David Lobell (Stanford University) and co-workers have related changes in crop yields to observed climatic shifts over the past thirty years. They found that long-term temperature changes are having a greater impact on yields in major agricultural areas than shifts in rainfall patterns. A grain trader might find this fact surprising. There is a well-known rule of thumb that crops benefit from plenty of rain during the vegetative (growth) stages and drier conditions during the fruiting/harvest stages. Low yields or poor quality occur if these conditions are not met. Therefore yield variability is often associated with rainfall variability. The finding by Lobell and co-workers is an example of how short-term variability can mask a longer-term underlying trend.

Nowadays climatic forecasts are made using state-of-the-art physics based models such as CFSv2. Where there is sufficient historical data, these models can also be used to recreate the state of the atmosphere in the past. The maps below show the trends in 2m temperature over land during 1982-2010. Trends were extracted from CFSv2 Reanalysis data using R‘s raster package and plotted using ggplot2 (“trends” means linear regression coefficients although there is markedly non-linearity in many places.)

The upper map is for December-January-February (DJF) and the lower for June-July-August (JJA). Globally, DJF warmed by ~0.36^oC/decade over land while JJA warmed somewhat less ~0.28^oC/decade. Winter in North America and Scandinavia warmed by several degrees during the period 1982-2010, whereas summer warming was much weaker. There are even some places where winter and summer trends are reversed. The US breadbasket states show little warming (even some cooling) during the summer  growing season, but this is far from the case in Central Europe or Russia.

Corresponding maps for rainfall look quite different:

While regional trends can be large ~ ±50mm/decade, there was no significant net wetting or drying trend over land.

The spatial and temporal structure of climatic shifts during 1982-2010 is much more complex than headline global warming numbers suggest. For agriculture, the details matter a great deal.

How severe are conditions in 2010 compared to previous Russian droughts and heat waves?

The plot^[2] shows monthly growing season precipitation versus temperature anomalies for wheat croplands 1948-2010. A positive index value indicates high cropland precipitation or temperature. June and July this year are clear outliers.

Gridded 200km climate data (NCEP Reanalysis) were re-projected^[1] to an equal area projection and standardized^[4]. Then a weighted average over the harvested area for the year 2000 (data from C. Monfreda et al) was carried out.

__________________________________________________

[1] USDA World Agriculture Report, August 2010 http://www.fas.usda.gov/psdonline/circulars/production.pdf

[2] made using smoothScatter() base R graphics.

[3] raster map calculations using raster package by Robert J. Hijmans & Jacob van Etten.

[4] Monthly standardized precipitation and standardized temperature indices.

GlobCover Example

Puntarenas is a province on the pacific coast of Costa Rica.  The province has a typical mix of tropical land cover. This includes some spectacular examples of Pacific Rainforest, notably on the Osa Peninsula. Puntarenas has an area of ≈ 11,000 sq. km or about 120,000 GlobCover pixels.

13 land cover types are present in the GlobCover map below. The barplot on the right shows the total amounts present in each class.

The GlobCover legend (above) has mixed land cover classes, where more than one biome occurs  inside a map pixel. This is especially true in the man-made biomes (agriculture) . For example, there are three cropland land cover types depending on the relative amounts of other vegetation present.

GlobCover map making in R

R is a programming language, not a specialised geographic information system (GIS) such as GRASS or commercial packages. However applications of R to spatial problems is a growth industry.^[2]

A GlobCover map similar to the above can be produced for any area of interest. The Geospatial Data Abstraction Library (GDAL) should be installed on your system. FWTools is the place to go. You also need R packages sp and rgdal installed. The regional GLOBCOVER map for Central America can be downloaded from ESA here. GlobCover is in GeoTiff format i.e. a Tiff image file which contains georeferencing information. The following GDAL command (from command line, or run from R using shell) creates a 4° x 4° submap centred on Costa Rica.

gdalwarp GLOBCOVER_200412_200606_V2.2_CentralAmerica_Reg.tif -te -86 8 -82 12 costaRica.tif


costaRica.tif is read into R using the rgdal package:

library(rgdal)
costa <- readGDAL("costaRica.tif")

costa has class SpatialGridDataFrame, which is a class defined in the package sp (loaded when rgdal is loaded).

