Improved streamflow simulations by coupling soil moisture analytical relationship in EnKF based hydrological data assimilation framework

Improved streamflow simulations by coupling soil moisture analytical relationship in EnKF based hydrological data assimilation framework

Accepted Manuscript Improved streamflow simulations by coupling Soil Moisture Analytical Relationship in EnKF based hydrological data assimilation fr...

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Accepted Manuscript

Improved streamflow simulations by coupling Soil Moisture Analytical Relationship in EnKF based hydrological data assimilation framework RAAJ Ramsankaran , Amol Patil PII: DOI: Reference:

S0309-1708(18)30113-1 https://doi.org/10.1016/j.advwatres.2018.08.010 ADWR 3183

To appear in:

Advances in Water Resources

Received date: Revised date: Accepted date:

9 February 2018 23 July 2018 19 August 2018

Please cite this article as: RAAJ Ramsankaran , Amol Patil , Improved streamflow simulations by coupling Soil Moisture Analytical Relationship in EnKF based hydrological data assimilation framework, Advances in Water Resources (2018), doi: https://doi.org/10.1016/j.advwatres.2018.08.010

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Highlights  Coupled SMAR model with EnKF to update root zone soil moisture for improving streamflow.  Study involves both synthetic and real data experiments.  SMOS and ASCAT soil moisture retrievals are used for assimilation.  Proposed approach enhances the assimilation efficiency for streamflow simulations.  Streamflow simulations are improved but only to a moderate level.

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Improved streamflow simulations by coupling Soil Moisture Analytical Relationship in EnKF based hydrological data assimilation framework Abstract

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The present study investigates the potential of coupled Soil Moisture Analytical Relationship

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(SMAR) and Ensemble Kalman Filter (EnKF) based surface soil moisture data assimilation

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for improving the streamflow simulations. For this purpose, synthetic and real data

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assimilation experiments were carried out using Soil and Water Assessment Tool (SWAT)

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hydrological model in two different sub-catchments lying in the Krishna River basin, India.

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Here, the satellite-based surface soil moisture estimates from Soil Moisture and Ocean

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Salinity (SMOS) and Advanced Scatterometer (ASCAT) are used for assimilation. Results of

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the synthetic experiment show that the use of physically based SMAR scheme coupled with

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EnkF for updating profile soil moisture has better ability to improve the surface flow,

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groundwater flow and consequently streamflow over the covariance-based updates using

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EnKF only. Likewise, the real data assimilation experiment also shows SMAR-EnKF

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assimilation strategy performs better than the EnKF only updates for simulating streamflow.

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However, in both the synthetic as well as real data experiment, the improvements are only

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moderate. This restricted success in improving streamflow simulations indicate that updating

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only the soil moisture through any updating scheme adopted here is not sufficient to reduce

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the effect of the errors in model forcing on subsequent simulation days.

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Keywords: Data assimilation, EnKF, ASCAT, SMOS, SMAR, Soil moisture, Streamflow,

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SWAT

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1. Introduction

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Soil moisture is an essential climate variable and a key component of the water cycle

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supporting terrestrial ecosystem. From hydrological viewpoint, soil water has fundamental

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role in partitioning of the rainfall into surface and subsurface runoff, subsequently controlling the water movement, evapotranspiration and groundwater recharge. Considering the

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importance of long term soil moisture data for hydrological and climatological studies, in the

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past decade many satellite missions have been dedicated for accurate spatiotemporal

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measurements/estimations of soil moisture. The examples include Soil Moisture Ocean

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Salinity (SMOS) (Kerr et al., 2001), Advanced Microwave Scanning Radiometer for Earth

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observation science (AMSR-E) (Njoku et al., 2003), Advanced Microwave Scanning

ACCEPTED MANUSCRIPT Radiometer - 2 (AMSR-2) (Imaoka et al., 2010), the Soil Moisture Active Passive (SMAP)

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(Entekhabi et al., 2010) and Advanced Scatterometer (ASCAT) (Wagner et al., 2013).

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However, these satellite measurements are limited to top few centimeters of the soil profile.

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Most of the hydrological applications require the root zone soil moisture estimates for

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defining antecedent soil moisture conditions. Therefore, several studies have explored the

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potential of surface soil moisture estimates to update subsurface soil moisture in hydrological

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models by using data assimilation techniques (For example: Pauwels et al., 2002; Crow et al.,

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2005; Brocca et al., 2010; Chen et al., 2011; Han et al., 2012; Lievens et al., 2015, Massari et

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al., 2018).

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Among the various data assimilation techniques used in hydrological applications, Ensemble

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Kalman Filter (EnKF) (Evensen, 1994; Burgers et al., 1998; Houtekamer and Mitchell, 1998)

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has been widely utilised for updating the root zone soil moisture estimates using surface

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observations because of its capacity to deal with non-linear models (Ryu et al., 2009; Chen et

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al., 2011; Han et al., 2012; Lievens et al., 2015). EnKF updates the subsurface soil moisture

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from surface observations based on the forecasted error covariance between surface and

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subsurface soil moisture estimates. Hence, it solely depends on the ability of the model

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physics to generate the forecast error covariance for surface and subsurface soil moisture

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states. Kumar et al. in 2009 performed a suite of synthetic experiments using four different

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land surface models (Catchment, Mosaic, Noah and Community Land Model (CLM)), and

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found that the root zone soil moisture estimation can be more skilful when using models that

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exhibit better coupling between surface to root zone soil moisture. Moreover, they found that

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overestimating the surface to root zone coupling in the assimilation system can provide more

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robust skill improvement in the root zone soil moisture estimation. Similarly, Li et al., (2010)

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have used higher vertical correlation in WEB-SVAT model while perturbing the soil moisture

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states for improving the vertical coupling between surface and subsurface soil moisture and

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shown that it can improve the profile soil moisture estimates. However, a study by Chen et

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al., (2011) using SWAT model and EnKF technique have shown that despite high vertical error correlation, the EnKF was able to update the root zone soil moisture moderately with

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limited improvements in streamflow simulations. Han et al., (2012) conducted a synthetic

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study using SWAT model and found limited improvements in the streamflow. Recently, Patil

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and Ramsankaran, (2017) conducted an EnkF based assimilation study using SWAT model

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and shown that perturbing the field capacity of soil can improve the coupling between the

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surface to subsurface layers, however, it just led to moderate improvement only in the

ACCEPTED MANUSCRIPT assimilation performance. Similarly, past studies by Albergel et al., (2017), Fairbairn et al.,

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(2015) have shown that although the Kalman filter-based assimilation techniques are useful

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to update the profile soil moisture, their performance in streamflow improvement is still

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limited. All this studies emphasis upon the need to assess more on the added value of

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satellite-based soil moisture estimates for improving streamflow simulations. Considering the

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limited success in the past efforts (Li et al., 2010; Chen et al., 2011; Patil and Ramsankaran,

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2017), it seems new strategies for assimilating satellite soil moisture estimates are need to be

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developed to further improve the streamflow simulations.

