Data assimilation methods in the Earth sciences

Although remote sensing data are often plentiful, they do not usually satisfy the users’ needs directly. Data assimilation is required to extract information about geophysical fields of interest from the remote sensing observations and to make the data more accessible to users. Remote sensing may provide, for example, measurements of surface soil moisture, snow water equivalent, snow cover, or land surface (skin) temperature. Data assimilation can then be used to estimate variables that are not directly observed from space but are needed for applications, for instance root zone soil moisture or land surface fluxes. The paper provides a brief introduction to modern data assimilation methods in the Earth sciences, their applications, and pertinent research questions. Our general overview is readily accessible to hydrologic remote sensing scientists. Within the general context of Earth science data assimilation, we point to examples of the assimilation of remotely sensed observations in land surface hydrology.     

Towards the estimation root-zone soil moisture via the simultaneous assimilation of thermal and microwave soil moisture retrievals

The upcoming deployment of satellite-based microwave sensors designed specifically to retrieve surface soil moisture represents an important milestone in efforts to develop hydrologic applications for remote sensing observations. However, typical measurement depths of microwave-based soil moisture retrievals are generally considered too shallow (top 2–5 cm of the soil column) for many important water cycle and agricultural applications. Recent work has demonstrated that thermal remote sensing estimates of surface radiometric temperature provide a complementary source of land surface information that can be used to define a robust proxy for root-zone (top 1 m of the soil column) soil moisture availability. In this analysis, we examine the potential benefits of simultaneously assimilating both microwave-based surface soil moisture retrievals and thermal infrared-based root-zone soil moisture estimates into a soil water balance model using a series of synthetic twin data assimilation experiments conducted at the USDA Optimizing Production Inputs for Economic and Environmental Enhancements (OPE³) site. Results from these experiments illustrate that, relative to a baseline case of assimilating only surface soil moisture retrievals, the assimilation of both root- and surface-zone soil moisture estimates reduces the root-mean-square difference between estimated and true root-zone soil moisture by 50% to 35% (assuming instantaneous root-zone soil moisture retrievals are obtained at an accuracy of between 0.020 and 0.030 m³ m⁻³). Most significantly, improvements in root-zone soil moisture accuracy are seen even for cases in which root-zone soil moisture retrievals are assumed to be relatively inaccurate (i.e. retrievals errors of up to 0.070 m³ m⁻³) or limited to only very sparse sampling (i.e. one instantaneous measurement every eight days). Preliminary real data results demonstrate a clear increase in the R² correlation coefficient with ground-based root-zone observations (from 0.51 to 0.73) upon assimilation of actual surface soil moisture and tower-based thermal infrared temperature observations made at the OPE³ study site.     

Initialisation of Land Surface Variables for Numerical Weather Prediction

Land surface processes and their initialisation are of crucial importance for Numerical Weather Prediction (NWP). Current land data assimilation systems used to initialise NWP models include snow depth analysis, soil moisture analysis, soil temperature and snow temperature analysis. This paper gives a review of different approaches used in NWP to initialise land surface variables. It discusses the observation availability and quality, and it addresses the combined use of conventional observations and satellite data. Based on results from the European Centre for Medium-Range Weather Forecasts (ECMWF), results from different soil moisture and snow depth data assimilation schemes are shown. Both surface fields and low-level atmospheric variables are highly sensitive to the soil moisture and snow initialisation methods. Recent developments of ECMWF in soil moisture and snow data assimilation improved surface and atmospheric forecast performance.     

Requirements of a global near-surface soil moisture satellite mission: accuracy,repeat time,and spatial resolution

Soil moisture satellite mission accuracy, repeat time and spatial resolution requirements are addressed through a numerical twin data assimilation study. Simulated soil moisture profile retrievals were made by assimilating near-surface soil moisture observations with various accuracy (0, 1, 2, 3, 4, 5 and 10%v/v standard deviation) repeat time (1, 2, 3, 5, 10, 15, 20 and 30 days), and spatial resolution (0.5, 6, 12 18, 30, 60 and 120 arc-min). This study found that near-surface soil moisture observation error must be less than the model forecast error required for a specific application when used as data assimilation input, else slight model forecast degradation may result. It also found that near-surface soil moisture observations must have an accuracy better than 5%v/v to positively impact soil moisture forecasts, and that daily near-surface soil moisture observations achieved the best soil moisture and evapotranspiration forecasts for the repeat times assessed, with 1–5 day repeat times having the greatest impact. Near-surface soil moisture observations with a spatial resolution finer than the land surface model resolution (∼30 arc-min) produced the best results, with spatial resolutions coarser than the model resolution yielding only a slight degradation. Observations at half the land surface model spatial resolution were found to be appropriate for our application. Moreover, it was found that satisfying the spatial resolution and accuracy requirements was much more important than repeat time.     

