</td></tr><tr><td>2.2 MODEL SPECIFICATIONS</td><td>4</td></tr><tr><td>3 PRODUCT VALIDATION</td><td>5</td></tr><tr><td>3.1 EUROPE</td><td>6</td></tr><tr><td>3.2 GLOBAL</td><td>18</td></tr><tr><td>4 PRODUCT ASSESSMENT AGAINST STATE-OF-THE-ART RZSM PRODUCTS</td><td>20</td></tr><tr><td>4.1 SWI</td><td>20</td></tr><tr><td>4.2 ERA5-LAND</td><td>22</td></tr><tr><td>4.3 SMAP LEVEL 4</td><td>23</td></tr><tr><td>5 STUDY CONCLUSION</td><td>28</td></tr><tr><td>6 OUTLOOK: NEXT STEPS</td><td>29</td></tr><tr><td>7 REFERENCES</td><td>30</td></tr></table>
## List of Figures

Figure 1: Overview of all ISMN stations used for the global validation of the datasets

Figure 2: Validation of all produced datasets and reference datasets of SWI and ERA5-Land showing correlations of absolute values of the datasets to ISMN data over Europe for the three soil layer depths. Validation metrics in Tab. 2

Figure 3: Validation of all produced datasets and reference datasets of SWI and ERA5-Land showing uRMSD of absolute values of the datasets to ISMN data over Europe for the three soil layer depths. Validation metrics in Tab. 3

Figure 4: Comparison of the performance of surface soil moisture open-loop runs (y-axis) and the one of CCI surface soil moisture COMBINED v6.1 (x-axis) (A and C) and how the assimilation of SSM impacts the performance of the results (B and D), whereat blue colours indicate an improvement of the validation results by SSM assimilation to the open-loop run and red colours show a higher performance of the open-loop run over SSM assimilation run

Figure 5: Anomaly validation of all produced datasets and reference datasets of SWI and ERA5-Land showing correlations of absolute values of the datasets to ISMN data over Europe for the three soil layer depths. Validation metrics in Tab. 4

Figure 6: Anomaly validation of all produced datasets and reference datasets of SWI and ERA5-Land showing uRMSD of absolute values of the datasets to ISMN data over Europe for the three soil layer depths. Validation metrics in Tab. 5

Figure 7: Comparison of the performance of surface soil moisture anomalies of open-loop runs (y-axis) and the one of CCI surface soil moisture COMBINED v6.1 (x-axis) (A and C) and how the assimilation of SSM impacts the performance of the results (B and D), whereat blue colours indicate an improvement of the validation results by SSM assimilation to the open-loop run and red colours show a higher performance of the open-loop run over SSM assimilation run

Figure 8: Performance changes of the joint assimilation of LAI & SSM vs. OL run of Noah-MP per climate class. Each violin plot represents the differences of the correlations using the joint LAI & SSM and OL. Validation metrics in Tab. 6. Overview of climate class abbreviations in Tab. 7

Figure 9: Performance changes of the joint assimilation of LAI & SSM vs. OL run of Noah-MP per land cover class (based on CCI-LC map). Each violin plot represents the differences of the correlations using the joint LAI & SSM and OL. Validation metrics in Tab. 8. Table 8: Validation metrics corresponding to Fig. 9. Median shows the difference of correlations between the two datasets Noah-MP joint assimilation of LAI&SSM and Noah-MP OL run per land cover class. The p-value shows the result of a t-test comparing these two datasets. P-values lower than 0.05 indicate statistically significant differences between the datasets. Only median differences larger than 0.00 are shown

Figure 10: Performance changes of the joint assimilation of LAI & SSM vs. OL run of ISBA per climate class. Each violin plot represents the differences of the correlations using the joint LAI & SSM and OL. Validation metrics in Tab. 9. Overview of climate class abbreviations in Tab. 7
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Figure 11: Performance changes of the joint assimilation of LAI & SSM vs. OL run of ISBA per land cover class (based on CCI-LC map). Each violin plot represents the differences of the correlations using the joint LAI & SSM and OL. Validation metrics in Tab. 10

Figure 12: Comparison of the validation of the OL run and the joint LAI & SSM assimilation runs. The color of the points represent the improvement of the validation obtained through DA. Blue colors indicate an improvement of DA, whereas for red points the OL result has a better performance

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Figure 13: Selected timeseries in southern France (ISMN station Cabrieres d'Avignon from SMOSMANIA) of the model results showing the differences of OL, assimilation runs, and SSM retrievals (ESA CCI COMBINED v6.1) for surface and root-zone soil moisture

Figure 14: Global validation of the produced datasets, SWI, and ERA5-Land. Showing the correlations of the individual datasets to ISMN data. Validation metrics in Tab. 11

Figure 15: Global validation of the produced datasets, SWI, and ERA5-Land. Showing uRMSD of the individual datasets to ISMN data. Validation metrics in Tab. 12

Figure 16: Comparison of the validations of Noah-MP, ISBA, SWI, and ERA5-Land. The first violin plot shows the changes in Pearson's R from the ISBA joint assimilation run to its OL run. The remaining violins show the changes comparing Noah-MP OL to its assimilation runs as well as a comparison to SWI, ERA5-Land and ISBA OL. P-val shows the results of the t-tests comparing the respective datasets

Figure 17: Comparison of the anomaly validations of Noah-MP, ISBA, SWI, and ERA5-Land. The first violin plot shows the changes in Pearson's R from the ISBA joint assimilation run to its OL run. The remaining violins show the changes comparing Noah-MP OL to its assimilation runs as well as a comparison to SWI, ERA5-Land and ISBA OL. P-val shows the results of the t-tests comparing the respective datasets
Figure 18: Validation of ERA5 Land and SMAP L4 for their original depths over Europe, showing the correlations of the individual datasets and ISMN data

Figure 19: Validation of all produced datasets and reference datasets of SWI, ERA5-Land, and SMAP L4 validated over the period of 2015-2019. It shows the correlations of absolute values of the datasets to ISMN data over Europe for the three soil layer depths. Validation metrics in Tab. 13

Figure 20: Validation of all produced datasets and reference datasets of SWI, ERA5-Land, and SMAP L4 validated over the period of 2015-2019. It shows uRMSD of absolute values of the datasets to ISMN data over Europe for the three soil layer depths. Validation metrics in Tab. 14

Figure 21: Validation of all produced datasets and reference datasets of SWI, ERA5-Land, and SMAP L4 validated over the period of 2015-2019. It shows the correlations of anomalies of the datasets to ISMN data over Europe for the three soil layer depths. Validation metrics in Tab. 15

Figure 22: Validation of all produced datasets and reference datasets of SWI, ERA5-Land, and SMAP L4 validated over the period of 2015-2019. It shows uRMSD of the anomalies of the datasets to ISMN data over Europe for the three soil layer depths. Validation metrics in Tab. 16

Figure 23: Global validation of the produced datasets, SWI, ERA5-Land, and SMAP L4. Showing the correlations of the individual datasets to ISMN data – validated for the period 2015-2019. Validation metrics in Tab. 17

## List of Tables

Table 1: Overview of all produced datasets for this study including the assimilated products and the spatial extent of the model run 5

Table 2: Validation metrics corresponding to Fig. 2, showing median correlation, its interquartile range (IQR) and the number of observations (N) 9

Table 3: Validation metrics corresponding to Fig. 3, showing median uRMSD, its interquartile range (IQR) and the number of observations (N) 10

Table 4: Validation metrics corresponding to Fig. 4, showing median correlation, its interquartile range (IQR) and the number of observations (N) 11

Table 5: Validation metrics corresponding to Fig. 5, showing median uRMSD, its interquartile range (IQR) and the number of observations (N) 12

Table 6: Validation metrics corresponding to Fig. 6. Median shows the difference of correlations between the two datasets Noah-MP joint assimilation of LAI&SSM and Noah-MP OL run per climate class. The p-value shows the result of a t-test comparing these two datasets. P-values lower than 0.05 indicate statistically significant differences between the datasets. Only median differences larger than 0.00 are shown 13

Table 7: Climate classes abbreviations 14

Figure 9: Performance changes of the joint assimilation of LAI & SSM vs. OL run of Noah-MP per land cover class (based on CCI-LC map). Each violin plot represents the differences of the correlations using the joint LAI & SSM and OL. Validation metrics in Tab. 8 Table 8: Validation metrics corresponding to Fig. 9. Median shows the difference of correlations between the two datasets Noah-MP joint assimilation of LAI&SSM and Noah-MP OL run per land cover class. The p-value shows the result of a t-test comparing these two datasets. P-values lower
than 0.05 indicate statistically significant differences between the datasets. Only median differences larger than 0.00 are shown 14

Table 9: Validation metrics corresponding to Fig. 10. Median shows the difference of correlations between the two datasets ISBA joint assimilation of LAI&SSM and ISBA OL run per climate class. The p-value shows the result of a t-test comparing these two datasets. P-values lower than 0.05 indicate statistically significant differences between the datasets. Only median differences larger than 0.00 are shown 15

Table 10: Validation metrics corresponding to Fig. 11. Median shows the difference of correlations between the two datasets ISBA joint assimilation of LAI&SSM and ISBA OL run per land cover class. The p-value shows the result of a t-test comparing these two datasets. P-values lower than 0.05 indicate statistically significant differences between the datasets. Only median differences larger than 0.00 are shown 16

Table 11: Validation metrics corresponding to Fig. 15, showing median correlation, its interquartile range (IQR) and the number of observations (N) 19

Table 12: Validation metrics corresponding to Fig. 15, showing median uRMSD, its interquartile range (IQR) and the number of observations (N) 20

Table 13: Validation metrics corresponding to Fig. 19, showing median correlation, its interquartile range (IQR) and the number of observations (N) 25

Table 14: Validation metrics corresponding to Fig. 20, showing median uRMSD, its interquartile range (IQR) and the number of observations (N) 25

Table 15: Validation metrics corresponding to Fig. 21, showing median correlation, its interquartile range (IQR) and the number of observations (N) 26

Table 16: Validation metrics corresponding to Fig. 22, showing median uRMSD, its interquartile range (IQR) and the number of observations (N) 27

Table 17: Validation metrics corresponding to Fig. 23, showing median correlations, its interquartile range (IQR) and the number of observations (N) 28
Acronyms

