Variational Data Assimilation Approach Research Articles

Retrieving compressive sea ice strength in the Beaufort Sea using the inverse visco-plastic model

We apply a simplified 2d Visco-Plastic (VP) sea ice model with a spatially variable representation of the sea ice rheological parameters for retrieving maximum compressive sea ice strength from satellite and in situ observations. A set of Observing System Simulation Experiments (OSSEs) demonstrates feasibility of optimizing rheological parameter of the VP sea ice model through the variational data assimilation approach during the periods of strong sea ice convergence if accurate sea ice observations are available. Following this strategy, the developed variational data assimilation VP model was applied to the sea ice velocity (https://nsidc.org/data/nsidc-0116/versions/4), sea ice concentration (https://nsidc.org/data/) and CryoSat-2 sea ice thickness observations collected in the vicinity of three moorings in the Beaufort Sea during periods of intensive sea ice convergence. Ice velocities from moorings and atmospheric wind speed (NCEP-NCAR) were used as well. Our results show that conventional maximum compressive sea ice strength (Hibler, 1979) may depend on sea ice thickness or other parameters partly controlled by the sea ice thickness, which is driven by the seasonal cycle.

A variational data assimilation approach for sparse velocity reference data in coarse RANS simulations through a corrective forcing term

The Reynolds-averaged Navier–Stokes (RANS) equations provide a computationally efficient method for solving fluid flow problems in engineering applications. However, the use of closure models to represent turbulence effects can reduce their accuracy. To address this issue, recent research has explored data-driven techniques such as data assimilation and machine learning.An efficient variational data assimilation (DA) approach is presented to enhance steady-state eddy viscosity based RANS simulations. To account for model deficiencies, a corrective force term is introduced in the momentum equation. In the case of only velocity reference data, this term can be represented by a potential field and is divergence-free. The DA implementation relies on the discrete adjoint method and approximations for efficient gradient evaluation.The implementation is based on a two-dimensional coupled RANS solver in OpenFOAM, which is extended to allow the computation of the adjoint velocity and pressure as well as the adjoint gradient. A gradient-based optimizer is used to minimize the difference between the simulation results and the reference data. To evaluate this approach, it is compared with alternative data assimilation methods for canonical stationary two-dimensional turbulent flow problems. For the data assimilation, sparsely distributed reference data from averaged high-fidelity simulation results are used.The results suggest that the proposed method achieves the optimization goal more efficiently compared to applying data assimilation for obtaining the eddy viscosity, or a field modifying the eddy viscosity, directly. The method works well for different reference data configurations and runs efficiently by leveraging coarse meshes.

Sensor placement for data assimilation of turbulence models using eigenspace perturbations

We present an approach to sensor placement for turbulent mean flow data assimilation in the context of Reynolds-averaged Navier–Stokes (RANS) simulations. It entails generating a spatial uncertainty map through the eigenspace perturbations (ESPs) of the baseline turbulence model (e.g., the k−ω shear stress transport model) to quantify the epistemic structural errors in the model. A novel greedy search algorithm is proposed to place sensors targeting regions of highest uncertainty in the spatial uncertainty map generated from ESP. The algorithm is computationally efficient (e.g., computational cost negligible compared to a RANS solution) and is both easy to implement and tune. It involves two hyper-parameters (a constraint to avoid sensor clustering and the number of sensors) which we investigate in-depth. A variational (adjoint-based) data assimilation approach is used for flow reconstruction. The proposed strategy was tested on three two-dimensional wall-bounded flows (Reynolds number ranging 5.6×103–9.36×105) involving flow separation and reattachment. For the wall-mounted hump case, we found that data assimilation using 33 sensors with our proposed sensor placement algorithm reduced the average velocity prediction error by 60% vs 38% with a simple uniform placement of sensors. Furthermore, we found that we could achieve 61% error reduction using our algorithm with only three sensors. Notably, in all tested cases, the error reduction using our method for sensor placement was close in accuracy to the instances where the entire flow field data were used for flow reconstruction, which involved two to three orders of magnitude more data points than the placed sensors.

