GMDDGeoscientific Model Development DiscussionsGMDDGeosci. Model Dev. Discuss.1991-962XCopernicus GmbHGöttingen, Germany10.5194/gmdd-8-4781-2015Modelling spatial and temporal vegetation variability with the
Climate Constrained Vegetation Index: evidence of CO2
fertilisation and of water stress in continental interiorsLosS. O.s.o.los@swansea.ac.ukhttps://orcid.org/0000-0002-1325-3555Department of Geography, Swansea
University, Swansea SA2 8PP UKS. O. Los (s.o.los@swansea.ac.uk)22June2015864781482120May201526May2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://gmd.copernicus.org/preprints/8/4781/2015/gmdd-8-4781-2015.htmlThe full text article is available as a PDF file from https://gmd.copernicus.org/preprints/8/4781/2015/gmdd-8-4781-2015.pdf
A model was developed to simulate spatial, seasonal
and interannual variations in vegetation in response to temperature,
precipitation and atmospheric CO2 concentrations; the model
addresses shortcomings in current implementations. The model uses
the minimum of 12 temperature and precipitation constraint functions
to simulate NDVI. Functions vary based on the Köppen–Trewartha
climate classification to take adaptations of vegetation to climate
into account. The simulated NDVI, referred to as the climate
constrained vegetation index (CCVI), captured the spatial
variability (0.82<r<0.87), seasonal variability (median r=0.83) and interannual variability (median global r=0.24) in
NDVI. The CCVI simulated the effects of adverse climate on
vegetation during the 1984 drought in the Sahel and during dust
bowls of the 1930s and 1950s in the Great Plains in North
America. A global CO2 fertilisation effect was found in NDVI
data, similar in magnitude to that of earlier estimates (8 % for
the 20th century). This effect increased linearly with simple ratio,
a transformation of the NDVI. Three CCVI scenarios, based on
climate simulations using the representative concentration pathway
RCP4.5, showed a greater sensitivity of vegetation towards
precipitation in Northern Hemisphere mid latitudes than is currently
implemented in climate models. This higher sensitivity is of
importance to assess the impact of climate variability on
vegetation, in particular on agricultural productivity.
Introduction
Spatial, seasonal and interannual variations in
vegetation in response to climate affect vegetation photosynthesis and
the global carbon cycle, hydrological cycle and energy
budget. Feedbacks between the land surface (soil moisture and
vegetation) on the one hand and the atmosphere (water, carbon and
energy fluxes) on the other can enhance or mitigate the effects of
climate variability or can improve forecasting of precipitation
. The
realistic simulation of spatial and temporal variability in vegetation
is therefore important, but the ability to do so is limited in current
land-surface parameterisations and ecosystem models. For example,
, using the community land model
(CLM) version 3 found a difference of
up to 3 months between modelled and measured timing of maximum leaf
area. tested 14 commonly used
land-surface parameterizations on 10 sites across North America and
found large discrepancies between seasonal and interannual variations
in observed and modelled leaf area index
(LAI). found that leaf seasonality simulated
with the Joint UK Land Environment Simulator (JULES)
south of the Sahara
did not match satellite observations.
calculated spatial correlations between Northern Hemisphere (>30∘ N) LAI from 11 earth system models and satellite derived
LAI; these correlations varied between 0.21<r<0.66; i.e. at
best 44 % of the spatial variance in observed leaf area index was
explained. There is therefore a clear need for improved simulations of
spatial and temporal variability of vegetation in models.
Temporal and spatial variability in vegetation parameters (leaf area
index or associated parameters) is generally modelled as a function of
temperature, e.g. growing degree days, and of soil moisture or drought
stress . Other, related approaches exist,
e.g. Lieth's Miami model estimates annual potential net primary
productivity (NPP) as the minimum of two constraints; one dependent on
mean annual temperature and the other on annual precipitation
. The Miami model captures spatial and temporal
variations in NPP well although some interannual
variability in NPP is lost . The Miami model
uses an annual time step, although adaptations exist to obtain
smaller, e.g. monthly time steps . The Reconstructed
Vegetation Index (RVI) simulates
monthly NDVI values from monthly precipitation and temperature using
an empirical model that is optimised for each location across the
global land surface. The RVI reproduces spatial, seasonal and
interannual variability well . A disadvantage of
the RVI is that equations are optimised for current climatic
conditions. It is therefore likely that the RVI is less suitable for
simulations where climate deviates from current conditions. Examples
are glacial periods or climate regimes that may occur if atmospheric
CO2 concentrations and global temperatures continue to rise.