<table><tr><td>AMI</td><td>Active Microwave Instrument</td></tr><tr><td>ASCAT</td><td>Advanced Scatterometer (Metop)</td></tr><tr><td>CCI</td><td>Climate Change Initiative</td></tr><tr><td>CCN</td><td>Contract Chance Notice</td></tr><tr><td>CDF</td><td>Cumulative Distribution Function</td></tr><tr><td>CGLS</td><td>Copernicus Global Land service</td></tr><tr><td>CNRM</td><td>Centre National de Recherches Météorologiques</td></tr><tr><td>ECMWF</td><td>European Centre for Medium Range Weather Forecasting</td></tr><tr><td>ECV</td><td>Essential Climate Variable</td></tr><tr><td>ERA</td><td>European Reanalysis (ECMWF)</td></tr><tr><td>ERS</td><td>European Remote Sensing Satellite (ESA)</td></tr><tr><td>ESA</td><td>European Space Agency</td></tr><tr><td>GLEAM</td><td>Global Land Evaporation, the Amsterdam Methodology</td></tr><tr><td>HPC</td><td>High Performance Computing</td></tr><tr><td>HRSM</td><td>High Resolution Soil Moisture from Sentinel data</td></tr><tr><td>IEM</td><td>Integral Equation Model</td></tr><tr><td>ISBA</td><td>Interactions between Soil, Biosphere, and Atmosphere</td></tr><tr><td>ISBA-CTRIP</td><td>ISBA- CNRM- Total Runoff Integrating Pathways</td></tr><tr><td>ISMN</td><td>International Soil Moisture Network</td></tr><tr><td>LAI</td><td>Leaf Area Index</td></tr><tr><td>LDAS</td><td>Land Data Assimilation System</td></tr><tr><td>LIS</td><td>Land Information System</td></tr><tr><td>LSM</td><td>Land Surface Model</td></tr><tr><td>MPP</td><td>Milestone Payment Plan</td></tr><tr><td>NASA</td><td>National Aeronautics and Space Administration</td></tr><tr><td>NDVI</td><td>Normalized Differenced Vegetation Index</td></tr><tr><td>Noah-MP</td><td>Noah-Multi-parameterization</td></tr><tr><td>OL</td><td>Open-loop</td></tr><tr><td>QA4SM</td><td>Quality Assurance for Soil Moisture</td></tr><tr><td>R&D</td><td>Research and Development</td></tr><tr><td>RZSM</td><td>Root Zone Soil Moisture</td></tr><tr><td>SAR</td><td>Synthetic Aperture Radar</td></tr><tr><td>SMAP</td><td>Soil Moisture Active and Passive mission</td></tr><tr><td>SMOS</td><td>Soil Moisture and Ocean Salinity</td></tr><tr><td>SoW</td><td>Statement of Work</td></tr><tr><td>SSM</td><td>Surface Soil Moisture</td></tr><tr><td>SWI</td><td>Soil Water Index</td></tr><tr><td>TDR</td><td>Time Domain Reflectometry</td></tr><tr><td>uRMSD</td><td>Unbiased Root Mean Square Deviation</td></tr><tr><td>VH</td><td>Vertical-Horizontal polarisation</td></tr><tr><td>VOD</td><td>Vegetation Optical Depth</td></tr><tr><td>VODCA</td><td>VOD Climate Archive</td></tr><tr><td>VV</td><td>Vertical-Vertical polarisation</td></tr></table>
WBS Work Breakdown Structure

WCM Water Cloud Model

WP Work Package
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# Scope of Document

This document provides the deliverable D7.1, version 1.0, ESA CCI R&D CCN 1; Study Report, Task 1 Root Zone Soil Moisture Product (RZSM). Version 1 of this report introduced the scope and goal of the study (section 1), presented the study methodology (section 2), and outlined the product validation (section 3).

The final three sections: presenting the product assessment, the study conclusion, and an outlook for the next steps towards integrating the study results in CCI activities are revised now for version 2.0.

# 1 Introduction

While the surface soil moisture (SSM) products delivered by ESA CCI have proven valuable contributions to many climate applications, particularly carbon and vegetation modellers have expressed a strong interest in long-term satellite-based root-zone soil moisture products for linking vegetation phenology and biomass carbon allocation to moisture availability in the soil (Dorigo et al. 2017). While simple purely data-driven approaches have been developed to mimic the infiltration process by means of an exponential filter (Albergel et al. 2008, Pasik et al. 2020), this methodology neglects important soil water loss processes, such as bare soil evaporation, plant transpiration, and capillary rise. Hence, process-based models are required to transfer more realistically the surface measurements to deeper soil layers in order to improve surface energy, water and carbon flux simulations. It is understood that this would add model structure to the derived product and the satellite-derived product can no longer be considered an independent reference for model evaluation. However, the main envisaged use of the ESA CCI root-zone product is not model evaluation but to provide a state-of-the-art microwave satellite-driven product. For model evaluation, a host of exclusively satellite-based soil moisture products is available for that end.

Numerous studies have shown the benefit of microwave-based surface soil moisture retrievals, brightness temperatures, or backscatter to update root-zone soil moisture (Liu et al., 2011, Draper et al., 2012, Carrera et al., 2015, De Lannoy and Reichle, 2016a,b, Reichle et al., 2019). Albergel et al. (2018), showed that the assimilation of CCI surface soil moisture to constrain the interactions between Soil, Biosphere, and Atmosphere (ISBA) land surface model (LSM) coupled with the CNRM (Centre National de Recherches Météorologiques) version of the Total Runoff Integrating Pathways (ISBA-CTRIP) continental hydrological system has a neutral to positive impact on (i) soil moisture itself (ii) agricultural statistics over France, (iii) river discharge, (iv) land evapotranspiration (compared to the Global Land Evaporation Amsterdam Model (GLEAM) project) and (v) gross primary production and evapotranspiration (compared to spatially gridded observations based estimates of up-scaled from the FLUXNET
<figure><img src="image_5.png" /></figure>

network). However, the study also showed that the assimilation of LAI generally had a stronger impact. Also, Kumar et al. (2019) found a positive impact of assimilating leaf area index on top of assimilating soil moisture alone in the Noah-MP model and obtained even better performance when adding microwave vegetation optical depth (VOD; Kumar et al., 2020).

In this study, we assimilate and assess the added value of satellite-based retrievals of CCI Soil Moisture, LAI, and VOD, by assimilating them both individually and in combination. To assess the impact of the model choice, we do this for two land surface models: (1) the Noah-Multi-parameterization (Noah-MP) and (2) the ISBA LSM. The LSMs differ in their model structure (e.g. soil layering) and process parameterization (e.g. plant water stress), and come with their own data assimilation scheme. The different implementations impact final performance and can provide useful insights for the optimization of each RZSM analysis. Investigating two fundamentally different LSMs can provide deeper insights into the synergies between models and observations by revealing which processes and parameters are affected most by the assimilation of observational information, which may in turn aid the future development of both model and satellite products.

Soil moisture data assimilation can be performed using L1 backscatter or brightness temperature measurements, or L2/3 soil moisture retrievals (e.g., De Lannoy and Reichle, 2016a, Lievens et al., 2017, Muñoz-Sabater et al. 2019, Albergel et al. 2020). While the former typically uses a radiative transfer model to relate the L1 satellite measurements to the modelled soil moisture estimates, in the latter approach this is already done by the retrieval algorithm of the assimilated L2/3 product. The first approach has the advantage of being physically consistent (Reichle et al., 2019), but increases the complexity of the assimilation system, whereas the second approach suffers more from biases between various retrieval products. However, in the past, the ESA CCI soil moisture teams have put great efforts into assessing and harmonizing soil moisture retrievals from different sensors in order to create consistent merged products (Mittelbach et al. 2014, Gruber et al. 2015, Gruber et al. 2019). Hence, it is sensible to leverage this work by assimilating the harmonized soil moisture retrievals. Moreover, little is known about the L1 assimilation of vegetation optical depth, which would add yet another unknown to the system. Hence, in this project we will assimilate both soil moisture and vegetation retrieval products directly.

The activity is made to investigate the requirements and R&D activities needed for the development of a root-zone soil moisture product. The following items will be specifically addressed:

1. Develop and evaluate a long term (2002-2019), root-zone soil moisture product with daily and 0.25° resolution, by constraining the Noah-MP and ISBA land surface models through assimilation of EO Climate Data Records, i.e., the joint assimilation of the ESA CCI soil moisture product latest version (combined product or its individual contributing data products) and two products related to vegetation productivity, i.e.
<figure><img src="image_6.png" /></figure>

Leaf Area Index from optical remote sensing data and Vegetation Optical Depth from passive microwave remote sensing.

2. Assess the impact of assimilating one observation type alone (soil moisture or vegetation) versus a combination of both (soil moisture and vegetation) on root-zone soil moisture over Europe. Note that the evaluation is limited to surface and root-zone soil moisture, but all other land surface variables are also updated (indirectly) via surface soil moisture or vegetation data assimilation.

# 2 Study Methodology

## 2.1 Land Surface Model

At the land surface, soil moisture and vegetation processes are constantly interacting. In an LSM, the dynamical simulation of soil moisture and vegetation is therefore crucial and done via closure relations of the water, energy and carbon cycles. Because of model uncertainties, the modelling of soil moisture and vegetation will benefit from any observational constraints either on soil moisture or vegetation provided by satellite observations.

### 2.1.1 Noah-MP

The Noah-Multiparameterization (Noah-MP) is a land surface model with a long track record of dynamical soil moisture and vegetation simulation (Niu et al., 2011). Forced by surface meteorology, Noah-MP is able to dynamically simulate spatially distributed soil moisture for different soil depths (adjustable but most commonly: 0-10 cm, 10-40 cm, 40-100 cm, and 100-200 cm) and vegetation leaf carbon mass, which is directly related to above-ground biomass and LAI. Noah-MP is embedded in the NASA Land Information System (LIS, Kumar et al., 2006). LIS already enables the assimilation of selected satellite retrievals such as soil moisture and LAI (Kumar et al., 2019). The assimilation of VOD retrievals is only in its infancy (Kumar et al., 2020), but a preliminary scheme has been implemented in LIS to merge enhanced (9-km) SMAP VOD retrievals with dynamic vegetation simulations of Noah-MP.

The CCI+ team builds upon the LIS framework, which already runs successfully on the KU Leuven High Performance Cluster (HPC), both for research at KU Leuven and joint TU Wien-KU Leuven research. Noah-MP is used in several projects either in model-only or data assimilation mode. Here we propose to use Noah-MP and LIS to assimilate ESA-CCI SSM, Copernicus Global Land service (CGLS) LAI and the multi-sensor, multi-frequency VOD Climate Archive (VODCA; Moesinger et al., 2020). Specifically, we run experiments in which soil moisture and each of the vegetation products are assimilated individually and experiments in which soil moisture and either LAI or VOD observations are combined. Preparative works for these experiments include the optimization of the connection between the prognostic
<figure><img src="image_7.png" /></figure>

vegetation variables and VOD retrievals. Since VOD is not directly simulated by the model, the VOD retrievals are rescaled into the LAI space via seasonally varying Cumulative Distribution Function (CDF) matching (Kumar et al., 2020). SSM observations are rescaled too using a seasonally varying CDF matching. The assimilation is performed with a 1-dimensional (column-based) ensemble-based filter. This filter diagnoses the forecast error covariances from perturbed soil moisture and vegetation variables at individual 25-km grid cells and balances it with the corresponding assimilated retrieval uncertainty to compute analysis updates for the whole soil moisture profile and all vegetation variables of that 25-km grid cell. Perturbations are applied to meteorological forcing, soil moisture and vegetation variables with different temporal autocorrelation lengths in order to account for the much higher temporal autocorrelation of vegetation variables.

### 2.1.2 ISBA

The ISBA land surface model is embedded in the SURFEX modelling platform (Masson et al. 2013). The latter contains data assimilation routine for land analysis. A python environment was built to manage the data flow, from satellite-derived observations to be assimilated to the display of open-loop (OL) and analysis simulation results. The combination of these elements is called LDAS-Monde (Albergel et al. 2017). This open-source tool has now reached a high technical readiness level and is now being transferred to operational services of Meteo-France. The current version of LDAS-Monde is able to assimilate true LAI values from the Copernicus Global Land service (CGLS) with or without the joint assimilation of ASCAT-derived SSM products disseminated by CGLS. LDAS-Monde can be adapted to ingest other sources of data.

A unique capability of LDAS-Monde is the possibility to analyse the root-zone soil moisture (RZSM) at several depths by assimilating LAI and SSM, or LAI alone, or SSM alone. Recent tests have shown that microwave VOD estimates can be customized to be used as a proxy for true LAI. A seasonal CDF-matching technique can be used for this purpose. The advantage of microwave VOD products is that they benefit from the all-weather capability of low-frequency microwave sensors.

In this work, ESA CCI SSM is assimilated together with the CGLS LAI in order to produce a global multi-layer RZSM product. A seasonally varying CDF-matching is applied to SSM observations but LAI is assimilated as is.

