A REGRESSION APPROACH TO STUDY THE NATURAL LAWS AND PHENOLOGICAL CALENDARS IN THE UNITED STATES OF AMERICA, THROUGHOUT THE LONGITUDE 84ºW
Phenology and Hopkin’s Law
Dinesh Shrestha, South Dakota State University
I am interested in verifying the Hopkin’s Law, that the time of occurrence of a given periodical event in life activity in temperate North America is at the general average rate of 4 days for each 1 degree of latitude, 5 degrees of longitude, 400 feet of altitude, later northward, eastward and upward in the spring and early summer, and the reverse in late summer and autumn. The study area lies in the central USA, the latitude ranging from 29°N to 46°N along the longitude 84°W, and covers five states, running south to north: Georgia, Tennessee, Kentucky, Ohio, and Michigan. The study focuses on seasonal patterns from south to north of the United State, comparing these patterns with the Hopkins Law of Phenology. This comparison, and the study’s results were not as predicted: the seasonal patterns often did not follow the law but tended to follow the law at the point of latitude and longitude aforementioned. The NDVI imagery obtained from WELD Distribution System was analyzed in ENVI 4.8 software to determine the First Day of Spring (FSD). The FSD was then plotted against the latitude which gave a curve that best fits Hopkin’s Law. The obtained result shows the FSD at the southern-most latitude (29°N) on the 97th day of the year, and the northern-most latitude (46°N) is on the 129th day of the year which is close to Hopkin’s Law (85%).
Keywords: NDVI, Day of Year, Hopkin’s Law of Phenology, Weld Distribution System, First Day of Spring, curve fitting, longitude and latitude.
A season is a division of the year, marked by changes in weather, ecology and hours of daylight (Bennet, 2012). Seasons result from the yearly orbit of the Earth around the Sun and the tilt of the Earth’s rotational axis relative to the plane of the orbit. During May, June, and July, the northern hemisphere is exposed to more direct sunlight because the hemisphere faces the sun. The same is true of the southern hemisphere in November, December, and January. It is the tilt of the Earth that causes the Sun to be higher in the sky during the summer months which increases the solar flux. However, due to seasonal lag, June, July, and August are the hottest months in the northern hemisphere and December, January, and February is the hottest months in the southern hemisphere. Moreover, different human activities and natural disturbances have effects in the dynamics of ecosystems causing the alteration in the phenological process. For instance, the modification of vegetation cover, with a predominant clearing of natural vegetation, may have a long-term impact on sustainable food production, freshwater and forest resources, the climate and human welfare (Foley et al., 2007).
Phenology is a branch of science dealing with the relations between climate and the timing of biological phenomena, such as bud burst, leaf out and plant flowering. It is the study of the timing of recurring biological phases, the causes of their timing with regard to biotic and abiotic forces, and the interrelation of phases of the same or different species.” Many phenological relations exist in folklore. Jackson et al. (2001) cite the aphorism, “seed should be sown when oak leaves are as big as sow’s ears”, for example.
Andrew Delmar Hopkins (1857-1948) was a prominent scholar that has had a lasting effect on phenology for his contributions, mainly Hopkins Law. Hopkins Law states that, “… the time of occurrence of a given periodical event in life activity in temperate North America is at the general average rate of 4 days for each 1 degree of latitude, 5 degrees of longitude, 400 feet of altitude, later northward, eastward and upward in the spring and early summer, and the reverse in late summer and autumn”. This means that the further west from the Atlantic Coast, the further north, or higher in the elevation a site, the later spring arrives.
Phenological metrics describe the phenology of vegetation growth as observed by satellite imagery. Some standard metrics derived are Onset of greening, Onset of senescence, Timing of Maximum of the Growing Season, Growing season length, and so forth. In Figure 1, Greenup Onset is the beginning of measurable photosynthesis. The start of spring is the period when photosynthesis rate is rapid. The plants are growing green and getting more green leaves. The Greenup Phase is the duration of photosynthetic activity, or say the time frame from the start of the season until the maturity onset. During maturity phase, the plants are fully grown and have maximum leaves and maximum photosynthesis process takes place. The phase, when the plants begin to shade off the leaves and the photosynthesis rate, is seized is Senescence Onset and Senescent Phase. During dormancy onset and dormant phase the photosynthesis rate are minimum and plants exhibit minimum greenness. This is because of shading of the leaves.