A related issue is that a range of land-surface parameterizations and
ecosystem models use current representations of land cover to derive
biophysical parameters . These representations cannot be used without
modification for scenarios under different climate regimes.
In the present study, a model was developed that uses atmospheric
CO2 concentrations, precipitation and temperature as inputs to
simulate spatial, seasonal and interannual variability in leaf area
and associated parameters globally (Sect. ). The model
can be applied to a range of climate scenarios, including those from
the recent geological past as well as climate change scenarios with
increased atmospheric CO2 concentrations and elevated
temperatures. Equations describing the constraints of precipitation
and temperature on NDVI were derived for each of the six main
Köppen–Trewartha climate zones A–F
(Sect. ). These equations used different lags – up to
3 months and annual for precipitation and up to two months for
temperature. Analogous to the Miami model , the
minimum of the precipitation and temperature constraints was selected
to represent the NDVI. The resulting estimate of NDVI was referred to
as the climate constrained vegetation index (CCVI;
Sect. ). An adjustment was made for non-linearities
between the simulated CCVI and observed (1982–1999) NDVI
(Sect. ). In Sect. the CCVI fields
were tested against AVHRR data (1982–1999, i.e. compared to the same
data used to derive the CCVI model), against MODIS data (2001–2010,
which were not used to derive the CCVI model), phenology data at local
sites – predominantly from the second half of the 20th century – and
the global, monthly reconstructed vegetation index
1901–2006;. When tested on
well-known extreme events – the North American dust bowl during the
1930s and 1950s and the 1984 drought in the Sahel, south of the Sahara
– the CCVI simulates a large decrease in NDVI
(Sect. ). A CO2 fertilisation effect on NDVI
was estimated from residuals between model and observations
(Sect. ). Application of the CCVI to climate change
scenarios indicated a greater sensitivity of vegetation to changes in
precipitation in the interiors of North America and Eurasia than found
in other land-surface parameterisations (Sect. ).
Data
The fused Advanced Very High Resolution Radiometer (AVHRR; 1982–1999)
and Moderate Resolution Imaging Spectroradiometer (MODIS; 2001–2010)
Fourier Adjusted, Solar and sensor zenith angle corrected,
Interpolated and Reconstructed (FASIR) Normalised Difference
Vegetation Index (NDVI) data for 1982–2010 were used
. This data set is corrected for sensor
degradation of the AVHRRs, bidirectional effects, atmospheric
scattering and absorption; outliers are removed and missing data
filled in
The Climate Research Unit (CRU) time series (TS) monthly, global air
surface temperature and precipitation data version 3.21 at 0.5∘×0.5∘ were used . The data set
extends from 1901 to 2013.
Mauna Loa monthly atmospheric CO2 concentrations for
1958–2010 were obtained from NOAA
and were extended back to 1901
with the annual CO2 records from the Law Dome DE08,
DE08-2, and DSS ice cores .
Three gridded monthly precipitation, temperature and leaf area index
products based on representative concentration pathway RCP4.5 climate
simulations over 2006–2100 were obtained for the Max Planck Institute
Earth System Model , the Met Office
Hadgem-CC model and the NSF/DOE NCAR (National
Center for Atmospheric Research Community Earth System Model coupled
to the BioGeochemical Cycles model (CESM1-BGC)
. The scenarios form part of the coupled model
intercomparison project phase 5 (CMIP 5)
. These fields, together with the 4.5
mid-year greenhouse gas concentrations for 2006–2100
were used to simulate global, monthly CCVI
(Sect. ).
Method
The six major Köppen–Trewartha climate regions
(Sect. ) were used to allow for climate dependent
variations in precipitation and temperature constraints on NDVI
(Sect. ). The CCVI was calculated at monthly time step,
but higher temporal resolution can be obtained by using moving monthly
windows over a shorter, e.g. daily, time step.
Köppen–Trewartha classification
The Köppen–Trewartha (KT) classification was used to stratify the
globe into similar climatic regions because it closely resembles the
distribution of global vegetation cover and can be derived using only
precipitation and temperature data. Implementation of this
classification scheme in ecosystem models and land-surface
parameterisations is therefore straightforward. The KT classification
adapts to different climate regimes and can be updated on an annual
basis in transient model simulations.