Imaging with spatio-temporal modelling to characterize the dynamics of plant-pathogen lesions.

Within-host spread of pathogens is an important process for the study of plant-pathogen interactions. However, the development of plant-pathogen lesions remains practically difficult to characterize beyond the common traits such as lesion area. Here, we address this question by combining image-based phenotyping with mathematical modelling. We consider the spread of Peyronellaea pinodes on pea stipules that were monitored daily with visible imaging. We assume that pathogen propagation on host-tissues can be described by the Fisher-KPP model where lesion spread depends on both a logistic growth and an homogeneous diffusion. Model parameters are estimated using a variational data assimilation approach on sets of registered images. This modelling framework is used to compare the spread of an aggressive isolate on two pea cultivars with contrasted levels of partial resistance. We show that the expected slower spread on the most resistant cultivar is actually due to a significantly lower diffusion coefficient. This study shows that combining imaging with spatial mechanistic models can offer a mean to disentangle some processes involved in host-pathogen interactions and further development may allow a better identification of quantitative traits thereafter used in genetics and ecological studies.

A data‐driven optimal control method for endoplasmic reticulum membrane compartmentalization in budding yeast cells

In this paper, we propose a variational data assimilation approach for including data measurements in the simulation of the mobility of fluorescently labeled molecules in the yeast endoplasmic reticulum. The modeling framework aims to provide numerical evidence for compartmentalization in the endoplasmic reticulum. Experimental data are collected and an optimal control problem is formulated as a regularized inverse problem. To our knowledge, this is the first attempt to introduce an optimization formulation constrained by partial differential equations to study the kinetics of fluorescently labeled molecules in budding yeast. We derive the optimality conditions and use an optimize‐then‐discretize approach. A gradient descent algorithm allows accurate estimation of unknown key parameters in different cellular compartments. The numerical results support the empirical barrier index theory suggesting the presence of a physical diffusion barrier that compartmentalizes the endoplasmic reticulum membrane by limiting the exchange of proteins between the mother and its growing bud. We report several numerical experiments on real data and geometry, with the aim of illustrating the accuracy and efficiency of the method. Furthermore, a relationship between the size ratio of mother and bud compartments and the barrier index ratio is provided.

Forecast Sensitivity-based Observation Impact (FSOI) in an analysis–forecast system of the California Current Circulation

Forecast Sensitivity-based Observation Impacts (FSOI) in an analysis–forecast​ system of the California Current System (CCS) are quantified using an adjoint-based approach. The analysis–forecast system is based on the Regional Ocean Modeling System (ROMS) and a 4-dimensional variational (4D-Var) data assimilation approach. FSOI was applied to four different metrics of forecast skill that target important features of the CCS circulation along the central California coast. A particular focus of the FSOI analysis is the impact of assimilation of measurements of the radial component of surface currents from a network of high frequency (HF) radars since this is a new data stream in the near-real-time system considered here. On average, ∼50–60% of all observations assimilated into the model yielded improvements in the forecast skill. Conversely, the remaining ∼40–50% of data degrade the forecasts, in line with similar findings in numerical weather prediction systems. Much of the improvement in forecast skill arises from remotely sensed observations, including HF radar data; on average only ∼50% of in situ measurements contribute to a reduction in forecast error. This is partly due to the large volume of remote sensing observations compared to in situ observations. However, in situ observations are an order of magnitude more impactful than remotely sensed data when viewed in terms of the average impact per observation.

Mean wind flow reconstruction of a high-rise building based on variational data assimilation using sparse pressure measurements

The paper investigates the applicability of the variational data assimilation approach to reconstruct three-dimensional wind flows around a high-rise building model, and provides guidelines towards an efficient reconstruction. The objective is to determine the best distributed control parameters based on the Reynolds-averaged-Navier–Stokes (RANS) model coupled with pressure data. The strategy considers a distributed additive forcing control parameter, acting on the momentum equation and/or the transport equation of turbulent dissipations, where the closure is performed. To avoid unphysical solutions and accelerate the optimization convergence a Sobolev gradient descent regularization is proposed and compared with penalty techniques. The proposed data assimilation framework is applied to a realistic wind engineering estimation problem combining sparse wall pressure measurements with a routinely used industrial three-dimensional RANS numerical code. Results demonstrate that wall-pressure data is a meaningful enough piece of information to recover accurately the wake flow extension. A hybrid control parameter on the transport of the dissipation and the momentum equations leads to very precise results, whereas the Sobolev gradient descent direction gives efficient regularization and a fast convergence. These findings can be useful for future application of such a data assimilation technique to wind engineering problems.

