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We explore two questions about integral domains of the form Z [ d ] = { a + b d | a , b ∈ Z } , where d ≠ 1 is square-free, meaning not divisible by the square of a prime. 1. Is there a reasonable ...

Eutrophication is a severe environmental problem in the most inland lakes. Taihu Lake, the third largest freshwater lake in China, is one of the most eutrophic lakes. Increased phosphorus concentra...

Particle size distribution (PSD) is an important characterization parameter of the particle size structure of suspended particles, which is vulnerable to human activities such as sand dredging. In this study, sand dredging numbers were evaluated by the accumulated radiance algorithm using the night-time light composite data of the visible infrared imaging radiometer suite, and the PSD slope was derived by band ratio algorithm of Landsat-8/operational land imager (OLI) imagery. Then, the influence of sand mining on PSD slope was analyzed. We draw several crucial findings. First, the ratio of ${\boldsymbol{R}_{{{\bf rs}}({{{\bf Red}}})}}$ to ${\boldsymbol{R}_{{{\bf rs}}({{{\bf Green}}})}}$ based on OLI imagery was capable of retrieving PSD slope with good robustness ( R 2 = 0.71, p n = 41) and verified acceptance (mean absolute percentage error = 4.29%, root mean square error = 0.19, n = 20), and the PSD slope in HZL was lower in summer than in the other seasons from 2014 to 2017. Second, The night active vessels extracted from the night-time images show that sand dredging activities began at the outlet of Chengzi Lake (CZL) in April 2012, spread to the whole lake between 2014 and 2016, and then stopped in the northeast region in March 2017 due to the strict control of the local government. Third, the PSD slope is strongly influenced by sand mining, which is positively correlated with the number of sand dredgers ( R 2 = 0.92), i.e., the PSD slope increases 0.21 per 100 working sand dredgers in CZL.

Tracking the spatiotemporal dynamics of particulate phosphorus concentration (C

The chlorophyll-a (Chl-a) concentration of eutrophic lakes fluctuates significantly due to the disturbance of wind and anthropogenic activities on the water body. Consequently, estimation of the Chl-a concentration has become an immense challenge. Due to urgent demand and rapid development in high-resolution earth observation systems, it has become crucial to assess hyperspectral satellite imagery capabilities on inland water monitoring. The Orbita hyperspectral (OHS) satellite is the latest hyperspectral sensor with both high spectral and spatial resolution (2.5 nm and 10 m, respectively), which could provide great potential for remotely estimating the concentration of Chl-a for inland waters. However, there are still some deficiencies that are mainly manifested in the Chl-a concentration remote sensing retrieval model assessment and accuracy validation, as well as signal-to-noise ratio (SNR) estimation of OHS imagery for inland waters. Therefore, the radiometric performance of OHS imagery for water quality monitoring is evaluated in this study by comparing different atmospheric correction models and the SNR with several remote sensing images. Several crucial findings can be drawn: (1) the three-band model ((1/B15-1/B17)B19) developed by OHS imagery is most suitable for estimating the Chl-a concentration in Dianchi Lake, with the root-mean-square error (RMSE) and the mean absolute percentage error (MAPE) of 15.55 µg/L and 16.31%, respectively; (2) the applicability of the FLAASH (Fast Line-of-sight Atmospheric Analysis of Spectral Hypercubes) atmospheric correction model for OHS imagery in a eutrophic plateau lake (Dianchi Lake) was better than the 6S (Second Simulation of Satellite Signal in the Solar Spectrum) model, and QUAC (Quick Atmospheric Correction) model, as well as the dark pixel method; (3) the SNR of the OHS imagery was similar to that of Hyperion imagery and was significantly higher than SNR of the HSI imagery; (4) the spatial resolution showed slight influence on the SNR of the OHS imagery. The results show that OHS imagery could be applied to remote sensing retrieval of Chl-a in eutrophic plateau lakes and presents a new tool for dynamic hyperspectral monitoring of water quality.