In Table the rules are set out to obtain the 6 major KT
classes (A–F). Class BS serves, in the present study, as an
intermediate between class A and B and contains 50 % of
both. Two modifications were made to the KT classification. The first
was that cold deserts were grouped into class D, E or F because
analysis of temperature constraints on NDVI showed that at low
temperatures NDVI values were higher in cold deserts than in warm
deserts (Sect. ). The second modification was that
transitions between classes C and D, D and E and E and F were
considered to be continuous.
Continuous transitions between classes C, D, E and F were modelled
using the total number of months during a 30 year period with mean
temperature above 10 ∘C, NT>10, rather than the total
number of months from a 30 year average climatology commonly
used in the KT classification scheme. The total number of months above
10 ∘C was divided by the length of the time period
(30 years); NT>10 becomes thus a fraction. The continuous
transitions were calculated as follows: 25 and 75 % values were
calculated from the NT>10 frequency distributions for the classes
C, D, E and F. Transitions between C and D were changed proportionally
from the 25 % value of C (lower number of warm days in class C) to
the 75 % value of D (higher number of warm days in class
D). Transitions between D and E and E and F were calculated
similarly. The continuous transitions ensured smooth changes in CCVI
values across KT classes (Sect. ).
Table provides a comparison of the SIB classification
developed by EROS Data Center and the major
KT classes derived in the present study (using the discrete KT
classification). The agreement is for the most part logical and
misclassifications occur only in a few instances, e.g. for evergreen
broad leaf trees in KT classes D–F) and for trees with ground cover,
ground cover and shrubs with ground cover – in KT class B. The
occurrence of agriculture in KT class F is unlikely as well.
Climate constraints on NDVI
The approach to simulate NDVI was based on that of the Miami model
. The Miami model calculates annual potential net
primary productivity (NPP) as the minimum of two constraints; one
based on temperature and the other on precipitation (Fig. 1). The
spatial and temporal variations in Miami NPP correlate well with those
in satellite observations , although not all
variability is captured and NPP derived from satellite data appears
more realistic . One limitation using just 2
functions to predict NDVI for the globe is that adaptations of
vegetation to different climate regimes cannot be taken into account
(Sect. ).
A leaf seasonality model, implemented in a land-surface model or
ecosystem model, can only use antecedent conditions as
input. Therefore, the model was set up to calculate end-of-month NDVI
values (rather than average monthly values that represent the middle
of the month) from average monthly temperature and total monthly
precipitation. End-of-month NDVI values were calculated as the average
of month t and month t+1. For precipitation seven constraints on
NDVI were calculated and for temperature five. The constraints were
calculated for individual months at different lags as well as for
combinations of multiple months and in one case (precipitation) the
total annual value was used (Table ). The number of
combinations of months included was based on a sensitivity analysis on
a sample data set; inclusion of the last case (average total
precipitation over past 3 months) resulted in only a small
improvement. For each of the cases included, the independent variable
(precipitation or temperature) was divided into 64 intervals and the
95 percentiles of NDVI distributions were calculated for each
interval. Separate cases were considered for ascending NDVI
(NDVIt>NDVIt+1) and descending NDVI
(NDVIt<NDVIt+1), since hysteresis is frequently
observed in the response of NDVI to climate.
Figure shows examples of precipitation and
temperature constraints for ascending NDVI and several KT
classes. Note that for colder KT classes, the temperatures around the
freezing point show higher NDVI values; e.g. the class E NDVI value
around the freezing point is about 0.4 whereas the class C NDVI value
is around 0.2.
Segmented regression
Equations describing the 95th NDVI percentile as a function of climate
were estimated using segmented regression
. Segmented
regression has several advantages: inflation of deviations from the
mean model is smaller for linear segments than for quadratic or higher
order polynomials. In addition, segmented regression is flexible and
can be used without a priori knowledge of a relationship between two
variables (e.g. logarithmic, exponential or quadratic). Finally,
compared to the use of polynomial functions, segmented regression is
less likely to give pathological predictions for values outside the
range for which the functions were derived. There is a disadvantage to
segmented regression in that it has a subjective element – the number
of segments is chosen by the user – and solutions obtained for the
same number of segments are not unique because breakpoints between
segments are calculated using a random number generator. Solutions are
often close, however. For the present application, it was thought that
the advantages, i.e. greater flexibility and smaller errors,
outweighed the disadvantages, i.e. introducing a degree of
arbitrariness.
