This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

Nitrate-N (

Globally, more than 1.5 billion people rely on groundwater as their primary source of drinking water [

The long-term behavior of nitrate-N in groundwater shows variability in space and time. The spatio-temporal variability of nitrate-N in groundwater is influenced by the interaction among multiple geophysical factors, such as source availability, precipitation pattern, thickness and composition of the vadose zone [

There are several approaches to quantify the trends and persistence of a system variable (e.g., nitrate-N) across spatio-temporal scales. For instance, Assaf and Saadeh [

As a result, we have developed an entropy-based approach jointly with the Hurst exponent to explore the trends and persistence of nitrate-N in groundwater to inform and develop optimal groundwater sampling and remediation strategies, in two different hydrogeologic settings: the Ogallala and Trinity Aquifers in Texas. The specific objectives of this study are to (1) analyze the persistence of nitrate-N contamination and examine decadal variability in nitrate-N at three spatial scales (fine, intermediate and coarse) in the Ogallala and Trinity Aquifers and (2) develop and present a new metric for identifying hot spots of nitrate (

To analyze the trends and persistence of nitrate-N in groundwater, we utilized the entropy theory and the Hurst exponent. We further developed an index that quantifies the distribution of hot spots (>10 mg/L of

For a variable with a probability density function (PDF),

The function

We define a new index, the “normalized risk index” (

The range of

Harold E. Hurst was a British hydrologist, who first used the range analysis of time series data in hydrology. He analyzed the time series for trends and persistence by dividing the time series into shorter sub-time series and rescaling ranges of each sub-time series [

There are various methods (such as rescaled range, regression on periodogram, Whittle estimator, aggregated variances) to estimate the Hurst coefficient in the literature [

Compute the mean

Detrend the series by subtracting mean

Calculate the summation of all detrended series

Rescale the range, by dividing the range by the standard deviation.

Calculate the mean of the rescaled range for all sub-series of length

Finally, the value of the Hurst exponent is obtained using an ordinary least square regression with

We conducted this study in two different hydro-geologic settings: (1) the Ogallala Aquifer, which is an unconfined aquifer and a principal source of water for agricultural, municipal and industrial development; and (2) the Trinity Aquifer, which is partially confined and a principal source of water in four densely inhabited urban centers: San Antonio, Austin, Fort Worth and Dallas metropolitan areas in Texas. Previous studies (such as [

The Ogallala Aquifer is the largest groundwater system in North America. The Ogallala Aquifer spreads across eight states: South Dakota, Nebraska, Wyoming, Colorado, Kansas, Oklahoma, New Mexico and Texas [

The Trinity Group Aquifer is a prime water-bearing entity in north-central, central and southwest-central Texas, extends over more than 106,190 km

Map showing the Ogallala Aquifer (

The nitrate-N data were obtained from the Texas Water Development Board [

The Trinity and Ogallala Aquifers are two contrasting hydrogeologic settings, as shown in (

The nitrate-N concentrations (1940 to 2008) are shown in the (

The Hurst exponent (

Probability distribution functions (PDFs) of the Hurst exponent of nitrate-N in the (

In the Ogallala Aquifer, PDFs show that

Further analysis of

For understanding the temporal variability of nitrate-N over different decades, an inter-decadal variation of nitrate-N was analyzed (

In the Ogallala Aquifer, overall decadal mean nitrate-N has increased at all scales from 1940 to 1970, which may be because of a higher use of fertilizers to improve agricultural productivity since the 1940s. After 1970, overall mean nitrate-N has decreased at both fine and coarse scales (

Decadal analysis of the mean and standard deviation (SD) for nitrate-N in the Trinity Aquifer across (

Decadal analysis of normalized marginal entropy (

The normalized risk index (

Normalized risk index (

Aquifers | Grid | Normalized Risk Index (%) |
---|---|---|

Ogallala | Fine | 67.8 |

Intermediate | 64.2 | |

Coarse | 39.1 | |

Trinity | Fine | 75.3 |

Intermediate | 61.3 | |

Coarse | 40.9 |

Results show that a larger number of hot spots of nitrate-N contamination exist at the fine scale as compared to intermediate or coarse scales. Thus, at the fine scale (particularly around the transitional zones), automated sampling that helps to provide data at a smaller interval should be used to monitor nitrate-N contamination in groundwater. Furthermore, trends of nitrate-N in groundwater are more persistent at intermediate and coarse scales. This result suggests that a few sampling sites at a relatively larger interval will be needed at these scales to monitor groundwater quality. In other words, these results can, therefore, be used to design metrics for optimal groundwater monitoring, management and remediation strategies for nitrate-N. An example of such an application is provided below.