Three-dimensional variational assimilation of Lidar extinction profiles: Application to PM2.5 prediction in north China

The capability of assimilating aerosol optical properties (AOP) using the three-dimensional variational (3DVAR) data assimilation (DA) approach is developed for the Weather Research and Forecasting (WRF) model's data assimilation (WRFDA) system by introducing WRF-Chem-based AOP observation operator and its tangent linear and adjoint. The new AOP DA capability of WRFDA- Chem is firstly applied to assimilate Lidar extinction coefficient profiles in Beijing City from 26 February to March 5, 2019. Cycling strategy of Lidar DA is important to allow a substantial positive impact on surface PM2.5 forecast over the whole evaluation domain (D02, 100 times area of Beijing city covered by the eight Lidar sites) for the entire 24-h forecast range. Compared to the control run without aerosol DA, the mean RMSE reduction and correlation coefficient increase of surface PM2.5 forecast can be up to 15% for the one-day partial cycling strategy. Lidar DA exhibits a clear benefit in improving the vertical distribution of aerosols over Beijing when comparing to surface PM2.5 DA. With the very limited coverage of Lidar data, however, adding Lidar data above surface PM2.5 data (covering the whole D02) does not show the further improvement of surface PM2.5 forecast over D02.

Estimation of Turbulent Heat Fluxes and Gross Primary Productivity by Assimilating Land Surface Temperature and Leaf Area Index

AbstractIn this study, land surface temperature (LST) and leaf area index (LAI) observations are merged with a coupled two‐source surface energy budget–vegetation dynamic model (TSEB–VDM) via a variational data assimilation (VDA) system to predict turbulent heat fluxes and gross primary productivity (GPP). The TSEB and VDM are coupled by relating photosynthesis in the VDM to transpiration in the TSEB equation. Unknown parameters of the VDA approach are the neutral bulk heat transfer coefficient (CHN), evaporative fractions for soil and canopy (EFS and EFC), and specific leaf area (cg). The VDA approach is evaluated at six AmeriFlux sites with distinct vegetative and climatic characteristics. The modeled sensible (H) and latent (LE) heat fluxes, and GPP agree well with the corresponding eddy covariance measurements in different environmental conditions. The six‐site average root mean square error (RMSE) of estimated daily H, LE, and GPP is 42.2 W m−2, 51.5 W m−2, and 1.8 gC m−2 d−1, respectively. The outcomes show that the developed VDA approach is able to exploit the implicit information in the sequences of LST and LAI measurements to estimate H, LE, and GPP. Our findings also indicate that the estimates of the H and LE are more sensitive to uncertainties in LST measurements, while the GPP retrievals are more affected by uncertainties in the LAI observations.

Reconstruction of remotely sensed daily evapotranspiration data in cloudy-sky conditions