Particulate organic matter (POM) plays an important role in biological pumping as a source of energy and nutrients in aquatic systems, as well as being the mechanism for algal bloom formation. However, research on its sources and composition, particularly the research on the contribution of algae in the bloom season, is still insufficient. In this study, the sources and composition of the POM in the surface water of Lake Taihu during the algal bloom season were quantitatively analysed. Dual stable carbon (δ13C) and nitrogen (δ15N) isotopes revealed that the algae were not the only sources of POM during algal blooms, and their contributions were inconsistent in the different lake regions. On average, algae made up 57.2% of the POM in Lake Taihu. Due to wind farms and nutrient runoff, algal POM was mainly concentrated in Meiliang Bay, Gonghu Bay and Central Taihu. The proportions of algal POM in the western estuary area and East Taihu were the smallest with a minimum of 10.8%. The proportion of terrestrial POM in the surface water and vertical sections was 18.3% and 40.0%, respectively. Furthermore, the highest value was 76.8%, which accounted for a large proportion in the algal bloom season. The terrestrial POM that came from rivers was mainly concentrated in the western part of Lake Taihu, while the resuspension of sediments also increased the proportion of terrestrial sources in the surface water. Affected by the distribution of the vegetation in Lake Taihu, the proportion of macrophyte POM in East Taihu was higher than that of algal sources. Although the contribution of endogenous POM might further increase due to the dual effects of climate change and eutrophication, our isotopic evidence suggested that terrestrial POM cannot be ignored, even in the algal bloom season.

Terrestrial humic-like substances (Peak C), the main constituent of chromophoric dissolved organic matter (CDOM), which is one of the optically active constituents present in water, is a good indicator of the ecological statuses of global aquatic ecosystems. In this study, the optical relationship between the absorption spectrum and the fluorescence spectrum of CDOM were investigated in a total of 168 samples collected from Lakes Taihu and Chaohu, and four components of the fluorescence spectrum were identified. There are significant positive correlations between the component arising from Peak C and the specific ultraviolet absorbance at 254 nm (SUVA), and the absorption coefficient of CDOM at 443 nm (a(443)), whereas the correlation between this component and the ratio of two absorption coefficients of CDOM (M) is negative. In addition, total nitrogen (TN), total phosphorus (TP), chlorophyll a and dissolved organic carbon (DOC) were shown to increase significantly with the increase in Peak C, highlighting the importance of the Peak C affecting the water quality in inland lakes. An optical algorithm was developed, which can be used to estimate the fluorescence intensity of Peak C based on R r s (B6) and R r s (B11) of the Ocean and Land Color Instrument (OLCI); the validation dataset showed that the mean absolute percentage error (MAPE) is 28% and the root mean square error (RMSE) is 0.13 QSU. This algorithm was successfully applied to OLCI images and used to analyze the distribution of Peak C in Lake Taihu. The resulting map indicated that the fluorescence intensity of Peak C was significantly higher near the lake entrance than in East Taihu, and the terrestrial input in the estuary area in the west is marked larger than other regions in Taihu Lake.

High-frequency and reliable data on cyanobacteria blooming over a long time period is crucial to identify the outbreak mechanism of blooms and to forecast future trends. However, in cloudy and rainy areas, it is difficult to retrieve useful satellite images, especially in the rainy season. To address this problem, we used data from the HJ-1/CCD (Chinese environment and disaster monitoring and forecasting satellite/charge coupled device), GF-1/WFV (Chinese high-resolution satellite/wide field of view), and Landsat-8/OLI (Operational Land Imager) satellites to generate a time series of the bloom area from 2009 to 2016 in Dianchi Lake, China. We then correlated the responses of bloom dynamics to meteorological factors. Several findings can be drawn: (1) a higher bloom frequency and a larger bloom area occurred in 2011, 2013, and 2016, compared to the other years; (2) the frequency of blooms peaked in April, August, and November each year and expanded from north to south starting in July; (3) air temperature in spring and sunshine hours in summer greatly correlated to the yearly bloom area; (4) wind speed and sunshine hours strongly affected the short-term expansion of blooms and thereafter influenced the monthly bloom scale; and (5) rainfall had a strong short-term influence on the occurrence of blooms. Cyanobacteria blooms often occurred when wind speeds were less than 2.35 ± 0.78 m/s in the dry season and 2.01 ± 0.75 m/s in the rainy season, when there were 48 to 72 h of sunshine in the dry season and 35 to 57 h of sunshine in the rainy season, and when there was more than 10 mm of daily precipitation.