## 2.2 Model Specifications

Both models are run to produce mean daily (0:00 UTC +/- 12 h) soil moisture values in m³/m³ for three soil moisture layers: 0-10cm, 10-40cm, and 40-100cm. The temporal coverage is from 2002-2019 with a spatial resolution of 0.25°. ERA5 is used as meteorological forcing. The
assimilated datasets are ESA CCI COMBINED soil moisture v6.1, CGLS LAI v2, and VODCA VOD X-Band. Model runs are produced globally for ISBA OL, ISBA SSM & LAI joint assimilation, and Noah-MP OL. Further results are produced over Europe (latitude 29.875 N to 71.625 N; longitudes 11.375 W to 40.125 E, cf. Fig. 12) using Noah-MP for the following assimilation runs: SSM, LAI, scaled LAI, VOD, and the joint assimilation runs of SSM & LAI and SSM & VOD (Tab. 1).

<table><caption>Table 1: Overview of all produced datasets for this study including the assimilated products and the spatial extent of the model run</caption><thead><tr><th></th><th>OL</th><th>SSM</th><th>LAI</th><th>LAI Scaled</th><th>VOD</th><th>SSM & LAI</th><th>SSM & VOD</th></tr></thead><tbody><tr><th>Noah-MP</th><td>Global</td><td>Europe</td><td>Europe</td><td>Europe</td><td>Europe</td><td>Europe</td><td>Europe</td></tr><tr><th>ISBA</th><td>Global</td><td>-</td><td>-</td><td>-</td><td>-</td><td>Global</td><td>-</td></tr></tbody></table>

## 3 Product Validation

All datasets are validated using pytesmo (publicly available validation software which is a part of QA4SM: https://github.com/TUW-GEO/pytesmo). The QA4SM (https://qa4sm.eu/) framework brings together the software, (reference) data and infrastructure that is necessary for the evaluation of new SM products following community best practices (Gruber et al., 2020). QA4SM provides pre-processed soil moisture data from multiple sources (satellite, in-situ, reanalyses). For the validation it uses the in-situ soil moisture data from the International Soil Moisture Network (ISMN) (Dorigo et al. 2021) (Fig. 1). The presented results and conclusions, therefore, are confined to the locations of the used ISMN stations. For the global validation, this is mainly driven by stations in the US and Eurasia. Several different validation metrics for comparing the datasets to in-situ measurement are calculated (mean squared error, bias, Spearman's Rho, residual sum of squares, etc.) for both the absolute soil moisture values and the inter-annual anomalies. This report focuses on Pearson's R and unbiased root mean square deviation (uRMSD). First, the results over Europe are presented and afterwards compared to the global results of the OL runs of ISBA and Noah-MP as well as the joint assimilation run of LAI & SSM of ISBA. In addition, our produced datasets are compared to existing RZSM datasets: ERA5-Land data (volumetric soil water layers), SMAP Level 4 soil moisture version 5 (Reichle et al. 2020), and a Soil Water Index dataset (SWI) which is a proxy for RZSM based on the ESA CCI COMBINED v. 6.1 product (see Section 4). Hence, these datasets are validated using the same validation scheme. All these datasets and our results are validated over the whole time series from 2002-2019, except the validation including SMAP L4 global surface and root zone soil moisture geophysical data (Reichle et al. 2020). It must be noted that a limitation of this validation exercise is that SM correlation or uRMSD scores tell
<figure><img src="image_8.png" /></figure>

nothing about the impact of the assimilation on the quality of the simulated fluxes (e.g. evapotranspiration).

<figure><img src="image_9.png" /><figcaption>Figure 1: Overview of all ISMN stations used for the global validation of the datasets</figcaption></figure>

## 3.1 Europe

The correlations of the produced datasets to ISMN measurements over Europe are around 0.6 for the uppermost soil layer (0-10cm) and the lowest layer (40-100cm) and between 0.65 and 0.71 for the middle soil layer (Fig. 2 and Tab. 2). The impact of assimilation is relatively low showing improvements of maximally 0.01. Both results of ISBA (OL and joint LAI & SSM assimilation) obtain higher performances than all Noah-MP model runs over Europe, yet the differences are not statistically significant (Fig. 15 and Tab. 12).

Looking at the validation using anomalies, the correlations are evidently lower: surface soil moisture gets correlations of 0.52 to 0.55, sub-surface (10-40cm) 0.51 to 0.55, and root-zone from 0.43 to 0.48 (Fig. 5 and Tab. 4). For the lower two layers (10-40cm and 40-100cm) data assimilation leads to larger improvements than for the validation using absolute values. ISBA improves by 0.01 for the sub-surface layer and by 0.02 for the lowest layer, whereas the correlations of Noah-MP and ISMN increases by 0.02 comparing OL and joint VOD & SSM assimilation for the middle layer, and even 0.05 for the lowest layer using joint LAI & SSM assimilation. Largest improvements are obtained when assimilating SSM either alone or jointly with LAI or VOD for Noah-MP and the joint assimilation using ISBA. Generally, LAI and VOD only assimilations lead to slightly lower correlations than when using SSM.

A similar pattern can be seen when looking at uRMSD. An overall good performance of the models regarding absolute values is indicated by uRMSD smaller than 0.053 m³m⁻³ for 0-10 cm, smaller than 0.042 m³m⁻³ for 10-40 cm, and even below 0.033 m³m⁻³ or 40-100 cm (Fig. 3
<figure><img src="image_10.png" /></figure>

and Tab. 3). The impact of data assimilation is again not large. The validation of the anomalies shows a larger impact of the assimilation, especially of the ones using SSM, showing the largest improvements for subsurface soil moisture (-0.002 m³m⁻³ for joint VOD SSM assimilation compared to OL) (Fig. 6 and Tab. 5).

A potential explanation why the assimilation of SSM has a small impact can be seen in Fig. 4. For most locations, the OL run of both models have higher correlations to in-situ soil moisture than the assimilated ESA CCI SSM (all pixels above the red dotted line in Fig. 4). At such locations the model can hardly learn anything from the assimilated SSM data and the correlations of the model run including SSM assimilation are rather decreasing. Only pixels which lay below the red line in Fig. 4 have the potential of significant improvement through SSM assimilation. At such locations the performance of the assimilation runs is usually better than of the OL (indicated by positive values of DA-OL in Fig. 4). It has been shown in other studies that the high quality of open-loop soil moisture of other models compared to satellite-based soil moisture limit performance improvements using data assimilation in that respect (Martens et al., 2017). However, a well-designed data assimilation system may be able to extract useful signals from the assimilated data (Reichle et al., 2014). This is indicated by the validation of the anomalies. The model is indeed able to learn from the SSM observations with a lower performance than the OL run. Most pixels are above the red dotted line, indicating a higher performance of the OL than the observations. Yet, many of those pixels still show an improved performance of the assimilation run over the OL run of Noah-MP (Fig. 7). In addition, it can be seen that the impact of SSM assimilation is rather lower on ISBA than on Noah-MP (Fig. 4 & 7). Overall, it can be stated, that neither of the assimilation runs lead to significant changes in model performance (Fig. 15 and Tab. 12).

In a next step, it is analysed if there are significant impacts of the assimilation for certain land cover or climate classes (Fig. 8 to 11 and Tab. 6 to 10). It can be seen that there are no significant differences between the performance of the assimilation runs compared to the OL for any climate or land cover class. However, for many classes no significant conclusions can be made due to the small number of ISMN stations available. Classes with enough stations like cropland, tree cover (CCI-LC value 12 and 70), grassland, shrub, and urban, respectively Cfb, Dfb, and Dfc for climate, show no significant differences in the datasets when applying a t-test (Fig. 8 to 11 and Tab. 6 to 10).

The spatial distribution of the impacts of assimilation confirms the larger impact of assimilation on Noah-MP compared to ISBA (Fig. 12). For Noah-MP there are several clustering regions with increasing or decreasing correlations. Especially the region in northern and eastern Romania shows many increasing correlations for surface soil moisture of Noah-MP, whereas the correlations to the stations in Finland are decreasing. For subsurface soil moisture, assimilation has either a neutral or positive impact. In the lowest soil layer, there are some positive impacts in Poland, southern Germany and Italy but similarly many negative
<figure><img src="image_11.png" /></figure>

impacts in Finland, France, and Denmark. ISBA results show for many stations a negative impact of assimilation for surface soil moisture. There are more locations with a positive impact in the deeper layers.

The time-series of the model results (Fig. 13) show similar tendencies as seen in the validation results. First, there is again a minor impact of assimilation on modelled surface and root-zone soil moisture results from ISBA. The impact of assimilation on surface soil moisture of Noah-MP is not large either, even though SSM retrievals show large deviations from modelled OL soil moisture and have much larger short-term fluctuations (Fig. 13). There is a larger impact of assimilation on Noah-MP root-zone soil moisture. Still SSM assimilation alone does not alter the model output a lot, but both joint assimilations significantly impact the modelled soil moisture. For LAI&SSM, the short-term variations are not affected much, but over the scale of some months soil moisture deviates from OL results. VOD&SSM results show current limitations in the use of VOD for assimilation. The impact is large, and it seems that much noise is added to the modelled root-zone soil moisture.

<figure><img src="image_12.png" /><figcaption>Figure 2: Validation of all produced datasets and reference datasets of SWI and ERA5-Land showing correlations of absolute values of the datasets to ISMN data over Europe for the three soil layer depths. Validation metrics in Tab. 2</figcaption></figure>
<table><caption>Table 2: Validation metrics corresponding to Fig. 2, showing median correlation, its interquartile range (IQR) and the number of observations (N)</caption><thead><tr><th>Pearson's R</th><th>ISBA OL</th><th>ISBA LAI&SM</th><th>NoahMP OL</th><th>NoahMP SM</th><th>NoahMP LAI</th><th>NoahMP LAI s</th><th>NoahMP VOD</th><th>NoahMP LAI&SM</th><th>NoahMP VOD&SM</th><th>ESA CCI SWI</th><th>ERA5 Land</th></tr></thead><tbody><tr><td rowspan="3">0-10</td><td>Median</td><td>0,61</td><td>0,62</td><td>0,59</td><td>0,59</td><td>0,59</td><td>0,60</td><td>0,59</td><td>0,59</td><td>0,59</td><td>0,57</td><td>0,60</td></tr><tr><td>IQR</td><td>0,29</td><td>0,30</td><td>0,27</td><td>0,28</td><td>0,27</td><td>0,27</td><td>0,27</td><td>0,28</td><td>0,28</td><td>0,31</td><td>0,32</td></tr><tr><td>N</td><td>621</td><td>621</td><td>621</td><td>621</td><td>621</td><td>621</td><td>621</td><td>621</td><td>621</td><td>621</td><td>621</td></tr><tr><td rowspan="3">10-40</td><td>Median</td><td>0,70</td><td>0,71</td><td>0,65</td><td>0,66</td><td>0,65</td><td>0,65</td><td>0,65</td><td>0,66</td><td>0,66</td><td>0,61</td><td>0,67</td></tr><tr><td>IQR</td><td>0,29</td><td>0,28</td><td>0,28</td><td>0,28</td><td>0,28</td><td>0,27</td><td>0,28</td><td>0,29</td><td>0,29</td><td>0,32</td><td>0,29</td></tr><tr><td>N</td><td>482</td><td>482</td><td>482</td><td>482</td><td>482</td><td>482</td><td>482</td><td>482</td><td>482</td><td>482</td><td>482</td></tr><tr><td rowspan="3">40-100</td><td>Median</td><td>0,62</td><td>0,62</td><td>0,59</td><td>0,58</td><td>0,59</td><td>0,59</td><td>0,59</td><td>0,58</td><td>0,59</td><td>0,53</td><td>0,61</td></tr><tr><td>IQR</td><td>0,36</td><td>0,35</td><td>0,33</td><td>0,38</td><td>0,33</td><td>0,32</td><td>0,33</td><td>0,35</td><td>0,36</td><td>0,35</td><td>0,36</td></tr><tr><td>N</td><td>180</td><td>180</td><td>180</td><td>180</td><td>180</td><td>180</td><td>180</td><td>180</td><td>180</td><td>180</td><td>180</td></tr></tbody></table>