A land surface data assimilation framework using the land information system: Description and applications

The Land Information System (LIS) is an established land surface modeling framework that integrates various community land surface models, ground measurements, satellite-based observations, high performance computing and data management tools. The use of advanced software engineering principles in LIS allows interoperability of individual system components and thus enables assessment and prediction of hydrologic conditions at various spatial and temporal scales. In this work, we describe a sequential data assimilation extension of LIS that incorporates multiple observational sources, land surface models and assimilation algorithms. These capabilities are demonstrated here in a suite of experiments that use the ensemble Kalman filter (EnKF) and assimilation through direct insertion. In a soil moisture experiment, we discuss the impact of differences in modeling approaches on assimilation performance. Provided careful choice of model error parameters, we find that two entirely different hydrological modeling approaches offer comparable assimilation results. In a snow assimilation experiment, we investigate the relative merits of assimilating different types of observations (snow cover area and snow water equivalent). The experiments show that data assimilation enhancements in LIS are uniquely suited to compare the assimilation of various data types into different land surface models within a single framework. The high performance infrastructure provides adequate support for efficient data assimilation integrations of high computational granularity.     

Numerical investigation of the impact of uncertainties in satellite rainfall estimation and land surface model parameters on simulation of soil moisture

This study aims at evaluating the uncertainty in the prediction of soil moisture (1D, vertical column) from an offline land surface model (LSM) forced by hydro-meteorological and radiation data. We focus on two types of uncertainty: an input error due to satellite rainfall retrieval uncertainty, and, LSM soil-parametric error. The study is facilitated by in situ and remotely sensed data-driven (precipitation, radiation, soil moisture) simulation experiments comprising a LSM and stochastic models for error characterization. The parametric uncertainty is represented by the generalized likelihood uncertainty estimation (GLUE) technique, which models the parameter non-uniqueness against direct observations. Half-hourly infra-red (IR) sensor retrievals were used as satellite rainfall estimates. The IR rain retrieval uncertainty is characterized on the basis of a satellite rainfall error model (SREM). The combined uncertainty (i.e., SREM + GLUE) is compared with the partial assessment of uncertainty. It is found that precipitation (IR) error alone may explain moderate to low proportion of the soil moisture simulation uncertainty, depending on the level of model accuracy—50–60% for high model accuracy, and 20–30% for low model accuracy. Comparisons on the basis of two different sites also yielded an increase (50–100%) in soil moisture prediction uncertainty for the more vegetated site. This study exemplified the need for detailed investigations of the rainfall retrieval-modeling parameter error interaction within a comprehensive space-time stochastic framework for achieving optimal integration of satellite rain retrievals in land data assimilation systems.     

Satellite based estimates of terrestrial water storage variations in Turkey

In recent years, the Gravity Recovery and Climate Experiment (GRACE) has provided a new tool to study terrestrial water storage variations (TWS) at medium and large spatial scales, providing quantitative measures of TWS change. Linear trends in TWS variations in Turkey were estimated using GRACE observations for the period March 2003 to March 2009. GRACE showed a significant decrease in TWS in the southern part of the central Anatolian region up to a rate of 4 cm/year. The Global Land Data Assimilation System (GLDAS) model also captured this TWS decrease event but with underestimated trend values. The GLDAS model represents only a part of the total TWS variations, the sum of soil moisture (2 m column depth) and snow water equivalent, ignoring groundwater variations. Therefore, GLDAS model derived TWS variations were subtracted from GRACE derived TWS variations to estimate groundwater storage variations. Results revealed that decreasing trends of TWS observed by GRACE in the southern part of central Anatolia were largely explained by the decreasing trends of groundwater variations which were confirmed by the limited available well groundwater level data in the region.     

