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by: Giovani Ullrich PhD


Giovani Ullrich PhD
GPA 3.5

Mark Kaiser

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About this Document

Mark Kaiser
Class Notes
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This 7 page Class Notes was uploaded by Giovani Ullrich PhD on Saturday September 26, 2015. The Class Notes belongs to STAT 690B at Iowa State University taught by Mark Kaiser in Fall. Since its upload, it has received 31 views. For similar materials see /class/214400/stat-690b-iowa-state-university in Statistics at Iowa State University.




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Date Created: 09/26/15
Limnological Time Series Limnology is the study of lakes7 focusing largely on the variables that govern the primary productivity in lakes7 both natural and manmade called reservoirs Pri mary productivity equates to a large extent with the amount of algae found in a lake or reservoir Algae are simple plants and are the source of energy for many inverte brates7 as well as sh lf algae become overly abundant7 however7 a lake or reservoir may become 77unhealthy 7 suffering from anoxic conditions7 general unsightliness eg7 green scum7 and reduced life expectancy Limnologists may be primarily con cerned with physiological processes at the cellular level and the detailed chemical and biological reactions that occur at this ne scale7 or they may be more 77 holistic77 in their approach7 observing phenomena at a larger scale7 even across lakes within a region or the world Of fundamental concern to holistic limnologists are levels of algae and the factors on which the growth of these plants depend Algal biomass is generally taken as proportional to the concentration of chlorophyll the green stuff in plants in a water sample The most important factors involved in governing the level of algal biomass chlorophyll concentration are the primary plant nutrients phosphorus and nitrogen7 and the availability of light although carbon7 temperature7 lake morphology7 and other factors can sometimes be important A common study design for limnologists taking a holistic approach is that of a 77limnological survey 7 in which a collection of lakes in a given region are sampled several times often 3 or 4 during the course of a year7 and often during only the summer growing season in the temperate zone such as North America A typical analysis will consider 77seasonal average77 values of the variables measured7 resulting in a single data point for each lake which is then taken as representative of the condition of that lake during the year of observation As concern about individual lakes and reservoirs increased7 various regulatory bodies eg USEPA or local regulatory 77 water quality boards began setting lim its on certain important water quality variables which if exceeded would prompt mandatory corrective actions such as additional treatment of municipal waste wa ter This led in turn to questions about the appropriate manner to set such limits and the appropriate frequency with which to sample lakes to determine whether they were in 77compliance with the regulatory limits or not Protocols for sampling associated with regulatory standards are often determined in an ad hoc manner with less consideration of what the measurements imply about the health of a lake than the logistical constraints of time money and sampling effort required The use of seasonal means to represent the condition of a lake and the imple mentation of regulatory limits both assume that the procedures used to sample lakes do indeed result in observed values that are 77characteristic77 of a lake at least within a given year If this premise is not true both the standard design of limnological survey studies and the sampling of lakes to determine compliance with regulatory limits are called into question But not a great deal is known about how water quality variables in a single lake vary over time Seldom is a single lake sampled frequently within a year let alone across years Very little limnological data come from sampling of lakes in the winter The study from which our data come for this project was designed to look in tensively at a single lake over time The data consist of daily measurements of total phosphorus total nitrogen chlorophyll and turbidity in a lake located in central Missouri Also available are rainfall data from a nearby weather station and water temperature data These variables were measured each day from 19 May 1992 to 19 December 1996 There are no missing values making this a unique data set to use in assessing daily and seasonal changes in water chemistry variables In fact this data set may represent the highest temporal resolution ever to be observed over a long time span for the variables of total phosphorus total nitrogen and chlorophyll in a lake The potential drawback of course is that the data are for only one lake Plots of water temperature chlorophyll phosphorus and nitrogen over time are presented in Figures 1 4 respectively Our objective is to determine a suitable model to describe the way these variables change over time If possible it would be great to be able to further relate these variables to each other but attempts to do this have to date proven to be unsuccessful Some of the large spikes in the series for phosphorus and chlorophyll have been identi ed as corresponding with events known to in uence lakes For example the phosphorus series of Figure 3 has several occurences of a steep increase followed by something that looks like an exponential decay These events have been matched with turnover events in the lake Turnover happens in the fall During the summer warmer water remains above colder water because warmer water is less dense than colder water Much of the phosphorus that washes into the lake sinks to the bottom where it remains trapped in the lower layer of colder water As the lake cools in the fall the surface water evenutally reaches the same temperature as the lower water and then with all of the water in the lake being the same density the water mixes freely A large amount of phosphorus that had been trapped in the lower portion of the lake then is brought into the water column Traditional time series models have not proved adequate to describe the patterns seen in Figures 1 4 One alternative is to make use of Bayesian dynamic models We will describe these models and their analysis in more detail as this project progresses 30 I 25 20 I 3 Water Temperature 15 0 500 1000 1500 Observation No Figure 1 Water temperature in Lake Woodrail Observation 1 is 19 May 1992 Chlorophyll 20 30 4O 50 60 70 I 10 0 500 1000 1500 Observation No Figure 2 Chlorophyll in Lake Woodrail Observation 1 is 19 May 1992 Phosphorus 60 80 l I 40 0 500 1000 1500 Observation No Figure 3 Phosphorus in Lake Woodrail Observation 1 is 19 May 1992 Nitrogen 08 10 12 06 0 500 1000 1500 Observation No Figure 4 Nitrogen in Lake Woodrail Observation 1 is 19 May 1992


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