The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

Trend-preserving blending of passive and active microwave soil moisture retrievals

Landslide susceptibility mapping using downscaled AMSR-E soil moisture: A case study from Cleveland Corral, California, US

The Tropical Rainfall Measuring Mission (TRMM) is a joint space mission between NASA and the Japan Aerospace Exploration Agency (JAXA) designed to monitor and study tropical rainfall. In this study, the daily rainfall from TRMM has been utilized to simulate the soil moisture content up to 30 cm vertical soil profile of at an interval depth of 15 cm by using the HYDRUS 1D numerical model for the three plots. The simulated soil moisture content using ground-based rainfall and TRMM-derived rainfall measurements indicate an agreeable goodness of fit between the both. The Nash–Sutcliffe efficiency using ground-based and TRMM-derived rainfall was found in the range of 0.90–0.68 and 0.70–0.40, respectively. The input data sensitivity analysis of precipitation combined with different irrigation treatment indicates a high dependency of soil moisture content with rainfall input. The overall analysis reveals that TRMM rainfall is promising for soil moisture prediction in absence of ground-based measurements of soil moisture.

Evaluation of TRMM rainfall for soil moisture prediction in a subtropical climate

https://ntrs.nasa.gov/api/citations/20150014256/downloads/20150014256.pdf

Assessment of SMOS soil moisture retrieval parameters using tau-omega algorithms for soil moisture deficit estimation

. In this paper, 7 years (during the growing season (April–October) of 2002–2008) of the Advanced Microwave Scanning Radiometer (AMSR-E) data taken at a frequency of 6.9 GHz for night observations at both polarizations are processed and used to conduct 7 years of surface soil moisture dataset for an arid area, in Northwestern China. This soil moisture dataset can contribute to better understanding the climate change and forecast modeling for this area. Based on the first-order radiative transfer model calculation, a unique method for estimating surface soil moisture over the study area is developed. Considering extremely complex topography over the study area, we have to present a parameterization of surface roughness at the 6.9 GHz and spatial resolution of the AMSR-E using the annual minimum MPDI (Microwave Polarization Difference Index). For validation purpose, the comparisons of soil moisture patterns with precipitation fields are made. The results indicate the evolutions of soil moisture estimated from the AMSR-E and antecedent ground daily precipitations are in a good agreement. Furthermore, a series of rainfall traces is captured over the Taklimakan Desert. Comparisons of the estimated values of soil moisture with the ground observations are also made for two reprehensive sites over 2002–2004. The results indicate there has a good agreement between them, with higher correlation coefficients (R=0.649, 0.604) and RMSE (3.5, 5.4%), and the soil moisture product derived from the AMSR-E is realistic and acceptable. This new long time series of estimated soil moisture will prove valuable for other studies of climate change and model evaluation.

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Surface soil moisture estimates from AMSR-E observations over an arid area, Northwest China

Low-frequency microwave satellite observations are sensitive to land surface soil moisture (SM). Using satellite microwave brightness temperature observations to improve SM simulations of numerical weather, climate and hydrological predictions is one of the most active research areas of the geoscience community. In this paper, Yan and Jins’ (J Radio Sci 19(4):386–392, 2004) theory on the relationship between satellite microwave remote sensing polarization index and SM is used to estimate land surface SM values from the advanced microwave scanning radiometer-E (AMSR-E) brightness temperature data. With consideration of soil texture, surface roughness, optical thickness, and the monthly means of NASA AMSR-E SM data products, the regional daily land surface SM values are estimated over the eastern part of the Qinghai-Tibet Plateau. The resulting SM retrievals are better than the NASA daily AMSR-E SM product. The retrieved SM values are generally lower than the ground measurements from the Maqu Station (33.85°N, 102.57°E) and the Tanglha Station (33.07°N, 91.94°E) and the US NCEP reanalysis data, but the temporal variations of the retrieved SM demonstrate more realistic response to the observed precipitation events. In order to improve the land surface SM simulating ability of the weather research and forecasting model, the retrieved SM was assimilated into the Noah land surface model by the Newtonian relaxation (NR) method. A direct insertion method was also applied for comparison. The results indicate that fine-tuning the quality factor in the NR method improves the simulated SM values most for desert areas, followed by grasslands, and shrub and grass mixed zones at the regional scale. At the temporal scale, the NR method decreased the root mean square error between the simulated SM and actual observed SM by 0.03 and 0.07 m3/m3 at the Maqu and Tanglha Stations, respectively, and the temporal variation of simulated SM values was much closer to the ground-measured SM values.

