Divergence and Curl of COVID19 Spreading in the Lower Peninsula of Michigan

This paper explores the COVID19 transmission pattern and circulation dynamics in the Euclidean space at the lower peninsula of Michigan by using the divergence and curl concept in vector field. The COVID19 transmission volume flux can be calculated for each county by using vector divergence. The results shows Wayne county had the highest divergence (162660), the Kent county had the second highest divergence (152540), and the Saginaw county had the third highest divergence (103240), the divergence is positive which means the COVID19 virus was transmitted from these counties to other places. The results also shows Monroe county had the lowest divergence (-187843), the Allegan county had the second lowest number in divergence (-90824), the divergence is negative which means the COVID19 virus was transmitted from other places to these counties. The circulation of the virus is also calculated by using vector curl. The positive curl means that the virus has circulated in a counter-clockwise direction, and the negative curl means the virus has circulated in a clockwise direction. The divergence is an operator of the COVID19 transmission vector field, which produces a scalar field giving the quantity of the transmission vector field’s source at each location. The COVID19 spreading volume density of the outward flux of transmission field is represented by divergence around a given location. The curl is an operator of the COVID19 transmission field, which describes the circulation of a transmission vector field. The curl at a location in COVID19 transmission field is represented by a vector whose length and direction denote the magnitude and axis of the maximum circulation. The curl of a transmission field is formally defined as the circulation density at each location of COVID19 transmission field.

Inter-annual Variability of Snowfall in the Lower Peninsula of Michigan

Winter snowfall, particularly lake-contributed snowfall, has a significant impact on the society and environment in the Great Lakes regions including transportation, tourism, agriculture, and ecosystem. Understanding the inter-annual variability of snowfall will provide sound basis for local community safety management and reduce its environmental impacts on agriculture and ecosystems. This study attempts to understand the trend and inter-annual variability in snowfall in the Lower Peninsula of Michigan (LPM) using statistical analysis based on snowfall measurements from eight weather stations. Our study demonstrates that snowfall has significantly increased from 1932 to 2015. Correlation analysis suggests that regional average air temperatures have a strong negative relationship with snowfall in the LPM. On average, approximately 27% of inter-annual variability in snowfall can be explained by regional average air temperatures. ENSO events are also negatively related to snowfall in the LPM and can explain ~8% of inter-annual variability. The North Atlantic Oscillation (NAO) does not have strong influence on snowfall. Composite analysis demonstrates that on an annual basis, more snowfall occurs during the years with higher maximum ice cover (MIC) than during the years with lower MIC in Lake Michigan. Higher MIC is often associated with lower air temperatures which are negatively related to snowfall. This study could provide insight on future snow related climate model improvement and weather forecasting.

Rating the potential suitability of habitat in Michigan stream reaches for Arctic grayling

Arctic Grayling Thymallus arcticus were historically found throughout the northern half of Michigan’s Lower Peninsula but were extirpated from the state by 1936. By addressing issues from previous reintroduction efforts and employing instream rearing (Remote Site Incubator) approach to stocking, numerous partners are working to reintroduce Arctic Grayling to Michigan with hopes of reestablishing self-sustaining populations. With over 47,000 km of coldwater stream habitat in the state and limited numbers of eggs for reintroductions, a prioritization framework was needed to provide a standardized, fine-scale method for rating suitability of streams for reintroductions. Through facilitated discussions with stakeholders and experts, we developed an overall prioritization framework for rating Michigan streams with components evaluating a reach’s thermal, instream habitat, biological, and connectivity characteristics. Within the context of this broader framework, we developed the habitat rating component for assessing suitability of instream conditions for egg, fry, juvenile, and adult life stages of Arctic Grayling. Life-stage specific habitat metrics and scoring criteria from this effort were used to rate habitat conditions for 45 reaches in tributaries of Michigan’s Manistee River, enabling identification of reaches likely having instream habitat most suitable for Arctic Grayling. Numbers of reaches meeting or exceeding 60%, 70%, and 80% of the maximum score for overall habitat suitability were 31, 8, and 1. Upon completion of the fish assemblage and connectivity components, the prioritization framework and habitat rating process described here will be used for comparing suitability among streams throughout the historic range of Arctic Grayling in Michigan and guiding reintroduction efforts. Though it will take considerable time before instream habitat suitability criteria can be evaluated for all life stages of Arctic Grayling in Michigan, the collaborative stream prioritization framework developed for Arctic Grayling reintroduction can be readily adapted to reintroduction efforts for other species elsewhere.

Divergence and Curl of COVID19 Spreading in Lower Peninsula of Michigan

Divergence and Curl concept in vector field is applied to the COVID19 spreading data for Lower Peninsula of Michigan State, U.S.A. The Divergence is an operator of COVID19 transmission vector field, which produces a scalar field giving the quantity of transmission vector field’s source at each location. The COVID19 spreading volume density of the outward flux of transmission field is represented by divergence around a given location. The Curl is an operator of COVID19 transmission field, which describes the circulation of a transmission vector field. The Curl at a location in COVID19 transmission field is represented by a vector whose length and direction denote the magnitude and axis of the maximum circulation. The curl of a transmission field is formally defined as the circulation density at each location of COVID19 transmission field. From data analysis of divergence of curl of Lower Michigan Peninsula, the COVID19 transmission volume flux and circulation can be identified for each County. Summary: This paper is to use vector Divergence and Curl concept to apply to COVID19 confirmed cases in Lower Peninsula of Michigan, U.S.A.

