Solving geoinformatics parametric polynomial systems using the improved Dixon resultant

Improvements in computational and observational technologies in geoinformatics, e.g., the use of laser scanners that produce huge point cloud data sets, or the proliferation of global navigation satellite systems (GNSS) and unmanned aircraft vehicles (UAVs), have brought with them the challenges of handling and processing this “big data”. These call for improvement or development of better processing algorithms. One way to do that is integration of symbolically presolved sub-algorithms to speed up computations. Using examples of interest from real geoinformatic problems, we will discuss the Dixon-EDF resultant as an improved resultant method for the symbolic solution of parametric polynomial systems. We will briefly describe the method itself, then discuss geoinformatics problems arising in minimum distance mapping (MDM), parameter transformations, and pose estimation essential for resection. Dixon-EDF is then compared to older notions of “Dixon resultant”, and to several respected implementations of Gröbner bases algorithms on several systems. The improved algorithm, Dixon-EDF, is found to be greatly superior, usually by orders of magnitude, in both CPU usage and RAM usage. It can solve geoinformatics problems on which the other methods fail, making symbolic solution of parametric systems feasible for many problems

Independent patterns of water mass anomalies over Australia from satellite data and models.

The Gravity Recovery and Climate Experiment (GRACE) products allow the quantification of total water storage (TWS) changes at global to regional scales. However, the quantity measured by GRACE represents mass signals integrated over vertical columns, requiring their separation into their original sources. Such a separation is vital for Australia, for which GRACE estimates are affected by leakage from the surrounding oceans. The independent component analysis (ICA) method that uses higher-order statistics, is implemented here to separate GRACE-derived water storage signals over the Australian continent from its surrounding oceans, covering from October 2002 to May 2011. The performance of ICA applied to GRACE is then compared to the ICA of WaterGAP Global Hydrology Model (WGHM) and the ICA of the Australian Water Resources Assessment (AWRA) system. To study the influence of rainfall variability on the derived independent patterns, use is made of Tropical Rainfall Measuring Mission (TRMM) data set, from January 2000 to May 2011. Implementing ICA on GRACE-TWS showed a remarkable improvement in separating the continental hydrological signals from the surrounding oceanic anomalies, which was not achievable using a conventional principle component analysis. Reconstructing the continental TWS changes using only those independent components of GRACE that were located over the continent showed a high correlation with WGHM-TWS and AWRA-TWS. Mass concentrations over the oceans and particularly S2 semi-diurnal aliased pattern were separated as independent modes.Correlation analysis between the independent components of GRACE and climate teleconnections showed that the mass anomalies over the northern ocean, Gulf of Carpentaria and north-eastern parts of Australia were significantly correlated with the El Niño-Southern Oscillation, while those over south and south-eastern parts of Australia were mainly linked to the Indian Ocean Dipole

The influence of low frequency sea surface temperature modes on delineated decadal rainfall zones in Eastern Africa region

Influence of low frequency global Sea Surface Temperatures (SSTs) modes on decadal rainfall modes over Eastern Africa region is investigated. Fore-knowledge of rainfall distribution at decadal time scale in specific zones is critical for planning purposes. Both rainfall and SST data that covers a period of 1950–2008 were subjected to a ‘low-pass filter’ in order to suppress the high frequency oscillations. VARIMAX-Rotated Principal Component Analysis (RPCA) was employed to delineate the region into decadal rainfall zones while Singular Value Decomposition (SVD) techniques was used to examine potential linkages of these zones to various areas of the tropical global oceans. Ten-year distinct decadal signals, significant at 95% confidence level, are dominant when observed in-situ rainfall time series are subjected to spectral analysis. The presence of variability at El Niño Southern Oscillation (ENSO)-related timescales, combined with influences in the 10–12 year and 16–20 year bands were also prevalent. Nine and seven homogeneous decadal rainfall zones for long rainfall season i.e. March-May (MAM) and the short rainfall season i.e. October-December (OND), respectively, are delineated. The third season of June–August (JJA), which is mainly experienced in western and Coastal sub-regions had eight homogenous zones delineated. The forcing of decadal rainfall in the region is linked to the equatorial central Pacific Ocean, the tropical and South Atlantic Oceans, and the Southwest Indian Ocean. The high variability of these modes highlighted the significant roles of all the global oceans in forcing decadal rainfall variability over the region