In remote sensing analyses of water colour, suspended particle size is an important optical parameter that also plays an important role in inland and coastal biogeochemical processes. Knowledge of ...

Total phosphorus (TP) is an important factor of eutrophication. The accurate monitoring of TP concentration is conducive to the management of water environments. To improve the accuracy of TP remote sensing inversion, this paper improved and studied the following three aspects. First, a new optical classification method was constructed to classify water into two different types. Compared with other classification methods, the proposed method can be more effective for improving the accuracy of TP inversion. Second, data regression analysis and fitting (DRF), back propagation neural network (BP) and random forest (RF) were used to build TP inversion models based on the different water type. The validation results indicated that the DRF performed best, with the highest precision for all water types, and was suitable for TP inversion. Finally, the performance of the classification and inversion algorithms on Sentinel-3 data was evaluated and one image was acquired for mapping the TP concentration in Taihu Lake. All in all, this study improves the accuracy of TP inversion by combining the new classification algorithm with DRF. This is significant for the development of class-based water quality parameter inversion algorithms for water color remote sensing, and this approach can be applied in the effective management and control of the eutrophication of lake environments.

The Secchi disk depth (ZSD) plays a critical role in describing water clarity. Several studies have shown linkages between Three Gorges Dam (TGD) and the downstream lacustrine ecosystem in the middle and lower Yangtze River basin. However, the potential influence on the ZSD fluctuation in the entire anthropogenic reservoirs of Three Gorges (ER) and Dongting Lake (DTL) has not been reported, possibly due to technical obstacles in obtaining statistically significant spatial and temporal results. We addressed this challenge by using remote sensing technology: the Landsat 8 Operational Land Imager (OLI). We proposed a new, robust remote-sensing algorithm to estimate ZSD from OLI imagery using red and green band-ratio, leading to MAPE of 21.68% and RMSE of 0.076m for ZSD ranging from 0.1m to 1.05m. After satisfactory image-based validation, the algorithm was implemented on OLI data to derive ZSD patterns over ER and DTL from 2013 to 2017. Several crucial findings can be drawn: 1) Spatial-temporal patterns of ZSD exhibited notable fluctuations over both ER and DTL, and they also demonstrated a significant correlation with each other because of the opposite temporal cycle of ZSD fluctuations between ER and DTL; 2) Temporally, monthly fluctuations of ZSD between ER and DTL had opposite temporal cycles, which was mainly attributed to the surface runoff and sediment discharge driven by the outbound runoff variations of TGD. Spatially, the heterogeneity of the ZSD pattern in ER might have resulted from the different geographical regions being divided by large anthropologic hydrological facilities, such as TGD; 3) The relationship between ZSD and total suspended matter (TSM) showed a significant negative correlation, as did the relationship between ZSD and Kd(490). These findings demonstrate that TSM often plays a principal role in light attenuation of extremely turbid inland waters; 4) An inversed phenomenon of water clarity was observed at the intersection of DTL and the Yangtze River around Chenglingji site (YRAC), which was due to the opposite temporal cycle of ZSD fluctuations between DTL and ER after the impoundment of TGD; and 5) Owing to the analysis of noise-equivalent ZSD, OLI data can be used to derive ZSD, since the imagery uncertainty is 0.07m by means of our band-ratio algorithm, which demonstrates similar results to MODIS. The proposed ZSD-derived algorithm in this study could be suitable for other turbid lakes or reservoirs to formulate related strategies of water quality management in the middle and lower Yangtze River basin, and the unveiled findings here improve our understanding of ZSD spatiotemporal fluctuations in large river-connected lakes, such as Poyang Lake.

