Q & A

Weather and climate influence our lives daily. Whether it’s deciding to bring a jacket and umbrella on a walk or causing life-threatening issues like food insecurity and conflict abroad, these phenomena have both short- and long-term impacts.

Individual efforts to observe weather in North America began in the mid-17th century, and there were groups of volunteer observers in the U.S.A. since 1776. The U.S. Surgeon General James Tilton ordered Army posts across the U.S.A. in 1814 to begin meteorological observations, giving rise to the first observing network in North America, which was formalized by the Smithsonian Institution in 1849 and the National Weather Service was established in 1870. In Europe, Fernando II de Medici – the Grand Duke of Tuscany from 1621 to 1670 – established a meteorological observations network in ten cities, among them Florence, the home of the Medicis; the collected data were sent to Florence at regular intervals. A few stations in Central England have measured surface air temperature since 1659, but the more reliable record is since 1772. In 1854, the U.K. Government established the U.K. Meteorological Office. The British East India Company established several meteorological observatories in India beginning in 1785, followed by other observatories in the first half of the 19th century. The India Meteorological Department was established in 1875 as a branch of the colonial government. Then, in late 19th and early 20th centuries, national meteorological services were established in many countries in Europe and Asia, although meteorological measurements were started in some countries much earlier. Therefore, reliable instrument-measured observations of precipitation and temperature are available in many countries for well over 100 years.

The recorded history of oceanographic observations goes back to at least the 15th century and Christopher Columbus had also observed a hurricane in the Atlantic. There are other records of shipboard measurements of various oceanographic phenomena and of meteorological phenomena observed at sea. The Challenger expedition in 1872-76 was probably the first, organized, around-the-world cruise that made extensive oceanographic observations. Regular measurements of sea-surface temperatures (SSTs), however, did not begin till the 1850s. In the beginning, most SST observations were made at regular times along shipping routes from Europe to Africa, Asia, and North America. Geographical coverage even in these regions was generally sparse and uneven. The two World Wars in the 20th century interrupted regular measurements; and the opening of the Suez (1869) and Panama (1914) Canals permanently changed shipping routes and, therefore, geographical coverage of oceanographic measurements. In the Pacific Ocean, sparsity of shipping routes and the World Wars made possible regular observations only after the 1940s. Changes in SST measurement instruments and methods also complicated quantitative use of the available data. Some scientists have invested substantial efforts in adjusting land surface air temperature and SST data to correct for biases and changes in measurement techniques.

The vast majority of these measurements have been made with thermometers (temperatures), anemometers (winds), rain gauges (rain), snow depth scales (snow), and barometers (air pressure). Since the advent of Earth-orbiting satellites, temperatures and winds at various heights in the atmosphere, rain and snow, water vapor, atmospheric constituents, vegetation cover, and other parameters have been estimated with remote sensing instruments also. These instruments measure visible and infrared radiations reflected or emitted by the Earth and the atmosphere. Using known physics of how these radiations interact with various atmospheric constituents, temperatures and other parameters are then estimated from the radiation measurements. Ground-based and satellite-based radars are also used to remotely estimate liquid and solid precipitations. Regardless of whether a measuring instrument senses a parameter with physical contact or remotely, a very substantial and careful effort is made to calibrate the instrument against precise sources of parameters, and then a calibrated instrument’s measurements are validated by independent measurements not used in the calibration process. Thus, the measurement of weather and climate parameters involves hundreds of thousands of people around the world every day whose main job it is to make these measurements and provide them for weather and climate analyses and predictions.

Two main climate variables or parameters of interest to lay people are precipitation (rain, snow, or other forms) and temperature. Climate scientists are also interested in studying patterns of variations in time series of other parameters such as winds, ocean temperatures, snow and vegetation covers, and soil moisture. Many techniques developed for data analysis in other fields have been applied or adapted to climate variability analysis. This is an overview of some frequently used techniques.

