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Predictions Within and Across Aquatic Systems using Statistical Methods and Models
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, LUVAL. (Miljöanalys)
2015 (English)Doctoral thesis, comprehensive summary (Other academic)Alternative title
Prediktioner inom och mellan akvatiska system med statistiska metoder och modeller (Swedish)
Abstract [en]

Aquatic ecosystems are an essential source for life and, in many regions, are exploited to a degree which deteriorates their ecological status. Today, more than 50 % of the European lakes suffer from an ecological status which is unsatisfactory. Many of these lakes require abatement actions to improve their status, and mathematical models have a great potential to predict and evaluate different abatement actions and their outcome. Several statistical methods and models exist which can be used for these purposes; however, many of the models are not constructed using a sufficient amount or quality of data, are too complex to be used by most managers, or are too site specific. Therefore, the main aim of this thesis was to present different statistical methods and models which are easy to use by managers, are general, and provide insights for the development of similar methods and models.

To reach the main aim of the thesis several different statistical and modelling procedures were investigated and applied, such as genetic programming (GP), multiple regression, Markov Chains, and finally, well-used criteria for the r2 and p-value for the development of a method to determine temporal-trends. The statistical methods and models were mainly based on the variables chlorophyll-a (chl-a) and total phosphorus (TP) concentrations, but some methods and models can be directly transferred to other variables.

The main findings in this thesis were that multiple regressions overcome the performance of GP to predict summer chl-a concentrations and that multiple regressions can be used to generally describe the chl-a seasonality with TP summer concentrations and the latitude as independent variables. Also, it is possible to calculate probabilities, using Markov Chains, of exceeding certain chl-a concentrations in future months. Results showed that deep water concentrations were in general closely related to the surface water concentrations along with morphometric parameters; these independent variables can therefore be used in mass-balance models to estimate the mass in deep waters. A new statistical method was derived and applied to confirm whether variables have changed over time or not for cases where other traditional methods have failed. Finally, it is concluded that the statistical methods and models developed in this thesis will increase the understanding for predictions within and across aquatic systems.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2015. , 59 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1300
Keyword [en]
Lake, Water quality, Chlorophyll-a, Total phosphorus, Seasonality, Morphometry, Regression model, Probability, Markov chain, Genetic programming, Temporal-trend
National Category
Earth and Related Environmental Sciences Environmental Sciences Oceanography, Hydrology, Water Resources Probability Theory and Statistics
Research subject
Earth Science with specialization in Environmental Analysis
Identifiers
URN: urn:nbn:se:uu:diva-263283ISBN: 978-91-554-9362-2 (print)OAI: oai:DiVA.org:uu-263283DiVA: diva2:859133
Public defence
2015-11-27, Hambergsalen, Villavägen 16, Uppsala, 10:00 (English)
Opponent
Supervisors
Available from: 2015-11-05 Created: 2015-09-30 Last updated: 2015-11-10
List of papers
1. A Comparison Between Regression Models and Genetic Programming for Predictions of Chlorophyll-a Concentrations in Northern Lakes
Open this publication in new window or tab >>A Comparison Between Regression Models and Genetic Programming for Predictions of Chlorophyll-a Concentrations in Northern Lakes
2016 (English)In: Environmental Modelling and Assessment, ISSN 1420-2026, E-ISSN 1573-2967, Vol. 21, no 2, 221-232 p.Article in journal (Refereed) Published
Abstract [en]

Chlorophyll-a (chl-a) concentrations are often used as a proxy for water quality problems as well as phytoplankton blooms. Available chl-a models range from simple phosphorus loading models to complex regression and dynamic models. A comparison of multiple regression models was made with genetic programming (GP) techniques to predict chl-a concentrations over a large range of 104 Swedish lakes. Independent variables used were lake area, mean depth, iron, latitude, ammonium, nitrogen + nitrate, pH, phosphate, secchi depth, silicon, temperature, total phosphorus, total nitrogen and total organic carbon. GP is a method based on the Darwinian evolution theory. This implies that a program will be able to test different mathematical equations, iterating and improving each equation using fundamental ideas from evolution theory to increase the predictive power. A good correspondence was found between the multiple regression and the GP modelling approach. No significant improvement of the predictive power was found using GP, and it is therefore recommended that multiple regression methods should be preferred when predicting chl-a concentrations as these models tend to be less complex and the modelling approach is easier to use. Results from GP were in some cases more accurate compared to multiple regressions; however, the best model was created by multiple regressions which used concentrations of total phosphorus, total nitrogen and latitude as independent variables. These findings will be an important note for limnologists and modelling managers when developing future models of chl-a concentrations in lakes.