The unavailability of thermal infrared satellite observations in cloudy conditions has limited the spatial distribution and temporal coverage of remotely sensed evapotranspiration (ET) data. As a result, a number of approaches have been developed to reconstruct remotely sensed daily ET data in cloudy-sky conditions. Despite the wide application of these approaches, no work has been conducted to compare their performance over a wide variety of climatic and vegetative conditions. In this study, three commonly used ET reconstruction approaches namely, reference ET fraction (EToF), land surface temperature reconstruction (LSTR), and variational data assimilation (VDA) are used to obtain daily ET data under cloudy conditions. The abovementioned three approaches are applied to the Heihe River Basin (HRB) in the northwest of China during the growing season in 2015. The HRB covers an area of approximately 1,432,000 km2 and contains various land covers. The large aperture scintillometer (LAS) and eddy covariance (EC) measurements are used to evaluate performance of the abovementioned three methods over the grassland, cropland, and riparian forest sites in the HRB. The results show that the EToF approach underestimates ET at the grassland and riparian sites in cloudy days because of the negatively biased ET/ETo (where ETo is the reference evapotranspiration) in clear-sky days. The VDA approach overestimates ET in cloudy-sky conditions because of the overpredicted evaporative fraction values. The LSTR approach overestimates ET due to the under-reconstructed LST in cloudy day. The mean absolute percentage difference (MAPD) and root mean square error (RMSE) statistical metrics are used to compare performance of the three approaches The LSTR (MAPD = 43.1% and RMSE = 1.3 mm/day) and VDA (MAPD = 46.7% and RMSE = 1.4 mm/day) approaches slightly outperform EToF (MAPD = 46.6% and RMSE = 1.5 mm/day). The RMSEs of reconstructed ET values by EToF, VDA, and LSTR increase respectively from 1.6, 1.2, and 1.5 (mm/day) to 2.2, 1.9, and 2.0 (mm/day) as the number of consecutive cloudy days increases from 1 to 3. These outcomes suggest that synergistic use of space-borne microwave and thermal infrared LST observations into remote sensing-based ET methods can improve the reconstruction of ET data under cloudy conditions.

Improved decadal predictions of East Asian summer monsoon with a weakly coupled data assimilation scheme

AbstractThe East Asian summer monsoon (EASM) has undergone significant decadal variations since the late 1970s, which greatly affects regional economic and societal activities. However, most available EASM predictions are limited to seasonal to interannual scales, with indistinctive improvements. This study significantly improves decadal prediction skills of the 10‐year‐averaged EASM index (EASMI) and related decadal variations of the East China summer precipitation anomalies (ECSPAs) in the 10‐member decadal prediction experiments started once a year from 1960 to 2005 using a coupled climate model. These improvements are mainly attributed to the use of more realistic and well‐balanced initial conditions (ICs) from a weakly coupled data assimilation system that incorporates the monthly mean atmospheric reanalysis data into the model using the dimension‐reduced projection four‐dimensional variational data assimilation approach, a kind of four‐dimensional ensemble‐variational hybrid method. The atmospheric initialization ameliorates the ICs of Pacific Decadal Oscillation (PDO) through the air‐sea coupling, and thus leads to better PDO hindcasts and forecasts (under the representative concentration pathway 4.5). The improved PDO hindcasts (forecasts) result in more accurate hindcasts (forecasts) of land‐sea thermal contrast, and thus have significant impacts on the EASMI. The improved decadal predictions of the EASMI then contribute to the ameliorated prediction on decadal variations of the spatial distribution of ECSPAs. This study highlights the importance of ICs for a coupled model in reasonably presenting decadal variabilities of the EASMI.

Numerical linear algebra in data assimilation

AbstractData assimilation is a method that combines observations (ie, real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system and thereby the model output. The model is usually represented by a discretized partial differential equation. The data assimilation problem can be formulated as a large scale Bayesian inverse problem. Based on this interpretation we will derive the most important variational and sequential data assimilation approaches, in particular three‐dimensional and four‐dimensional variational data assimilation (3D‐Var and 4D‐Var) and the Kalman filter. We will then consider more advanced methods which are extensions of the Kalman filter and variational data assimilation and pay particular attention to their advantages and disadvantages. The data assimilation problem usually results in a very large optimization problem and/or a very large linear system to solve (due to inclusion of time and space dimensions). Therefore, the second part of this article aims to review advances and challenges, in particular from the numerical linear algebra perspective, within the various data assimilation approaches.