Water storage changes and climate variability within the Nile Basin between 2002-2011

Understanding water storage changes within the Nile’s main sub-basins and the related impacts of climate variability is an essential step in managing its water resources. The Gravity Recovery And Climate Experiment (GRACE) satellite mission provides a unique opportunity to monitor changes in total water storage (TWS) of large river basins such as the Nile. Use of GRACE-TWS changes for monitoring the Nile is, however, difficult since stronger TWS signals over the Lake Victoria Basin (LVB) and the Red Sea obscure those from smaller sub-basins making their analysis difficult to undertake. To mitigate this problem, this study employed Independent Component Analysis (ICA) to extract statistically independent TWS patterns over the sub-basins from GRACE and the Global Land Data Assimilation System (GLDAS) model. Monthly precipitation from the Tropical Rainfall Measuring Mission (TRMM) over the entire Nile Basin are also analysed by ICA. Such extraction enables an in-depth analysis of water storage changes within each sub-basin and provides a tool for assessing the influence of anthropogenic as well as climate variability caused by large scale ocean–atmosphere interactions such as the El Niño Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD).Our results indicate that LVB experienced effects of both anthropogenic and climate variability (i.e., a correlation of 0.56 between TWS changes and IOD at 95% confidence level) during the study period 2002–2011, with a sharp drop in rainfall between November and December 2010, the lowest during the entire study period, and coinciding with the drought that affected the Greater Horn of Africa. Ethiopian Highlands (EH) generally exhibited a declining trend in the annual rainfall over the study period, which worsened during 2007–2010, possibly contributing to the 2011 drought over GHA. A correlation of 0.56 was found between ENSO and TWS changes over EH indicating ENSO’s dominant influence. TWS changes over Bar-el-Ghazal experienced mixed increase–decrease, with ENSO being the dominant climate variability in the region during the study period. A remarkable signal is noticed over the Lake Nasser region indicating the possibility of the region losing water not only through evaporation, but also possibly through over extraction from wells in the Western Plateau (Nubian aquifer)

Potential impacts of climate and environmental change on the stored water of Lake Victoria Basin and economic implications

The changing climatic patterns and increasing human population within the Lake Victoria Basin (LVB), together with overexploitation of water for economic activities call for assessment of water management for the entire basin. This study focused on the analysis of a combination of available in situ climate data, Gravity Recovery and Climate Experiment (GRACE), Tropical Rainfall Measuring Mission (TRMM) observations, and high resolution Regional Climate simulations during recent decade(s) to assess the water storage changes within LVB that may be linked to recent climatic variability/changes and anomalies. We employed trend analysis, principal component analysis (PCA), and temporal/spatial correlations to explore the associations and covariability among LVB stored water, rainfall variability, and large-scale forcings associated with El-Niño/Southern Oscillation (ENSO) and Indian Ocean Dipole (IOD). Potential economic impacts of human and climate-induced changes in LVB stored water are also explored.Overall, observed in situ rainfall from lake-shore stations showed a modest increasing trend during the recent decades. The dominant patterns of rainfall data from the TRMM satellite estimates suggest that the spatial and temporal distribution of precipitation have not changed much during the period of 1998–2012 over the basin consistent with in situ observations. However, GRACE-derived water storage changes over LVB indicate an average decline of 38.2 mm/yr for 2003–2006, likely due to the extension of the Owen Fall/Nalubale dam, and an increase of 4.5 mm/yr over 2007–2013, likely due to two massive rainfalls in 2006–2007 and 2010–2011. The temporal correlations between rainfall and ENSO/IOD indices during the study period, based on TRMM and model simulations, suggest significant influence of large-scale forcing on LVB rainfall, and thus stored water. The contributions of ENSO and IOD on the amplitude of TRMM-rainfall and GRACE-derived water storage changes, for the period of 2003–2013, are estimated to be ~2.5 cm and ~1.5 cm, respectively