Before we begin any analysis, it is very important to decide why we want to do it. Also, we should judge whether the available data are suitable for the purpose(s) we have in mind. If possible, it helps to frame questions we want to address to the data. The selection of technique(s) and interpretation of results depend on the questions. It can be very instructive to inspect a time series visually before putting it through rigorous analysis. A visual inspection can tell us if there is a linear trend (increasing or decreasing) in the time series, if there are prominent cycles in the time series, and if there are discontinuities in the time series. If there is a linear trend from the beginning to the end of the time series, the slope and intercept of the trend should be estimated and the trend should be removed from the time series before applying any analysis technique. Then, if one of the questions we framed is “Are there prominent cycles and what are their periods?”, we should apply some type of spectrum analysis technique which shows strengths of cycles (or oscillations) as a function of cycle period. Each technique has positive and negative aspects which must guide the selection and later interpretation of results. Some commonly used techniques are Fourier, Singular Spectrum, and Multi-Taper Method. Results from these techniques can be plotted as a graph of oscillation frequency (or period) on the x-axis and the strength of each oscillation on the y-axis. Results from each of these techniques should be compared with chance occurrence of prominent cycles; such comparisons are known as assessment of statistical significance of results. Results can also be checked qualitatively against “poor man’s spectrum analysis” in which the total length of a time series is divided by the number of prominent peaks (or valleys) in the time series. This ratio gives an estimate of the most prominent cycle period in the time series. In an extension of spectrum analysis techniques known as filtering, unwanted cycle periods (or oscillation frequencies) can be removed and only the remaining components of a time series can be examined. For example, if we want to study only the climate variability with cycle periods longer than 10 years, we can filter out shorter periods and only the variability longer than 10 years can be studied.

If there are two time series of equal lengths and if we want to see if the two are statistically related, we can estimate the correlation coefficient between them. This coefficient can be calculated for simultaneous correlation and also for time delays (known as lags) between the two series by sliding one series with respect to the other. For example, suppose we want to know if rain at two locations 100 km apart is related to each other, we can estimate lagged correlation coefficients between the two rain time series. If the storm causing the rain in both locations is moving from west to east, the western location will experience rain first and then the eastern location will experience it after some time. The lagged coefficients may show this time delay. As in most statistical analysis techniques, it is very important to compare correlation coefficient results with an assessment of chance occurrence to ascertain reality of the correlation.

Extending the previous example further, let’s say that there are more than two time series on an x-y grid, with a time series at each node of the grid. So, now we have 3-dimensional data to analyze. If we want to know if there are dominant patterns in these data, we can apply an extended version of the correlation coefficient analysis. We can select one reference point in the x-y grid and estimate correlation coefficient between the reference point and all grid points. This will give us a map of correlation coefficients which may indicate if there is a large-scale pattern extending around the reference grid point. Such correlation maps can be constructed for several reference points to see if there are dominant patterns in the data. In a more advance technique known as the Empirical Orthogonal Function or Principal Component analysis, a matrix made up of such correlation coefficients can be analyzed to identify dominant patterns defined by their strengths (or variances) and the time evolution of each pattern can also be calculated.

Air and water are fluids.  Therefore, motions and temperatures of atmosphere and ocean are governed by principles of fluid dynamics and thermodynamics.  These principles are formulated in terms of mathematics.  Since the motions and temperatures are functions of several variables such as space (longitude, latitude) and time, the so-called laws of motion and temperature are express time and space evolutions of winds, ocean currents, and temperatures as differential equations.  These equations also incorporate laws of thermodynamics because air and water absorb as well as give up heat.  Other differential equations govern evolutions of water vapor, chemical constituents, and salt in the oceans.  Since water can exist in air as solid, liquid, or vapor depending on air temperature, processes which convert any of these phases to other phases are also included in the governing equation for water vapor as are processes of evaporation and precipitation (rain, snow, or other forms of precipitation).  Processes which form clouds, which dissipate momentum by friction, which transfer heat, and which change salt content of ocean water are also included in the governing equations.  Finally, an equation describing expansion/contraction of air or water column is also included in the governing equations.

These equations contain non-linear terms, derivatives with respect to time and space co-ordinates, and localized heat-momentum-water transfer processes, so they cannot be solved analytically and have to be solved numerically.  There are various numerical methods of solving these equations, but the simplest method is to define a longitude-latitude-height grid centered on the geographical area of interest and to “solve” the governing equations at each grid point by approximating derivative terms as finite differences.  Numerical methods have been developed which conserve momentum, heat, and other physical quantities as required by the principles of fluid dynamics and thermodynamics.  The last requirement is to define motion, temperature, salt, water vapor, etc. conditions at the boundaries of the grid domain.  These governing equations are then solved with powerful computers.  The finer the grid spacing, the larger the computing power needed to solve the governing equations.

For short term weather forecasting, only the atmosphere model is used and boundary conditions such as land and snow cover, and ocean temperature are kept fixed; these are usually based on observed data for the region of interest.  For long term climate simulation and forecasting, an atmosphere model is coupled to ocean and land models such that variables of these models interact in space and time, and boundary conditions are fixed for the entire atmosphere-ocean-land system being modeled.  Besides climate simulation and forecasting, such coupled climate models are also used in estimating potential impacts of changes in land cover-land use, urbanization, desertification, forestation/de-forestation, and changes in atmospheric constituents such as CO₂, methane, and volcanic material.  Potential effects of changes in incoming solar radiation are also estimated with coupled climate models.  Such models require much more computing power compared to short term weather forecasting models.