Bloom occurrence probability prediction is a critical issue for freshwater resource management and protection. As the mechanism of algal blooms is not understood, the construction of prediction model mainly depends on statistical data. Therefore, knowledge on prior bloom occurrence derived from statistical data plays a significant role in establishing a prediction model. In this study, a naive Bayesian model incorporating prior information was constructed to predict algal bloom occurrence probabilities 1–7 days in advance under different weather conditions in Dianchi Lake. The proposed model utilised the following data from the MODIS images, the floating algae index (FAI) for the previous 7 days and five meteorological variables (mean wind speed, air pressure, relative humidity on the prediction day, accumulated sunshine hours in the previous 3 days, and accumulated air temperature in the previous 7 days). The prior probabilities of each pixel were calculated on a monthly timescale to highlight the bloom’s temporal-spatial differences, and the 1–7 day posterior probabilities were calculated by combining the prior and conditional probabilities. The predictive effect was tested by the area under the receiver-operating characteristic curve (AUC), and the results showed the number of pixels with estimation predictions classified as ‘Good+’ and ‘Excellent’ were 91.3%, 91.4%, 82.7%, 83.3%, 89.0%, 86.6%, and 90.0% for the predictions on days 1–7, respectively. Additionally, the independent validation datasets showed that the percentage of correctly classified instances (CCI%) of approximately 90% of the pixels were greater than 50%. The proposed algal bloom prediction model based on the naive Bayesian method has pixel-level prediction abilities, is applicable to other inland water systems, and can provide a reference for water environment risk forecasting and management.

Knowledge of tempo-spatial dynamics of water quality and its response to river flow is important for the management of lake water quality because river discharge associated with rainstorms can be an important source of pollutants to the estuary. Total phosphorus (TP), chlorophyll a (Chl-a), and total suspended matter (TSM) are important indexes of water quality and important factors influencing eutrophication and algal blooms. In this study, remote sensing was used to monitor these indexes to investigate the effects of river discharge on the estuary of Taihu Lake by the largest inflow river which is Chendong River using a total of 136 Geostationary Ocean Color Images (GOCI). In situ datasets collected during the four cruise experiments on Taihu Lake between 2011 and 2015 were used to develop the TP, Chl-a, and TSM inversion models based on simple empirical algorithms: 154 points for TP (mg/L), 114 for Chl-a (μg/L), and 181 for TSM (mg/L). The spatial and temporal changes of the concentration of the three parameters in the Chendong River estuary were analyzed by combining the GOCI data, the flow of the Chendong River, and meteorological data throughout the year in 2014. The several key findings are as follows: (1) In summer and autumn, TP, Chl-a, and TSM contents were significantly higher than in winter and spring. TP and Chl-a have a few similar distribution characteristics. And organic suspended matter in summer was the main reason for the increase of the TSM concentration. (2) The severe surface erosion in the rivers cannot be ignored; the high erodibility is an important factor in the increase of TP and TSM concentrations in the estuary. The concentration of the water quality parameter showed exponential decay with distance from the shore. The concentration decreased slowly after 12 km and then remained essentially constant. (3) TP content in the Chendong River estuary decreased under steady flow inputs and dramatically increased when the flow became large. The increase in Chl-a content was linked to higher levels of TP and good weather conditions after the rain event. Higher flow rates mainly play a dilution role for the Chl-a concentration. Erosion of the surface soil via rainfall is a major source of TSM to the estuary. This paper firstly analyzes tempo-spatial dynamics of water quality and its response to river flow in estuary of Taihu Lake, helps to further understand the impact of river input on lake water quality, and is important for lake eutrophication.

There are a few studies working on the vertical distribution of TSM, however, understanding the underwater profile of TSM is of great benefit to the study of biogeochemical processes in the water column that still require further research. In this study, three data-gathering expeditions were conducted in Lake Hongze (HZL), China, between 2016 and 2018. Based on the in situ optical and biological data, a multivariate linear stepwise regression method was applied for retrieval of the surface horizontal distribution of TSM (TSM0.2) using GOCI (Geostationary Ocean Color Imager) data. Then, the estimation model of vertical structure of underwater TSM was constructed using layer-by-layer recursion. This study drew several crucial findings: (1) the approach proposed in this paper generated very high goodness of fit results, with determination coefficients (R2) of 0.83 (p

