Soil moisture retrieval over agricultural fields from L-band multi-incidence and multitemporal PolSAR observations using polarimetric decomposition techniques

Surface soil moisture (SM) retrieval over agricultural areas from polarimetric synthetic aperture radar (PolSAR) has long been restricted by vegetation attenuation, simplified polarimetric scattering modelling, and limited SAR measurements. This study proposes a modified polarimetric decomposition framework to retrieve SM from multi-incidence and multitemporal PolSAR observations. The framework is constructed by combining the X-Bragg model, the extended double Fresnel scattering model and the generalised volume scattering model (GVSM). Compared with traditional decomposition models, the proposed framework considers the depolarisation of dihedral scattering and the diverse vegetation contribution. Under the assumption that SM is invariant for the PolSAR observations at two different incidence angles and that vegetation scattering does not change between two consecutive measurements, analytical parameter solutions, including the dielectric constant of soil and crop stem, can be obtained by solving multivariable nonlinear equations. The proposed framework is applied to the time series of L-band uninhabited aerial vehicle synthetic aperture radar data acquired during the Soil Moisture Active Passive Validation Experiment in 2012. In this study, we assess retrieval performance by comparing the inversion results with in-situ measurements over bean, canola, corn, soybean, wheat and winter wheat areas and comparing the different performance of SM retrieval between the GVSM and Yamaguchi volume scattering models. Given that SM estimation is inherently influenced by crop phenology and empirical parameters which are introduced in the scattering models, we also investigate the influence of surface depolarisation angle and co-pol phase difference on SM estimation. Results show that the proposed retrieval framework provides an inversion accuracy of RMSE<6.0% and a correlation of R≥0.6 with an inversion rate larger than 90%. Over wheat and winter wheat fields, a correlation of 0.8 between SM estimates and measurements is observed when the surface scattering is dominant. Specifically, stem permittivity, which is retrieved synchronously with SM also shows a linear relationship with crop biomass and plant water content over bean, corn, soybean and wheat fields. We also find that a priori knowledge of surface depolarisation angle, co-pol phase difference and adaptive volume scattering could help to improve the performance of the proposed SM retrieval framework. However, the GVSM model is still not fully adaptive because the co-pol power ratio of volume scattering is potentially influenced by ground scattering.This work was supported by the National Natural Science Foundation of China [grant numbers 61971318, 41771377, 41901286, 42071295, 41901284, U2033216]; the China Postdoctoral Science Foundation [grant number 2018M642914]. This work was supported in part by the Spanish Ministry of Science and Innovation, the State Agency of Research (AEI), and the European Funds for Regional Development (EFRD) under Project TEC2017-85244-C2-1-P

On the Use of Generalized Volume Scattering Models for the Improvement of General Polarimetric Model-Based Decomposition

Recently, a general polarimetric model-based decomposition framework was proposed by Chen et al., which addresses several well-known limitations in previous decomposition methods and implements a simultaneous full-parameter inversion by using complete polarimetric information. However, it only employs four typical models to characterize the volume scattering component, which limits the parameter inversion performance. To overcome this issue, this paper presents two general polarimetric model-based decomposition methods by incorporating the generalized volume scattering model (GVSM) or simplified adaptive volume scattering model, (SAVSM) proposed by Antropov et al. and Huang et al., respectively, into the general decomposition framework proposed by Chen et al. By doing so, the final volume coherency matrix structure is selected from a wide range of volume scattering models within a continuous interval according to the data itself without adding unknowns. Moreover, the new approaches rely on one nonlinear optimization stage instead of four as in the previous method proposed by Chen et al. In addition, the parameter inversion procedure adopts the modified algorithm proposed by Xie et al. which leads to higher accuracy and more physically reliable output parameters. A number of Monte Carlo simulations of polarimetric synthetic aperture radar (PolSAR) data are carried out and show that the proposed method with GVSM yields an overall improvement in the final accuracy of estimated parameters and outperforms both the version using SAVSM and the original approach. In addition, C-band Radarsat-2 and L-band AIRSAR fully polarimetric images over the San Francisco region are also used for testing purposes. A detailed comparison and analysis of decomposition results over different land-cover types are conducted. According to this study, the use of general decomposition models leads to a more accurate quantitative retrieval of target parameters. However, there exists a trade-off between parameter accuracy and model complexity which constrains the physical validity of solutions and must be further investigated.This work was supported in part by National Nature Science Foundation of China under Grant 41531068, 41371335, 41671356 and 41274010, the Spanish Ministry of Economy and Competitiveness and EU FEDER under Project TIN2014-55413-C2-2-P, and China Scholarship Council under Grant 201406370079