Administative boundaries for Costa Rica were obtained from Global Administrative Areas www.gadm.org (see Revolution R blog post)

con <- url("http://gadm.org/data/rda/CRI_adm1.RData")
load(con)
close(con)

Costa Rican provinces are now contained in the object gadm of class SpatialPolygonsDataFrame. The boundaries of Puntarenas province (excluding Cocos Island) are extracted as follows:

Polygons(list(Polygon(gadm@polygons[[6]]@Polygons[[27]]@coords),Polygon(gadm@polygons[[6]]@Polygons[[25]]@coords)),"puntarenas")
temp <- SpatialPolygons(list(temp),proj4string=CRS(proj4string(gadm)))
punt.sp <- SpatialPolygonsDataFrame(temp, data.frame(cbind(2,2), row.names=c("puntarenas")))  # puntarenas


The overlay() method  is used to extract the land cover map puntarenas from costa:

puntarenas <- costa
puntarenas.overlay <- overlay(costa,punt.sp)  # 1 in interior of puntarenas polygons, 0 outside
puntarenas$band1 <- costa$band1*puntarenas.overlay

Unfortunately overlay() is rather slow, because it applies point.in.polygon() to the entire raster. Eventually puntarenas appears as a SpatialGridDataFrame which can be plotted using standard R tools such as image().

The code needed to generate the above plot is here.

footnotes

[1] For example, the International Biosphere-Geosphere Programme (IGBP) land cover legend used 17 biomes. The University of Maryland map used 14 biomes. At much lower resolution, numerical weather forecasting models such as US National Center for Climate Prediction Global Forecasting System (NCEP-GFS) also use alternative schemes.

[2] Roger S. Bivand, Edzer J. Pebesma, and Virgilio Gómez-Rubio. Applied Spatial Data Analysis with R. Springer, New York, 2008

]]> http://joewheatley.net/mapping-biomes/feed/ 3 http://joewheatley.net/black-swan-white-mountain/ http://joewheatley.net/black-swan-white-mountain/#comments Tue, 26 May 2009 16:31:13 +0000 joe http://joewheatley.net/?p=329 Everyone knows that tree rings mark annual variations in tree growth. Biomass production is influenced by climatic variability  (precipitation,temperature, sunlight) or disease, pests, fire etc. Tree rings can be measured very accurately and used to recover information about past climate over thousands of years.

The World Data Center for Paleoclimate (NOAA) maintains a  tree ring database. As well as raw data on growth rings for individual trees, the database contains “chronology” files labelled  ***.crn. These files contain annual growth data averaged over small stands of trees, and indexed relative to the mean growth. Thus an index value of 1000 is average growth, index lower than 1000 is below average growth etc. Here is a simple R script which uploads the chronology file  “ca535.crn” file into a time-series treeRing.ts. ca535.crn describes annual growth in an ancient Bristlecone Pine forest in the White Mountains of California from 6000 BC to 1979 AD. The world’s oldest known (non-clonal) tree  is a member of the stand of Bristlecone Pines making up this index. The area is known as Methuselah Grove.

You can click on the plot below to see a full-screen version.

Most of the volatility in the growth of Bristlecone Pines in the White Mountains is due to drought. The investigator Edmund Schulman wrote “There is something a little fantastic in the persistent ability of a 4,000-year-old tree to shut up shop almost everywhere throughout its stem in a very dry year, and faithfully to reawaken to add many new cells in a favorable year.” (1958). With so much high quality data (7980 points), many interesting questions can be asked about climatic variability at this location. For example, a statistical model can be built relating recent tree ring growth to observed precipitation and temperature, say. Such models are used to extract information about historical climate.

The following R commands produce a histogram of tree ring growth values (probability distribution) as well as a smooth curve fit:

library(MASS)
truehist(treeRing.ts,nbins=50,main="Distribution of Growth Index at Methuselah Grove",font.main=2,font.axis=2,font.lab=3,xlab="Growth Index",ylab="Density");
lines(density(treeRing.ts),lwd=2)

The distribution approximates a bell-shaped curve, but there is a pronounced “fat-tail” on the low growth side. For example, there  is only one year with growth index > 1900, but there are 44 years with growth < 100.

If you only ever read one book about statistics, make sure it is Nassim Taleb’s book The Black Swan. Fat-tailed distributions (such as drought impact on Bristlecone Pines) are the norm in complex systems. Many of Taleb’s examples are from finance and economics. However geophysical time-series, such as precipitation levels, often have this property. When making inferences from data, it is important to decide in advance what kind of process you are likely to be dealing with. A process where there is no clear constraint on the outcome (such as a physical conservation law) is likely to be subject to fat-tail events.