Regional soil moisture retrievals and simulations from assimilation of satellite microwave brightness temperature observations

Forecasting aircraft turbulence accurately is of vital importance for route optimization and flight safety. The common methods including TI index and L-P are usually used to predict aircraft turbulence by diagnosing the strength of atmospheric turbulence, not taking into account the impact of aircraft itself and other elements, and can only be applied to the products with low horizontal resolutions. By considering factors that affect the aircraft lift, a new diagnostic index method, S Index (SI) method, is designed in this paper for aircraft turbulence, which can be applicable to high-resolution NWP products or analysis products. SI method mainly focuses on the factors that impact aircraft turbulence such as flight speed, wing loading, vertical velocity of air flow, horizontal wind speed, air density. The paper also provides a method of determining parameters based on the existing experience and mathematical techniques which are combined with aircraft reports and high-resolution NWP results. In addition, pointing to the level flight and takeoff/landing stages, SI analysis and calculation are carried out, respectively. To validate the application scope of the accuracy of SI method objectively, the physical quantity of turbulence area ratio (TAR), which is a statistical parameter to describe the ratio of turbulence area and the overall diagnostic region, is defined. In the case that the horizontal and vertical resolutions of weather research and forecasting (WRF) forecasts are 9 km and 300 m, respectively, the diagnostic results of SI show that for the stage of level flight, when the TAR ratio is 41 %, the overall forecast accuracy of aircraft turbulence can reach 74 %, of which the accuracy of moderate turbulence forecast is 60 % and the severe 27 %. For the stage with 20° elevation during the process of takeoff and landing, when the TAR ratio is 40 %, the overall forecast accuracy can get to 63 %, of which the accuracies of moderate and severe turbulence are 41 and 14 %, respectively.

A diagnostic method for aircraft turbulence based on high-resolution numerical weather prediction products

Accurate assignment of model and observation errors is crucial for the successful application of land surface data assimilation algorithms. Poorly-specified model and observation errors can significantly degrade assimilation results. In 2008, Reichle et al. developed an operational procedure to adaptively tune model and observation errors. In this paper, we modified and applied Reichle’s procedure in the Noah land surface model to assimilate observed surface soil moisture data. Numerical simulations showed that: (1) the best estimate of model and observation errors appears when the empirical factor β equals 1.02; (2) the Reichle procedure can be deployed to adaptively tune errors if their true values change slowly; and (3) convergence of the Reichle procedure was improved using better initial errors achieved by iterative computations.

Application and improvement of an adaptive ensemble Kalman filter for soil moisture data assimilation

. As the satellite microwave remote sensed brightness temperature is sensitive to land surface soil moisture (SM) and SM is a basic output variable in model simulation, it is of great significance to use the brightness temperature data to improve SM numerical simulation. In this paper, the theory developed by Yan et al. (2004) about the relationship between satellite microwave remote sensing polarization index and SM was used to estimate the land surface SM from AMSR-E (Advanced Microwave Scanning Radiometer – Earth Observing System) brightness temperature data. With consideration of land surface soil texture, surface roughness, vegetation optical thickness, and the AMSR-E monthly SM products, the regional daily land surface SM was estimated over the eastern part of the Qinghai-Tibet Plateau. The results show that the estimated SM is lower than the ground measurements and the NCEP (American National Centers for Environmental Prediction) reanalysis data at the Maqu Station (33.85° N, 102.57° E) and the Tanglha Station (33.07° N, 91.94° E), but its regional distribution is reasonable and somewhat better than that from the daily AMSR-E SM product, and its temporal variation shows a quick response to the ground daily precipitations. Furthermore, in order to improve the simulating ability of the WRF (Weather Research and Forecasting) model to land surface SM, the estimated SM was assimilated into the Noah land surface model by the Newtonian relaxation (NR) method. The results indicate that, by fine tuning of the quality factor in NR method, the simulated SM values are improved most in desert area, followed by grassland, shrub and grass mixed zone. At temporal scale, Root Mean Square Error (RMSE) values between simulated and observed SM are decreased 0.03 and 0.07 m 3 /m 3 by using the NR method in the Maqu Station and the Tanglha Station, respectively.

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Xiaokang Shi

Papers

Surface soil moisture estimates from AMSR-E observations over an arid area, Northwest China

Regional soil moisture retrievals and simulations from assimilation of satellite microwave brightness temperature observations

A diagnostic method for aircraft turbulence based on high-resolution numerical weather prediction products

Application and improvement of an adaptive ensemble Kalman filter for soil moisture data assimilation

Application of satellite microwave remote sensed brightness temperature in the regional soil moisture simulation