Global Terrestrial Water Storage Changes and Connections to ENSO Events

Improved data quality of extended record of the Gravity Recovery and Climate Experiment (GRACE) satellite gravity solutions enables better understanding of terrestrial water storage (TWS) variations. Connections of TWS and climate change are critical to investigate regional and global water cycles. In this study, we provide a comprehensive analysis of global connections between interannual TWS changes and El Niño Southern Oscillation (ENSO) events, using multiple sources of data, including GRACE measurements, land surface model (LSM) predictions and precipitation observations. We use cross-correlation and coherence spectrum analysis to examine global connections between interannual TWS changes and the Niño 3.4 index, and select four river basins (Amazon, Orinoco, Colorado, and Lena) for more detailed analysis. The results indicate that interannual TWS changes are strongly correlated with ENSO over much of the globe, with maximum cross-correlation coefficients up to ~0.70, well above the 95% significance level (~0.29) derived by the Monte Carlo experiments. The strongest correlations are found in tropical and subtropical regions, especially in the Amazon, Orinoco, and La Plata basins. While both GRACE and LSM TWS estimates show reasonably good correlations with ENSO and generally consistent spatial correlation patterns, notably higher correlations are found between GRACE TWS and ENSO. The existence of significant correlations in middle–high latitudes shows the large-scale impact of ENSO on the global water cycle.     

Analysis and partitioning of terrestrial water storage in the Yellow River source region

In order to increase the capability to understand and quantify the spatial differences in terrestrial water storage (TWS), and to reflect the unique energy balance processes and soil freeze–thaw mechanisms in the Qinghai-Tibet Plateau (QTP), this study improved the energy balance processes of the water and energy transfer processes model, including its surface radiation calculations and snowmelt module. By integrating these improvements, a water and energy transfer processes model in Qinghai-Tibet Plateau (WEP-QTP) for the Yellow River source region (YRSR) is developed. Using the improved WEP-QTP model to perform simulations, we assessed the daily changes in snow cover, soil moisture (SM), permafrost (PM), and groundwater storage (GWS) in the YRSR. Our analysis revealed an increase in TWS of 0.24 mm/yr from 1961 to 2020. Snow water equivalent (SWE), SM, PM, and GWS have proportional contributions of 8.33%, 216.67%, −154.17%, and 29.17% to the increased TWS, respectively. SM is the primary component of TWS. Temperature (T), precipitation (P), evapotranspiration (E), and solar radiation (Rs) influence the spatiotemporal variations in TWS, as well as those of its components. The increase in P is the primary cause for the rise in TWS, SWE, and SM, while the increase in T predominantly contributes to the decrease in PM. Furthermore, permafrost degradation and climate-induced warming and humidification lead to increased infiltration, resulting in elevated GWS.     

Root-zone soil moisture estimation from assimilation of downscaled Soil Moisture and Ocean Salinity data

The crucial role of root-zone soil moisture is widely recognized in land–atmosphere interaction, with direct practical use in hydrology, agriculture and meteorology. But it is difficult to estimate the root-zone soil moisture accurately because of its space-time variability and its nonlinear relationship with surface soil moisture. Typically, direct satellite observations at the surface are extended to estimate the root-zone soil moisture through data assimilation. But the results suffer from low spatial resolution of the satellite observation. While advances have been made recently to downscale the satellite soil moisture from Soil Moisture and Ocean Salinity (SMOS) mission using methods such as the Disaggregation based on Physical And Theoretical scale Change (DisPATCh), the assimilation of such data into high spatial resolution land surface models has not been examined to estimate the root-zone soil moisture. Consequently, this study assimilates the 1-km DisPATCh surface soil moisture into the Joint UK Land Environment Simulator (JULES) to better estimate the root-zone soil moisture. The assimilation is demonstrated using the advanced Evolutionary Data Assimilation (EDA) procedure for the Yanco area in south eastern Australia. When evaluated using in-situ OzNet soil moisture, the open loop was found to be 95% as accurate as the updated output, with the updated estimate improving the DisPATCh data by 14%, all based on the root mean square error (RMSE). Evaluation of the root-zone soil moisture with in-situ OzNet data found the updated output to improve the open loop estimate by 34% for the 0–30 cm soil depth, 59% for the 30–60 cm soil depth, and 63% for the 60–90 cm soil depth, based on RMSE. The increased performance of the updated output over the open loop estimate is associated with (i) consistent estimation accuracy across the three soil depths for the updated output, and (ii) the deterioration of the open loop output for deeper soil depths. Thus, the findings point to a combined positive impact from the DisPATCh data and the EDA procedure, which together provide an improved soil moisture with consistent accuracy both at the surface and at the root-zone.     