Application Of Polarimetric SAR For Surface Parameter Inversion And Land Cover Mapping Over Agricultural Areas

In this thesis, novel methodology is developed to extract surface parameters under vegetation cover and to map crop types, from the polarimetric Synthetic Aperture Radar (PolSAR) images over agricultural areas. The extracted surface parameters provide crucial information for monitoring crop growth, nutrient release efficiency, water capacity, and crop production. To estimate surface parameters, it is essential to remove the volume scattering caused by the crop canopy, which makes developing an efficient volume scattering model very critical. In this thesis, a simplified adaptive volume scattering model (SAVSM) is developed to describe the vegetation scattering as crop changes over time through considering the probability density function of the crop orientation. The SAVSM achieved the best performance in fields of wheat, soybean and corn at various growth stages being in convert with the crop phenological development compared with current models that are mostly suitable for forest canopy. To remove the volume scattering component, in this thesis, an adaptive two-component model-based decomposition (ATCD) was developed, in which the surface scattering is a X-Bragg scattering, whereas the volume scattering is the SAVSM. The volumetric soil moisture derived from the ATCD is more consistent with the verifiable ground conditions compared with other model-based decomposition methods with its RMSE improved significantly decreasing from 19 [vol.%] to 7 [vol.%]. However, the estimation by the ATCD is biased when the measured soil moisture is greater than 30 [vol.%]. To overcome this issue, in this thesis, an integrated surface parameter inversion scheme (ISPIS) is proposed, in which a calibrated Integral Equation Model together with the SAVSM is employed. The derived soil moisture and surface roughness are more consistent with verifiable observations with the overall RMSE of 6.12 [vol.%] and 0.48, respectively

Aboveground Biomass Retrieval in Tropical and Boreal Forests Using L-Band Airborne Polarimetric Observations

Forests play a crucial part in regulating global climate change since their aboveground biomass (AGB) relates to the carbon cycle, and its changes affect the main carbon pools. At present, the most suitable available SAR data for wall-to-wall forest AGB estimation are exploiting an L-band polarimetric SAR. However, the saturation issues were reported for AGB estimation using L-band backscatter coefficients. Saturation varies depending on forest structure. Polarimetric information has the capability to identify different aspects of forest structure and therefore shows great potential for reducing saturation issues and improving estimation accuracy. In this study, 121 polarimetric decomposition observations, 10 polarimetric backscatter coefficients and their derived observations, and six texture features were extracted and applied for forest AGB estimation in a tropical forest and a boreal forest. A parametric feature optimization inversion model (Multiple linear stepwise regression, MSLR) and a nonparametric feature optimization inversion model (fast iterative procedure integrated into a K-nearest neighbor nonparameter algorithm, KNNFIFS) were used for polarimetric features optimization and forest AGB inversion. The results demonstrated the great potential of L-band polarimetric features for forest AGB estimation. KNNFIFS performed better both in tropical (R2 = 0.80, RMSE = 22.55 Mg/ha, rRMSE = 14.59%, MA%E = 12.21%) and boreal (R2 = 0.74, RMSE = 19.82 Mg/ha, rRMSE = 20.86%, MA%E = 20.19%) forests. Non-model-based polarimetric features performed better compared to features extracted by backscatter coefficients, model-based decompositions, and texture. Polarimetric observations also revealed site-dependent performances

Estimation de l’humidité du sol en milieu agricole par combinaison des données polarimétriques radar en bande C et des micro-ondes passives en bande L