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One possible strategy is to use some independent subsurface soil moisture estimation

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relationships coupled in data assimilation framework. Till date there are three methods

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available (viz. exponential filter, linear relationship and Soil Moisture Anlytical Relationship

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(SMAR)) to estimate root zone soil moisture dynamics from surface measurements (Wagner

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et al., 1999; Albergel et al., 2008; Manfreda et al., 2014). These studies were primarily

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focused on increasing the applicability of the satellite-based soil moisture retrievals for

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estimating root zone soil moisture estimates using time series of the surface measurements.

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Wagner et al., (1999) proposed an exponential filter which depends on only one parameter

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and its recursive formulation was given by the Albergel et al., (2008). Use of exponential

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filter from Albergel et al., 2008 for estimating subsurface soil moisture prior to assimilation

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in a hydrologic model with vertically lumped soil profile has been reported by previous

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studies (Brocca et al., 2010; Massari et al., 2015). Brocca et al., (2012) carried out an

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assimilation of surface and root zone soil moisture products obtained by the exponential filter

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developed by Albergel et al., (2008) and shown that the vertically extended soil moisture

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estimates have resulted clear improvements in the assimilation performance. Recently,

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Manfreda et al., (2014) proposed a new physically based approach called Soil Moisture

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Analytical Relationship (SMAR) for estimating root zone soil moisture. This approach is

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dependent on total seven parameters relating to the physical characteristics of the soil profile.

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However, they also shown that these seven parameters can be further assigned to physically consistent four parameters and calibration of these four parameters on historic time series

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gave good performance for simulating root zone soil moisture. Recently, Baldwin et al.,

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(2017) have effectively used the SMAR approach to predict the root zone soil moisture for

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conterminous United States and proposed SMAR-EnKF model to consider the regional scale

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biases.

ACCEPTED MANUSCRIPT Considering the recent availability of physically based independent subsurface soil moisture

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estimation relationships like SMAR, it is sensible to explore the efficacy of the SMAR based

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subsurface soil moisture estimates when coupled with EnKF assimilation to enhance skill

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improvement of hydrological models. At the same time it is also important to analyse such

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assimilation schemes especially in the widely used hydrological models like SWAT which

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has already reported suboptimal assimilation performance for improving streamflow

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simulations. Hence, to understand and evaluate the performance of EnKF to update the

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profile soil moisture of SWAT hydrological model when coupled with SMAR soil moisture

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estimates, a detailed analysis has been carried out using both synthetic as well as real data

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assimilation experimental runs. To validate the applicability of the proposed approach under

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varied catchment characteristics, real data analysis has been carried out in two catchments in

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Krishna river basin, India. Following this introduction (Sec.1), in Sec.2, a description of the

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study area, dataset used and a brief introduction on SWAT hydrologic model are given along

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with the overall methodology adopted. Section 3 discusses the results obtained for synthetic

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and real data experiments. Finally, the summary, conclusions and future directions are

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discussed in Sec. 4.

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2. Study Area, Data and Methods

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2.1 Study Area and Datasets

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Figure 1: Location map of the study area(s) along with depiction of stream networks, landuse

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and stream gauging stations

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To test the proposed methodology, two catchments in Krishna River basin, India are selected

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in the present study as shown in Fig (1). The first catchment is of the Wyra river (Fig.1a) covering an area of 1650 Km2 up to Madhira river gauging site. Major landuse in this

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catchment is agriculture (70.6%) followed by deciduous forests (14.1%), rangeland (6.2%),

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pasture (5%), urban (1.7%), waterbodies (1.5%) and others (0.9%). Most soils in the study

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area are clayey loam and clay. The catchment receives an average annual rainfall of 1090

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mm. Out of which 90% rainfall is generally received within June to October monsoon period.

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The second catchment is of the Varada River (Fig. 1b), which covers an area of 5092 Km2 up

ACCEPTED MANUSCRIPT to Marol river gauging site. Major land use in this catchment are agriculture (77.5%)

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followed by deciduous forests (10.7%), pasture (5.3%), evergreen forest (4.5%), and others

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(2%). Major soil type in this this catchment are Clayey Loam and Sandy Clayey loam. This

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catchment lies in the leeward side of the Western Ghats and receives 1560 mm average

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annual rainfall.

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The details of the Land Use Land Cover (LULC), Digital Elevation Model (DEM), soil

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datasets, meteorological forcing datasets, and observed streamflow and soil moisture datasets

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for both selected catchments are given in Table 1. Rainfall data for both the study catchments

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have been obtained from rain gauge observations. For Wyara catchment, gridded rainfall

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obtained from India Metrological Department (IMD) Pai et al., (2014) has been used. For

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Varada catchment, Tahasil (Taluk level) daily average rainfall data obtained from Karnataka

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State Natural Disaster Monitoring Centre (KSNDMC) has been used. Among thematic

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datasets, Food and Agriculture (FAO), World Harmonized Soil Dataset (HWSD)

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(FAO/IIASA/ISRIC/ISSCAS/JRC, 2009) with two-layer soil information (0-30 cm and 30 to

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100 cm) is used for Wyara Catchment. For Varada Catchment, soil map from National

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Bureau of Soil Survey and Land Use Planning (NBSS & LUP) is used. Based on the

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requirement of the data assimilation experiments, for both catchments, only two layers of soil

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profile with 0-5 cm top layer and 5 to 100 cm root zone layer were prepared using weighted

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averaging of original soil profile information. To test the proposed methodology in a robust

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manner and to endorse the validity of the results, a detailed analysis have been carried out

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using two different satellite-based soil moisture products. Therefore, depending on the data

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availability, the Soil Moisture and Ocean Salinity (SMOS) mission level 3 (L3) and

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Advanced Scatterometer (ASCAT) version H113 soil moisture products are used in the

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present study. The SMOS soil moisture products provided by CATDS (Centre Aval de

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Traitement des Données) are available since January 2010 with spatial resolution of 0.25o x

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0.25o. Among the available data quality flags, it is found that the data quality index (DQX) of

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the retrieval algorithm and the radio frequency interference (RFI) from local illumination sources are dominant in the present study area and hence, they were used for defining

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observation errors. The ASCAT H113 product is combination of Metop-A and Metop-B

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satellites with spatial sampling of 0.125o x 0.125o (later resampled at 0.25o x 0.25o). These

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products are distributed by EUMETSAT Satellite Application Facility on Support to

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Operational Hydrology and Water Management (H-SAF). Among the data quality flags in

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ASCAT, soil moisture error (sm_noise) is used for defining the observation errors. All other

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datasets such as DEM, landuse/landcover map for both catchments are from common source

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as given in Table 1.