Intercomparison of the JULES and CABLE land surface models through assimilation of remotely sensed soil moisture in southeast Australia

Numerous land surface models exist for predicting water and energy fluxes in the terrestrial environment. These land surface models have different conceptualizations (i.e., process or physics based), together with structural differences in representing spatial variability, alternate empirical methods, mathematical formulations and computational approach. These inherent differences in modeling approach, and associated variations in outputs make it difficult to compare and contrast land surface models in a straight-forward manner. While model intercomparison studies have been undertaken in the past, leading to significant progress on the improvement of land surface models, additional framework towards identification of model weakness is needed. Given that land surface models are increasingly being integrated with satellite based estimates to improve their prediction skill, it is practical to undertake model intercomparison on the basis of soil moisture data assimilation. Consequently, this study compares two land surface models: the Joint UK Land Environment Simulator (JULES) and the Community Atmosphere Biosphere Land Exchange (CABLE) for soil moisture estimation and associated assessment of model uncertainty. A retrieved soil moisture data set from the Soil Moisture and Ocean Salinity (SMOS) mission was assimilated into both models, with their updated estimates validated against in-situ soil moisture in the Yanco area, Australia. The findings show that the updated estimates from both models generally provided a more accurate estimate of soil moisture than the open loop estimate based on calibration alone. Moreover, the JULES output was found to provide a slightly better estimate of soil moisture than the CABLE output at both near-surface and deeper soil layers. An assessment of the updated membership in decision space also showed that the JULES model had a relatively stable, less sensitive, and more highly convergent internal dynamics than the CABLE model.     

The influence of groundwater representation on hydrological simulation and its assessment using satellite‐based water storage variation

The interaction between surface water and groundwater is an important aspect of hydrological processes. Despite its importance, groundwater is not well represented in many land surface models. In this study, a groundwater module with consideration of surface water and groundwater dynamic interactions is incorporated into the distributed biosphere hydrological (DBH) model in the upstream of the Yellow River basin, China. Two numerical experiments are conducted using the DBH model: one with groundwater module active, namely, DBH_GW and the other without, namely, DBH_NGW. Simulations by two experiments are compared with observed river discharge and terrestrial water storage (TWS) variation from the Gravity Recovery and Climate Experiment (GRACE). The results show that river discharge during the low flow season that is underestimated in the DBH_NGW has been improved by incorporating the groundwater scheme. As for the TWS, simulation in DBH_GW shows better agreement with GRACE data in terms of interannual and intraseasonal variations and annual changing trend. Furthermore, compared with DBH_GW, TWS simulated in DBH_NGW shows smaller decreases during autumn and smaller increases in spring. These results suggest that consideration of groundwater dynamics enables a more reasonable representation of TWS change by increasing TWS amplitudes and signals and as a consequence, improves river discharge simulation in the low flow seasons when groundwater is a major component in runoff. Additionally, incorporation of groundwater module also leads to wetter soil moisture and higher evapotranspiration, especially in the wet seasons.     

基于光学与被动微波遥感的青藏高原地区土壤水分反演

青藏高原地区高精度的土壤水分反演对高原能水循环、全球大气循环研究有着极大的影响.因此,获取青藏高原土壤水分时空布信息是一个迫切需要解决的问题.温度植被干旱指数(TVDI),是基于光学与热红外遥感通道数据反演土壤水分的重要方法,但在研究区域较大、地表覆盖格局差异显著时,TVDI模型反演精度会受到地表温度(Ts)等因素的影响.被动微波AMSR-E数据精确记录了像元内的土壤水分信息,但空间分辨率低.本文利用同时期的MODIS与被动微波数据,发展了针对青藏高原地区高精度土壤水分反演算法.首先,在TVDI模型中,利用修正型土壤调整植被指数(MSAVI)代替归一化植被指数(NDVI),以改进NDVI易饱和的缺点;其次,利用ASTER GDEM数据,对地形高程和纬度差异引起的地表温度变化进行了校正;然后,通过神经网络训练建立基于TVDI、被动微波以及辅助气象数据的土壤水分反演模型,并应用该模型反演了青藏高原地区三个观测网(CAMP/Tibet、玛曲和那曲)的土壤水分;最后,利用实测土壤水分数据对反演结果进行验证,结果表明该模型的精度均方根误差(RMSE)数值可达到0.031~0.041 m~3·m~(-3).本文还应用该算法反演了青藏高原连续的土壤水分的空间分布,并比较了土壤水分的变化趋势与实测降水变化趋势,结果表明二者变化量的正负关系一致.     