Land target-based atmospheric correction methods over inland waters are an effective alternative method for when the standard or improved atmospheric correction method that is based on water is invalid. The type of aerosol model that is selected and land dark target that is distinguished are two key factors that could determine the atmospheric correction’s accuracy. We present an improved land target-based iterative method [denoted as dense dark vegetation (DDV)-WC] for the atmospheric correction of Moderate Resolution Imaging Spectroradiometer (MODIS) over Lake Taihu. The improvements include the use of aerosol models in Optical Properties of Aerosols and Clouds (OPAC), which fully consider the impact of relative humidity (RH) on aerosol properties, and a rigorous land dark target selection rule (DDV-WC-Selection). The DDV-WC algorithm includes three steps: the selection of DDV pixels from lakeshore areas, the retrieval of the aerosol optical thickness (AOT) at 550 nm ( $AO{T_{550}}$ ) for the selected DDV pixels, and the retrieval of the remote sensing reflectance ( ${R_{rs}}$ ) over water. The $AO{T_{550}}$ inversion accuracy of different aerosol models in OPAC is tested in Lake Taihu. The “continental clean model” has the best performance compared with five other aerosol models for every month of the year. Therefore, the aerosol model of the DDV-WC algorithm is fixed to the “continental clean model” in Lake Taihu because of its stable and excellent performance. When using the “continental clean model” to perform these retrievals, the DDV pixels selection (DDV-WC-Selection) in the DDV-WC method ( ${\text {MRE}}({\text {Mean}}\;{\text {Relative}}\;{\text {Error}}) = {14}.{63}\% $ ) is more reliable than the DDV pixels selection (DDV-Selection) in the MODIS V5.2 method ( ${\text {MRE}} = {17}.{24}\% $ ). The atmospheric correction of MODIS indicates that this approach produces superior performance in the green and red bands but poor results in the near-infrared (NIR) and blue bands. The MRE is only 13.15% at 645 nm. These findings illustrate that the DDV-WC algorithm is a practical MODIS atmospheric correction method for inland turbid waters.

The diffuse attenuation coefficient Kd(λ) is an important optical parameter that can be determined remotely. It plays a meaningful role in inland and coastal biogeochemical processes and aids in determining water quality. Four data-gathering expeditions were conducted in Lake Hongze (HZL), China, between 2015 and 2017. Based on the in situ optical and biological data, we constructed and evaluated a band ratio model for retrieving Kd(490) of HZL from MODIS/Aqua images between 2002 and 2016. Our results are as follows: (1) The developed algorithm, using the visible bands (Rrs(red)/Rrs(green)), performs robustly for Kd(490) estimation, with R2 of 0.82 and p

Atmospheric correction is an essential prerequisite for obtaining accurate inland water color information. An inland water atmospheric correction algorithm, ACbTC (Atmospheric Correction based on Turbidity Classification), was proposed in this study by using OLCI (Ocean and Land Color Instrument) and SLSTR (Sea and Land Surface Temperature Radiometer) synergistic observations for the first time. This method includes two main steps: (1) water turbidity classification by the GRA index (GRAdient of the spectrum index); and (2) atmospheric correction by synergistic use of OLCI and SLSTR images. The algorithm was validated with 72 in situ sampling sites in Lake Erhai, Lake Hongze, and Lake Taihu, and compared with other atmospheric correction methods, i.e., C2RCC (Case 2 Regional Coast Colour processor), MUMM (Management Unit of the North Seas Mathematical Models), FLAASH (Fast Line-of-sight Atmospheric Analysis of Hypercubes), POLYMER (POLYnomial based algorithm applied to MERIS), and BPAC (Bright Pixel Atmospheric Correction). The results show that (1) the GRA index performed better than the proposed turbidity classification indices, i.e., the Diff (spectral difference index) and the Tind (turbid index), in inland lakes by using the reflectance peak at 1020 nm in clean water; (2) the synergistic use of OLCI and SLSTR performed feasibly for atmospheric correction, and the ACbTC algorithm achieved full-band average values of the mean absolute percentage error (MAPE) = 29.55%, mean relative percentage error (MRPE) = 13.98%, and the root mean square of error (RMSE) = 0.0039 sr−1, which were more reliable than C2RCC, MUMM, FLAASH, POLYMER, and BPAC; and (3) the synergistic use of the 17th band (865 nm) on OLCI and the 5th band (1613 nm) on SLSTR are suitable for clean inland lakes, while both the 5th band (1613 nm) and 6th band (2250 nm) on SLSTR are advisable for the turbidity.

