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  • Author or Editor: T. M. L. Wigley x
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T. M. L. Wigley
and
Tu Qipu

Abstract

A new technique in statistical crop-climate analysis, the direct linking of spatial patterns of crop yield and spatial patterns of climate, is explored. Yield and climate data from networks of crop reporting districts and meteorological stations are decomposed into orthogonal components using principal components analysis. Each yield component is then expressed as a function of the climate components using multiple regression. These regression equations are then combined to give an equation which relates interannual variations in the spatial patterns of yield to interannual variations in the spatial patterns of selected climate variables. The method is illustrated using wheat yield data from 59 crop reporting districts in southwestern Western Australia covering the period 1929–75. The regression models are calibrated using data for the period 1929–65 and the results are verified using data for the period 1966–75. The climate contribution is shown to be highly significant, with winter precipitation being the most important variable. A single equation relating yield and climate patterns correctly reproduces the differing results obtained for separate parts of the study area by earlier workers. The influence of winter and autumn precipitation is nonlinear and, as a consequence, the study area divides into three zones: a high rainfall area where rainfall is generally more than optimum so that lower rainfall gives higher yields; a low rainfall area where rainfall is, on average, less than optimum so that positive rainfall anomalies are associated with higher yields; and an intermediate zone where average rainfall is close to optimum so that anomalies in either direction tend to suppress yields. Our analysis shows no evidence for any significant change in the sensitivity of wheat yields to climate in spite of a complete change in the variety of wheat cultivated.

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T. M. L. Wigley

Abstract

This paper presents the results of a numerical solution of the equations of moist plume rise and compares the trajectories of wet and dry cooling tower and scrubbed industrial plumes under a wide range of atmospheric stability conditions. Similar comparisons have been made previously by Wigley and Slawson, Hanna, and Weil, and the results of these authors are discussed. It is found that their results are all qualitatively correct, but that there are important quantitative differences between their results and the numerical solution. Previous approximate analytic results have shown that the critical lapse rate for the transition to unstable plume behavior for wet plumes is close to the saturated adiabatic lapse rate. The more-complete numerical solution confirms this result when one allows for the variation of the saturated adiabatic lapse rate with height. The approximate analytic formula for the maximum height of rise of dry plumes is also examined and found to overestimate plume rise by 6–20% when compared with the numerical solution.

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T. M. L. Wigley

Abstract

The one-dimensional theory for the condensation of buoyant plumes is extended to include supersaturation as an extra variable. An additional equation describing the dynamics of droplet growth is used to make the system tractable. Some simple mathematical results are obtained which allow one to relate the theory to, and so extend, a commonly used graphical representation of the condensation process. The theory is then simplified to a single nonlinear first-order differential equation for the condensed water content. This is solved numerically for a typical jet, scrubbed industrial plume and natural-draft cooling tower plume to obtain down-plume profiles of condensed water content, supersaturation and mean droplet size. High supersaturation is predicted in all three cases, corresponding to mean relative humidities of up to 170% (jet), 150% (scrubbed plume) and 105% (cooling tower). These results may be important in predicting the growth of “foreign” carry-over droplets in plumes from industrial sources or cooling towers. Predictions of plume length in these cases is found to be insensitive to supersaturation, but plume length is noticeably affected by supersaturation in the case of a jet. In the examples considered maximum mean droplet radii never exceed 10 μm which supports the belief that rain-out is caused primarily by carry-over from imperfect mist eliminators.

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T. M. L. Wigley

Abstract

The application of the maximum plume rise formula for bent-over industrial plumes to visible cooling tower plumes depends on the validity of two assumptions: the neglect of finite source size and the neglect of condensation effects. These produce errors which, in many cases, tend to compensate. The effect of finite source size is examined analytically and an alternative formula for maximum plume rise is derived.

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T. M. L. Wigley
and
P. R. Slawson

Abstract

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T. M. L. Wigley
and
P. R. Slawson

Abstract

The theory of moist bent-over plume behavior given by Csanady and by Wigley and Slawson is expanded and clarified to illustrate the differences between moist and dry plume behavior under various atmospheric stability conditions associated with linear gradients of temperature and humidity. If plume types are defined according to the behavior of a dry plume in stable, neutral and unstable conditions, then it is found, for example, that a condensed (or ‘wet’) plume rising in an atmosphere with lapse rate equal to the saturated adiabatic lapse rate will behave as a ‘neutral’ plume, while a dry plume in the same atmosphere will behave as a ‘stable’ plume. Also, while the condensed portion of a given plume rises according to one stability criterion, the re-evaporated portion may rise according to another.