<figure><img src="image_13.png" /><figcaption>Figure 3: Validation of all produced datasets and reference datasets of SWI and ERA5-Land showing uRMSD of absolute values of the datasets to ISMN data over Europe for the three soil layer depths. Validation metrics in Tab. 3</figcaption></figure>
<table><caption>Table 3: Validation metrics corresponding to Fig. 3, showing median uRMSD, its interquartile range (IQR) and the number of observations (N)</caption><thead><tr><th>uRMSD</th><th></th><th>ISBA OL</th><th>ISBA LAI&SM</th><th>NoahMP OL</th><th>NoahMP SM</th><th>NoahMP LAI</th><th>NoahMP LAI s</th><th>NoahMP VOD</th><th>NoahMP LAI&SM</th><th>NoahMP VOD&SM</th><th>ESA CCI SWI</th><th>ERA5 Land</th></tr></thead><tbody><tr><td rowspan="3">0-10</td><td>Median</td><td>0,052</td><td>0,053</td><td>0,052</td><td>0,051</td><td>0,051</td><td>0,052</td><td>0,051</td><td>0,051</td><td>0,051</td><td>0,055</td><td>0,053</td></tr><tr><td>IQR</td><td>0,041</td><td>0,041</td><td>0,039</td><td>0,040</td><td>0,040</td><td>0,039</td><td>0,040</td><td>0,040</td><td>0,040</td><td>0,039</td><td>0,041</td></tr><tr><td>N</td><td>621</td><td>621</td><td>621</td><td>621</td><td>621</td><td>621</td><td>621</td><td>621</td><td>621</td><td>621</td><td>621</td></tr><tr><td rowspan="3">10-40</td><td>Median</td><td>0,041</td><td>0,041</td><td>0,042</td><td>0,041</td><td>0,042</td><td>0,042</td><td>0,042</td><td>0,041</td><td>0,041</td><td>0,047</td><td>0,041</td></tr><tr><td>IQR</td><td>0,028</td><td>0,029</td><td>0,028</td><td>0,029</td><td>0,028</td><td>0,028</td><td>0,028</td><td>0,029</td><td>0,029</td><td>0,031</td><td>0,029</td></tr><tr><td>N</td><td>482</td><td>482</td><td>482</td><td>482</td><td>482</td><td>482</td><td>482</td><td>482</td><td>482</td><td>482</td><td>482</td></tr><tr><td rowspan="3">40-100</td><td>Median</td><td>0,032</td><td>0,032</td><td>0,032</td><td>0,032</td><td>0,033</td><td>0,032</td><td>0,033</td><td>0,033</td><td>0,032</td><td>0,036</td><td>0,033</td></tr><tr><td>IQR</td><td>0,034</td><td>0,036</td><td>0,034</td><td>0,036</td><td>0,034</td><td>0,034</td><td>0,034</td><td>0,036</td><td>0,036</td><td>0,036</td><td>0,031</td></tr><tr><td>N</td><td>180</td><td>180</td><td>180</td><td>180</td><td>180</td><td>180</td><td>180</td><td>180</td><td>180</td><td>180</td><td>180</td></tr></tbody></table>

<figure><img src="image_14.png" /><figcaption>Figure 4: Comparison of the performance of surface soil moisture open-loop runs (y-axis) and the one of CCI surface soil moisture COMBINED v6.1 (x-axis) (A and C) and how the assimilation of SSM impacts the performance of the results (B and D), whereat blue colours indicate an improvement of the validation results by SSM assimilation to the open-loop run and red colours show a higher performance of the open-loop run over SSM assimilation run</figcaption></figure>
<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /><figcaption>Figure 5: Anomaly validation of all produced datasets and reference datasets of SWI and ERA5-Land showing correlations of absolute values of the datasets to ISMN data over Europe for the three soil layer depths. Validation metrics in Tab. 4</figcaption></figure>

<table><caption>Table 4: Validation metrics corresponding to Fig. 5, showing median correlation, its interquartile range (IQR) and the number of observations (N)</caption><thead><tr><th>Pearson's R</th><th></th><th>ISBA OL</th><th>ISBA LAI&SM</th><th>NoahMP OL</th><th>NoahMP SM</th><th>NoahMP LAI</th><th>NoahMP LAI s</th><th>NoahMP VOD</th><th>NoahMP LAI&SM</th><th>NoahMP VOD&SM</th><th>ESA CCI</th><th>SWI</th><th>ERA5 Land</th></tr></thead><tbody><tr><td rowspan="3">0-10</td><td>Median</td><td>0,52</td><td>0,52</td><td>0,54</td><td>0,55</td><td>0,53</td><td>0,54</td><td>0,53</td><td>0,54</td><td>0,54</td><td>0,54</td><td>0,46</td><td>0,54</td></tr><tr><td>IQR</td><td>0,19</td><td>0,19</td><td>0,18</td><td>0,18</td><td>0,18</td><td>0,18</td><td>0,18</td><td>0,19</td><td>0,19</td><td>0,24</td><td>0,18</td></tr><tr><td>N</td><td>206</td><td>206</td><td>206</td><td>206</td><td>206</td><td>206</td><td>206</td><td>206</td><td>206</td><td>206</td><td>206</td></tr><tr><td rowspan="3">10-40</td><td>Median</td><td>0,54</td><td>0,55</td><td>0,51</td><td>0,52</td><td>0,51</td><td>0,51</td><td>0,51</td><td>0,53</td><td>0,54</td><td>0,39</td><td>0,52</td></tr><tr><td>IQR</td><td>0,21</td><td>0,22</td><td>0,21</td><td>0,21</td><td>0,22</td><td>0,21</td><td>0,23</td><td>0,22</td><td>0,21</td><td>0,22</td><td>0,23</td></tr><tr><td>N</td><td>214</td><td>214</td><td>214</td><td>214</td><td>214</td><td>214</td><td>214</td><td>214</td><td>214</td><td>214</td><td>214</td></tr><tr><td rowspan="3">40-100</td><td>Median</td><td>0,46</td><td>0,48</td><td>0,43</td><td>0,46</td><td>0,46</td><td>0,44</td><td>0,44</td><td>0,48</td><td>0,47</td><td>0,31</td><td>0,45</td></tr><tr><td>IQR</td><td>0,34</td><td>0,32</td><td>0,28</td><td>0,33</td><td>0,29</td><td>0,26</td><td>0,30</td><td>0,34</td><td>0,32</td><td>0,38</td><td>0,24</td></tr><tr><td>N</td><td>96</td><td>96</td><td>96</td><td>96</td><td>96</td><td>96</td><td>96</td><td>96</td><td>96</td><td>96</td><td>96</td></tr></tbody></table>
<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /><figcaption>Figure 6: Anomaly validation of all produced datasets and reference datasets of SWI and ERA5-Land showing uRMSD of absolute values of the datasets to ISMN data over Europe for the three soil layer depths. Validation metrics in Tab. 5</figcaption></figure>

<table><caption>Table 5: Validation metrics corresponding to Fig. 6, showing median uRMSD, its interquartile range (IQR) and the number of observations (N)</caption><thead><tr><th>uRMSD</th><th></th><th>ISBA OL</th><th>ISBA LAI&SM</th><th>NoahMP OL</th><th>NoahMP SM</th><th>NoahMP LAI</th><th>NoahMP LAI s</th><th>NoahMP VOD</th><th>NoahMP LAI&SM</th><th>NoahMP VOD&SM</th><th>ESA CCI SWI</th><th>ERA5 Land</th></tr></thead><tbody><tr><td rowspan="3">0-10</td><td>Median</td><td>0,047</td><td>0,047</td><td>0,046</td><td>0,046</td><td>0,046</td><td>0,046</td><td>0,046</td><td>0,045</td><td>0,046</td><td>0,051</td><td>0,046</td></tr><tr><td>IQR</td><td>0,028</td><td>0,027</td><td>0,024</td><td>0,025</td><td>0,024</td><td>0,024</td><td>0,024</td><td>0,025</td><td>0,025</td><td>0,028</td><td>0,025</td></tr><tr><td>N</td><td>206</td><td>206</td><td>206</td><td>206</td><td>206</td><td>206</td><td>206</td><td>206</td><td>206</td><td>206</td><td>206</td></tr><tr><td rowspan="3">10-40</td><td>Median</td><td>0,040</td><td>0,039</td><td>0,042</td><td>0,041</td><td>0,041</td><td>0,042</td><td>0,041</td><td>0,040</td><td>0,040</td><td>0,047</td><td>0,040</td></tr><tr><td>IQR</td><td>0,028</td><td>0,029</td><td>0,029</td><td>0,028</td><td>0,029</td><td>0,028</td><td>0,028</td><td>0,028</td><td>0,028</td><td>0,031</td><td>0,029</td></tr><tr><td>N</td><td>214</td><td>214</td><td>214</td><td>214</td><td>214</td><td>214</td><td>214</td><td>214</td><td>214</td><td>214</td><td>214</td></tr><tr><td rowspan="3">40-100</td><td>Median</td><td>0,030</td><td>0,029</td><td>0,030</td><td>0,029</td><td>0,029</td><td>0,030</td><td>0,029</td><td>0,029</td><td>0,029</td><td>0,033</td><td>0,031</td></tr><tr><td>IQR</td><td>0,032</td><td>0,029</td><td>0,034</td><td>0,033</td><td>0,034</td><td>0,034</td><td>0,034</td><td>0,034</td><td>0,033</td><td>0,028</td><td>0,030</td></tr><tr><td>N</td><td>96</td><td>96</td><td>96</td><td>96</td><td>96</td><td>96</td><td>96</td><td>96</td><td>96</td><td>96</td><td>96</td></tr></tbody></table>
<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

Figure 7: Comparison of the performance of surface soil moisture anomalies of open-loop runs (y-axis) and the one of CCI surface soil moisture COMBINED v6.1 (x-axis) (A and C) and how the assimilation of SSM impacts the performance of the results (B and D), whereat blue colours indicate an improvement of the validation results by SSM assimilation to the open-loop run and red colours show a higher performance of the open-loop run over SSM assimilation run

<figure><img src="image_21.png" /></figure>

Figure 8: Performance changes of the joint assimilation of LAI & SSM vs. OL run of Noah-MP per climate class. Each violin plot represents the differences of the correlations using the joint LAI & SSM and OL. Validation metrics in Tab. 6. Overview of climate class abbreviations in Tab. 7

Table 6: Validation metrics corresponding to Fig. 8. Median shows the difference of correlations between the two datasets Noah-MP joint assimilation of LAI&SSM and Noah-MP OL run per climate class. The p-value shows the result of a t-test comparing these two datasets. P-values lower than 0.05
indicate statistically significant differences between the datasets. Only median differences larger than 0.00 are shown