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Table 1. Datasets used in the present study Dataset

Source

Rainfall Forcing Variables

Temperature

Scale/Spatial Resolution

*IMD Gridded (Pai et al., 2014) *Karnataka State Natural Disaster Monitoring Centre IMD Gridded (Srivastava et al., 2009)

0.25 × 0.25

Interpolated using gauge data

Varies

Interpolated using gauge data

1 × 1

Humidity, NCEP–CFSR Wind Speed, 0.25 × 0.25 (Saha et al., 2010) Solar Radiation

Stream Discharge

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Thematic Data

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Soil moisture

ASCAT (Wagner et al., 2013) CWC Gauge (CWC, 2012)

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State Variables

SMOS L3 (Kerr et al., 2001)

Soil

Topography

NRSC (NRSC, 2008) FAO HWSD V1.2 (FAO, 2012) *NBSS&LUP (Sivaprasad et al., 1998) SRTM GDEM (Jarvis, 2008)

Remarks

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0.25 × 0.25

0.25 × 0.25 1:250,000

1:5,000,000

1:250,000 90 m

Interpolated using gauge data Reanalysis Passive microwave retrievals Passive microwave retrievals Observed gauge data Derived from AWiFS optical data Prepared from soil survey datasets Interferometric SAR product

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2.2 SWAT Hydrological model setup

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Soil and Water Assessment Tool (SWAT) is process-based, semi-distributed, continuous time

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hydrological model, which also simulates the crop growth, sediments and pollutants yield

ACCEPTED MANUSCRIPT from a catchment. All these modules are dependent mainly on the underlying hydrological

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model simulating all hydrological processes in a catchment. For considering the spatial

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heterogeneity, SWAT divides the entire catchment into smaller sub-basins. Each sub-basin is

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further sub-divided into virtual hydrological response units (HRU) representing areas with

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same land-use soil and slope information. All land surface processes are carried out at each

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HRU and final water balance is ensured. In the present study, the partitioning of rainfall into

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surface and sub-surface runoff is carried out using SCS Curve Number (CN) (SCS, 1972)

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method. Once the surface runoff is computed, the remaining water is allowed to flow through

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each soil layer. Water entering in the soil profile is routed using storage routing methodology

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at each HRU. During this, the storage routing methodology first fulfil the field water capacity

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of upper soil layer and calculate the excess soil water as,

(1)

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SWly,excess is the water content in a soil layer above the field capacity (mm), Qperc.ly is the

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amount of water percolating in lower soil layers (mm) and FCly is the depth of water in soil

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layer when it is at field capacity (mm). From the excess soil water (if available) the lateral

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flows are calculated as, (

where Ksat is saturated hydraulic conductivity (mm/h), is the drainable porosity of soil layer (mm/mm), and

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)

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(2)

is the steepness of a slope (m/m), is the hillslope length (m). Once

the lateral flow requirement is computed, this excess soil water is allowed to percolate to

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deeper soil layers considering the hydraulic conductivity of soil layer as given in Eq.(3),

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(



⌋)

(3)

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where ∆t is time step (h) and SATly is the depth of water in soil layer when completely saturated (mm). If the deeper layer is already saturated, then the percolation is restricted and

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the excess water is allowed to meet the surface runoff. Similarly, the percolation from the

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lowest layer meets the aquifer system and contributes to groundwater flow. All the processes

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related to flow generation (surface runoff, lateral flow and groundwater flow) are carried out

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at each HRU and then the different flow components are directly linked to sub-basin outlet

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based on lag routing function. Once the water enters in to channel, then it is routed to basin

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outlet using linear reservoir concept.

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2

v__ALPHA_BF

3

a__GW_DELAY

a__GWQMN

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v__GW_REVAP

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r__SOL_AWC()

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r__SOL_K() v__SURLAG

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v__CH_K2

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v__CH_N2

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v__REVAPMN

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v__ESCO

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SCS runoff curve number Baseflow alpha factor (days) Groundwater delay (days). Threshold depth of water in the shallow aquifer required for return flow to occur (mm) Groundwater “revap” coefficient Available water capacity of the soil layer Saturated hydraulic conductivity Surface runoff lag time Effective hydraulic conductivity in main channel Manning's “n” value for the main channel Threshold depth of water in the shallow aquifer for “revap” to occur (mm) Soil evaporation compensation factor Plant uptake compensation factor

0

1

0

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Range used for calibration

Calibrated value

3t3

Madhira -0.295

Marol -0.295

0 to 1

0.906

0.921

0 to 150

46.270

213.182

0

5000

-1000 to 1500

51.202

-79.485

0.02

0.2

0.02 to 0.2

0.020

0.121

0

1

t

0.344

0.293

0

2000

t

-0.068

0.214

0.05

24

0.5 to 24

5.538

9.963

0.01

500

0.02 to 300

17.645

228.171

0.01

0.3

0.02 to 0.3

0.192

0.088

0

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0 to 500

208.634

416.471

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0.209

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Description

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Table 2. Details of the calibrated SWAT parameters for Wyara and Varada catchments

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0 1 1 to 1 0.838 0.399 13 v__EPCO 228 The initials represent the method used for defining the parameter range in auto-calibration, r – relative change to 229

initial value, v – replacement of value within given range, a – absolute change with respect to the default value.

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In the present study, the SWAT hydrologic model is set up for Wyra and Varada catchments

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using the datasets described in Sec. 2.1. For a distributed application of the meteorological

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forcing, the catchment is divided into 33 sub-basins with areas varying from 20 Km2 to 100

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Km2 (Fig. 1a and 1b). For facilitating the assimilation of coarser grid satellite based soil

ACCEPTED MANUSCRIPT moisture retrievals at sub-basin level, one HRU per sub-basin is delineated as per dominant

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land use, soil type and slope class.

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Based on availability of rainfall and river discharge datasets, the SWAT hydrological model

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was calibrated for seven years (2003 to 2009) for Wyara catchment and four years (2006 to

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2009) for Varada catchment with extra two year spin up period. Model calibration was

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performed using the available observed discharge at basin outlets located at Madhira for

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Wyara catchment and Marol for Varada catchment (Fig. 1). Model input parameters were

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optimised using Sequential Uncertainty Fitting Algorithm (SUFI-2) in SWAT CUP

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(Abbaspour et al., 2004) to maximise the Nash Sutcliffe Efficiency (NSE) of the simulated

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streamflow. Total 13 model parameters were selected for calibration based on the past studies

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(Arnold et al., 2012; Abbaspour et al., 2015; Patil and Ramsankaran, 2017). Table 2

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summarises all calibrated model parameters, ranges used for their calibration and the final

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calibrated values.

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2.3 Soil Moisture Analytical Relationship (SMAR)

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To derive the subsurface soil moisture estimates from surface measurements, the Soil

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Moisture Analytical Relationship (SMAR) proposed by Manfreda et al., (2014) has been

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utilised. The SMAR is a physically based relation between surface and root zone soil

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moisture derived from soil water balance equations and having physically consistent

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parameter set which can be measured on the field or can be calibrated. SMAR defines the soil

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profile in two layers, surface layer equivalent to observation depth of satellite soil moisture (5

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cm – 10 cm) and root zone layer (60 cm to 150 cm). To calculate the water flux between two

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soil layers in absence of rainfall information, the flux from the surface to root zone layer can

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be considered significant only when the surface layer soil moisture exceeds its field capacity.