For each solution varying numbers of segments were tried using
different starting values. Solutions were visually inspected, and were
only selected when functions were gradually changing, had preferably
one maximum and had ascending NDVI at the low range of the independent
variable.
A potential pitfall in deriving the NDVI vs. temperature relationships
is that, by their very nature, the KT classes are defined for only
a limited range of temperatures and, as a result, fitted functions may
not reflect the true relationship at the high and low temperature
boundaries. Therefore 95 NDVI percentiles for temperatures of adjacent
classes were used, but with a much lower weighting, to guide the curve
fitting at the temperature boundaries. This affected function
estimation at the lower and/or upper end of the temperature range for
KT classes C, D, E and F.
CCVI was calculated as the minimum of 12 climate functions
representing the ascending NDVI; if CCVIt<CCVIt-1 the minimum of the 12 climate constraints for
descending NDVI was used. The observations showed that the minimum
monthly NDVI over the year was in about 95 % of the cases higher
than 60 % of the average of 12 preceding NDVI values. The minimum
of the CCVI was therefore set at 60 % of the 12 month
average. The version of the CCVI thus calculated is referred to as the
CCVI control.
CCVI adjustment
The CCVI control for 1982–1999 was compared with monthly FASIR NDVI
data of the same period. The comparison was carried out separately for
each KT class (A–F; 6 cases), both types of constraint (precipitation
or temperature limited; 2 cases) and ascending and descending CCVI (2
cases). Thus for a total of 6×2×2=24 cases, estimated
CCVI (independent variable) was compared with observed FASIR NDVI
(dependent variable). The independent variable was divided in 64
intervals and the average for each interval calculated. Adjustment
functions were calculated using segmented linear regression
(Fig. ) and the CCVI was adjusted accordingly. This
version of the CCVI is referred to as the CCVI adjusted
VCad.
The mean annual CCVI and the mean CCVI for January and July for the
period of 1982–1999 are shown in Fig. a, c, and
d and are compared with the FASIR NDVI data for the same periods
(Fig. b, d and f). Deviations between the two
products are in general small (ERMS=0.11 for January;
ERMS=0.12 for July and ERMS=0.09 for the
mean annual average; Fig. ). Relatively large
biases occur in high northern latitudes during winter when no
satellite observations are available and FASIR data are
interpolated. A bias up to 0.1 NDVI occurs during the summer in the
northern boreal forests where FASIR data are higher. However, it is
likely that, after the BRDF correction, a residual positive bias with
an absolute range between 0.03 and 0.05 NDVI remains in the FASIR NDVI
data in high latitudes and this explains 30
to 50 % of the bias in the CCVI.
CO2 fertilisation
found that about 40 % of the increase in NDVI
over 1982–1999 could be attributed to increased atmospheric
CO2 concentrations and 40 % to trends in climate,
predominantly temperature. The magnitude of the CO2
fertilisation effect on NDVI was estimated from residuals between
modelled RVI and observed NDVI. A similar approach can be used to
estimate CO2 fertilisation effect by comparing the CCVI and
NDVI. However, the match between CCVI and NDVI is not as close as
between RVI and NDVI and the estimation of the CO2
fertilisation effect was therefore adapted as follows. First, the
anomalies of the CCVI (departures from monthly means) were subtracted
from the FASIR NDVI to eliminate climate related variability in FASIR
NDVI. Then, the monthly adjusted FASIR NDVI and mean monthly observed
FASIR NDVI were converted to simple ratio using the transformation
SR=(NDVI+1)/(1-NDVI). For each 0.5∘×0.5∘ cell and month, the ratio between the adjusted
FASIR SR and mean monthly observed FASIR SR for 1982–1999 was
calculated. The ratios were aggregated by KT class and changes in the
ratio were expressed as functions of atmospheric CO2 concentrations
using robust linear regression
:
SR{Vi-anom(Vi,Cad)}SR{Vi,seas}=β0+β1[CO2]
with Vi all observed NDVI values for KT class A–E (excluding
transition zones; data for F were not included because the number of
observations was small); anom(Vi,Cad) the anomalies
of the adjusted CCVI (departure of monthly mean), and Vi,seas the seasonal (monthly mean) NDVI and SR the simple
ratio. Coefficients β0 and β1 show a close linear
relationship when plotted against mean SR for each KT class
(Fig. ):
β0=1.28551-0.25776×SR{Vi,j,t}β1=-7.950×10-4+7.119×10-4×SR{Vi,j,t}
The
CO2 fertilisation effect as a function of NDVI shows
saturation at high values because of the non-linear relationship
between NDVI and SR.