<table><caption>Table 7: Climate classes abbreviations</caption><thead><tr><th></th><th></th><th>Bsk</th><th>Cfa</th><th>Cfb</th><th>Csa</th><th>Csb</th><th>Dfa</th><th>Dfb</th><th>Dfc</th></tr></thead><tbody><tr><td rowspan="3">0-10</td><td>Median</td><td></td><td>0,01</td><td>0,01</td><td></td><td></td><td>0,02</td><td></td><td>-0,03</td></tr><tr><td>P-value</td><td>0,94</td><td>0,73</td><td>0,93</td><td>0,91</td><td>0,95</td><td>0,87</td><td>0,85</td><td>0,5</td></tr><tr><td>N</td><td>26</td><td>27</td><td>84</td><td>23</td><td>6</td><td>4</td><td>391</td><td>57</td></tr><tr><td rowspan="3">10-40</td><td>Median</td><td></td><td>0,01</td><td>0,01</td><td></td><td></td><td>0,01</td><td></td><td>-0,02</td></tr><tr><td>P-value</td><td></td><td>0,82</td><td>0,71</td><td>0,9</td><td>0,91</td><td></td><td>0,94</td><td>0,83</td></tr><tr><td>N</td><td></td><td>31</td><td>93</td><td>45</td><td>10</td><td></td><td>255</td><td>48</td></tr><tr><td rowspan="3">40-100</td><td>Median</td><td></td><td>0,06</td><td>0,01</td><td>0,01</td><td></td><td></td><td>0,01</td><td>0,01</td></tr><tr><td>P-value</td><td></td><td>0,86</td><td>0,86</td><td>0,82</td><td></td><td></td><td>0,75</td><td>0,92</td></tr><tr><td>N</td><td></td><td>3</td><td>40</td><td>7</td><td></td><td></td><td>107</td><td>23</td></tr></tbody></table>

<table><tr><td>BSk</td><td>cold arid steppe</td></tr><tr><td>Cfa</td><td>warm temperate climate, fully humid with hot summers</td></tr><tr><td>Cfb</td><td>warm temperate climate, fully humid with warm summers</td></tr><tr><td>Csa</td><td>warm temperate climate, with dry and hot summers</td></tr><tr><td>Csb</td><td>warm temperate climate, with dry and warm summers</td></tr><tr><td>Dfa</td><td>snow, fully humid with hot summers</td></tr><tr><td>Dfb</td><td>snow, fully humid with warm summers</td></tr><tr><td>Dfc</td><td>snow, fully humid with cool summers</td></tr><tr><td>ET</td><td>polar tundra</td></tr></table>

<figure><img src="image_22.png" /><figcaption>Figure 9: Performance changes of the joint assimilation of LAI & SSM vs. OL run of Noah-MP per land cover class (based on CCI-LC map). Each violin plot represents the differences of the correlations using the joint LAI & SSM and OL. Validation metrics in Tab. 8Table 8: Validation metrics corresponding to</figcaption></figure>
Fig. 9. Median shows the difference of correlations between the two datasets Noah-MP joint assimilation of LAI&SSM and Noah-MP OL run per land cover class. The p-value shows the result of a t-test comparing these two datasets. P-values lower than 0.05 indicate statistically significant differences between the datasets. Only median differences larger than 0.00 are shown

<table><thead><tr><th></th><th></th><th>10</th><th>11</th><th>12</th><th>20</th><th>30</th><th>40</th><th>60</th><th>70</th><th>90</th><th>100</th><th>110</th><th>130</th><th>180</th><th>190</th></tr></thead><tbody><tr><td rowspan="3">0-10</td><td>Median</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>-0,01</td><td>0,01</td><td>-0,03</td><td>-0,04</td><td></td><td>-0,02</td><td>0,02</td></tr><tr><td>P-value</td><td>0,86</td><td>0,98</td><td>0,99</td><td>0,92</td><td></td><td></td><td>0,93</td><td>0,78</td><td>0,84</td><td>0,51</td><td>0,79</td><td>0,94</td><td>0,73</td><td>0,81</td></tr><tr><td>N</td><td>346</td><td>4</td><td>29</td><td>7</td><td></td><td>1</td><td>11</td><td>67</td><td>12</td><td>9</td><td>7</td><td>46</td><td>34</td><td>45</td></tr><tr><td rowspan="3">10-40</td><td>Median</td><td>0,01</td><td></td><td></td><td></td><td>0,04</td><td></td><td></td><td>-0,01</td><td>0,01</td><td>-0,01</td><td>-0,02</td><td>-0,01</td><td>0,02</td><td>0,02</td></tr><tr><td>P-value</td><td>0,81</td><td>0,97</td><td>0,96</td><td></td><td>0,78</td><td>0,98</td><td>0,91</td><td>0,89</td><td>0,91</td><td>0,95</td><td>0,92</td><td>0,87</td><td>0,86</td><td>0,19</td></tr><tr><td>N</td><td>264</td><td>2</td><td>35</td><td></td><td></td><td>2</td><td>2</td><td>20</td><td>54</td><td>8</td><td>9</td><td>5</td><td>49</td><td>17</td><td>14</td></tr><tr><td rowspan="3">40-100</td><td>Median</td><td>-0,01</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0,01</td><td>0,07</td><td>0,04</td><td>-0,07</td><td>-0,01</td><td>0,09</td></tr><tr><td>P-value</td><td>0,71</td><td></td><td></td><td></td><td></td><td></td><td></td><td>0,96</td><td>0,99</td><td>0,67</td><td>0,7</td><td>0,71</td><td>0,9</td><td>0,09</td></tr><tr><td>N</td><td>106</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>42</td><td>6</td><td>4</td><td>3</td><td>8</td><td>4</td><td>5</td></tr></tbody></table>

<figure><img src="image_23.png" /></figure>

Figure 10: Performance changes of the joint assimilation of LAI & SSM vs. OL run of ISBA per climate class. Each violin plot represents the differences of the correlations using the joint LAI & SSM and OL. Validation metrics in Tab. 9. Overview of climate class abbreviations in Tab. 7

Table 9: Validation metrics corresponding to Fig. 10. Median shows the difference of correlations between the two datasets ISBA joint assimilation of LAI&SSM and ISBA OL run per climate class. The p-value shows the result of a t-test comparing these two datasets. P-values lower than 0.05 indicate
statistically significant differences between the datasets. Only median differences larger than 0.00 are shown

<table><thead><tr><th></th><th></th><th>Bsk</th><th>Cfa</th><th>Cfb</th><th>Csa</th><th>Csb</th><th>Dfa</th><th>Dfb</th><th>Dfc</th></tr></thead><tbody><tr><td rowspan="3">0-10</td><td>Median</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>P-value</td><td>0,65</td><td>1</td><td>0,77</td><td>0,99</td><td>0,98</td><td>0,99</td><td>0,86</td><td>0,96</td></tr><tr><td>N</td><td>26</td><td>27</td><td>84</td><td>23</td><td>6</td><td>4</td><td>391</td><td>57</td></tr><tr><td rowspan="3">10-40</td><td>Median</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0,01</td></tr><tr><td>P-value</td><td></td><td>0,99</td><td>0,77</td><td>0,82</td><td>0,97</td><td></td><td>0,65</td><td>0,93</td></tr><tr><td>N</td><td></td><td>31</td><td>93</td><td>45</td><td>10</td><td></td><td>255</td><td>48</td></tr><tr><td rowspan="3">40-100</td><td>Median</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0,01</td></tr><tr><td>P-value</td><td></td><td>-0,01</td><td></td><td>-0,01</td><td></td><td></td><td>0,75</td><td>0,94</td></tr><tr><td>N</td><td></td><td>3</td><td>40</td><td>7</td><td></td><td></td><td>107</td><td>23</td></tr></tbody></table>

<figure><img src="image_24.png" /><figcaption>Figure 11: Performance changes of the joint assimilation of LAI & SSM vs. OL run of ISBA per land cover class (based on CCI-LC map). Each violin plot represents the differences of the correlations using the joint LAI & SSM and OL. Validation metrics in Tab. 10</figcaption></figure>

Table 10: Validation metrics corresponding to Fig. 11. Median shows the difference of correlations between the two datasets ISBA joint assimilation of LAI&SSM and ISBA OL run per land cover class. The p-value shows the result of a t-test comparing these two datasets. P-values lower than 0.05 indicate statistically significant differences between the datasets. Only median differences larger than 0.00 are shown

<table><thead><tr><th></th><th></th><th>10</th><th>11</th><th>12</th><th>20</th><th>30</th><th>40</th><th>60</th><th>70</th><th>90</th><th>100</th><th>110</th><th>130</th><th>180</th><th>190</th></tr></thead><tbody><tr><td rowspan="3">0-10</td><td>Median</td><td>0,00</td><td>0,03</td><td>0,00</td><td>0,01</td><td></td><td></td><td>0,00</td><td>0,00</td><td>0,00</td><td>0,00</td><td>-0,01</td><td>-0,01</td><td>-0,03</td><td>-0,01</td></tr><tr><td>P-value</td><td>1</td><td>0,79</td><td>0,99</td><td>0,98</td><td></td><td></td><td>0,99</td><td>0,92</td><td>0,95</td><td>0,93</td><td>0,84</td><td>0,8</td><td>0,82</td><td>0,84</td></tr><tr><td>N</td><td>346</td><td>4</td><td>29</td><td>7</td><td></td><td>1</td><td>11</td><td>67</td><td>12</td><td>9</td><td>7</td><td>46</td><td>34</td><td>45</td></tr><tr><td rowspan="3">10-40</td><td>Median</td><td></td><td>0,03</td><td></td><td></td><td>-0,01</td><td>0,01</td><td></td><td></td><td>-0,01</td><td>0,01</td><td>0,02</td><td></td><td>0,01</td><td></td></tr><tr><td>P-value</td><td>0,85</td><td>0,83</td><td>0,99</td><td></td><td>0,98</td><td>0,95</td><td>0,96</td><td>0,98</td><td>0,92</td><td>0,94</td><td>0,88</td><td>0,99</td><td>0,81</td><td>0,54</td></tr><tr><td>N</td><td>264</td><td>2</td><td>35</td><td></td><td>2</td><td>2</td><td>20</td><td>54</td><td>8</td><td>9</td><td>5</td><td>49</td><td>17</td><td>14</td></tr><tr><td rowspan="3">40-100</td><td>Median</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>-0,01</td><td>0,04</td><td>0,02</td><td></td><td>0,07</td><td>-0,01</td></tr><tr><td>P-value</td><td>0,92</td><td></td><td></td><td></td><td></td><td></td><td></td><td>0,96</td><td>0,92</td><td>0,68</td><td>0,79</td><td>0,97</td><td>0,72</td><td>0,83</td></tr><tr><td>N</td><td>106</td><td></td><td></td><td></td><td></td><td></td><td></td><td>42</td><td>6</td><td>4</td><td>3</td><td>8</td><td>4</td><td>5</td></tr></tbody></table>
<figure><img src="image_25.png" /></figure>

<figure><img src="image_26.png" /></figure>

Figure 12: Comparison of the validation of the OL run and the joint LAI & SSM assimilation runs. The color of the points represent the improvement of the validation obtained through DA. Blue colors indicate an improvement of DA, whereas for red points the OL result has a
<figure><img src="image_27.png" /></figure>

better

<figure><img src="image_28.png" /></figure>

performance

<figure><img src="image_29.png" /></figure>

Figure 13: Selected timeseries in southern France (ISMN station Cabrieres d'Avignon from SMOSMANIA) of the model results showing the differences of OL, assimilation runs, and SSM retrievals (ESA CCI COMBINED v6.1) for surface and root-zone soil moisture

## 3.2 Global

The global validation of ISBA OL shows correlations from 0.57 for surface soil moisture, over 0.59 in subsurface to 0.54 in the lowest layer. Data assimilation increases the correlations for all three layers, but again only marginally (<=0.01). OL runs of Noah-MP show similar results. The correlations are decreasing with increasing soil depth from 0.602 in the top layer, over 0.59 in subsurface to 0.55 in root zone soil moisture (Fig. 16 and Tab. 11). For all model runs and soil depths uRSMD values are below 0.052 m³m⁻³ indicating a good model performance (Fig. 17 and Tab. 12). The validation using anomalies are lower than for absolute values and are strongly decreasing over the soil layers: surface soil moisture anomalies have correlations of 0.52 for ISBA OL, 0.52 for ISBA joint assimilation, and 0.54 for Noah-MP OL. Subsurface soil moisture anomalies still have a correlation for all model runs around 0.5 and the deepest layer shows median correlations of only around 0.41.