L’humidité du sol a un rôle majeur dans la régulation des éléments du climat (précipitations, température, H2O atmosphérique) et du cycle de l’eau. Pour étudier l’humidité du sol à l’échelle globale, la télédétection spatiale micro-onde présente un fort potentiel. Dans le cas du satellite Soil Moisture Active Passive (SMAP), les méthodes initialement développées permettaient d’obtenir trois produits d’humidité du sol : actif, passif et actif-passif avec une résolution spatiale fine de 3 km, grossière de 40 km et moyenne de 9 km, respectivement. Cependant, six mois après le lancement du satellite, son radar s’est détérioré, empêchant SMAP de générer des produits d’humidité du sol à fine et moyenne résolution spatiale. Dès lors, des équipes de recherche ont étudié la possibilité de combiner des mesures micro-ondes actives et passives avec des capteurs installés sur des plateformes différentes et opérant à des fréquences différentes. Ce projet propose une approche de combinaison des mesures micro-ondes actives et passives de satellites différents pour estimer l’humidité du sol à 1 km de résolution spatiale sur le site de la campagne terrain SMAPVEX16-MB, situé dans une zone agricole du Manitoba. La méthode est basée sur une désagrégation de la température de brillance (TB) de SMAP, de 40 km à 1 km de résolution spatiale, en utilisant les données polarimétriques en bande C de Radarsat-2 corrigées de l’effet de la végétation (la contribution de surface : Ps), plus sensible à l’humidité du sol. La contribution de surface (Ps) est obtenue en appliquant la décomposition polarimétrique de Freeman-Durden. Le résultat de la désagrégation est une température de brillance à 1 km de résolution spatiale, qui est ensuite utilisée dans l’algorithme du Single Chanel Algorithm pour estimer l’humidité du sol à 1 km de résolution spatiale. En ce qui concerne l’estimation de l’humidité du sol, pour tous les dix champs considérés, nous avons obtenu les meilleurs résultats en utilisant les TBV : coefficients de corrélation de Pearson (R) compris entre 0,42 et 0,86, p-values comprises entre 0,003 et 0,27 et erreurs quadratiques moyennes (RMSE) comprises entre 0,02 m3.m -3 et 0,05 m3.m -3. Lorsque nous utilisons les TBH pour estimer l’humidité du sol, nous obtenons : R compris entre 0,39 et 0,75, p-values comprises entre 0,02 et 0,30 et RMSE comprises entre 0,02 m3.m -3 et 0,15 m3.m -3. Ce projet nous a permis d’implémenter une méthode innovatrice de combinaison de données micro-ondes actives et passives pour l’étude de l’humidité du sol. L’approche proposée utilise les Ps au lieu de σ^0 contrairement à la plupart des méthodes que l’on trouve dans la littérature depuis la détérioration du radar de SMAP.Abstract : Soil moisture plays a major role in the regulation of climate elements (precipitation, temperature, atmospheric H2O) and water balance. To study the soil moisture at a global scale, spaceborne microwave remote sensing has a great potential. In the case of the Soil Moisture Active Passive (SMAP) satellite, the initially developed methods provided three soil moisture products : active, passive and active-passive with a fine spatial resolution of 3 km, coarse 40 km and medium 9 km, respectively. However, six months after the launch of the satellite, its radar failed, preventing SMAP from generating soil moisture products at fine (3 km) and medium (9 km) spatial resolutions. Since then, research teams have studied the possibility of combining active and passive measurements with sensors installed on different platforms and operating at different frequencies. This project proposes a combined approach of active and passive microwave measurements of different satellites to estimate soil moisture at 1 km spatial resolution at the SMAPVEX16-MB field campaign site, located in an agricultural area of Manitoba. The method is based on a disaggregation of the brightness temperature (TB) of SMAP, from 40 km to 1 km spatial resolution, using Radarsat-2 polarimetric C-band data corrected for vegetation effects. These are represented by the surface contribution (Ps), which is more sensitive to soil moisture and extracted by applying the polarimetric decomposition of Freeman-Durden (Freeman and Durden, 1998) to Radarsat-2 data. Regarding the estimation of the soil moisture, for all the ten fields considered, we obtained the best results by using TBV: (Pearson correlation R between 0.42 and 0.86, p-values between 0.003 and 0.27, and root mean square errors (RMSE) between 0.02 m3.m -3 and 0.05 m3.m -3). When TBH was used to estimate soil moisture, the results were less accurate (R between 0.39 and 0.75 p-values between 0.02 and 0.30; and RMSE between 0.02 m3.m -3 and 0.15 m3.m -3). This project allowed us to implement an innovative methodology using Ps instead of 0 in contrast to most of the approaches combining active and passive microwave data for soil moisture estimation, since the failure of the radar onboard SMAP