Forest Disturbance Types and Current Analogs for Historical Disturbance-Independent Forests

Forest classifications by disturbance permit designation of multiple types of both old growth forests and shorter-lived forests, which auto-replace under severe disturbance, and also identification of loss of the disturbance type and associated forest. Historically, fire and flooding disturbance regimes, or conversely, infrequent disturbance, produced unique forests such as disturbance-independent forests of American beech (Fagus grandifolia), eastern hemlock (Tsuga canadensis), and sugar maple (Acer saccharum) in the Eastern United States. However, disturbance has changed to primarily frequent mechanical overstory disturbance, resulting in novel forests. To demonstrate the transition to no-analog forests after disturbance change, I compared historical tree surveys (ca. 1837 to 1857) to current surveys in the Northern Lower Peninsula of Michigan. To establish widespread disturbance change effects, I also located where beech and hemlock are currently most abundant throughout the Eastern US compared to historical distribution of beech–hemlock forests. In the Northern Lower Peninsula of Michigan, beech and hemlock historically were about 30% of all trees, but currently, beech and hemlock are 2% of all trees. Red maple (Acer rubrum) increased from 1% to 11% of all trees and aspen (Populus) increased from 2% to 13% of all trees. The squared-chord difference between historical and current surveys was 0.40, or dissimilar forests. Areas with ≥20% beech and hemlock or ≥15% of either species decreased from about 52 million to 6 million hectares, with current distribution restricted to the Northeastern US. Current forests are dissimilar to historical forests, and this transition appears to be driven by disturbance regimes without historical analogs. Disturbance change may provide perspective in forest management for climate change.

Use of Geographic Information System Mapping in the Examination of Specialized Low Vision Resources and Areas of Need in Michigan

Introduction: The number of adults with visual impairments (i.e., blindness or low vision) is increasing, especially with the aging of the population. Although awareness of vision loss as a public health problem is growing, public health budgets are decreasing. This study exemplifies the use of publicly available secondary data and geographic information system (GIS) mapping to spatially map areas of potential higher risk for vision loss and identify where specialized, low vision resources are located, by county, in Michigan. Methods: County-level, publicly available data on risk factors for low vision (health and demographic) and specialized low vision resources (medical, rehabilitation, and community) are extracted from existing public health data sets and information published on the Internet. GIS mapping is applied to visually examine potential areas of disparity between need and resources. Results: Broadly speaking, counties in Michigan with the highest number of risk factors for low vision are clustered in the center of the Lower Peninsula and on the eastern and western ends of the Upper Peninsula. Areas that have fewer resources for low vision are clustered in the thumb area and the middle to upper part of the Lower Peninsula. Resources are concentrated near the state’s metropolitan areas (i.e., Detroit and suburbs, Kalamazoo, and Grand Rapids). Discussion: Maps can be helpful in locating areas of health disparities, but they need to be interpreted carefully such as by considering the county’s population size. Understanding the eligibility criteria of available services can help to uncover groups of persons not being served. Implications for practitioners: With increasing need for services and shrinking budgets, strategic planning may help alleviate anticipated shortfalls in available services. Use of publicly available data and GIS mapping may be an affordable and efficient method to identify areas of need and resources, for targeted public health efforts in vision.

Characterization of Diaporthe spp. associated with spruce decline on Colorado blue spruce in Michigan

Since 2006 there has been a decline in Colorado blue spruce (CBS; Picea pungens) planted as landscape trees and for Christmas tree production throughout the Lower Peninsula of Michigan, United States. This decline is characterized by a slow loss of needles in the lower portion of the tree starting at branch tips, followed by entire branch dieback which gradually progresses upwards over several years. This dieback has been linked to shallow branch cankers visible in the phloem when the bark layer is removed. Isolates in the fungal genus Diaporthe have been consistently isolated from lesion margins on symptomatic branches. Prior to the initial reports of declining CBS in landscape and Christmas trees, Diaporthe was only known as a nursery disease of CBS. To determine the species of Diaporthe linked to the decline of CBS in Michigan, seven gene regions were sequenced from a collection of Diaporthe isolates collected in 2011-2018 from CBS and other coniferous hosts. Subsequent phylogenetic analyses indicated that Diaporthe eres and a novel Diaporthe clade were present on symptomatic CBS in Michigan. The new species Diaporthe brevicancria nov. is described, and Koch’s postulates were confirmed for D. brevicancria nov. and D. eres. Diaporthe brevicancria nov. produced the largest cankers in greenhouse pathogenicity trials and dual inoculations of D. brevicancria nov. and D. eres produced intermediate cankers.