Utilization of satellite data in land surface hydrology: sensitivity and assimilation

This paper investigates the sensitivity of potential evapotranspiration to input meteorological variables, i.e. surface air temperature and surface vapor pressure. The sensitivity studies have been carried out for a wide range of land surface variables such as wind speed, leaf area index and surface temperatures. Errors in the surface air temperature and surface vapor pressure result in errors of different signs in the computed potential evapotranspiration. This result has implications for use of estimated values from satellite data or analysis of surface air temperature and surface vapor pressure in large‐scale hydrological modeling. The comparison of cumulative potential evapotranspiration estimates using ground observations and satellite observations over Manhattan, Kansas for a period of several months shows a variable difference between the two estimates. The use of satellite estimates of surface skin temperature in hydrological modeling to update the soil moisture using a physical adjustment concept is studied in detail, including the extent of changes in soil moisture resulting from the assimilation of surface skin temperature. The soil moisture of the 1 cm surface layer was adjusted by 0·9 mm over a 10‐day period as a result of a 3 K difference between the predicted and the observed surface temperature. This is a considerable amount given the fact that the top layer can hold only 5 mm of moisture. Copyright © 2001 John Wiley & Sons, Ltd.     

A land surface soil moisture data assimilation framework in consideration of the model subgrid-scale heterogeneity and soil water thawing and freezing

The Ensemble Kalman Filter (EnKF) is well known and widely used in land data assimilation for its high precision and simple operation. The land surface models used as the forecast operator in a land data assimilation system are usually designed to consider the model subgrid-heterogeneity and soil water thawing and freezing. To neglect their effects could lead to some errors in soil moisture assimilation. The dual EnKF method is employed in soil moisture data assimilation to build a soil moisture data as- similation framework based on the NCAR Community Land Model version 2.0 (CLM 2.0) in considera- tion of the effects of the model subgrid-heterogeneity and soil water thawing and freezing: Liquid volumetric soil moisture content in a given fraction is assimilated through the state filter process, while solid volumetric soil moisture content in the same fraction and solid/liquid volumetric soil moisture in the other fractions are optimized by the parameter filter. Preliminary experiments show that this dual EnKF-based assimilation framework can assimilate soil moisture more effectively and precisely than the usual EnKF-based assimilation framework without considering the model subgrid-scale heteroge- neity and soil water thawing and freezing. With the improvement of soil moisture simulation, the soil temperature-simulated precision can be also improved to some extent.     

Simultaneous estimation of soil moisture and hydraulic parameters using residual resampling particle filter

Land data assimilation (DA) has gradually developed into an important earth science research method because of its ability to combine model simulations and observations. Integrating new observations into a land surface model by the DA method can correct the predicted trajectory of the model and thus, improve the accuracy of state variables. It can also reduce uncertainties in the model by estimating some model parameters simultaneously. Among the various DA methods, the particle filter is free from the constraints of linear models and Gaussian error distributions, and can be applicable to any nonlinear and non-Gaussian state-space model; therefore, its importance in land data assimilation research has increased. In this study, a DA scheme was developed based on the residual resampling particle filter. Microwave brightness temperatures were assimilated into the macro-scale semi-distributed variance infiltration capacity model to estimate the surface soil moisture and three hydraulic parameters simultaneously. Finally, to verify the scheme, a series of comparative experiments was performed with experimental data obtained during the Soil Moisture Experiment of 2004 in Arizona. The results show that the scheme can improve the accuracy of soil moisture estimations significantly. In addition, the three hydraulic parameters were also well estimated, demonstrating the effectiveness of the DA scheme.     