Regularized variational data assimilation for bias treatment using the Wasserstein metric

AbstractThis article presents a new variational data assimilation (VDA) approach for the formal treatment of bias in both model outputs and observations. This approach relies on the Wasserstein metric, stemming from the theory of optimal mass transport, to penalize the distance between the probability histograms of the analysis state and an a priori reference dataset, which is likely to be more uncertain but less biased than both model and observations. Unlike previous bias‐aware VDA approaches, the new Wasserstein metric VDA (WM‐VDA) treats systematic biases of unknown magnitude and sign dynamically in both model and observations, through assimilation of the reference data in the probability domain, and can recover the probability histogram of the analysis state fully. The performance of WM‐VDA is compared with the classic three‐dimensional VDA (3D‐Var) scheme for first‐order linear dynamics and the chaotic Lorenz attractor. Under positive systematic biases in both model and observations, we consistently demonstrate a significant reduction in the forecast bias and unbiased root‐mean‐squared error.

Feasibility of Estimating Turbulent Heat Fluxes via Variational Assimilation of Reference-Level Air Temperature and Specific Humidity Observations

This study investigated the feasibility of partitioning the available energy between sensible (H) and latent (LE) heat fluxes via variational assimilation of reference-level air temperature and specific humidity. For this purpose, sequences of reference-level air temperature and specific humidity were assimilated into an atmospheric boundary layer model (ABL) within a variational data assimilation (VDA) framework to estimate H and LE. The VDA approach was tested at six sites (namely, Arou, Audubon, Bondville, Brookings, Desert, and Willow Creek) with contrasting climatic and vegetative conditions. The unknowns of the VDA system were the neutral bulk heat transfer coefficient (CHN) and evaporative fraction (EF). EF estimates were found to agree well with observations in terms of magnitude and day-to-day fluctuations in wet/densely vegetated sites but degraded in dry/sparsely vegetated sites. Similarly, in wet/densely vegetated sites, the variations in the CHN estimates were found to be consistent with those of the leaf area index (LAI) while this consistency deteriorated in dry/sparely vegetated sites. The root mean square errors (RMSEs) of daily H and LE estimates at the Arou site (wet) were 25.43 (Wm−2) and 55.81 (Wm−2), which are respectively 57.6% and 45.4% smaller than those of 60.00 (Wm−2) and 102.21 (Wm−2) at the Desert site (dry). Overall, the results show that the VDA system performs well at wet/densely vegetated sites (e.g., Arou and Willow Creek), but its performance degrades at dry/slightly vegetated sites (e.g., Desert and Audubon). These outcomes show that the sequences of reference-level air temperature and specific humidity have more information on the partitioning of available energy between the sensible and latent heat fluxes in wet/densely vegetated sites than dry/slightly vegetated sites.

Mapping regional evapotranspiration in cloudy skies via variational assimilation of all-weather land surface temperature observations

Recently, a number of studies estimated evapotranspiration (ET) via variational assimilation of land surface temperature (LST) data from Moderate Resolution Imaging Spectroradiometer (MODIS). Their unknown parameters are neutral bulk heat transfer coefficient (CHN) (that scales the sum of sensible and latent heat fluxes), and evaporative fraction (EF) (that represents the partitioning of available energy between sensible and latent heat fluxes). The variational data assimilation (VDA) approaches estimate CHN and EF by minimizing the difference between the MODIS LST observations and model estimates. The applicability of these studies is limited only to clear-sky conditions where MODIS LST data are available. Even when the sky is clear, they cannot robustly update the initial guess of EF (i.e., the a priori EF value) because of the low temporal resolution of MODIS LST data. This study overcomes these shortcomings by 1) using the random forest (RF) method to obtain a reasonable the a priori EF value, and 2) assimilating the all-weather LST data (which are obtained by merging thermal infrared and passive microwave observations) into the VDA approach. The VDA approach is applied to the Source Regions of Rivers (SRR) in southwest China with heavy cloud covers. Results show that the RF method obtains a reasonably accurate the a priori EF value. Compared to assimilating the MODIS LST product, assimilation of all-weather LST data lead to an improvement in the ET estimates, especially in regions with dense clouds. Comparison of ET estimates with the measurements at four sites (i.e., Dangxiong, Linzhi, Naqu, and Qomolangma) in the SRR shows that the VDA approach can accurately estimate ET in cloudy conditions. Finally, the three-cornered hat (TCH) method is employed to assess the relative uncertainty of ET estimates over the SRR.