The main difference of the global validation to the one over Europe is the overall lower correlations. Only surface soil moisture of Noah-MP OL performs similarly good for both absolute values and anomalies. In the lower two layers Pearson's R is around 0.06, 0.03
respectively for anomalies, lower. ISBA correlations decrease globally even with a magnitude of up to 0.11. The impact of the assimilation for ISBA is similarly low as the validation over Europe showed.

<figure><img src="image_30.png" /><figcaption>Figure 14: Global validation of the produced datasets, SWI, and ERA5-Land. Showing the correlations of the individual datasets to ISMN data. Validation metrics in Tab. 11</figcaption></figure>

<table><caption>Table 11: Validation metrics corresponding to Fig. 15, showing median correlation, its interquartile range (IQR) and the number of observations (N)</caption><thead><tr><th>Pearson's R Absolute</th><th>ISBA OL</th><th>ISBA LAI&SM</th><th>NoahMP OL</th><th>ESA CCI SW</th><th>ERA5 Land</th><th>Anomalies</th><th>ISBA OL</th><th>ISBA LAI&SM</th><th>NoahMP OL</th><th>ESA CCI SW</th><th>ERA5 Land</th></tr></thead><tbody><tr><td rowspan="3">0-10</td><td>Median</td><td>0,57</td><td>0,58</td><td>0,60</td><td>0,57</td><td>0,60</td><td>0,52</td><td>0,52</td><td>0,54</td><td>0,48</td><td>0,55</td></tr><tr><td>IQR</td><td>0,34</td><td>0,35</td><td>0,30</td><td>0,35</td><td>0,31</td><td>0,23</td><td>0,24</td><td>0,22</td><td>0,25</td><td>0,22</td></tr><tr><td>N</td><td>2261</td><td>2261</td><td>2261</td><td>2261</td><td>2261</td><td>937</td><td>937</td><td>937</td><td>937</td><td>937</td></tr><tr><td rowspan="3">10-40</td><td>Median</td><td>0,59</td><td>0,60</td><td>0,59</td><td>0,56</td><td>0,61</td><td>0,50</td><td>0,50</td><td>0,50</td><td>0,42</td><td>0,51</td></tr><tr><td>IQR</td><td>0,35</td><td>0,35</td><td>0,34</td><td>0,37</td><td>0,34</td><td>0,25</td><td>0,26</td><td>0,26</td><td>0,26</td><td>0,27</td></tr><tr><td>N</td><td>2284</td><td>2284</td><td>2284</td><td>2284</td><td>2284</td><td>1239</td><td>1239</td><td>1239</td><td>1239</td><td>1239</td></tr><tr><td rowspan="3">40-100</td><td>Median</td><td>0,54</td><td>0,55</td><td>0,55</td><td>0,46</td><td>0,54</td><td>0,41</td><td>0,40</td><td>0,41</td><td>0,34</td><td>0,42</td></tr><tr><td>IQR</td><td>0,36</td><td>0,35</td><td>0,39</td><td>0,44</td><td>0,37</td><td>0,37</td><td>0,36</td><td>0,37</td><td>0,37</td><td>0,37</td></tr><tr><td>N</td><td>1073</td><td>1073</td><td>1073</td><td>1073</td><td>1073</td><td>716</td><td>716</td><td>716</td><td>716</td><td>716</td></tr></tbody></table>
<figure><img src="image_31.png" /></figure>

<figure><img src="image_32.png" /><figcaption>Figure 15: Global validation of the produced datasets, SWI, and ERA5-Land. Showing uRMSD of the individual datasets to ISMN data. Validation metrics in Tab. 12</figcaption></figure>

<table><caption>Table 12: Validation metrics corresponding to Fig. 15, showing median uRMSD, its interquartile range (IQR) and the number of observations (N)</caption><thead><tr><th>uRMSD</th><th>Absolute</th><th>ISBA OL</th><th>ISBA LAI&SM</th><th>NoahMP OL</th><th>SWI</th><th>ERA5 Land</th><th>Anomalies</th><th>ISBA OL</th><th>ISBA LAI&SM</th><th>NoahMP OL</th><th>SWI</th><th>ERA5 Land</th></tr></thead><tbody><tr><td rowspan="3">0-10</td><td>Median</td><td>0,052</td><td>0,052</td><td>0,051</td><td>0,053</td><td>0,051</td><td></td><td>0,054</td><td>0,054</td><td>0,053</td><td>0,057</td><td>0,053</td></tr><tr><td>IQR</td><td>0,033</td><td>0,033</td><td>0,030</td><td>0,033</td><td>0,031</td><td></td><td>0,036</td><td>0,036</td><td>0,033</td><td>0,033</td><td>0,033</td></tr><tr><td>N</td><td>2261</td><td>2261</td><td>2261</td><td>2261</td><td>2261</td><td></td><td>937</td><td>937</td><td>937</td><td>937</td><td>937</td></tr><tr><td rowspan="3">10-40</td><td>Median</td><td>0,042</td><td>0,042</td><td>0,043</td><td>0,046</td><td>0,042</td><td></td><td>0,044</td><td>0,043</td><td>0,044</td><td>0,048</td><td>0,043</td></tr><tr><td>IQR</td><td>0,029</td><td>0,030</td><td>0,030</td><td>0,033</td><td>0,031</td><td></td><td>0,031</td><td>0,032</td><td>0,032</td><td>0,034</td><td>0,032</td></tr><tr><td>N</td><td>2286</td><td>2286</td><td>2286</td><td>2286</td><td>2286</td><td></td><td>1239</td><td>1239</td><td>1239</td><td>1239</td><td>1239</td></tr><tr><td rowspan="3">40-100</td><td>Median</td><td>0,033</td><td>0,033</td><td>0,033</td><td>0,037</td><td>0,034</td><td></td><td>0,033</td><td>0,033</td><td>0,032</td><td>0,035</td><td>0,034</td></tr><tr><td>IQR</td><td>0,033</td><td>0,032</td><td>0,033</td><td>0,034</td><td>0,033</td><td></td><td>0,031</td><td>0,031</td><td>0,032</td><td>0,034</td><td>0,032</td></tr><tr><td>N</td><td>1076</td><td>1076</td><td>1076</td><td>1076</td><td>1076</td><td></td><td>716</td><td>716</td><td>716</td><td>716</td><td>716</td></tr></tbody></table>

# 4 Product Assessment against state-of-the-art RZSM products

## 4.1 SWI

The SWI dataset was implemented using an exponential filter on ESA CCI COMBINED v6.1 as described in Albergel et al. (2008). The resulting dataset consists of various t-values from 1 to 100 which represent the time constant used for the filtering. These t-values can be used to approximate soil layer depths, assuming that higher t-values represent deeper soil depths. The t-values were converted to soil layer depths to obtain the same soil layers as for the ISBA and Noah-MP model outputs. This conversion from t-values to soil layer depths is already
<figure><img src="image_33.png" /></figure>

based on ISMN data, by checking which t-values fit best to which ISMN station depths. Hence the validation is not independent of the modelling and will lead to a rather higher performance. Yet, the results show that over the validated locations Noah-MP and ISBA results clearly outperform SWI over Europe (Figs. 1,2,4, and 5, Tab. 2 to 5). Looking at Fig. 16 and 17 shows that the correlations with ISMN data over Europe significantly improves using Noah-MP compared to SWI. The median Pearson's R of SWI and in-situ measurements is around 0.05 lower than the median Pearson's R of Noah-MP OL and the in-situ observations for all soil layers, showing p-values < 0.005. All other comparisons of Noah-MP OL to ISBA OL, the assimilation runs of Noah-MP and ERA5-Land do not have any significant differences in correlations (Fig. 16 & 17).

<figure><img src="image_34.png" /></figure>

Figure 16: Comparison of the validations of Noah-MP, ISBA, SWI, and ERA5-Land. The first violin plot shows the changes in Pearson's R from the ISBA joint assimilation run to its OL run. The remaining violins show the changes comparing Noah-MP OL to its assimilation runs as well as a comparison to SWI, ERA5-Land and ISBA OL. P-val shows the results of the t-tests comparing the respective datasets
<figure><img src="image_35.png" /></figure>

<figure><img src="image_36.png" /></figure>

**Figure 17:** Comparison of the anomaly validations of Noah-MP, ISBA, SWI, and ERA5-Land. The first violin plot shows the changes in Pearson's R from the ISBA joint assimilation run to its OL run. The remaining violins show the changes comparing Noah-MP OL to its assimilation runs as well as a comparison to SWI, ERA5-Land and ISBA OL. P-val shows the results of the t-tests comparing the respective datasets

## 4.2 ERA5-Land

The comparison to ERA5-Land brings along some challenges due to the different depths of the soil layers. ERA5-Land uses soil layers spanning from 0-7cm, 7-28cm, and 28-100cm. These are slightly shifted to the depths used for the datasets produced here. However, as it still covers a similar range, ERA5-Land is in a first step validated over the same depths as used here (0-10cm, 10-40cm, and 40-100cm). In a next step, ERA5-Land is validated over the depths it is established for (Fig. 18).

The first validation results using ISMN data over the depths of Noah-MP and ISBA show a similar performance of ERA5-Land to the results produced in this study. The correlations in the uppermost layer are 0.6 and, therefore, slightly higher than for Noah-MP but lower than ISBA. In the second layer, ISBA outperforms ERA5-Land by having correlations of around 0.03
<figure><img src="image_37.png" /></figure>

higher than ERA5-Land and 0.05 than Noah-MP OL. For the deepest layer, the correlations are again similar with ISBA still having the best performance (Tab. 2 and Fig. 2). However, neither of these differences are significant (Fig. 16). The same holds for the correlations of the anomalies, which lay too in a similar range. For the uppermost layer ERA5-Land and Noah-MP have the same correlations and are around 0.02 higher than ISBA. For the lower two layers ISBA is best, outperforming ERA5-Land by around 0.01. Again, none of these differences are significant (Fig. 17). The validation using uRMSD reveals a similar pattern, indicating that the datasets developed here represent soil moisture similarly well as ERA5-Land over these soil layers in Europe. On a global scale, ERA5-Land seems to perform a bit better, however, is still in the range of the datasets established in this study (Fig. 14 & 15 and Tab. 11 & 12). The correlations are not significantly increasing when validating ERA5-Land over its original depth (Fig. 18).

<figure><img src="image_38.png" /><figcaption>Figure 18: Validation of ERA5 Land and SMAP L4 for their original depths over Europe, showing the correlations of the individual datasets and ISMN data</figcaption></figure>

## 4.3 SMAP Level 4

The product assessment using SMAP Level 4 data (from hereon called SMAP), brings along a similar challenge as ERA5-Land. It is developed to represent depths of 0-5cm for surface soil moisture and 0-100cm for root zone soil moisture. Hence the validation is done in the same way as ERA5-Land, once using the depths of ISBA and Noah-MP and once for the depths it is established for. In the first case, root zone soil moisture of SMAP is used twice for depths of 10-40cm and 40-100cm. In addition, SMAP data is only available since March 2015, hence the validation period is set to 2015-2019 which leads to slightly different results to the ones presented so far.
<figure><img src="image_39.png" /></figure>

Validation results over the three soil layers used in this study show a similar performance of SMAP to Noah-MP OL for surface and root zone soil moisture regarding absolute values. Over subsurface soil moisture it performs worse than the other datasets (Fig. 19 & 20 and Tab. 13 & 14). Looking at soil moisture anomalies, SMAP has among the highest performance for all layers. In the uppermost layer it performs slightly better than all other datasets. In the lowest layer, SMAP clearly outperforms Noah-MP model runs. In the second layer it performs similarly as Noah-MP. ISBA OL and the assimilation run of ISBA have the best performance in the lowest two layers (Fig. 21 & 22 and Tab. 15 & 16). As for ERA5-Land, the validation of SMAP does not perform significantly better over its original depths (Fig. 18).