Developing Parameter Constraints for Radar-based SWE Retrievals

Terrestrial snow is an important freshwater reservoir with significant influence on the climate and energy balance. It exhibits natural spatiotemporal variability which has been enhanced by climate change, thus it is important to monitor on a large scale. Active microwave, or radar remote sensing has shown frequency-dependent promise in this regard, however, interpretation remains a challenge. The aim of this thesis was to develop constraints for radar based SWE retrievals which characterize and limit uncertainty with a focus on the underlying physical processes, snowpack stratigraphy, the influence of vegetation, and effects of background scattering. The University of Waterloo Scatterometer (UWScat) was used to make measurements at 9.6 and 17.2 GHz of snow and bare ground in a series of field-based campaigns in Maryhill and Englehart, ON, Grand Mesa, CO (NASA SnowEx campaign, year 1), and Trail Valley Creek, NT. Additional measurements from Tobermory, ON, and Churchill, MB (Canadian Snow and Ice Experiment) were included. The Microwave Emission Model for Layered Snowpacks, Version 3, adapted for backscattering (MEMLS3&a) was used to explore snowpack parameterization and SWE retrieval and the Freeman-Durden three component decomposition (FD3c) was used to leverage the polarimetric response. Physical processes in the snow accumulation environment demonstrated influence on regional snowpack parameterization and constraints in a SWE retrieval context with a single-layer snowpack parameterization for Maryhill, ON and a two-layer snowpack parameterization for Englehart, ON resulting in a retrieval RMSE of 21.9 mm SWE and 24.6 mm SWE, respectively. Use of in situ snow depths improved RMSE to 12.0 mm SWE and 10.9 mm SWE, while accounting for soil scattering effects further improved RMSE by up to 6.3 mm SWE. At sites with vegetation and ice lenses, RMSE improved from 60.4 mm SWE to 21.1 mm SWE when in situ snow depths were used. These results compare favorably with the common accuracy requirement of RMSE ≤ 30 mm and underscore the importance of understanding the driving physical processes in a snow accumulation environment and the utility of their regional manifestation in a SWE retrieval context. A relationship between wind slab thickness and the double-bounce component of the FD3c in a tundra snowpack was introduced for incidence angles ≥ 46° and wind slab thickness ≥ 19 cm. Estimates of wind slab thickness and SWE resulted in an RMSE of 6.0 cm and 5.5 mm, respectively. The increased double-bounce scattering was associated with path length increase within a growing wind slab layer. Signal attenuation in a sub-canopy SWE retrieval was also explored. The volume scattering component of the FD3c yielded similar performance to forest fraction in the retrieval with several distinct advantages including a real-time description of forest condition, accounting for canopy geometry without ancillary information, and providing coincident information on forest canopy in remote locations. Overall, this work demonstrated how physical processes can manifest regional outcomes, it quantified effects of natural inclusions and background scattering on SWE retrievals, it provided a means to constrain wind slab thickness in a tundra environment, and it improved characterization of coniferous forest in a sub-canopy SWE retrieval context. Future work should focus on identifying ice and vegetation conditions prior to SWE retrieval, testing the spatiotemporal validity of the methods developed herein, and finally, improving the integration of snowpack attenuation within retrieval efforts

Re-evaluating Scattering Mechanisms in Snow-Covered Freshwater Lake Ice Containing Bubbles Using Polarimetric Ground-based and Spaceborne Radar Data