Estimation of Turbulent Heat Fluxes via Assimilation of Air Temperature and Specific Humidity into an Atmospheric Boundary Layer Model

AbstractA number of studies have used time series of air temperature and specific humidity observations to estimate turbulent heat fluxes. These studies require the specification of surface roughness lengths for heat and momentum (that are directly related to the neutral bulk heat transfer coefficientCHN) and/or ground heat flux, which are often unavailable. In this study, sequences of air temperature and specific humidity are assimilated into an atmospheric boundary layer model within a variational data assimilation (VDA) framework to estimateCHN, evaporative fraction (EF), turbulent heat fluxes, and atmospheric boundary layer (ABL) height, potential temperature, and humidity. The developed VDA approach needs neither the surface roughness parameterization (as it is optimized by the VDA approach) nor ground heat flux measurements. The VDA approach is tested over the First International Satellite Land Surface Climatology Project Field Experiment (FIFE) site in the summers of 1987 and 1988. The results indicate that the estimated sensible and latent heat fluxes agree fairly well with the corresponding measurements. For FIFE 1987 (1988), the daily sensible and latent heat fluxes estimates have a root-mean-square error of 25.72 W m−2(27.77 W m−2) and 53.63 W m−2(48.22 W m−2), respectively. In addition, the ABL height, specific humidity, and potential temperature estimates from the VDA system are in good agreement with those inferred from the radiosondes both in terms of magnitude and diurnal trend.

Estimation of surface heat fluxes via variational assimilation of land surface temperature, air temperature and specific humidity into a coupled land surface-atmospheric boundary layer model

Numerous studies have estimated surface heat fluxes by assimilating land surface temperature (LST) observations (as the state variable of land surface). A number of other studies have focused on the estimation of surface energy balance components by assimilating air temperature and specific humidity (as the state variables of atmosphere) into an atmospheric boundary layer model. This study advances these existing data assimilation approaches by the synergistic assimilation of LST, air temperature, and specific humidity into a coupled land surface-atmospheric boundary layer model. The unknown parameters are the neutral bulk heat transfer coefficient (CHN) and evaporative fraction (EF). CHN scales the sum of turbulent heat fluxes, and EF represents their partitioning. The developed approach is tested at the First International Satellite Land Surface Climatology Project Field Experiment (FIFE) site in the summer of 1987 and 1988. The results indicate that the new approach performs well in both wet and dry periods because it uses the implicit information in both the land surface and atmospheric state variables (i.e., LST, air temperature, and specific humidity). The root-mean-square-errors (RMSEs) of estimated daily sensible and latent heat fluxes are 21.80 Wm−2 (22.10 Wm−2) and 39.32 Wm−2 (36.89 Wm−2) for FIFE 87 (88). The corresponding mean-absolute-percentage-errors (MAPEs) are 22.16% (18.64%) and 13.98% (13.44%) for FIFE 87 (88). The new variational data assimilation (VDA) system outperforms the previous studies that assimilated either LST or air temperature/specific humidity. For FIFE 87, this study decreases the RMSEs of daily sensible and latent heat fluxes estimates by 12.5% and 24.4% compared to assimilating only LST, and by 15.2% and 26.7% compared to assimilating only air temperature and specific humidity. A similar improvement is obtained for FIFE 88. The atmospheric boundary layer height, potential temperature, and specific humidity estimates from the VDA approach are also in good agreement with the corresponding radiosonde observations, and can capture their variations during the course of the day.

Mapping Regional Turbulent Heat Fluxes via Assimilation of MODIS Land Surface Temperature Data into an Ensemble Kalman Smoother Framework