Select the region in US Consortium and order the NDVI, Day of Year and Cloud Data from WELD website 2011 CONSUS Spring image for 11 points along the longitude 84ºW. Each line of the 11 locations order the monthly WELD 2011 data for ~1X1º area. Then, the data were downloaded. The downloaded data should be organized into separate folders. Data were renamed per the name of the months, if necessary. Data were saved in a separate folder. For each ordered ~1X1º area, a single pixel 30m vegetation/soil pixel that for the months January, February through July is predominantly NOT water, cloud, snow, urban, or missing was located. Then, the WELD NDVI and Day of Year pixel values for each month (Jan to July) were collected. The above 2 steps were repeated for all 11 areas. The prime objective is to define the first day of spring from monthly NDVI and Day of Years values. The study area lies in the central USA, the latitude ranging from 29°N to 46°N along the longitude 84°W, and covers five states, running south to north: Georgia, Tennessee, Kentucky, Ohio, and Michigan (Figure 2). The study focuses on seasonal patterns from south to north, comparing these patterns with the Hopkins Law of Phenology.
The entire project involves three major steps as shown in figure 3: (1) Image interpretation and data analysis using ENVI software, (2) Analysis of the output and comparison with the Hopkin’s Law, and, (3) Presentation of the output and preparing the map in Arc GIS. All three steps require the skilled manpower with adequate knowledge in ENVI software, Google Earth, Arc GIS, Excel, and Mathematics (Regression and RMSE). The project would also demand the adequate knowledge in Phenology and Hopkin’s Law.
The first step was to locate the working area and download the data, and then work with ENVI software to process the image. Image interpretation and data analysis using ENVI software are categorized into four steps. The first step is to order and download the data. For this, I selected the region in US Consortium and ordered the NDVI, Day of Year and Cloud Data from WELD website 2011 CONSUS Spring image for 11 points along the longitude 84ºW. After I downloaded the data, the second step was Pre-processing the data I organized and renamed the data into separate folders and saved them in a separate folder. The third step was processing, where I extracted the WELD NDVI and Day of Year pixel values for each month (Jan to July) for all 11 areas. The fourth step was Post-processing where the data was plotted in the graph (X-axis showing the Day of year and Y-axis showing the NDVI). Table 1 and Figure 4 give the graph showing the FSD for the point P8 (Clermont, Georgia). The FSD is DAY 105 i.e. April 15th, in this location. The method adopted is NDVIratio = (NDVI-NDVImin) / (NDVImax-NDVImin. The First Day of Spring (FSD) was then determined and a final graph showing, X- axis as the derived First Day of Spring (FSD) and Y- Axis as the latitude of the area was plotted (Table 2 and Figure 5).
2.2 Data Analysis
There are different methods adopted to study Phenology. A diversity of satellite measures and methods has been developed. These methods can be divided into four main categories: (1) NDVI Thresholding (absolute or relative values), (2) Derivatives (temporal derivatives i.e. slopes), (3) Smoothing Algorithms, (4) Model fit (NDVI curve fitting- regression, splines). I adopted first two methods.
The NDVI is an index used to identify vegetation and its health through the Levels of chlorophyll detected in the leaves. NDVI is calculated from the visible and near-infrared light reflected by vegetation. Healthy vegetation absorbs most of the incoming visible light, and reflects a large portion (about 25%) of the near infra-red (NIR) light, but a low portion in the red band (RED). Unhealthy or sparse vegetation reflects more visible light and less NIR light. To apply the NDVI, the following formula is used: NDVI = (NIR – RED) / (NIR + RED).
The NDVI is a common and widely used transformation for the enhancement of vegetation information. It is used to measure vegetation cover characteristics and incorporated into many forest assessment studies. It can be used for an accurate description of land cover, vegetation classification and vegetation phenology. In some cases, multi-resolution imagery and integrated analysis method were included along with NDVI for land cover classification. Temporal dynamics of the NDVI or adding an NDVI image with the multispectral image is also useful in differentiating the vegetation. The classification accomplishing of NDVI using GIS software depend on remotely sensed satellite data as the primary information source. However, the WELD gives us the NDVI processed image so that we should not spend much time in NDVI calculations.
The threshold selection is commonly based on a normal distribution characterized by its mean and its standard deviation threshold values are scene-dependent; they should be calculated dynamically based on the image content. However, the thresholds can be determined by three approaches: (1) interactive, (2) statistical and (3) supervised. In the first approach, thresholds are interactively determined visual tests. The second approach is based on statistical measures from the histogram of techniques for selecting appropriate thresholds are based on the modeling of the signal and noise, which is carried out in this study (Brink, A. D., and N. E. Pendock, 1996). Third, the supervised approach derives thresholds based on a training set of change and no-change pixels.