On a global scale (Fig. 23 and Tab. 17), all model runs are performing similarly for absolute values in the top and bottom layer. In the second layer, ISBA and Noah-MP have higher correlations than SMAP for absolute values and anomalies. In the top layer, SMAP outperforms ISBA and Noah-MP for anomalies and in the lowest layer ISBA has slightly higher correlations than SMAP, which in return slightly outperforms Noah-MP.

<figure><img src="image_40.png" /><figcaption>**Figure 19:** Validation of all produced datasets and reference datasets of SWI, ERA5-Land, and SMAP L4 validated over the period of 2015-2019. It shows the correlations of absolute values of the datasets to ISMN data over Europe for the three soil layer depths. Validation metrics in Tab. 13</figcaption></figure>
<figure><img src="image_41.png" /></figure>

<table><caption>Table 13: Validation metrics corresponding to Fig. 19, showing median correlation, its interquartile range (IQR) and the number of observations (N)</caption><thead><tr><th></th><th>Pearson's R</th><th>ISBA OL</th><th>ISBA LAI&SM</th><th>NoahMP OL</th><th>NoahMP SM</th><th>NoahMP LAI</th><th>NoahMP LAI s</th><th>NoahMP VOD</th><th>NoahMP LAI&SM</th><th>NoahMP VOD&SM</th><th>ESA CCI SWI</th><th>ERA5 Land</th><th>SMAP</th></tr></thead><tbody><tr><td rowspan="3">0-10</td><td>Median</td><td>0,61</td><td>0,61</td><td>0,61</td><td>0,61</td><td>0,60</td><td>0,61</td><td>0,61</td><td>0,60</td><td>0,60</td><td>0,58</td><td>0,60</td><td>0,60</td></tr><tr><td>IQR</td><td>0,34</td><td>0,34</td><td>0,30</td><td>0,31</td><td>0,29</td><td>0,30</td><td>0,29</td><td>0,31</td><td>0,31</td><td>0,34</td><td>0,34</td><td>0,32</td></tr><tr><td>N</td><td>493</td><td>493</td><td>493</td><td>493</td><td>493</td><td>493</td><td>493</td><td>493</td><td>493</td><td>493</td><td>493</td><td>493</td></tr><tr><td rowspan="3">10-40</td><td>Median</td><td>0,72</td><td>0,72</td><td>0,66</td><td>0,67</td><td>0,67</td><td>0,67</td><td>0,66</td><td>0,67</td><td>0,67</td><td>0,63</td><td>0,67</td><td>0,61</td></tr><tr><td>IQR</td><td>0,32</td><td>0,31</td><td>0,29</td><td>0,30</td><td>0,30</td><td>0,28</td><td>0,30</td><td>0,30</td><td>0,30</td><td>0,33</td><td>0,33</td><td>0,32</td></tr><tr><td>N</td><td>342</td><td>342</td><td>342</td><td>342</td><td>342</td><td>342</td><td>342</td><td>342</td><td>342</td><td>342</td><td>342</td><td>342</td></tr><tr><td rowspan="3">40-100</td><td>Median</td><td>0,67</td><td>0,67</td><td>0,60</td><td>0,58</td><td>0,60</td><td>0,60</td><td>0,60</td><td>0,59</td><td>0,58</td><td>0,58</td><td>0,65</td><td>0,59</td></tr><tr><td>IQR</td><td>0,24</td><td>0,25</td><td>0,27</td><td>0,34</td><td>0,36</td><td>0,36</td><td>0,37</td><td>0,32</td><td>0,33</td><td>0,33</td><td>0,29</td><td>0,33</td></tr><tr><td>N</td><td>110</td><td>110</td><td>110</td><td>110</td><td>110</td><td>110</td><td>110</td><td>110</td><td>110</td><td>110</td><td>110</td><td>110</td></tr></tbody></table>

<figure><img src="image_42.png" /><figcaption>Figure 20: Validation of all produced datasets and reference datasets of SWI, ERA5-Land, and SMAP L4 validated over the period of 2015-2019. It shows uRMSD of absolute values of the datasets to ISMN data over Europe for the three soil layer depths. Validation metrics in Tab. 14</figcaption></figure>

<table><caption>Table 14: Validation metrics corresponding to Fig. 20, showing median uRMSD, its interquartile range (IQR) and the number of observations (N)</caption><thead><tr><th>uRMSD</th><th></th><th>ISBA OL</th><th>ISBA LAI&SM</th><th>NoahMP OL</th><th>NoahMP SM</th><th>NoahMP LAI</th><th>NoahMP LAI s</th><th>NoahMP VOD</th><th>NoahMP LAI&SM</th><th>NoahMP VOD&SM</th><th>ESA CCI SWI</th><th>ERA5 Land</th><th>SMAP</th></tr></thead><tbody><tr><td rowspan="3">0-10</td><td>Median</td><td>0,052</td><td>0,052</td><td>0,050</td><td>0,050</td><td>0,050</td><td>0,050</td><td>0,050</td><td>0,050</td><td>0,050</td><td>0,053</td><td>0,052</td><td>0,052</td></tr><tr><td>IQR</td><td>0,046</td><td>0,047</td><td>0,045</td><td>0,047</td><td>0,045</td><td>0,044</td><td>0,045</td><td>0,046</td><td>0,045</td><td>0,046</td><td>0,048</td><td>0,044</td></tr><tr><td>N</td><td>493</td><td>493</td><td>493</td><td>493</td><td>493</td><td>493</td><td>493</td><td>493</td><td>493</td><td>493</td><td>493</td><td>493</td></tr><tr><td rowspan="3">10-40</td><td>Median</td><td>0,037</td><td>0,037</td><td>0,040</td><td>0,039</td><td>0,040</td><td>0,040</td><td>0,040</td><td>0,039</td><td>0,039</td><td>0,041</td><td>0,039</td><td>0,042</td></tr><tr><td>IQR</td><td>0,031</td><td>0,030</td><td>0,029</td><td>0,031</td><td>0,029</td><td>0,029</td><td>0,030</td><td>0,031</td><td>0,030</td><td>0,034</td><td>0,033</td><td>0,031</td></tr><tr><td>N</td><td>342</td><td>342</td><td>342</td><td>342</td><td>342</td><td>342</td><td>342</td><td>342</td><td>342</td><td>342</td><td>342</td><td>342</td></tr><tr><td rowspan="3">40-100</td><td>Median</td><td>0,032</td><td>0,032</td><td>0,035</td><td>0,036</td><td>0,035</td><td>0,035</td><td>0,035</td><td>0,037</td><td>0,037</td><td>0,039</td><td>0,034</td><td>0,035</td></tr><tr><td>IQR</td><td>0,028</td><td>0,028</td><td>0,036</td><td>0,038</td><td>0,036</td><td>0,036</td><td>0,037</td><td>0,035</td><td>0,036</td><td>0,034</td><td>0,030</td><td>0,029</td></tr><tr><td>N</td><td>110</td><td>110</td><td>110</td><td>110</td><td>110</td><td>110</td><td>110</td><td>110</td><td>110</td><td>110</td><td>110</td><td>110</td></tr></tbody></table>
<figure><img src="image_43.png" /></figure>

<figure><img src="image_44.png" /><figcaption>Figure 21: Validation of all produced datasets and reference datasets of SWI, ERA5-Land, and SMAP L4 validated over the period of 2015-2019. It shows the correlations of anomalies of the datasets to ISMN data over Europe for the three soil layer depths. Validation metrics in Tab. 15</figcaption></figure>

<table><caption>Table 15: Validation metrics corresponding to Fig. 21, showing median correlation, its interquartile range (IQR) and the number of observations (N)</caption><thead><tr><th></th><th>Pearson's R</th><th>ISBA OL</th><th>ISBA LAI&SM</th><th>NoahMP OL</th><th>NoahMP SM</th><th>NoahMP LAI</th><th>NoahMP LAI s</th><th>NoahMP VOD</th><th>NoahMP LAI&SM</th><th>NoahMP VOD&SM</th><th>ESA CCI SWI</th><th>ERA5 Land</th><th>SMAP</th></tr></thead><tbody><tr><td rowspan="2">0-10</td><td>Median</td><td>0,58</td><td>0,57</td><td>0,55</td><td>0,56</td><td>0,55</td><td>0,56</td><td>0,55</td><td>0,56</td><td>0,56</td><td>0,53</td><td>0,58</td><td>0,60</td></tr><tr><td>IQR</td><td>0,19</td><td>0,19</td><td>0,20</td><td>0,20</td><td>0,20</td><td>0,20</td><td>0,20</td><td>0,21</td><td>0,21</td><td>0,26</td><td>0,18</td><td>0,25</td></tr><tr><td rowspan="2">10-40</td><td>N</td><td>106</td><td>106</td><td>106</td><td>106</td><td>106</td><td>106</td><td>106</td><td>106</td><td>106</td><td>106</td><td>106</td><td>106</td></tr><tr><td>Median</td><td>0,61</td><td>0,59</td><td>0,52</td><td>0,54</td><td>0,55</td><td>0,53</td><td>0,53</td><td>0,55</td><td>0,55</td><td>0,46</td><td>0,55</td><td>0,54</td></tr><tr><td rowspan="2">40-100</td><td>IQR</td><td>0,29</td><td>0,27</td><td>0,26</td><td>0,25</td><td>0,27</td><td>0,26</td><td>0,26</td><td>0,25</td><td>0,26</td><td>0,32</td><td>0,25</td><td>0,20</td></tr><tr><td>N</td><td>109</td><td>109</td><td>109</td><td>109</td><td>109</td><td>109</td><td>109</td><td>109</td><td>109</td><td>109</td><td>109</td><td>109</td></tr><tr><td></td><td>Median</td><td>0,55</td><td>0,58</td><td>0,47</td><td>0,46</td><td>0,47</td><td>0,47</td><td>0,46</td><td>0,45</td><td>0,45</td><td>0,33</td><td>0,49</td><td>0,53</td></tr><tr><td></td><td>IQR</td><td>0,26</td><td>0,24</td><td>0,28</td><td>0,28</td><td>0,31</td><td>0,28</td><td>0,28</td><td>0,29</td><td>0,31</td><td>0,34</td><td>0,20</td><td>0,22</td></tr><tr><td></td><td>N</td><td>33</td><td>33</td><td>33</td><td>33</td><td>33</td><td>33</td><td>33</td><td>33</td><td>33</td><td>33</td><td>33</td><td>33</td></tr></tbody></table>
<figure><img src="image_45.png" /></figure>

<figure><img src="image_46.png" /><figcaption>Figure 22: Validation of all produced datasets and reference datasets of SWI, ERA5-Land, and SMAP L4 validated over the period of 2015-2019. It shows uRMSD of the anomalies of the datasets to ISMN data over Europe for the three soil layer depths. Validation metrics in Tab. 16</figcaption></figure>