Keyword
Chlorophyll-a, Lake, Multiple regression, Genetic programming
National Category
Earth and Related Environmental Sciences Environmental Sciences
Research subject
Earth Science with specialization in Environmental Analysis
Identifiers
urn:nbn:se:uu:diva-263171 (URN)10.1007/s10666-015-9480-4 (DOI)000371612600005 ()
Available from: 2015-09-28 Created: 2015-09-28 Last updated: 2017-12-01Bibliographically approved
2. Predicting median monthly chlorophyll-a concentrations
Open this publication in new window or tab >>Predicting median monthly chlorophyll-a concentrations
2013 (English)In: Limnologica, ISSN 0075-9511, E-ISSN 1873-5851, Vol. 43, no 3, 169-176 p.Article in journal (Refereed) Published
Abstract [en]

Chlorophyll-a (Chl-a) is a plant pigment which is used in many environmental monitoring programs as a water quality indicator for lakes. However, monthly Chl-a data are often lacking in many monitored lakes as measurements are concentrated to certain periods of the year. This study investigates two methods of how monthly Chl-a medians can be predicted (i) new monthly regression models from median summer total phosphorus concentrations and latitude, (ii) and with monthly constants added to regression models from the literature. Data from 308 lakes were used and the trophic status of the lakes ranged from oligotrophic to hypertrophic, they were located from northern Sweden (Europe) to southern Florida (North America). These models may be useful for understanding the general Chl-a seasonality in lakes and for managing lakes in which Chl-a measurements are not made over the whole year.

Place, publisher, year, edition, pages
Elsevier, 2013
Keyword
Chlorophyll-a, Seasonality, Lake, Phosphorus, Regression model, Statistical model
National Category
Environmental Sciences
Research subject
Earth Science with specialization in Environmental Analysis
Identifiers
urn:nbn:se:uu:diva-197880 (URN)10.1016/j.limno.2012.08.011 (DOI)000319240700005 ()
Available from: 2013-04-05 Created: 2013-04-05 Last updated: 2017-12-06Bibliographically approved
3. Probabilities of monthly median chlorophyll-a concentrations in subarctic, temperate and subtropical lakes
Open this publication in new window or tab >>Probabilities of monthly median chlorophyll-a concentrations in subarctic, temperate and subtropical lakes
2013 (English)In: Environmental Modelling & Software, ISSN 1364-8152, E-ISSN 1873-6726, Vol. 41, 199-209 p.Article in journal (Refereed) Published
Abstract [en]

High concentrations of chlorophyll-a (chl-a) during summer are by definition a common problem in eutrophicated lakes. Several models have been designed to predict chl-a concentrations but are unable to estimate the probability of predicted concentrations or concentration spans during subsequent months. Two different methods were developed to compute the probabilities of obtaining a certain chl-a concentration. One method is built on discrete Markov chains and the other method on a direct relationship between median chl-a concentrations from two months. Lake managers may use these methods to detect and counteract the risk of high chl-a concentrations and algal blooms during coming months. Both methods were evaluated and applied along different scenarios to detect the probability to exceed chl-a concentration in different coming months. The procedure of computing probabilities is strictly based on general statistics which means that neither method is constrained for chl-a but can also be used for other variables. A user-friendly software application was developed to facilitate and extend the use of these two methods.