Lakes are a prominent feature of the sub-Arctic and Arctic regions of North America, covering up to 40% of the landscape. Seasonal ice cover on northern lakes afford habitat for several flora and fauna species, and provide drinking water and overwintering fishing areas for local communities. The presence of lake ice influences lake-atmosphere exchanges by modifying the radiative properties of the lake surface and moderating the transfer of heat to the atmosphere. The thermodynamic aspects of lakes exhibit a pronounced effect on weather and regional climate, but are also sensitive to variability in climate forcings such as air temperature and snow fall, acting as proxy indicators of climate variability and change. To refine the understanding of lake-climate interactions, improved methods of monitoring lake ice properties are needed. Manual lake ice monitoring stations have dropped significantly since the 1990s and existing stations are restricted to populated and coastal regions. Recently, studies have indicated the use of radar remote sensing as a viable option for the monitoring of small lakes in remote regions due to its high spatial resolution and imaging capability independent of solar radiation or cloud cover. Active microwave radar in the frequency range of 5 – 10 GHz have successfully retrieved lake ice information pertaining to the physical status of the ice cover and areas that are frozen to bed, but have not been demonstrated as effective for the derivation of on-ice snow depth. In the 10 – 20 GHz range, radar has been shown to be sensitive to terrestrial snow cover, but has not been investigated over lakes. Utilizing a combination of spaceborne and ground-based radar systems spanning a range of 5 – 17 GHz, simulations from the Canadian Lake Ice Model (CLIMo), and ice thickness information from a shallow water ice profiler (SWIP), this research aimed to further our understanding of lake ice scattering sources and mechanisms for small freshwater lakes in the sub-Arctic. Increased comprehension of scattering mechanisms in ice advances the potential for the derivation of lake ice properties, including on-ice snow depth, lake ice thickness and identification of surface ice types. Field observations of snow-covered lake ice were undertaken during the winter seasons of 2009-2010 and 2010-2011 on Malcolm Ramsay Lake, near Churchill Manitoba. In-situ snow and ice observations were coincident with ground-based scatterometer (UW-Scat) and spaceborne synthetic aperture radar (SAR) acquisitions. UW-Scat was comprised of two fully polarimetric frequency modulated continuous wave (FMCW) radars with centre frequencies of 9.6 and 17.2 GHz (X- and Ku-bands, respectively). SAR observations included fine-beam fully polarimetric RADARSAT-2 acquisitions, obtained coincident to UW-Scat observations during 2009-2010. Three experiments were conducted to characterize and evaluate the backscatter signatures from snow-covered freshwater ice coincident to in-situ snow and ice observations. To better understand the winter backscatter (σ°) evolution of snow covered ice, three unique ice cover scenarios were observed and simulated using a bubbled ice σ° model. The range resolution of UW-SCAT provided separation of microwave interaction at the snow/ice interface (P1), and within the ice volume (P2). Ice cores extracted at the end of the observation period indicated that a considerable σ° increase at P2 of approximately 10 – 12 decibels (dB) HH/VV at X- and Ku-band occurred coincident to the timing of tubular bubble development in the ice. Similarly, complexity of the ice surface (high density micro-bubbles and snow ice) resulted in increased P1 σ° at X- and Ku-band at a magnitude of approximately 7 dB. P1 observations also indicated that Ku-band was sensitive to snowpack overlying lake ice, with σ° exhibiting a 5 (6) dB drop for VV (HH) when ~ 60 mm SWE is removed from the scatterometer field of view. Observations indicate that X-band was insensitive to changes in overlying snowpack within the field of view. A bubbled ice σ° model was developed using the dense medium radiative transfer theory under the Quasi-Crystalline Approximation (DMRT-QCA), which treated bubbles as spherical inclusions within the ice volume. Results obtained from the simulations demonstrated the capability of the DMRT model to simulate the overall magnitude of observed σ° using in-situ snow and ice measurements as input. This study improved understanding of microwave interaction with bubble inclusions incorporated at the ice surface or within the volume. The UW-Scat winter time series was then used to derive ice thickness under the assumption of interactions in range occurring at the ice-snow and ice-water interface. Once adjusted for the refractive index of ice and slant range, the distance between peak returns agreed with in-situ ice thickness observations. Ice thicknesses were derived from the distance of peak returns in range acquired in off-nadir incidence angle range 21 - 60°. Derived ice thicknesses were compared to in-situ measurements provided by the SWIP and CLIMo. Median ice thicknesses derived using UW-Scat X- and Ku-band observations agreed well with in-situ measurements (RMSE = 0.053 and 0.045 m), SWIP (RMSE = 0.082 and 0.088 m) and Canadian Lake Ice Model (CLIMo) simulations using 25% of terrestrial snowpack scenario (RMSE = 0.082 and 0.079), respectively. With the launch of fully polarimetric active microwave satellites and upcoming RADARSAT Constellation Mission (RCM), the utility of polarimetric measurements was observed for freshwater bubbled ice to further investigate scattering mechanisms identified by UW-Scat. The 2009-2010 time series of UW-Scat and RADARSAT-2 (C-band) fully polarimetric observations coincident to in-situ snow and ice measurements were acquired to identify the dominant scattering mechanism in bubbled freshwater lake ice. Backscatter time series at all frequencies show increases from the ice-water interface prior to the inclusion of tubular bubbles in the ice column based on in-situ observations, indicating scattering mechanisms independent of double-bounce scatter, contrary to the longstanding hypothesis of double-bounce scatter off tubular bubbles and the ice-water interface. The co-polarized phase difference of interactions at the ice-water interface from both UW-Scat and SAR observations were centred at 0°, indicating a scattering regime other than double bounce. A Yamaguchi three-component decomposition of the time series suggested the dominant scattering mechanism to be single-bounce off the ice-water interface with appreciable surface roughness or preferentially oriented facets. Overall, this work provided new insight into the scattering sources and mechanisms within snow-covered freshwater lake ice containing spherical and tubular bubbles