<table><caption>Table 16: Validation metrics corresponding to Fig. 22, showing median uRMSD, its interquartile range (IQR) and the number of observations (N)</caption><thead><tr><th>uRMSD</th><th></th><th>ISBA OL</th><th>ISBA LAI&SM</th><th>NoahMP OL</th><th>NoahMP SM</th><th>NoahMP LAI</th><th>NoahMP LAI s</th><th>NoahMP VOD</th><th>NoahMP LAI&SM</th><th>NoahMP VOD&SM</th><th>ESA CCI SWI</th><th>ERA5 Land</th><th>SMAP</th></tr></thead><tbody><tr><td rowspan="3">0-10</td><td>Median</td><td>0,044</td><td>0,045</td><td>0,044</td><td>0,043</td><td>0,043</td><td>0,043</td><td>0,043</td><td>0,043</td><td>0,043</td><td>0,045</td><td>0,045</td><td>0,042</td></tr><tr><td>IQR</td><td>0,023</td><td>0,024</td><td>0,021</td><td>0,021</td><td>0,020</td><td>0,021</td><td>0,021</td><td>0,021</td><td>0,021</td><td>0,023</td><td>0,020</td><td>0,023</td></tr><tr><td>N</td><td>106</td><td>106</td><td>106</td><td>106</td><td>106</td><td>106</td><td>106</td><td>106</td><td>106</td><td>106</td><td>106</td><td>106</td></tr><tr><td rowspan="3">10-40</td><td>Median</td><td>0,036</td><td>0,036</td><td>0,041</td><td>0,040</td><td>0,040</td><td>0,041</td><td>0,041</td><td>0,039</td><td>0,039</td><td>0,042</td><td>0,041</td><td>0,040</td></tr><tr><td>IQR</td><td>0,025</td><td>0,026</td><td>0,027</td><td>0,027</td><td>0,028</td><td>0,028</td><td>0,027</td><td>0,027</td><td>0,026</td><td>0,031</td><td>0,026</td><td>0,023</td></tr><tr><td>N</td><td>109</td><td>109</td><td>109</td><td>109</td><td>109</td><td>109</td><td>109</td><td>109</td><td>109</td><td>109</td><td>109</td><td>109</td></tr><tr><td rowspan="3">40-100</td><td>Median</td><td>0,033</td><td>0,031</td><td>0,033</td><td>0,031</td><td>0,033</td><td>0,033</td><td>0,033</td><td>0,031</td><td>0,034</td><td>0,040</td><td>0,040</td><td>0,034</td></tr><tr><td>IQR</td><td>0,029</td><td>0,029</td><td>0,035</td><td>0,035</td><td>0,035</td><td>0,035</td><td>0,035</td><td>0,034</td><td>0,034</td><td>0,037</td><td>0,034</td><td>0,040</td></tr><tr><td>N</td><td>33</td><td>33</td><td>33</td><td>33</td><td>33</td><td>33</td><td>33</td><td>33</td><td>33</td><td>33</td><td>33</td><td>33</td></tr></tbody></table>
<figure><img src="image_47.png" /></figure>

<figure><img src="image_48.png" /><figcaption>Figure 23: Global validation of the produced datasets, SWI, ERA5-Land, and SMAP L4. Showing the correlations of the individual datasets to ISMN data – validated for the period 2015-2019. Validation metrics in Tab. 17</figcaption></figure>

<table><caption>Table 17: Validation metrics corresponding to Fig. 23, showing median correlations, its interquartile range (IQR) and the number of observations (N)</caption><thead><tr><th>Pearson's R Absolute</th><th>ISBA OL</th><th>ISBA LAI&amp;SWI</th><th>NoahMP OL</th><th>ESA CCI</th><th>SWI ERA5 Land</th><th>SMAP</th><th>Anomalies</th><th>ISBA OL</th><th>ISBA LAI&amp;SWI</th><th>NoahMP OL</th><th>ESA CCI</th><th>SWI ERA5 Land</th><th>SMAP</th></tr></thead><tbody><tr><td rowspan="3">0-10</td><td>Median</td><td>0.63</td><td>0.64</td><td>0.64</td><td>0.64</td><td>0.64</td><td>0.64</td><td></td><td>0.51</td><td>0.51</td><td>0.51</td><td>0.51</td><td>0.53</td><td>0.54</td></tr><tr><td>IQR</td><td>0.29</td><td>0.29</td><td>0.27</td><td>0.30</td><td>0.29</td><td>0.30</td><td></td><td>0.29</td><td>0.31</td><td>0.28</td><td>0.28</td><td>0.26</td><td>0.29</td></tr><tr><td>N</td><td>1450</td><td>1450</td><td>1450</td><td>1450</td><td>1450</td><td>1450</td><td></td><td>503</td><td>503</td><td>503</td><td>503</td><td>503</td><td>503</td></tr><tr><td rowspan="3">10-40</td><td>Median</td><td>0.65</td><td>0.66</td><td>0.64</td><td>0.62</td><td>0.66</td><td>0.62</td><td></td><td>0.49</td><td>0.49</td><td>0.47</td><td>0.44</td><td>0.49</td><td>0.46</td></tr><tr><td>IQR</td><td>0.29</td><td>0.29</td><td>0.31</td><td>0.31</td><td>0.30</td><td>0.30</td><td></td><td>0.34</td><td>0.36</td><td>0.34</td><td>0.30</td><td>0.33</td><td>0.31</td></tr><tr><td>N</td><td>1391</td><td>1391</td><td>1391</td><td>1391</td><td>1391</td><td>1391</td><td></td><td>464</td><td>464</td><td>464</td><td>464</td><td>464</td><td>464</td></tr><tr><td rowspan="3">40-100</td><td>Median</td><td>0.56</td><td>0.57</td><td>0.53</td><td>0.49</td><td>0.53</td><td>0.56</td><td></td><td>0.40</td><td>0.39</td><td>0.27</td><td>0.34</td><td>0.40</td><td>0.40</td></tr><tr><td>IQR</td><td>0.39</td><td>0.40</td><td>0.43</td><td>0.51</td><td>0.44</td><td>0.46</td><td></td><td>0.45</td><td>0.47</td><td>0.46</td><td>0.42</td><td>0.44</td><td>0.47</td></tr><tr><td>N</td><td>642</td><td>642</td><td>642</td><td>642</td><td>642</td><td>642</td><td></td><td>323</td><td>323</td><td>323</td><td>323</td><td>323</td><td>323</td></tr></tbody></table>

## 5 Study Conclusion

In the frame of this study, several new assimilation products were developed to estimate root zone soil moisture. Two land surface models were used, and three datasets (Tab. 1) were assimilated in different combinations and setups to evaluate the impact of data assimilation on root zone soil moisture modelling. The results were validated using ISMN data and compared to existing root zone soil moisture datasets of ERA5-Land and SMAP L4. The
<figure><img src="image_49.png" /></figure>

validation showed that the OL runs of both models already have a good performance for all three soil layers. Both OL runs show a significantly better correspondence with the ISMN data than ESA CCI COMBINED v6.1. Therefore, assimilating ESA CCI soil moisture did not help to significantly improve the performance of the models with respect to ISMN data in terms of correlation and uRMSD. The assimilation of LAI and VOD did not help to do so neither, and, in the case of VOD, even reduced the skill. However, the assimilation had an impact (not shown) on the simulated land surface fluxes and on RZSM in terms of volumetric soil moisture and water storage. The largest improvements in performance due to data assimilation were obtained to estimate subsurface soil moisture anomalies using Noah-MP by assimilating SSM either alone or jointly with VOD or LAI. For most other assimilation runs there were only small improvements. The lower improvements of the performance using joint assimilation with ISBA are possibly related to the already slightly higher performance of the OL run compared to Noah-MP OL, or to different model and observation error characterizations. Given the circumstances of the lower performance of ESA CCI soil moisture, it is remarkable though, that the model performance still increased, which is indeed a promise of data assimilation: even when assimilating inferior data, a well-designed data assimilation system may be able to extract useful signals from the assimilated data (Reichle et al., 2014). The comparison of the two models, ISBA and Noah-MP, to existing root zone soil moisture datasets showed that the results produced here perform similarly as ERA5-Land and SMAP.

A plausible explanation why the assimilation of ESA CCI SM did not add much skill above that of a model-only OL is because the forcing data over Europe have a very high quality. Over areas where fewer meteorological stations are available a stronger impact may be expected, as the quality of the forcing data depends on the availability of meteorological stations, and is rather lower with fewer stations.

Conversely, the assimilation of ESA CCI SM adds a lot of skill compared to the ESA CCI SM product alone. The assimilation improves the surface soil moisture, and provides consistent estimates of root-zone soil moisture, vegetation and other geophysical variables.

## 6 Outlook: Next Steps

The results presented in this study provide a good basis to further push the development of root zone soil moisture products through data assimilation. It has been shown that the two land surface models are well able to provide root zone soil moisture estimations. Data assimilation has not led to significantly improved products over model-only simulations, but it does add significant value over the ESA CCI SM retrieval product. Going forward, the assimilation impact could be improved by developing new observation operators for VOD or assimilating other products focusing on backscatter observations or the slope of the backscatter incidence angle relationship. Special attention will be required for the error characterisation of the assimilated products. In addition, further activities in that direction
<figure><img src="image_50.png" /></figure>

should focus on regions with a lower quality of forcing data to test the assumption of an increasing impact of soil moisture assimilation in such areas. In such areas the benefit of data assimilation can be evaluated via instrumental variable techniques, using independent retrieval products. The latter is likely only feasible when assimilating either the active or passive ESA CCI SM product.

Regarding a potential publication of the datasets on the ESA open data portal, it can be recommended to either use the joint assimilation runs of LAI & SSM of ISBA or of Noah-MP, because they showed the overall best performance and the best available root-zone product to complement the ESA CCI surface soil moisture product. A combination of the two datasets from both data assimilation systems is not recommended.

## 7 References

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Albergel, C. and Zheng, Y. and Bonan, B. and Dutra, E. and Rodriguez-Fernandez, N. and Munier, S. and Draper, C. and de Rosnay, P. and Munoz-Sabater, J. and Balsamo, G. and Fairbairn, D. and Meurey, C. and Calvet, J.-C. Earth Syst. Sci., 24, 4291–4316, 2020, https://doi.org/10.5194/hess-24-4291-2020

Albergel, C., S. Munier, D. J. Leroux, H. Dewaele, D. Fairbairn, A. L. Barbu, E. Gelati, W. Dorigo, S. Faroux, C. Meurey, P. Le Moigne, B. Decharme, J.-F. Mahfouf, J.-C. Calvet: Sequential assimilation of satellite-derived vegetation and soil moisture products using SURFEX_v8.0: LDAS-Monde assessment over the Euro-Mediterranean area, Geosci. Model Dev., 10, 3889–3912, https://doi.org/10.5194/gmd-10-3889-2017, 2017

Carrera, M. L., S.Bélair, and B.Bilodeau, 2015: The Canadian Land Data Assimilation System (CaLDAS): Description and synthetic evaluation study. J. Hydrometeor., 16, 1293–1314, https://doi.org/10.1175/JHM-D-14-0089.1.

De Lannoy, G.J.M., Reichle, R.H., 2016a. Assimilation of SMOS brightness temperatures or soil moisture retrievals into a land surface model. Hydrol. Earth Syst. Sci. 20 (12), 4895–4911

De Lannoy, G.J.M., Reichle, R.H., 2016b. Global assimilation of multiangle and multipolarization SMOS brightness temperature observations into the GEOS-5 catchment land surface model for soil moisture estimation. J. Hydrometeorol. 17 (2), 669–691

Dorigo et al (2017), ESA CCI Soil Moisture for improved Earth system understanding: State-of-the art and future directions, Remote Sensing of Environment, Volume 203, 2017, Pages 185-215, ISSN 0034-4257, https://doi.org/10.1016/j.rse.2017.07.001.
<figure><img src="image_51.png" /></figure>

Dorigo, W., Himmelbauer, I., Aberer, D., Schremmer, L., Petrakovic, I., Zappa, L., ... & Sabia, R. (2021). The International Soil Moisture Network: serving Earth system science for over a decade. Hydrology and earth system sciences, 25(11), 5749-5804. Draper et al., Geophysical Research Letters, vol. 39, p. L04401, 2012. https://doi.org/10.1029/2011GL050655

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