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An operational definition of a statistically meaningful trend
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, LUVAL. (Miljöanalys)
Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, LUVAL. (Miljöanalys)
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.

Place, publisher, year, edition, pages
2011. Vol. 6, no 4, e19241- p.
Keyword [sv]
trend, trendanalys
National Category
Earth and Related Environmental Sciences
Research subject
Statistics
Identifiers
URN: urn:nbn:se:uu:diva-152876DOI: 10.1371/journal.pone.0019241ISI: 000290020700044OAI: oai:DiVA.org:uu-152876DiVA: diva2:414230
Available from: 2011-05-04 Created: 2011-05-02 Last updated: 2015-11-10Bibliographically approved
In thesis
1. Determining Chlorophyll-a Concentrations in Aquatic Systems with New Statistical Methods and Models
Open this publication in new window or tab >>Determining Chlorophyll-a Concentrations in Aquatic Systems with New Statistical Methods and Models
2011 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Chlorophyll-a (chl-a) concentration is an indicator of the trophic status and is extensively used as a measurement of the algal biomass which affects the level of eutrophication in aquatic systems. High concentration of chl-a may indicate high biomass of phytoplankton which can decrease the quality of water or eliminate important functional groups in the ecosystem. Predicting chl-a concentrations is desirable to understand how great impact chl-a may have in aquatic systems for different scenarios during long-time periods and seasonal variation. Several models of predicting annual or summer chl-a concentration have been designed using total phosphorus, total nitrogen or both in combination as in-parameters. These models have high predictive power but are not constructed for evaluating the long-term change or predicting the seasonal variation in a system since the input parameters often are annual values or values from other specific periods. The models are in other words limited to the range where they were constructed. The aim with this thesis was to complement these models with other methods and models which gives a more appropriate image of how the chl-a concentration in an aquatic system acts, both in a short as well as a long-time perspective. The results showed that with a new method called Statistically meaningful trend the Baltic Proper have not had any change in chl-a concentrations for the period 1975 to 2007 which contradicts the old result observing the p-value from the trend line of the raw data. It is possible to predict seasonal variation of median chl-a concentration in lakes from a wide geographically range using summer total phosphorus and latitude as an in-parameter. It is also possible to predict the probability of reaching different monthly median chl-a concentrations using Markov chains or a direct relationship between two months. These results give a proper image of how the chl-a concentration in aquatic systems vary and can be used to validate how different actions may or may not reduce the problem of potentially harmful algal blooms.

Abstract [sv]

Koncentrationen av klorofyll-a (chl-a) är en indikator på vilken trofinivå ett akvatiskt system har och används som ett mått på algbiomassa som påverkar övergödningen i akvatiska system. Höga koncentrationer av chl-a i sjöar kan indikera hög biomassa av fytoplankton och försämra kvalitén i vattnet eller eliminera viktiga funktionella grupper i ett ekosystem. Det är önskvärt att kunna prediktera chl-a koncentrationer för att förstå hur stor påverkan chl-a kan ha för olika scenarier i akvatiska system under längre perioder samt under säsongsvariationer. Flera modeller har tagits fram som predikterar årsvärden eller sommarvärden av chl-a koncentrationer och i dessa ingår totalfosfor, totalkväve eller en kombination av båda som inparametrar. Dessa modeller har hög prediktiv kraft men är inte utvecklade för att kunna utvärdera förändringar över längre perioder eller prediktera säsongsvariationer i ett system eftersom inparametrarna ofta är årsmedelvärden eller värden från andra specifika perioder. Modellerna är med andra ord begränsade till den domän som de togs fram för. Målet med denna avhandling var att komplettera dessa modeller med andra metoder och modeller vilket ger en bättre förståelse för hur chl-a koncentrationer i akvatiska system varierar, både i ett kortsiktigt och ett längre perspektiv. Resultaten visade att med en ny metod som kallas för Statistiskt meningsfull trend så har egentliga Östersjön inte haft någon förändring av chl-a koncentrationer under perioden 1975 till 2007 vilket motsäger tidigare resultat då p-värdet tas fram från en trendlinje av rådata. Det är möjligt att prediktera säsongsvariationer av median chl-a koncentrationer i sjöar från en bred geografisk domän med totalfosfor från sommar och latitud som inparametrar. Det är även möjligt att beräkna sannolikhetenav ett predikterat värde för olika månadsmedianer av chl-a koncentrationer med Markovkedjor eller ett direkt samband mellan två månader. Dessa resultat ger en reell förståelse för hur chl-a koncentrationer i akvatiska system varierar och kan användas till att validera hur olika åtgärder kan eller inte kan reducera problemet av de potentiellt skadliga algblomningarna.

Place, publisher, year, edition, pages
Uppsala: Institutionen för geovetenskaper, Uppsala universitet, 2011. 25 p.
Keyword
Chlorophyll-a, statistical models, aquatic systems, lakes
National Category
Environmental Sciences
Identifiers
urn:nbn:se:uu:diva-160303 (URN)978-91-506-2241-6 (ISBN)
Available from: 2011-11-14 Created: 2011-10-20 Last updated: 2011-11-14Bibliographically approved
2. Predictions Within and Across Aquatic Systems using Statistical Methods and Models
Open this publication in new window or tab >>Predictions Within and Across Aquatic Systems using Statistical Methods and Models
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Prediktioner inom och mellan akvatiska system med statistiska metoder och modeller
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
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:nbn:se:uu:diva-263283 (URN)978-91-554-9362-2 (ISBN)
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

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