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SMAR assumes that soil water above field capacity in surface layer moves down to root zone

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layer in one day (Green and Ampt, 1911; Laio, 2006) and horizontal and lateral flows are

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negligible and hence, assumed to be zero. Therefore, the infiltration flux from surface layer to root zone layer can occur instantaneously and the fraction of saturation infiltrating to root zone layer, ( ) can be given as, ( )

{

( )

( ) ( )

(4)

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where,

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saturation of surface layer at field capacity. Once the infiltrating water to deeper layer is

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known, the root zone soil moisture can be computed using discrete form SMAR equation as,

[-] is the relative saturation of the surface soil layer,

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where,

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saturation of root zone soil layer at wilting point,

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and

)

+

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layer,

( )(

)

(

)]

(5)

[-] is the relative

is the current time step. The parameters

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where

)

)

(6)

[mm/day] is the soil water loss coefficient accounting all losses at root zone soil [-] and

[-] are the soil porosity for surface and root zone layers and

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(

[(

[-] is the relative saturation of the root zone soil layer,

can are given as,

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)

)

( )

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*( (

(

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[-] is the relative soil

[mm] and

[mm] are the depth of soil layer at surface and root zone layers. Therefore, parameter

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[day-1] is a water loss coefficient which controls the daily root zone water loss and given as

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ratio of the water loss coefficient to the total root zone storage. Parameter

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diffusivity coefficient and given as the ratio of surface soil storage to root zone soil storage.

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Considering the parameters

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contributes the amount of moisture lost over a given time step and second square bracket of

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the Eq. 5 represents the amount of moisture diffused from surface to root zone layer. In the

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present study, due to the absence of field data the four parameters such as

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were only calibrated for each sub-basin following Manfreda et al., (2014). To keep the

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calibration period different than the assimilation experiment, calibration of the SMAR was

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carried out using January 2014 to December 2015 datasets during synthetic and real data

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experiments. A calibration was performed using Particle Swarm Optimization (PSO)

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approach to match the SWAT simulated long term subsurface soil moisture with NSE as an

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,

,

and

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and , it can be said that the first square bracket of Eq. 5

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[-] is the

objective function. 2.4 Data Assimilation

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2.4.1 EnKF

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EnKF is a Monte Carlo approximation of the standard Kalman Filter (Kalman, 1960). EnKF

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is sequential data assimilation technique that updates the model predictions by optimally

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merging the observations. To do this, EnKF explicitly computes the error covariance of

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model predictions and observations using Monte Carlo approach and produces an analysis

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estimate which is the Best Linear Unbiased Estimate (BLUE) of the priors. The brief

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description of EnKF update procedure is given below.

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At given time step , the ensemble model forecast can be given as, (

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)

(7)

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where

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noise representing overall errors in model forecasts including errors in forcing,

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parametrisation and model physics. The superscript represents the ensemble matrix with –

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sign for prior and + sign for posterior. Similarly, the observation ensemble can be derived

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using model forecast as,

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̂

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where

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model predicted observation and

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independent of model errors. Given this information, the data assimilation step in the EnKF

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can be given as,

represents the ensemble of model forcing and

is

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represents nonlinear model,

(8)

̂

)

is noise representing errors in the observation and

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(

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is the observation operator, mapping the model states to the observations, ̂ is the

(9)

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where

309

assimilation i.e. analysis,

is an observation ensemble generated using observation

310

covariance matrix

is Kalman Gain ensuring Best linear Unbiased estimate of

311

model forecast and observation and given as,

314 315 316

PT

where

(10)

is the covariance of the model predicted observation ensemble obtained from

and

AC

313

and

CE

312

is an ensemble of model state after

ED

is an forecasted ensemble state,

is the cross covariance of the model forecast and observation prediction.

2.4.2 Synthetic Experiment Firstly, to understand and evaluate the ability of the proposed SMAR based EnKF

317

assimilation scheme for improving the SWAT streamflow simulations, a synthetic data

318

assimilation experiment was carried out at Wyara river catchment. For this purpose, four

319

model runs such as true, open loop, EnKF, SMAR-EnKF were carried out in synthetic

320

experiment. The calibrated SWAT model run from June 2010 to Dec 2013 in deterministic

321

mode is considered as true run (true scenario). After that, the SMAR model was calibrated

ACCEPTED MANUSCRIPT using synthetically generated observations (from true surface soil moisture) as input to

323

predict the model simulated root zone soil moisture. For generation of the open loop synthetic

324

run, the true scenario was perturbed and the calibrated SWAT model was run in an ensemble

325

mode using a degraded precipitation and soil moisture to represent a realistic erroneous

326

model run. During EnKF assimilation run, a synthetically generated ensemble observations

327

were used for updating the ensemble of surface and subsurface soil moisture estimates with

328

the help of inherent covariance based updating procedure in the EnKF. During the SMAR-

329

EnKF assimilation run the SWAT simulated ensemble of surface soil moisture and

330

subsurface soil moisture were updated using the ensemble of synthetic observations and

331

SMAR derived ensemble of subsurface soil moisture estimates respectively with the help of

332

EnKF. It shall be noted that during SMAR-EnKF assimilation run the surface and sub-surface

333

observations were assimilated independently to each layer.

334

For generation of open loop run, spatially homogeneous and temporally uncorrelated

335

multiplicative Gaussian noise of zero mean and 0.3 mm/mm standard deviation was applied

336

to the rainfall data. Similarly, zero mean and 0.05mm/mm and 0.15mm/mm standard

337

deviation Gaussian noise was added to the surface and subsurface layer soil moisture during

338

model simulations to account the model as we all as the input parameter uncertainties. During

339

the open loop run, the SWAT model was run with a 100 member ensemble realisation for

340

generation of ensemble forecast. Since the actual error in the input and model uncertainties

341

are known during synthetic experiment, through testing of any assimilation scheme is

342

possible. Accordingly, the error characteristics used for degrading rainfall and soil moisture

343

as mentioned earlier were applied for generation of rainfall and soil moisture ensembles as

344

well. Following Patil and Ramsankaran, (2017) the field capacity of the soil was also

345

perturbed with Gaussian noise of zero mean and 0.1 mm/mm standard deviation for both

346

surface and subsurface soil layers to maintain minimum ensemble spread during high rainfall

347

days. Following Flores et al., (2010) Lain hypercube sampling technique was used for

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generation of random number for all types of sampling in the present study. To maintain the quality of the ensembles generated, rainfall variable was considered as semi-restricted and

350

soil moisture was considered as fully restricted variables for ensemble model simulations as

351

suggested by Turner et al., (2007). Similarly, following Ryu el al., (2009) biases due to

352

ensemble model run were corrected using simple delta change method. For generating

353

synthetic observations with observation errors, the simulated surface soil moisture obtained in

354

the true scenario was degraded using fixed Gaussian noise of zero mean and 0.3 mm/mm

ACCEPTED MANUSCRIPT standard deviation. These synthetic observations were used for assimilation purpose during

356

EnKF and SMAR-EnKF assimilation runs with same observation error covariance used for

357

degrading them. Following Chen et al., (2011) a vertical error correlation of one was used for

358

perturbing soil moisture states during EnKF run. To account for the effect of differences in

359

random errors generated to produce open loop run due to different random seed, all synthetic

360

model runs such as open loop, SMAR-EnKF and EnKF were repeated over 25 times to

361

generate an ensemble of simulations. This ensemble of simulations would allow us to

362

evaluate the expected model performance during both EnKF and SMAR-EnKF assimilation

363

runs.