In this section, an example of a practical field application of the proposed entropy approach is presented. Although this example is focused on designing sampling strategies for nitrate contamination in groundwater, the following approach is generic enough in nature for designing the optimal sampling strategy to track groundwater quality. The first step in any monitoring well network design requires collecting preliminary data on potential sites or hot spots of nitrate in aquifers. Various approaches have been suggested in the literature for identifying strategic locations for monitoring groundwater. For example, Al-Zabet [

The second step in designing the optimal sampling strategy is to determine sampling frequency for various contaminants. Because data collection, processing and analysis can be expensive, it is desirable that the sampling frequency be cost effective. There are various criteria, such as land use change and groundwater fluctuations, that are used to determine sampling frequency for monitoring. However, it is essential to find redundancies in observations and to outline the sampling frequency without losing any significant information. To test the redundancy in the sampling frequency, we computed

Change in normalized marginal entropy (

Aquifers | Sampling Strategy | |
---|---|---|

Ogallala | Base case | 89.3 |

Removing one alternate sample | 89.3 | |

Removing two alternate samples | 63.8 | |

Removing 10% (randomly) | 88.7 | |

Removing 20% (randomly) | 88.7 | |

Removing 50% (randomly) | 85.2 | |

Removing 75% (randomly) | 60.0 | |

Trinity | Base case | 92.4 |

Removing one alternate sample | 92.2 | |

Removing two alternate samples | 91.9 | |

Removing 10% (randomly) | 91.7 | |

Removing 20% (randomly) | 91.7 | |

Removing 50% (randomly) | 91.9 | |

Removing 75% (randomly) | 90.4 |

Nitrate contamination in groundwater shows multi-scalar variability in space and time. However, a systematic approach to characterize the spatio-temporal variability of nitrate in groundwater has been lacking. This study uses entropy theory and the Hurst exponent to identify the trends and persistence of nitrate-N at different spatial scales (fine, intermediate and coarse) in the Trinity and Ogallala Aquifers of Texas.

Results suggest that nitrate-N in groundwater shows a scale phenomenon in both space and time. The trends of nitrate-N variability show long-term persistence at the intermediate and coarse scales. At the fine scale, there is a fluctuation in the trends of nitrate-N, especially in the transitional areas, where the interaction between rivers and aquifer is prominent, or in the zones that are characterized by the presence of local flow systems. Furthermore, agricultural lands are more prone to nitrate-N contamination than urban areas due to the application of fertilizers. Furthermore, outcrop or unconfined aquifers become more susceptible to contamination of nitrate-N if inorganic sources of nitrate-N (e.g., fertilizers) are present.

This study also highlights how entropy techniques and the Hurst exponent can be used to design decision-making tools for water quality monitoring and management. An improved monitoring of nitrate-N contamination of groundwater can be achieved by having densely-located sampling sites and collecting samples at smaller time intervals in transitional areas, such as the river-aquifer interface. In contrast, at intermediate and coarse scales, sparsely-located sampling sites that collect nitrate-N samples at larger time intervals are adequate. Furthermore, we presented an example application for designing monitoring strategies for nitrate in groundwater. The example demonstrated how the entropy-based approach along with the Hurst exponent can be used to identify strategic sampling locations and outline cost-effective sampling frequency by capturing the characteristic distribution of nitrate in groundwater, without losing any significant information. Although we applied the entropy technique and the Hurst exponent to understand the multi-scalar behavior of nitrate-N in groundwater, this approach should readily be transferable to other contaminated aquifers and catchments.

This research was supported by the EPA 319(h) grant for Total Maximum Daily Load (TMDL) in Texas streams and partly supported by the National Institute of Environmental Health Sciences (Grant 5R01ES015634), the Texas Water Resources Institute and Texas A&M support account number 02130003. The content is solely the responsibility of the authors and does not necessarily represent the official views of the funding agencies.

Dipankar Dwivedi did this work as part of his PhD dissertation, and Binayak P. Mohanty provided guidance. Both authors have read and approved the final manuscript.

The authors declare no conflict of interest.