Advanced techniques for classification of polarimetric synthetic aperture radar data

With various remote sensing technologies to aid Earth Observation, radar-based imaging is one of them gaining major interests due to advances in its imaging techniques in form of syn-thetic aperture radar (SAR) and polarimetry. The majority of radar applications focus on mon-itoring, detecting, and classifying local or global areas of interests to support humans within their efforts of decision-making, analysis, and interpretation of Earth’s environment. This thesis focuses on improving the classification performance and process particularly concerning the application of land use and land cover over polarimetric SAR (PolSAR) data. To achieve this, three contributions are studied related to superior feature description and ad-vanced machine-learning techniques including classifiers, principles, and data exploitation. First, this thesis investigates the application of color features within PolSAR image classi-fication to provide additional discrimination on top of the conventional scattering information and texture features. The color features are extracted over the visual presentation of fully and partially polarimetric SAR data by generation of pseudo color images. Within the experiments, the obtained results demonstrated that with the addition of the considered color features, the achieved classification performances outperformed results with common PolSAR features alone as well as achieved higher classification accuracies compared to the traditional combination of PolSAR and texture features. Second, to address the large-scale learning challenge in PolSAR image classification with the utmost efficiency, this thesis introduces the application of an adaptive and data-driven supervised classification topology called Collective Network of Binary Classifiers, CNBC. This topology incorporates active learning to support human users with the analysis and interpretation of PolSAR data focusing on collections of images, where changes or updates to the existing classifier might be required frequently due to surface, terrain, and object changes as well as certain variations in capturing time and position. Evaluations demonstrated the capabilities of CNBC over an extensive set of experimental results regarding the adaptation and data-driven classification of single as well as collections of PolSAR images. The experimental results verified that the evolutionary classification topology, CNBC, did provide an efficient solution for the problems of scalability and dynamic adaptability allowing both feature space dimensions and the number of terrain classes in PolSAR image collections to vary dynamically. Third, most PolSAR classification problems are undertaken by supervised machine learn-ing, which require manually labeled ground truth data available. To reduce the manual labeling efforts, supervised and unsupervised learning approaches are combined into semi-supervised learning to utilize the huge amount of unlabeled data. The application of semi-supervised learning in this thesis is motivated by ill-posed classification tasks related to the small training size problem. Therefore, this thesis investigates how much ground truth is actually necessary for certain classification problems to achieve satisfactory results in a supervised and semi-supervised learning scenario. To address this, two semi-supervised approaches are proposed by unsupervised extension of the training data and ensemble-based self-training. The evaluations showed that significant speed-ups and improvements in classification performance are achieved. In particular, for a remote sensing application such as PolSAR image classification, it is advantageous to exploit the location-based information from the labeled training data. Each of the developed techniques provides its stand-alone contribution from different viewpoints to improve land use and land cover classification. The introduction of a new fea-ture for better discrimination is independent of the underlying classification algorithms used. The application of the CNBC topology is applicable to various classification problems no matter how the underlying data have been acquired, for example in case of remote sensing data. Moreover, the semi-supervised learning approach tackles the challenge of utilizing the unlabeled data. By combining these techniques for superior feature description and advanced machine-learning techniques exploiting classifier topologies and data, further contributions to polarimetric SAR image classification are made. According to the performance evaluations conducted including visual and numerical assessments, the proposed and investigated tech-niques showed valuable improvements and are able to aid the analysis and interpretation of PolSAR image data. Due to the generic nature of the developed techniques, their applications to other remote sensing data will require only minor adjustments