GRACE terrestrial water storage data assimilation based on the ensemble four-dimensional variational method PODEn4DVar:Method and validation

Seasonal and interannual changes in the Earth's gravity field are mainly due to mass exchange among the atmosphere,ocean,and continental water sources.The terrestrial water storage changes,detected as gravity changes by the Gravity Recovery and Climate Experiment(GRACE) satellites,are mainly caused by precipitation,evapotranspiration,river transportation and downward infiltration processes.In this study,a land data assimilation system LDAS-G was developed to assimilate the GRACE terrestrial water storage(TWS) data into the Community Land Model(CLM3.5) using the POD-based ensemble four-dimensional variational assimilation method PODEn4 DVar,disaggregating the GRACE large-scale terrestrial water storage changes vertically and in time,and placing constraints on the simulation of vertical hydrological variables to improve land surface hydrological simulations.The ideal experiments conducted at a single point and assimilation experiments carried out over China by the LDAS-G data assimilation system showed that the system developed in this study improved the simulation of land surface hydrological variables,indicating the potential of GRACE data assimilation in large-scale land surface hydrological research and applications.     

Evaluation of snow models in terrestrial biosphere models using ground observation and satellite data: impact on terrestrial ecosystem processes

Snow is important for water management, and an important component of the terrestrial biosphere and climate system. In this study, the snow models included in the Biome‐BGC and Terrestrial Observation and Prediction System (TOPS) terrestrial biosphere models are compared against ground and satellite observations over the Columbia River Basin in the US and Canada and the impacts of differences in snow models on simulated terrestrial ecosystem processes are analysed. First, a point‐based comparison of ground observations against model and satellite estimates of snow dynamics are conducted. Next, model and satellite snow estimates for the entire Columbia River Basin are compared. Then, using two different TOPS simulations, the default TOPS model (TOPS with TOPS snow model) and the TOPS model with the Biome‐BGC snow model, the impacts of snow model selection on runoff and gross primary production (GPP) are investigated. TOPS snow model predictions were consistent with ground and satellite estimates of seasonal and interannual variations in snow cover, snow water equivalent, and snow season length; however, in the Biome‐BGC snow model, the snow pack melted too early, leading to extensive underpredictions of snow season length and snow covered area. These biases led to earlier simulated peak runoff and reductions in summer GPP, underscoring the need for accurate snow models within terrestrial ecosystem models. Copyright © 2007 John Wiley & Sons, Ltd.     

Detection of Continental Hydrology and Glaciology Signals from GRACE: A Review

Since its launch in March 2002, the Gravity Recovery and Climate Experiment (GRACE) has provided a global mapping of the time-variations of the Earth’s gravity field. Tiny variations of gravity from monthly to decadal time scales are mainly due to redistributions of water mass inside the surface fluid envelops of our planet (i.e., atmosphere, ocean and water storage on continents). In this article, we present a review of the major contributions of GRACE satellite gravimetry in global and regional hydrology. To date, many studies have focused on the ability of GRACE to detect, for the very first time, the time-variations of continental water storage (including surface waters, soil moisture, groundwater, as well as snow pack at high latitudes) at the unprecedented resolution of ~400–500 km. As no global complete network of surface hydrological observations exists, the advances of satellite gravimetry to monitor terrestrial water storage are significant and unique for determining changes in total water storage and water balance closure at regional and continental scales.     

Improving the estimation of hydrological states in the SWAT model via the ensemble Kalman smoother: Synthetic experiments for the Heihe River Basin in northwest China

Data assimilation as a method to predict variables, reduce uncertainties and explicitly handle various sources of uncertainties has recently received widespread attention and has been utilized to combine in situ and remotely sensed measurements with hydrological models. However, factors that significantly influence the capability of data assimilation still need testing and verifying. In this paper, synthetic surface soil moisture data are assimilated into the Soil and Water Assessment Tool (SWAT) model to evaluate their impact on other hydrological variables via the ensemble Kalman smoother (EnKS), using data from the Heihe River Basin, northwest China. The results show that the assimilation of surface soil moisture can moderately improve estimates of deep layer soil moisture, surface runoff and lateral flow, which reduces the negative influences of erroneous forcing and inaccurate parameters. The effects of the spatially heterogeneous input data (land cover and soil type) on the performance of the data assimilation technique are noteworthy. Moreover, the approaches including inflation and localization are specifically diagnosed to further extend the capability of the EnKS.