Quantifying the impacts of ENSO and IOD on rain gauge and remotely sensed precipitation products over Australia

Large-scale ocean-atmospheric phenomena like the El Niño Southern Oscillation (ENSO) and Indian Ocean Dipole (IOD) have significant influence on Australia's precipitation variability. In this study, multi-linear regression (MLR) and complex empirical orthogonal function (CEOF) analyses were applied to isolate (i) the continental precipitation variations likely associated with ENSO and IOD, here referred to as 'ENSO/IOD mode', and (ii) the variability not associated with ENSO/IOD (the 'non-ENSO/IOD mode'). The first is of interest due to its dominant influence on inter-annual variability, while the second may reveal lower frequency variability or trends. Precipitation products used for this study included gridded rainfall estimates derived by interpolation of rain gauge data from the Australian Bureau of Meteorology (BoM), two satellite remote sensing products (CHIRP and TRMM TMPA version 7), and two weather forecast model re-analysis products (ERA-Interim and MERRA). The products covered the period 1981-2014 except TMPA (1998-2014). Statistical and frequency-based inter-comparisons were performed to evaluate the seasonal and long-term skills of various rainfall products against the BoM product. The results indicate that linear trends in rainfall during 1981-2014 were largely attributable to ENSO and IOD. Both intra-annual and seasonal rainfall changes associated with ENSO and IOD increased from 1991 to 2014. Among the continent's 13 major river basins, the greatest precipitation variations associated with ENSO/IOD were found over the Northern and North East Coast, while the smallest contributions were for Tasmania and the South West Coast basins. We also found that although the assessed products show comparable spatial variability of rainfall over Australia, systematic seasonal differences exist that were more pronounced during the ENSO and IOD events

The use of NDVI and its Derivatives for Monitoring Lake Victoria’s Water Level and Drought Conditions

Normalized Difference Vegetation Index (NDVI), which is a measure of vegetation vigour, and lake water levels respond variably to precipitation and its deficiency. For a given lake catchment, NDVI may have the ability to depict localized natural variability in water levels in response to weather patterns. This information may be used to decipher natural from unnatural variations of a given lake’s surface. This study evaluates the potential of using NDVI and its associated derivatives (VCI (vegetation condition index), SVI (standardised vegetation index), AINDVI (annually integrated NDVI), green vegetation function (F g ), and NDVIA (NDVI anomaly)) to depict Lake Victoria’s water levels. Thirty years of monthly mean water levels and a portion of the Global Inventory Modelling and Mapping Studies (GIMMS) AVHRR (Advanced Very High Resolution Radiometer) NDVI datasets were used. Their aggregate data structures and temporal co-variabilities were analysed using GIS/spatial analysis tools. Locally, NDVI was found to be more sensitive to drought (i.e., responded more strongly to reduced precipitation) than to water levels. It showed a good ability to depict water levels one-month in advance, especially in moderate to low precipitation years. SVI and SWL (standardized water levels) used in association with AINDVI and AMWLA (annual mean water levels anomaly) readily identified high precipitation years, which are also when NDVI has a low ability to depict water levels. NDVI also appears to be able to highlight unnatural variations in water levels. We propose an iterative approach for the better use of NDVI, which may be useful in developing an early warning mechanisms for the management of lake Victoria and other Lakes with similar characteristics

Understanding the decline of water storage across the Ramser-Lake Naivasha using satellite-based methods