364

2.4.3 Real Data Experiment

365

To evaluate the proposed assimilation approach in real conditions, a real data experiment was

366

carried out in both the study catchments. In this experiment, the level 3 SMOS retrievals and

367

version H113 ASCAT retrievals (as described in Sec. 2.1) were used as observed soil

368

moisture estimates. Both these observations were spatially averaged using area weighted

369

averaging approach to represent the sub-basin level soil moisture and then bias corrected

370

using the model simulated long term surface layer soil moisture time series through mean-

371

variance bias correction approach (Lievens et al., 2015; Massari et al., 2015). It should be

372

noted that the SMAR model was calibrated using the bias corrected SMOS as well as

373

ASCAT observations for each catchment individually to match the SWAT simulated sub-

374

surface soil moisture as discussed in Sec. 2.3. During the real data experiment the SWAT

375

model simulations were carried out for the same assimilation period as that of synthetic run i.

376

e. from June 2010 to Dec 2013. The “open loop” run in the real data experiment is defined as

377

the calibrated SWAT model run with the ensemble model simulation with no data

378

assimilation. During data assimilation in real data study, two satellite-based soil moisture

379

retrievals (SMOS and ASCAT) were assessed separately for EnKF and SMAR-EnKF runs.

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Therefore, total five model runs were assessed in real data experiment namely open loop, EnKFSMOS, EnKFASCAT, SMAR-EnKFSMOS and SMAR-EnKFASCAT. During open loop run, the ensemble model simulations were generated by perturbing rainfall, soil moisture and soil

383

moisture field capacity with same input error covariance structure as used during the

384

synthetic experiment. Like synthetic EnKF run, a vertical error correlation of one was used

385

for perturbing soil moisture states during EnKF run in real data experiment as well. For

386

defining the observation error of SMOS retrievals, the observation error was linearly scaled

387

by using the data quality indices such as DQX and RFI, available with SMOS products.

ACCEPTED MANUSCRIPT 388

Therefore, ensemble of observation was represented by applying dynamic Gaussian noise to

389

the observed soil moisture with zero mean and standard deviation of

390

which is given as,

mm/mm

(11)

392

In both the study area(s), the DQX is varying from 0.01 to 0.1 and RFI is varying from 0.01

393

to 0.4. Considering the higher RFI in the study catchments and its subsequent effect on

394

SMOS soil moisture retrievals, a 30% observation uncertainty is assumed arbitrarily.

395

Accordingly, considering the DQX and RFI distributions in the available data, the

396

dimensionless parameters

397

represents the assumed 30% uncertainty i.e., 0.3 mm/mm. Similarly, the observation error for

398

ASCAT retrievals is defined by linearly scaling the soil moisture noise sm_noise provided

399

with ASCAT products. Similar to the SMOS observations, ensemble of ASCAT observations

400

were represented by applying dynamic Gaussian noise to the observed soil moisture with zero

401

mean and standard deviation of

are set to 1.5.in Eq. (8) so that the

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mm/mm which is given as,

402

(12)

In the present case, the sm_noise is varying from 0.02 to 0.06. Considering the relatively

404

robust soil moisture retrievals from ASCAT (as not much affected by RFI) compared to

405

SMOS soil moisture estimates, 10% uncertainty is assumed arbitrary. Therefore, to get the

406

average soil moisture error of 0.1 mm/mm the

407

2.5 Performance Evaluation

408

Performance of the model simulated streamflow were evaluated using RMSE, PBias, NSE

409

and assimilation efficiency (EFF). Most of these statistics are common and well known,

410

therefore formulations for assimilation efficiency (EFF) is only given here. Following

412

ED

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was set to 3 in the present study.

CE

AC

411

M

403

Aubert, (2003) the EFF metric is calculated as, [



(

)



(

)

]

(13)

413

Where,

414

and open loop run respectively. An EFF more than zero indicates that the assimilation run

415

shows better streamflow simulations than the open loop model simulations and vice versa.

416

and

are observed discharge, simulated discharge from assimilation run

ACCEPTED MANUSCRIPT 417 418 419 420

3. Results and Discussions

423

3.1 SMAR Calibration

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Figure 2: Boxplot of the calibrated values of four SMAR model parameters (a, b,

and

) along with corresponding NSE of the simulated sub-surface soil moisture in all sub

ED

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M

424

basins at a) Wyara catchment with synthetic observations as input b) Wyara catchment with

428

SMOS observations as input, c) Wyara catchment with ASCAT observations as input, d)

429

Varada catchment with SMOS observation as input and e) Varada catchment with ASCAT

430

observations as input.

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Distributions of the calibrated SMAR parameters along with NSE of the predicted soil

432

moisture at all sub-basins in Wyara and Varada catchments are plotted as boxplots in Fig 2.

433 434 435

AC

431

Fig. 2a represents the calibration performance while using synthetic observations as input for Wyara catchment. Figs. 2b-c and 2d-e show the calibration performance in Wyara and Vardha catchments respectively while using SMOS and ASCAT soil moisture estimates as

436

input. It shall be noted that the values of all the calibrated parameters of the SMAR model

437

shown in Fig. 2 are having similar ranges reported by Manfreda et al., (2014) for few

438

different observation sites, which gives some confidence in the calibration results in absence

439

of observed field data. The NSE (Fig.2) of the simulated subsurface soil moisture for both

440

catchments are well above 0.8 during all five calibration runs, highlighting the robustness of

ACCEPTED MANUSCRIPT SMAR algorithm to accurately simulate sub-surface soil moisture under different input soil

442

moisture characteristics. At the same time, it is noticed that the calibrated range of parameter

443

sfc1 (and parameter b in case of Wyara catchment) are significantly different for SMOS and

444

ASCAT soil moisture products in both study catchments (Fig. 2b -e). Even though the

445

calibration was performed using bias corrected data of each satellite product, this change in

446

calibrated values might be because of number of observations present in each surface soil

447

moisture dataset. For example, ASCAT has higher revisit time over both the study areas

448

when compared to SMOS revisit time. Therefore, field capacity of surface layer soil moisture

449

(sfc1 parameter) is showing higher sensitivity as it directly controls the amount of water

450

entering to root zone soil moisture from surface observations. To know how the SMAR

451

derived sub-surface soil moisture and SWAT simulated subsurface soil moisture are varying

452

in each sub-basin, a comparison of the same for each sub-basin is given in Figs. A1 to A5 of

453

the Appendix A. From Figs. A1 to A5 (given in Appendix A), it can be seen that the SMAR

454

estimated average subsurface soil moisture is in very good agreement with the SWAT

455

simulated soil moisture at layer 2 for most of the times in both catchments.

456

3.2 Synthetic Experiment

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Figure 4: Boxplot of NSE for different model simulated variables during 25 replications of the synthetic experiment for a) Open loop, b) EnKF and c) SMAR-EnKF run respectively

460

(See sec 3.2 for description of the variables).