In order to work with the phenology, the NDVI ratio is more accurate and widely practiced method. In this approach, first, we need to translate NDVI to a ratio based on the annual minimum and maximum as [NDVIratio = (NDVI -NDVImin) / (NDVImax – NDVImin)] and analyze the Greenup Onset for the particular pixel value (White et al., 1999). NDVI thresholding is the simplest method to determine FSD and LSD. The threshold is arbitrarily set at a certain level (e.g. 0.09, 0.17, 0.3, and so forth). However, across the conterminous US, NDVI threshold can vary from 0.08 to 0.40. Thus, it is inconsistent when applied towards large areas. 50% is the most often used threshold. The increase in greenness is believed to be most rapid at this threshold. Some believe that rapid growth is more important than first leaf occurrence or bud burst. Lower likelihood of soil – vegetation confusion than at lower thresholds.
2.2.2 Derivate is calculated based on 3 composites
We employ the recursive least squares procedure described by Hermance (in press) to create an average annual phenology by simultaneously fitting non-orthogonal low order polynomial and harmonic components while minimizing model roughness. The polynomial, typically 4th order, fits any instrument drift or long-term trends during the observation period, while the harmonic components, typically a 6th order series, fit the average phenology of the data. Harmonic analysis (specifically using Fourier series) has been shown to produce an accurate representation of a single year phenology across a range of land cover (Jakubauskas et al., 2001, Jakubauskas et al., 2002, Moody &Johnson, 2001). Here, we found that 6 harmonic components (periods of 1 year, 6 months, 4 months, 3 months, 2.4 months and 2 months) were sufficient to capture the variety of phenologies tested (e.g., differences in length of growing season and steepness of onset of greenness). However, the lack of dataset bound me to use the second order polynomial. NDVI ratio was then calculated: NDVIratio = (NDVI-NDVImin) / (NDVImax-NDVImin). The obtained curve was fitted with a second-degree polynomial curve: f(x) = ax2+bx+c. The FDS was determined considering 2 things: a) the point at which the fitted curve reached 50% NDVI threshold upward, or b) the point where NDVI value abruptly increased.
The graph partly confirms Hopkin’s Law of Phenology. The Hopkin’s law states that there is a 1-day delay for every 15 minutes of latitude upwards. Figure 7 shows the map showing the locations of all 11 points along with its land cover type, in the central USA, the latitude ranging from 29°N to 46°N along the longitude 84°W. There was a delay but not necessarily by 1 day in every 15 minutes. The number of days the FSD is being delayed is not consistent and does not always fit the law. There is a delay in the starting of spring as a function of latitude. The fitted line exhibits a correlation of is .596 i.e. 59.6% which can be considered acceptable. Some discrepancies observed are an underestimation at the first 36°N and at 39°N.
3.1.1 Possible natural source of discrepancies include:
The local starting of the agricultural season which may be linked to the local microclimate, such as crop types are unknown, the forest types were different (figure 6), and most of the land in the northern part was covered by snow for Jan, Feb and March months. This affected the NDVI. Some other factors may include local disturbance such as fire.
3.1.2 Possible technical sources of discrepancies:
The possible technical sources of discrepancies are as follows: the latitude 37N did not have data for July month, cloud cover that may impact the image processing, inconsistencies in pixel sampling (i.e. not evenly spaced northward or different distances from the longitude line to avoid missing data, and the polynomial curve fitted does not always work perfectly.
Hopkin’s law is considered to be the prime law to define the season pattern in the North America (White et al., 1999). Since the terrain, elevation and the land cover is not uniform throughout the continent, Hopkin’s Law does not always work. For vegetation mapping, the NDVI approach has been widely utilized in various sensors. However, the different characteristic of sensors would affect the classification results. Furthermore, the threshold selection is difficult for extracting vegetation information from various scenes. In this work, I have proposed an approach with a fixed-threshold scheme (NDVIratio) and a correlation approach, which can be suitable for WELD imagery and is illustrated with more accurate results than NDVI. My project results with WELD images partly confirms the theoretical inference of the proposed approach. In future work, I plan to extend the proposed approach to other high-resolution satellite images, e.g. QuickBird images, and to find a solid theoretical support for the fixed threshold scheme.
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LIST OF FIGURES
Figure 5: The graph showing the FSD for the point P8 (Clermont, Georgia). The FSD is determined to be DAY 105 i.e. April 15th, in this location. The method adopted is NDVIratio = (NDVI-NDVImin) / (NDVImax-NDVImin. The polynomial curve fitting gives R² = 0.9.
Figure 6: The graph showing the FSD for the point P8 (Clermont, Georgia). The FSD is determined to be DAY 105 i.e. April 15th, in this location. The method adopted is NDVIratio = (NDVI-NDVImin) / (NDVImax-NDVImin. The polynomial curve fitting gives R² = 0.9.