AbstractEstimation of turbulent heat fluxes via variational data assimilation (VDA) approaches has been the subject of several studies. The VDA approaches need an adjoint model that is difficult to derive. In this study, remotely sensed land surface temperature (LST) data from the Moderate Resolution Imaging Spectroradiometer (MODIS) are assimilated into the heat diffusion equation within an ensemble Kalman smoother (EnKS) approach to estimate turbulent heat fluxes. The EnKS approach is tested in the Heihe River Basin (HRB) in northwest China. The results show that the EnKS approach can estimate turbulent heat fluxes by assimilating low temporal resolution LST data from MODIS. The findings indicate that the EnKS approach performs fairly well in various hydrological and vegetative conditions. The estimated sensible (H) and latent (LE) heat fluxes are compared with the corresponding observations from large aperture scintillometer systems at three sites (namely, Arou, Daman, and Sidaoqiao) in the HRB. The turbulent heat flux estimates from EnKS agree reasonably well with the observations, and are comparable to those of the VDA approach. The EnKS approach also provides statistical information on the H and LE estimates. It is found that the uncertainties of H and LE estimates are higher over wet and/or densely vegetated areas (grassland and forest) compared to the dry and/or slightly vegetated areas (cropland, shrubland, and barren land).

Enhancing CFD-LES air pollution prediction accuracy using data assimilation

It is recognised worldwide that air pollution is the cause of premature deaths daily, thus necessitating the development of more reliable and accurate numerical tools. The present study implements a three dimensional Variational (3DVar) data assimilation (DA) approach to reduce the discrepancy between predicted pollution concentrations based on Computational Fluid Dynamics (CFD) with the ones measured in a wind tunnel experiment. The methodology is implemented on a wind tunnel test case which represents a localised neighbourhood environment. The improved accuracy of the CFD simulation using DA is discussed in terms of absolute error, mean squared error and scatter plots for the pollution concentration. It is shown that the difference between CFD results and wind tunnel data, computed by the mean squared error, can be reduced by up to three order of magnitudes when using DA. This reduction in error is preserved in the CFD results and its benefit can be seen through several time steps after re-running the CFD simulation. Subsequently an optimal sensors positioning is proposed. There is a trade-off between the accuracy and the number of sensors. It was found that the accuracy was improved when placing/considering the sensors which were near the pollution source or in regions where pollution concentrations were high. This demonstrated that only 14% of the wind tunnel data was needed, reducing the mean squared error by one order of magnitude.

Mapping regional turbulent heat fluxes via variational assimilation of land surface temperature data from polar orbiting satellites

Estimation of turbulent heat fluxes by assimilating sequences of land surface temperature (LST) measurements into variational data assimilation (VDA) frameworks has been the subject of several studies. The VDA approaches estimate turbulent heat fluxes by minimizing the difference between LST observations and estimations from the heat diffusion equation. The VDA methods have been tested only with high temporal resolution LST observations (e.g., from geostationary satellites) when applied at regional scales. Geostationary satellites can capture the diurnal cycle of LST, but they have a relatively low spatial resolution and mainly focus on low latitudes. To overcome these shortcomings, this study assimilates high spatial resolution LST data from polar orbiting satellites (e.g., Moderate Resolution Imaging Spectroradiometer, MODIS) into the combined-source (CS) and dual-source (DS) VDA schemes. An expression is developed to obtain an a priori evaporative fraction (EF) estimate from leaf area index (LAI) or apparent thermal inertia (ATI). The a priori EF estimate is used as an initial guess in the VDA approach. The results indicate that the VDA method is able to find the optimal value of EF by assimilating the low-temporal resolution MODIS LST data. The predicted turbulent heat fluxes from VDA are compared with the measurements from the large-aperture scintillometer at three sites (Arou, Daman, and Sidaoqiao) in the Heihe River Basin (located in northwest China). The findings indicate that the CS and DS VDA models perform well in various hydrological and vegetative conditions. The three-site-average root mean square errors (RMSEs) of sensible and latent heat fluxes estimates from the CS scheme are 37.44 W m−2 and 94.30 W m−2, respectively. The DS model reduces the abovementioned RMSEs by 19.82% and 21.37%, respectively. Overall, the results show that using the a priori EF estimate from the proposed expression in the VDA approach eliminates the need for the high resolution LST data from geostationary satellites, and allows the VDA method to estimate turbulent heat fluxes by assimilating LST data from polar orbiting satellites. Finally, several numerical tests are conducted to assess the effect of LST temporal sampling on the turbulent heat fluxes estimates. The results show that the LST measurement at 1400 Local Time (LT) has the most amount of information for partitioning the available energy into sensible and latent heat fluxes.