461

The results obtained from four model runs such as true, open loop, EnKF and SMAR-EnKF

462

carried out during the synthetic experiment at Wyara catchment are discussed herein. Out of

463

the four model runs mentioned above, three model runs such as open loop, EnKF and SMAR-

464

EnKF run were repeated 25 times to avoid the ambiguities due to different random number

ACCEPTED MANUSCRIPT seeds while assessing the model performance with respect to true run. Therefore, the SWAT

466

model is evaluated for these three model runs to assess its average performance in

467

computation of evapotranspiration (ET), surface runoff (SR), surface layer (layer 1) soil

468

moisture (S1), subsurface (layer 2) soil moisture (S2), profile soil moisture (SM), lateral flow

469

(LT), deep percolation from soil profile (DP), groundwater contribution from shallow aquifer

470

(GW) and streamflow (ST).

471

The distribution of NSE obtained for the aforementioned variables from 25 simulations are

472

shown as boxplots in Figs. 4a, b and c for open loop, EnKF and SMAR-EnKF run

473

respectively. The computation of NSE is done for all variables after taking the area weighted

474

average over entire basin except streamflow (ST) which represents channel routed

475

streamflow at basin outlet. By comparing NSE of the open loop run (Fig. 4a) and EnKF run

476

(Fig. 4b), it can be seen that the errors in the evapotranspiration (ET), surface soil moisture

477

(S1), subsurface soil moisture (S2) and profile soil moisture (SM) are significantly reduced in

478

EnKF run and thus resulted in much higher NSE values than the open loop run. However,

479

these updates were not fully conveyed to the updates in the surface runoff (SR), lateral flow

480

(LT) and streamflow (ST) and hence, they show only moderate improvements as compared to

481

the open loop run. Contrarily, it is observed that the NSE of groundwater (GW) was not

482

improved significantly during the EnKF run (Fig. 4b) than open loop run (Fig. 4a) which is

483

major contributor to the streamflow (around 62% in the true run). From Fig. 4c, it is observed

484

that the SMAR-EnKF scheme have also obtained very similar improvements for

485

evapotranspiration (ET), and soil moisture (S1, S2, and SM) like EnKF run (Fig. 4b) when

486

compared to the open loop run (Fig. 4a). Similarly, though the improvements in the surface

487

runoff (SR), lateral flow (LT), groundwater flow (GW), and streamflow (ST) during SMAR-

488

EnKF run (Fig 4c) are moderate when compared to open loop run (Fig. 4a), they are still

489

better than the EnKF run (Fig 4b). However, SMAR-EnKF model run gave relatively much

490

better improved NSE for groundwater (GW) flows. Perhaps, as a result of this improvement

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in NSE of the groundwater flow component (GW), the streamflow (ST) is showing better improvements during SMAR-EnKF (Fig. 4c) run than the EnKF run (Fig. 4b). The results of

493

this synthetic study are in accordance with the previous studies by Chen et al, 2011; Brocca et

494

al., 2012; Fairbairn et al., 2015; Masari et al., 2018 wherein they have stated that the surface

495

soil moisture assimilation scheme for updating soil moisture profile have resulted in moderate

496

to high improvements in sub-surface soil moisture while limited improvements in the

497

simulated streamflow.

ACCEPTED MANUSCRIPT Further, to understand why the streamflow (ST) is simulated better during SMAR-EnKF run

499

than the EnKF run, a qualitative analysis has been done using the time series plots shown in

500

Figs. 5a-g. Fig. 5a represents the time series of average rainfall pattern observed in the Wyra

501

basin, which was used for performing synthetic experiment. Figures 5b-g represent the time

502

series plot of area weighted average of the variables such as SM, SR, LT, DP, GW and ST

503

(except S1 and S2, as SM represents the sum of both) obtained from 25 simulations of open

504

loop, EnKF and SMAR-EnKF runs as well as the area weighted average of these variables

505

obtained from true run respectively.

506

From Fig. 5b, it is observed that during monsoon season (June to September) of each year,

507

the covariance-based updates of EnKF run have slightly underestimated the profile soil

508

moisture (SM) when compared with the true run. In the SWAT model, the curve number

509

(CN) computations are highly sensitive to soil moisture values when soil moisture is around

510

field capacity (Han et al., 2012; Patil and Ramsankaran, 2017). Therefore, the slight sub-

511

optimal performance of EnKF run during monsoon season has subsequently caused a

512

reduction in the lateral flow (LT) (Fig. 5d) and substantial reduction in the deep percolation

513

(DP) (yellow line in Fig. 5e), which is an inflow to the shallow aquifer in SWAT. This

514

reduction in the deep percolation (DP) during EnKF run has resulted in a significant drop in

515

the groundwater contribution from shallow aquifer (GW) for the entire simulation period as

516

shown in Fig. 5f. Therefore, it can be said that these reductions observed in LT, DP, GW

517

have resulted in decrease in streamflow (ST) estimates during EnKF run when compared to

518

true run as seen in Fig. 5g. From Fig. 5b, it is observed that the updates in the profile soil

519

moisture during SMAR-EnKF run are matching well with the true run in the monsoon season

520

(June to September) for each year and it is found to be better than EnKF run when compared

521

to true run. As a result of this, the improvement in the deep percolation (DP) (Fig. 5e) is

522

found to be better than the EnKF run for the entire simulation period. Considering the

523

significant contribution of groundwater flow (GW) to the streamflow, one can say that the

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above improvement in GW estimates could have resulted in more accurate estimates of the streamflow (ST) (Fig. 5g) as confirmed with the NSE plots in Fig. 4c.

526

To analyse the skill improvement of the simulated streamflow(s) at multiple stations, a

527

statistical evaluation of the simulated streamflow(s) obtained from all three model runs at

528

spatially distributed six internal sub-basin (ID’s 7, 18, 22, 26, 28, and 33) outlets has been

529

carried and thus obtained results are given in Table 3. The spatial location of these six sub-

530

basin outlets can be found in Fig. 1a (i.e. Wyara catchment). From Table 3 it can be seen that,

ACCEPTED MANUSCRIPT while both EnKF and SMAR-EnKF assimilation runs have produced better results than the

532

open loop run, SMAR-EnKF has outperformed EnKF run at five of the six outlet points

533

(except sub-basin ID 7) for all the metrices considered here. It is noteworthy to mention that

534

the overall assimilation efficiency (EFF) of the simulated streamflow at the outlet of the

535

catchment (i.e. sub-basin ID 33) is 18% for EnKF run whereas it is improved to 55% during

536

SMAR-EnKF run. While both assimilation schemes have produced improvements in the

537

simulated streamflow, the vertically extended subsurface soil moisture updates using coupled

538

SMAR-EnKF scheme presented here has shown that it has better capability to improve the

539

streamflow estimates. Nevertheless, it should be noted that the improvements in the NSE of

540

the simulated streamflow during both assimilation runs are still not substantially high than the

541

open loop run even during synthetic experiments. From another data assimilation experiment

542

representing an ideal assimilation condition (Refer Appendix B) where the surface and sub-

543

surface true observations were assimilated into the model using direct insertion approach, it

544

was found that the average improvement in streamflow NSE was 0.87 despite profile soil

545

moisture having NSE close to 1. This experiment which represents an ideal assimilation

546

condition reveals that the effect of the errors in forcing datasets cannot be fully corrected by

547

assimilating only the intermediate model state variables such as soil moisture as highlighted

548

by Massari et al., 2018 and Alvarez-Garreton et al., 2016. This might be another reason

549

which limited the model performance to a moderate level during EnKF and SMAR-EnKF

550

assimilation runs for streamflow simulations.