It has been postulated that Lake Naivasha, Kenya, has experienced a rapid decrease (and fluctuations) in its spatial extent and level between the years 2002 to 2010. Many factors have been advanced to explain this, with horticultural and floricultural activities, as well as climatic change, featuring prominently. This study offers a multi-disciplinary approach based on several different types of space-borne observations to look at the problem bedeviling Lake Naivasha, which is a Ramsar listed wetland of international importance. The data includes: (1) Gravity Recovery and Climate Experiment (GRACE) time-variable gravity field products to derive total water storage (TWS) variations within a region covering the Lakes Naivasha and Victoria basins; (2) precipitation records based on Tropical Rainfall Measurement Mission (TRMM) products to evaluate the impact of climate change; (3) satellite remote sensing (Landsat) images to map shoreline changes and to correlate these changes over time with possible causes; and (4) satellite altimetry observations to assess fluctuations in the lake’s level. In addition, data from an in situ tide gauge and rainfall stations as well as the output from the African Drought Monitor (ADM) model are used to evaluate the results.This study confirms that Lake Naivasha has been steadily declining with the situation being exacerbated from around the year 2000, with water levels falling at a rate of 10.2 cm/year and a shrinkage in area of 1.04 km2/year. GRACE indicates that the catchment area of 4°×4° that includes Lake Naivasha loses water at a rate of 1.6 cm/year for the period from August 2002 to May 2006, and 1.4 cm/year for the longer period of May 2002 to 2010. Examining the ADM outputs also supports our results of GRACE. Between the time periods 2000–2006 and 2006–2010, the lake surface area decreased by 14.43% and 10.85%, respectively, with a corresponding drop in the water level of 192 cm and 138 cm, respectively, over the same periods. Our results show a correlation coefficient value of 0.68 between the quantity of flower production and the lake’s level for the period 2002–2010 at 95% confidence level, indicating the probable impact of anthropogenic activities on the lake’s level drop

Motor Vehicles: Are they emerging threats to Lake Victoria and its environment?

Lake Victoria and its basin supports more than 30 million people, while its fishes are exported the world over. This second largest fresh water body is however experiencing stress due to eutrophication, sedimentation, declining levels and more recently the motor vehicle sector. This contribution examines the general pollution from motor vehicle and gives an in-depth analysis of motor vehicle washing along the lakeshore. The results indicate the water samples from the motor vehicle washing and urban runoff points to be slightly acidic (i.e., average pH of 6.7) and average Total at these points. The conductivity for the motor vehicle washing points averaged at 150 S/cm, while the urban runoffs point was more varied ranging from below 150 S/cm to over 400 S/cm (average 301 S/cm). A positive correlation coefficient of more than 0.7 is obtained between the total daily count of vehicles and each of the water quality parameter tested. This signifies a strong correlation between motor vehicle related activities and the pollution of the lake. In general, the motor vehicle industry is found to have a noticeable negativeeffect on the lake

GNSS remote sensing of the Australian tropopause

Radio occultation (RO) techniques that use signals transmitted by Global Navigation Satellite Systems (GNSS) have emerged over the past decade as an important tool for measuring global changes in tropopause temperature and height, a valuable capacity given the tropopause’s sensitivity to temperature variations. This study uses 45,091 RO data from the CHAMP (CHAllenging Minisatellite Payload, 80 months), GRACE (Gravity Recovery And Climate Experiment, 23 months) and COSMIC (Constellation Observing System for Meteorology, Ionosphere, and Climate, 20 months) satellites to analyse the variability of the tropopause’s height and temperature over Australia. GNSS RO temperature profiles from CHAMP, GRACE, and COSMIC are first validated using radiosonde observations provided by the Bureau of Meteorology (Australia). These are compared to RO soundings from between 2001 and 2007 that occurred within 3 h and 100 km of a radiosonde.The results indicate that RO soundings provide data of a comparable quality to radiosonde observations in the tropopause region, with temperature deviations of less than 0.5 ± 1.5 K. An analysis of tropopause height and temperature anomalies indicates a height increase over Australia as a whole of ca. 4.8 ± 1.3 m between September 2001 and April 2008, with a corresponding temperature decrease of −0.019 ± 0.007 K. A similar pattern of increasing height/decreasing temperature was generally observed when determining the spatial distribution of the tropopause height and temperature rate of change over Australia. Although only a short period has been considered in this study, a function of the operating time of these satellites, the results nonetheless show an increase in the height of the tropopause over Australia during this period and thus may indicate regional warming. Several mechanisms could be responsible for these changes, such as an increase in the concentration of greenhouse gases in the atmosphere, and lower stratospheric cooling due to ozone loss, both of which have been observed during the last decades