Although remote sensing technology has been widely used to monitor inland water bodies; the lack of suitable data with high spatial and spectral resolution has severely obstructed its practical development. The objective of this study is to improve the unmixing-based fusion (UBF) method to produce fused images that maintain both spectral and spatial information from the original images. Images from Environmental Satellite 1 (HJ1) and Medium Resolution Imaging Spectrometer (MERIS) were used in this study to validate the method. An improved UBF (IUBF) algorithm is established by selecting a proper HJ1-CCD image band for each MERIS band and thereafter applying an unsupervised classification method in each sliding window. Viewing in the visual sense—the radiance and the spectrum—the results show that the improved method effectively yields images with the spatial resolution of the HJ1-CCD image and the spectrum resolution of the MERIS image. When validated using two datasets; the ERGAS index (Relative Dimensionless Global Error) indicates that IUBF is more robust than UBF. Finally, the fused data were applied to evaluate the chlorophyll a concentrations (Cchla) in Taihu Lake. The result shows that the Cchla map obtained by IUBF fusion captures more detailed information than that of MERIS.

The diffuse attenuation coefficient, Kd(λ), is an important optical property. Environmental change and anthropogenic activities, however, have made it challenging to accurately assess Kd(λ) patterns in the extremely turbid inland waters. We addressed this challenge by using new Landsat 8 Operational Land Imager (OLI) imagery. For the bio-optical complexity of water, we proposed an empirical band-ratio algorithm for estimating Kd(490) using our in situ measurements. Based on the acceptable performance of an OLI image-based atmospheric correction and Kd(490) validation, the algorithm was then applied to OLI images to estimate Kd(490) patterns from April 2013 to April 2016, leading to several key findings: (1) Spatial-temporal patterns of Kd(490) varied significantly in Dongting Lake. The temporal heterogeneity of Kd(490) could be explained primarily by surface-runoff changes driven by regional precipitation. The spatial heterogeneity was due to sediment resuspension, resulting from sand dredging and shipping activities; (2) Kd(490) values that were inversed at the intersection of Dongting Lake and Yangtze River were observed for the first time near the Chengliji site and resulted from the opposing temporal cycle of Kd(490) variations between Dongting Lake and the Yangtze River; (3) There was a significant positive correlation between Kd(490) and total suspended matter (TSM). This confirms that TSM often plays a principal role in the attenuation of light in extremely turbid water bodies; (4) The empirical band-ratio algorithm worked well, not only for the broader Landsat archives, but also for the narrower Sentinel-2/3 for Kd(490) estimation, which demonstrates that the algorithm could be used to quantitatively monitor multi-decade records of Landsat observations and future applications of inland water quality in turbid inland waters, such as Dongting Lake and Poyang Lake.

Assessing the impacts of environmental change and anthropogenic activities on the historical and current total suspended matter (TSM) pattern in Dongting Lake, China, is a large challenge. We addressed this challenge by using more than three decades of Landsat data. Based on in situ measurements, we developed an algorithm based on the near-infrared (NIR) band to estimate TSM in Dongting Lake. The algorithm was applied to Landsat images to derive TSM distribution maps from 1978 to 2013 in the wet season, revealing significant inter-annual and spatial variability. The relationship of TSM to water level, precipitation, and wind speed was analyzed, and we found that: (1) sand mining areas usually coincide with regions that have high TSM levels in Dongting Lake; (2) water level and seven-day precipitation were both important to TSM variation, but no significant relationship was found between TSM and wind speed or other meteorological data; (3) the increased level of sand mining in response to rapid economic growth has deeply influenced the TSM pattern since 2000 due to the resuspension of sediment; and (4) TSM variation might be associated with policy changes regarding the management of sand mining; it might also be affected by lower water levels caused by the impoundment of the Three Gorges Dam since 2000.