551

Table 3: Comparison of RMSE, Bias, NSE and EFF performance indices for the simulated

552

streamflow at sub-basin ID 7, 18, 22, 26, 28 and 33 for open loop, EnKF and SMAR-EnKF

553

model runs during synthetic experiment at Wyara catchment

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Sub-Basin 7

18

22

26

Model Run Open Loop EnKF SMAR-EnKF Open Loop EnKF SMAR-EnKF Open Loop EnKF SMAR-EnKF Open Loop EnKF SMAR-EnKF

RMSE 1.91 1.35 1.45 10.00 8.92 6.46 12.37 9.27 9.13 15.94 15.27 10.10

Bias 0.24 -0.50 -0.56 0.60 -3.80 -1.33 2.27 -4.65 -4.28 0.83 -6.79 -1.94

NSE 0.40 0.70 0.65 0.43 0.56 0.76 0.34 0.64 0.64 0.46 0.51 0.78

EFF* 0.00 0.46 0.39 0.00 0.15 0.55 0.00 0.40 0.42 0.00 0.03 0.57

ACCEPTED MANUSCRIPT

28

33

28.84 25.47 19.05 34.28 30.27 22.45

3.22 -12.27 -6.32 3.92 -14.65 -7.20

0.42 0.56 0.74 0.44 0.57 0.75

0.00 0.18 0.54 0.00 0.18 0.55

*EFF is calculated with respect to the model performance in the open loop run

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Open Loop EnKF SMAR-EnKF Open Loop EnKF SMAR-EnKF

556

Figure 5: Time series plots of a) rainfall during the simulation period and b) profile soil

557

moisture (SM), c) surface runoff (SR), d) lateral flow (LT), e) deep percolation (DP), f)

558

groundwater flow (GW), and g) streamflow (ST) during True, Open Loop, EnKF and SMAR-

559

EnKF model runs

ACCEPTED MANUSCRIPT 3.3 Real Data Experiment

561

3.3(a) At Wyra Catchment: The results obtained from all five model runs viz. open loop,

562

EnKFSMOS, EnKFASCAT, SMAR-EnKFSMOS and SMAR-EnKFASCAT during the real data

563

experiment in Wyra catchment are shown as time series plots in Figs. 6a-f. Figures 6a-c

564

represent the area weighted average of the simulated soil moisture for layer one (S1) and the

565

layer two (S2) along with the simulated streamflow (Q) at the basin outlet respectively while

566

using SMOS observations for assimilation. Similarly, Figs.6d-f represent the same outputs

567

respectively while using ASCAT observations for assimilation.

568

From Figs. 6a and 6d it can be seen that the SMOS satellite have 2-3 days revisit time over

569

the study area while the ASCAT satellite have 1-2 days revisit time. It should be noted that

570

the surface soil moisture updates during EnKF and SMAR-EnKF run are same (Fig. 6a and

571

6d). It is mainly because, both assimilation runs update the surface layer soil moisture using

572

observations (either SMOS or ASCAT) under same forecast and observation errors. From

573

Fig. 6b and 6e it can be seen that the updates of the root zone soil moisture (S2) during EnKF

574

run possess more variations than open loop run and these variations are more dominant while

575

using ASCAT soil moisture retrievals which represents higher revisit time. At the same time,

576

this kind of fluctuations are less common in the subsurface soil moisture updates during

577

SMAR-EnKF assimilation runs (Fig. 6b and 6e) especially while using ASCAT soil moisture

578

for assimilation (Fig. 6e). This is because the subsurface soil moisture updates are

579

consistently augmented by the physically derived SMAR estimates. From Fig. 6c and 6f it

580

can be seen that the streamflow simulated during SMAR-EnKF runs are marginally better

581

match than EnKF runs. Moreover, significant updates in the simulated streamflow from both

582

assimilation runs are apparent during low flows than high flows. Table 4a shows statistical

583

evaluation results for the simulated streamflow from all five model runs in the real data

584

experiment at Wyra catchment. From this Table, it is seen that though both assimilation runs

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have better results than the open loop run, SMAR-EnKF assimilation scheme shows better performance than EnKF run in all the presented statistics. It is also seen that in Wyara catchment the SMOS soil moisture gave better assimilation efficiency (0.26 and 0.31 for

588

EnKF and SMAR-EnKF run respectively) over ASCAT soil moisture (0.21 and 0.24 for

589

EnKF and SMAR-EnKF run respectively).

590

3.3(b) At Varada Catchment: The results obtained from the real data experiment runs in

591

Varada catchment are shown in Figs. 7a-f. Here the nature of the surface soil moisture

ACCEPTED MANUSCRIPT assimilation (Fig 7a and 7d) is similar to Wyara catchment in terms of revisit time of SMOS

593

and ASCAT soil moisture and the closeness in the assimilated surface soil moisture during

594

EnKF and SMAR-EnKF runs. Likewise, the updates in the root zone soil moisture (S2) (Fig.

595

7b and 7e) are smoother during SMAR-EnKF over EnKF run as seen in the Wyara

596

catchment. However, while using ASCAT soil moisture for assimilation using EnKF scheme,

597

the fluctuations in updated S2 are relatively less in Varada catchment (Fig. 7e) than the

598

Wyara catchment (Fig. 6e). Among all assimilation runs, the simulated streamflow (Fig. 7c

599

and 7f) from SMAR-EnKF run matches well with observed streamflow. However, some

600

significant improvements are seen during low flows only. Table 4b shows statistical

601

evaluation results for the simulated streamflow obtained during all five model runs from the

602

real data experiment in Varada catchment. Contrary to the Wyara catchment, use of ASCAT

603

soil moisture gave better assimilation efficiency (0.20 and 0.27 for EnKF and SMAR-EnKF

604

run respectively) over SMOS observations (0.28 and 0.37 for EnKF and SMAR-EnKF run

605

respectively) in Varada catchment.

606

The overall results of the real data experiment from two study catchments clearly show the

607

enhanced ability of the SMAR-EnKF scheme to improve streamflow simulations than the

608

traditional EnKF scheme. These results are in accordance with the results seen during

609

synthetic experiment (Fig. 4 and Table 3). Further, a qualitative analysis of the simulated

610

streamflow shows that both the assimilation schemes could not improve the peak flows while

611

the low flows were improved marginally. These results are analogous to the earlier studies by

612

(Chen et al., 2014 and Alvarez-Garreton et al., 2016) where they found that the surface soil

613

moisture data assimilation using state correction scheme was able to improve the model

614

simulations during low flows only. Perhaps, the non-assurance of the observation and input

615

error variances during real data assimilation experiment might have hampered the

616

assimilation results to some extent. Additionally, the inability of state updating scheme to

617

entirely correct the errors due to inaccurate forcing (Massari et al., 2018 and Alvarez-

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Garreton et al., 2016) can be another reason for achieving only moderate improvements in the simulated streamflow.