The asymmetry in growth distribution in White Mountain Bristlecone Pines is due to the fact that higher than normal precipitation levels cannot boost growth beyond the limits set by available temperature, sunlight and plant physiology. Drought years, however, virtually eliminate growth.

Traditional farmers in drought-prone parts of the world are acutely aware of the fat-tailed distribution. Farming practices which appear sub-optimal to some, may in fact be adapted to the existence of fat-tails. Nassim Taleb points out that risk managers in banks tend to behave as though Black Swans do not exist.

In that sense, bankers know less about real-world statistics than subsistence farmers.

Computed values of  maize yield volatility for the top six producer countries are shown in the table below.

Maize Yield Volatilities

Yield volatility for the world’s top producer (the US) is surprisingly large at 9%. It is also apparent from the plot that there is little correlation in yield variations between countries, at least for the top six producers. This explains why the global yield volatility (5%) is substantially lower than individual country volatilities. Just as in finance, diversification lowers risk.

Belarus

What drives these relatively large annual fluctuations in maize yield? One of the most important factors influencing crop yields is climatic variability. Changes in precipitation, water vapour, temperature, cloud cover, frost, hail, snow-cover etc may affect harvest, depending on region and crop. However, management practices, such as fertiliser use, may also vary from season to season. Sometimes this is a large effect. For instance, crop yields in many Eastern block countries collapsed after break-up of the Soviet Union in 1991. The graph below illustrates this in the case of Belarus maize. Yields collapsed in 1993 and 1994, but have recovered strongly since. For the interval 1961-1991 the plot shows aggregate USSR data, because FAO does not have data for individual FSU states prior to 1992.

Zimbabwe

Zimbabwean maize yields (below) began to fall in the early 1980′s. While the fall is less dramatic than the case of Belarus, yields have not recovered due to local political factors. In contrast to neighbouring Zimbabwe,  South Africa shows a steady improvement typical of the Green Revolution.

Despite the different trends in Zimbabwe and South Africa, annual variations in yield are correlated. The reason is that both countries are strongly influenced by droughts associated with the El Nino Southern Oscillation (Equatorial Pacific sea surface temperature anomaly). This was pointed out in 1994 in an influential article article by Cane et al . The yield variations about trend line reflect climatic variability in Southern African countries.

Conclusions? It appears reasonable to decompose crop yield time-series into a smooth trend (reflecting the Green Revolution) and fluctuations about the trend. Annual variations are driven primarily by climate (e.g. Southern Africa maize) and sometimes by abrupt changes management practices (e.g. Belarus maize).

The graph shows global average yields of some major agricultural crops from 1961 to 2007. The source of the data is the Food and Agriculture Organisation (FAO) of the United Nations^[1]. The remarkable improvements in the yields of most major crops since the 1940s is known as the Green Revolution.  Per capita calorific food production has increased, as production has outpaced population growth during this period.

How has this doubling or tripling of agricultural yields been achieved? A major driver of high yield is the breeding and gradual adoption of new plant varieties with increased harvest index. The harvest index is the fraction by weight of the total above-ground biomass which contributes useful product (the grain from a rice plant, for example.)

Intensive farming methods, such as use of fertilizers, irrigation and pest control, are often required to make the new cultivars viable.

The benign outlook promised by the above graph seems to be contradicted by recent reports, such as United Nations Environment Programme GEO4^[2] report. Firstly while most crops and regions continue to show improved yields, there are physical limits on possible future gains in harvest fraction through plant breeding. Secondly, environmental constraints (and climate change) will increasingly impact agriculture in many parts of the world. According to one study^[3], more than 30% of terrestrial photosynthesis has already been appropriated by humans. Nearly 50% of the available rainwater resources are exploited by agriculture for crop irrigation.

The view that resource constraints (on crop yields, land area, water etc) are about to impact agriculture is a reversal of prevailing wisdom. It has been referred to as Green Revolution Fatigue. Is there evidence in the FAO data that the rate of yield improvement is slowing? The graph below shows that wheat yield growth is slowing and may be saturating.

[1] fao database, faostat

[2]united nations environment programme, GEO4 report

[3]human appropriation of net primary productivity, haberl et al