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T. M. L. Wigley
and
P. R. Slawson

Abstract

The theory of growth of dry plumes is extended to include the effects of moisture in both the vapor and liquid forms. A relation determining the point at which a moist plume first condenses is derived. Numerical solutions of this relation indicate that, under most atmospheric conditions, condensation either occurs very close to the stack or not at all. A method for predicting whether or not condensation will occur for arbitrary conditions of atmospheric relative humidity and initial temperature excess and relative humidity of the plume is given. The special case where the plume is initially saturated, corresponding to cooling tower effluents, is considered in more detail.

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J. M. Lough
,
T. M. L. Wigley
, and
J. P. Palutikof

Abstract

Scenarios for Europe in a warmer world, such as may result from increased atmospheric carbon dioxide levels, have been constructed using the early 20th century warming as an analogue. Mean temperature, Precipitation and pressure patterns for the period 1934–53 were compared with those for 1901–20. These are the warmest and cooler twenty-year periods this century based on Northern Hemisphere annual mean surface air temperature data, differing by 0.4°C. The climate scenarios show marked subregional scale differences from season to season, and individual season scenarios often show little similarity to the annual scenario. Temperature scenarios show warming for the annual mean and for spring, summer and autumn. The largest positive changes are found in higher latitudes. Winters over a large part of Europe are actually cooler and show greater interannual variability during the warmer period. These changes appear to be associated with a greater frequency of blocking activity. Precipitation changes occur in both directions in all seasons. There is, however, an overall tendency for spring and summer to be drier and autumn and winter to be wetter.

The climate scenarios are used to construct scenarios of the impact of a global warming on energy consumption and agriculture. Cooler winters alone would imply greater energy demand for space heating, but this is largely offset by warmer temperatures in spring and autumn which reduce the length of the heating season. Increased temperature variability combined with a general cooling during winter over north and northwestern Europe suggests a greater frequency of severe winters, and thus larger fluctuations in the demand for heating energy. The impact on agriculture is difficult to assess because of the complexity of crop-climate relationships and because of the importance of nonclimatic factors associated with technological change and, perhaps, with enhanced photosynthesis due to increased carbon dioxide concentrations. In northern latitudes, the increase in the length of the growing season would appear to be favorable for agriculture, but warmer summers drier springs and wetter autumns would be less favorable. A specific study was made of the effect of two different climate scenarios on crop yields in England and Wales with regression models constructed using a principal components regression technique. Most crops showed a decrease in yield for both warm-world scenarios, with largest decreases for hay yield and least effect on wheat yield. A similar regression analysis of French wine quality showed an improvement in the quality of Bordeaux and Champagne in a warmer world.

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T. M. L. Wigley
,
K. R. Briffa
, and
P. D. Jones

Abstract

In a number of areas of applied climatology, time series are either averaged to enhance a common underlying signal or combined to produce area averages. How well, then, does the average of a finite number (N) of time series represent the population average, and how well will a subset of series represent the N-series average? We have answered these questions by deriving formulas for 1) the correlation coefficient between the average of N time series and the average of n such series (where n is an arbitrary subset of N) and 2) the correlation between the N-series average and the population. We refer to these mean correlations as the subsample signal strength (SSS) and the expressed population signal (EPS). They may be expressed in terms of the mean inter-series correlation coefficient as
n,N 2nNNN
N 2Nr̄N
Similar formulas are given relating these mean correlations to the fractional common variance which arises as a parameter in analysis of variance. These results are applied to determine the increased uncertainty in a tree-ring chronology which results when the number of cores used to produce the chronology is reduced. Such uncertainty will accrue to any climate reconstruction equation that is calibrated using the most recent part of the chronology. The method presented can be used to define the useful length of tree-ring chronologies for climate reconstruction work. A second application considers the accuracy of area-average precipitation estimates derived from a limited network of raingage sites. The uncertainty is given in absolute terms as the standard error of estimate of the area-average expressed as a function of the number of gage sites and the mean inter-site correlation.
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P. D. Jones
,
S. C. B. Raper
, and
T. M. L. Wigley

Abstract

A new compilation of monthly mean surface air temperature data for the Southern Hemisphere for 1851–1984 is presented based on land-based meteorological station data. Where possible, the station data used in the analysis have been assessed for homogeneity. Only reliable or corrected station data have been used in calculating area averages. Grid point temperature estimates have been made by interpolating onto a 5° lat by 10° long grid for each month of the 134 years. For the period of best data coverage, 32% of the area of the Southern Hemisphere is covered. The reliability of hemispheric estimates is assessed for earlier periods when coverage is less than this maximum. Year-to-year estimates are considered reliable back to about 1890 and earlier estimates can indicate trends back to the 1860s. This new hemispheric compilation is compared with estimates of Southern Hemisphere marine data, and comparisons between land and marine data for both hemispheres are made and interpreted. The data show a long-term warming trend amounting to about 0.5°C over the past 100 years. The 1938–65 cooling trend that is so evident in the Northern Hemisphere data shows up only as a hiatus in the long-term warming of the Southern Hemisphere, pointing towards some hemispherically specific causal mechanism.

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