620

Table 4: Comparison of RMSE, Bias, NSE and EFF performance indices of the simulated

621

streamflow during real data experiment at a) Wyara and b) Varada catchment during Open

622

Loop run, EnKF run using SMOS observations (EnKFSMOS), SMAR-EnKF using SMOS

623

observations (SMAR-EnKFSMOS), EnKF run using ASCAT observations (EnKFASCAT), and

624

SMAR-EnKF run using ASCAT observations (SMAR-EnKFASCAT).

ACCEPTED MANUSCRIPT

Model Runs Open Loop EnKFSMOS SMAR-EnKFSMOS EnKFASCAT SMAR-EnKFASCAT

*EFF is calculated with respect to the model performance in the open loop run

626

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RMSE 33.424 28.704 27.685 29.675 29.038

(a) (b) Wyara Varada Bias NSE EFF* RMSE Bias NSE EFF* 6.829 0.225 0.000 110.249 82.840 0.521 0.000 -1.040 0.428 0.263 98.583 67.390 0.617 0.200 -2.857 0.468 0.314 94.173 60.296 0.650 0.270 -3.944 0.389 0.212 93.201 59.963 0.657 0.285 -4.720 0.415 0.245 87.319 52.755 0.699 0.373

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Figure 6: Time series plots for Wyra catchment from Open loop, EnKF and SMAR-EnKF

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model runs. (a) simulated soil moisture of layer 1 (S1) along with SMOS observations, (b)

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simulated soil moisture of layer 2 (S2), and (c) simulated streamflow at basin outlet along

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with observed streamflow when using SMOS observations as inputs. Similarly, (d) to (f)

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observations as inputs

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Figure 7: Same as Fig. 6 for Varada catchment

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4. Summary and Conclusions The present study proposes a new assimilation strategy by coupling Soil Moisture Analytical Relationship (SMAR) with EnKF for improving streamflow simulations. For this purpose,

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synthetic and real data assimilation experiments were carried out using SWAT hydrological

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model to systematically analyse the additional benefits of coupling the SMAR based

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subsurface soil moisture estimates in EnKF data assimilation framework. In synthetic

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experiment the proposed assimilation scheme is analysed under known forecast and

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observation error covariance at Wyra river catchment lying in Krishna basin, India. In real

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version retrievals were used for assimilating into SWAT hydrological model. All the real data

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experimental runs were carried out using the available data between June 2010 and Dec 2013

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at Wyara and Varada catchments lying in the Krishna River basin.

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The obtained results from synthetic experiment suggest that the physically based relationship

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like SMAR coupled with EnKF for (SMAR-EnKF run) can be successfully used to update the

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sub-surface soil moisture which helped to improve the model simulated flow components like

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surface runoff, lateral flows and groundwater flows better than EnKF only updates (EnKF

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run). These improvements during SMAR-EnKF run helped in producing reasonably better

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streamflow estimates than the traditional EnKF assimilation scheme. During the real data

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assimilation experiment, it is found that the physically consistent subsurface updates from

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SMAR-EnKF produced smoother subsurface soil moisture variations than the covariance-

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based updates by EnKF. Similar to the synthetic experiment, in real data experiment too the

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SMAR-EnKF assimilation strategy has shown improved streamflow estimates than EnKF run

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in both study catchments. At the same time the overall results indicate that though the

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proposed SMAR-EnKF assimilation scheme is able to improve the streamflow simulations,

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they are only moderate during both synthetic and real data experiments. It is found that these

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improvements were mainly coming from low flow components of the simulated streamflow.

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One of the possible reasons behind the moderate improvements in simulated streamflow

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could be because at the end of day the soil moisture updates are unable to fully compensate

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the errors in model simulated flow components (surface runoff, groundwater flow etc.) due to

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the errors in the forcing data (rainfall) at next day. Additionally, the initial uncertainty

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distributions assumed for forecast and observations might have also affected the results of

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real data assimilation in the present study, however, this has not been analysed herein.

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Finally, from the overall results it can be concluded that the limitations in the EnKF based

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surface soil moisture data assimilation practices for improving the streamflow simulations can be reasonably overcome by coupling appropriate independent profile soil moisture estimation approaches such as SMAR within the EnKF assimilation framework. This finding

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could be particularly useful for assimilating satellite soil moisture observations in studies

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such as land surface modelling, agricultural drought modelling which seeks accurate root

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zone soil moisture estimations. However, further detailed analysis should be carried out to

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confirm the suitability/ability of this proposed approach in different model structures and

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different climatic conditions.

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Acknowledgement

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The authors would like to acknowledge the three anonymous reviewers for their constructive comments to improve the article.

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Appendix A

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Figure A.1: Comparison of the relative subsurface soil moisture derived from SMAR using synthetic observations with SWAT simulated root zone soil moisture estimates during Jan 2014 to Dec 2015 at 33 sub basins of Wyra catchment

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Figure A.2: Comparison of the relative subsurface soil moisture derived from SMAR using SMOS observations with SWAT simulated root zone soil moisture estimates during Jan 2014 to Dec 2015 at 33 sub basins of Wyra catchment

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Figure A.3: Comparison of the relative subsurface soil moisture derived from SMAR using ASCAT observations with SWAT simulated root zone soil moisture estimates during Jan 2014 to Dec 2015 at 33 sub basins of Wyra catchment

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Figure A.4: Comparison of the relative subsurface soil moisture derived from SMAR using SMOS observations with SWAT simulated root zone soil moisture estimates during Jan 2014 to Dec 2015 at 31 sub basins of Varada catchment

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Figure A.5: Comparison of the relative subsurface soil moisture derived from SMAR using ASCAT observations with SWAT simulated root zone soil moisture estimates during Jan 2014 to Dec 2015 at 31 sub basins of Varada catchment

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Appendix B Figure B.1 shows the NSE for open loop and assimilation runs of SWAT model with ideal assimilation conditions where the observations and assimilation strategy are assumed to be perfect. It is to be noted that the open loop run of this experiment is same as that of the open loop run carried out in synthetic experiment as mentioned in Sec. 2.4.2. During data assimilation run, the model simulated surface and subsurface soil moisture states were

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updated by true soil moisture (i.e. without any observation error) using direct insertion assimilation strategy. From Fig.B1 it can be seen that, although the assimilation experiment updated the surface and subsurface soil moisture very accurately, these improvements did not helped in improvement of surface runoff, deep percolation and thus, streamflow. This is mainly because, updating the soil moisture states at end of a simulation day can only improve

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the antecedent soil moisture conditions, which will improve the partitioning of rainfall into surface and subsurface flow components during next simulation day. However, the errors in the rainfall during next rainy day are not removed by soil moisture assimilation and thus, resulted in moderate improvements in the model simulated runoff components such as

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Figure B.1: Boxplot of NSE for different model simulated variables for 25 repeated runs during synthetic experiment for a) Open loop run, b) Ideal assimilation run (Refer sec. 3.2 in the main manuscript for description of the variables).