3.2: Sampling over Space
- Page ID
- 31595
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Since the days of the Challenger expedition, shipboard oceanography has used a sampling approach based on grids of points stretched over a region of interest. As Thomson describes it, “At intervals as nearly uniform as possible, we established 362 observing stations” (Thomson 1878, p. xi). Thomson’s observing stations are now known as hydrographic stations, or simply stations. Each point on the grid represents a station. The line along which the ship moves from station to station is known as a transect. Hydrographic stations mark the spots where geological, chemical, physical, and biological measurements and samples may be taken. Of course, oceanographers may carry out measurements and take samples along the transect while underway, too. The number of stations and length of the transect depend on the number of days allotted to the expedition and the type and amount of work that the expedition team desires to carry out.
The distance between samples of different regions of the ocean—horizontally or vertically—defines the spatial resolution of the measurements. As someone living in the 21st century, you have undoubtedly witnessed increases in the spatial resolution of televisions and smartphone cameras. Spatial resolution defines the smallest object or feature that may be resolved or distinguished by the display or sensor in your television or smartphone camera—such as 4K resolution (and soon 8K and 16K). Similarly, for oceanographers, spatial resolution refers to the smallest features that may be distinguished in a particular set of data. At higher spatial resolution, oceanographers can identify an individual underwater mountain versus a blob of mountains. They can discriminate the fine details of different water temperatures (depicted as colors) instead of one blotch of the same temperature. Low spatial resolution occurs when oceanographers have to take samples far apart in distance or when a sensor can only measure broad swaths of the ocean. To obtain higher spatial resolution, oceanographers must take more samples in a given area or build sensors that detect smaller features. But there are limits.
Time, technology, and funding don’t always permit the highest spatial resolution. A compromise has to be made between where oceanographers sample and how much they sample: more locations with fewer samples at each location or fewer locations and more samples. Taking and processing more samples takes more time. Observing smaller details of the ocean demands better technology. But time and technology require money that is not always available.
An excellent example of the application of grid sampling can be found in the California Cooperative Oceanic Fisheries Investigation (CalCOFI), which has been conducting oceanographic surveys off the coast of California since 1949. The original grid in 1950 included hundreds of stations along the California coastline and parts of Baja. But since 2004 the survey has been limited to between 75 and 109 stations over a smaller area. Today CalCOFI samples an area of 73,184 square miles (189,547 km2), a considerable expanse but still less than 0.05 percent of the world ocean. Nevertheless, CalCOFI ranks as “the longest-running oceanographic monitoring program on the planet” (e.g., Koch 2019).
Combinations of technology and ships now provide an ability to sample the ocean at spatial scales spanning twelve orders of magnitude—from kilometers down to nanometers (e.g., Dickey 1990; Branson et al. 2016). The challenge for 21st-century oceanographers will be to connect the dots—to find the connections—between processes at each of those scales (e.g., Dickey 1991).