Place, publisher, year, edition, pages
Elsevier, 2013
Keyword
chlorophyll-a, predicting probability, markov chain, lake, chlorophyll-a, prediktion av sannolikheter, markovkedjor, sjöar
National Category
Environmental Sciences
Research subject
Earth Science with specialization in Environmental Analysis
Identifiers
urn:nbn:se:uu:diva-194311 (URN)10.1016/j.envsoft.2012.12.002 (DOI)000315974500019 ()
Available from: 2013-02-12 Created: 2013-02-12 Last updated: 2017-12-06Bibliographically approved
4. Predicting Total Nitrogen, Total Phosphorus, Total Organic Carbon, Dissolved Oxygen and Iron in Deep Waters of Swedish Lakes
Open this publication in new window or tab >>Predicting Total Nitrogen, Total Phosphorus, Total Organic Carbon, Dissolved Oxygen and Iron in Deep Waters of Swedish Lakes
2015 (English)In: Environmental Modelling and Assessment, ISSN 1420-2026, E-ISSN 1573-2967, Vol. 20, no 5, 411-423 p.Article in journal (Refereed) Published
Abstract [en]

In many lakes, the physical and chemical characteristics are monitored for surface waters but not for deep waters. Yet, deep waters may be important for understanding the dynamics of lake water chemistry variables over the year. In this study, multiple regression models have been created for five different variables, total phosphorus, total nitrogen, total organic carbon, dissolved oxygen (DO) and iron, in the deep water for 61 Swedish temperate or subarctic lakes. The investigated season was February to October, depending on the data availability. Regressions used the corresponding variables from the surface water as well as different morphometric parameters as independent variables. It was possible to construct meaningful models (r2 > 0.65; p < 0.05) for most of the variables and months. However, it was not possible to attain this criterion for some months regarding the DO concentration. Surface water concentrations were in general most important for predicting corresponding deep water concentrations. An exception was that during summer, DO differed considerably between surface waters and deep waters and voluminous lakes had particularly high DO concentrations in deep waters. No cross-systems relationship could be found between deepwater hypoxia and total phosphorus in deep waters during summer when phosphorus diffusion from sediments is most likely. A mass-balance modelling example was applied to illustrate the use of the produced models. These findings may provide a better understanding of the dynamics of these five variables in temperate or subarctic lakes.

Keyword
Lake, Morphometry, Mass-balance, Deep water, Water quality
National Category
Earth and Related Environmental Sciences Environmental Sciences
Research subject
Earth Science with specialization in Environmental Analysis
Identifiers
urn:nbn:se:uu:diva-263166 (URN)10.1007/s10666-015-9456-4 (DOI)000360554900001 ()
Available from: 2015-09-28 Created: 2015-09-28 Last updated: 2017-12-01Bibliographically approved
5. An operational definition of a statistically meaningful trend
Open this publication in new window or tab >>An operational definition of a statistically meaningful trend
2011 (English)In: PLoS ONE, ISSN 1932-6203, Vol. 6, no 4, e19241- p.Article in journal (Refereed) Published
Abstract [en]

Linear trend analysis of time series is standard procedure in many scientific disciplines. If the number of data is large, a trend may be statistically significant even if data are scattered far from the trend line. This study introduces and tests a quality criterion for time trends referred to as statistical meaningfulness, which is a stricter quality criterion for trends than high statistical significance. The time series is divided into intervals and interval mean values are calculated. Thereafter, r2 and p values are calculated from regressions concerning time and interval mean values. If r2≥0.65 at p≤0.05 in any of these regressions, then the trend is regarded as statistically meaningful. Out of ten investigated time series from different scientific disciplines, five displayed statistically meaningful trends. A Microsoft Excel application (add-in) was developed which can perform statistical meaningfulness tests and which may increase the operationality of the test. The presented method for distinguishing statistically meaningful trends should be reasonably uncomplicated for researchers with basic statistics skills and may thus be useful for determining which trends are worth analysing further, for instance with respect to causal factors. The method can also be used for determining which segments of a time trend may be particularly worthwhile to focus on.

Keyword
trend, trendanalys
National Category
Earth and Related Environmental Sciences
Research subject
Statistics
Identifiers
urn:nbn:se:uu:diva-152876 (URN)10.1371/journal.pone.0019241 (DOI)000290020700044 ()
Available from: 2011-05-04 Created: 2011-05-02 Last updated: 2015-11-10Bibliographically approved

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