Time series of mean annual values over 1901–2010 for both adjusted
CCVI and CO2 adjusted CCVI are shown in
Fig. . Note that filled (close to zero) values were
not included in the CCVI global average but were included in the
previously reported RVI average . The increase in
global mean CCVI compared to RVI over the 20th century is similar for
the CO2 fertilised scenarios, but is smaller in the CCVI
compared to the RVI when CO2 fertilisation is not included.
Results: testing and analysing the CCVI
Spatial correlations (Sect. ), seasonal correlations
and interannual correlations (Sect. ) were calculated
between CCVI on the one hand and NDVI or RVI on the other. Interannual
variations in CCVI were also compared with phenology data, mostly for
the latter part of the 20th century (Sect. ). The
response of the CCVI to two known extreme events was explored; the
dust bowl in North America during the 1930s and 1950s, and the drought
of the century in the Sahel south of the Sahara in 1984
(Sect. ). The response of the CCVI to climate change
scenarios was compared with the leaf seasonality simulations from
three Earth System Models (Sect. ).
Spatial correlation
Figure shows monthly spatial correlations over
time between FASIR NDVI on the one hand and RVI, CCVI (control) and
CCVI adjusted for bias on the other. The RVI shows the highest spatial
correlations, the adjusted CCVI the next highest and the CCVI control
the lowest. The RVI is tuned to the observed time series of
a particular cell and this tends to underestimate
or diminish the effect of errors in the RVI that should be present as
a result of errors in spatial interpolation of precipitation or
temperature.
Spatial correlations are on average higher for 1982–1999 because data
from this period were used to derive both the RVI and CCVI
models. A large decrease appears in the spatial correlation for the
RVI between the AVHRR (1982–1999) and MODIS period (2000–2010); this
decrease is more gradual in the CCVI. Potential causes for the
decrease in spatial correlation after 2000 are (1) that the quality of
gridded precipitation and temperature data diminishes over time as
a result of a decrease in the number of observations available, (2)
differences between the MODIS and AVHRR NDVI or (3) both. A minor but
interesting feature can be observed in the spatial correlations for
the CCVI; these correlations exhibit a saw tooth pattern with higher
correlations just after launch of subsequent NOAA satellites and
a decrease during their time of operation; thus correlations decrease
from 1982–1985 (NOAA-7), from 1985–1989 (NOAA-9), from 1990–1995
(NOAA-11) and from 1995–1999 (NOAA-14). This feature can be linked to
the gradual drift in overpass time to later times of the day and
residual BRDF effects .
Temporal correlation
Both seasonal and interannual temporal correlations were calculated
between FASIR NDVI on the one hand and RVI and CCVI on the
other. Seasonal correlations with FASIR NDVI were high for both RVI
and CCVI for 1982–1999, the period from which equations were derived,
and for 2001–2006; the period not used for model development
(Fig. ). The CCVI showed low correlations in
areas with small seasonal variations such as as in deserts and
tropical forests. Correlations for RVI in these areas were high; the
small variability in NDVI in these areas may not be related to
vegetation, however, but can be associated with other factors such as
variations in atmospheric water vapour over the Sahara
.
Temporal correlations for anomalies in RVI were high for 1982–1999
but lower for 2001–2006. Areas with high interannual variability
(semi arid regions and temperate regions) showed higher
correlations. The CCVI showed lower correlations for 1982–1999 than
the RVI but higher correlations for 2001–2006 indicating greater
skill in predicting interannual variations for periods not used to
derive the model.
The correlations between RVI control and CCVI control anomalies (the
control was used to reduce the effect of trends associated with
CO2 fertilisation on correlations) were compared for the
periods of 1901–1981, 1982–1999, 2001–2006 and 1982–2006 (Fig. ). Most
areas of high interannual variability showed high correlations between
RVI and CCVI.
Phenology time series
Figure shows frequency distributions of
correlations between either the leaf out date or the first day of
bloom with CCVI. Phenology data were obtained for lilac leaf out
and bloom in North America , Oak
in Germany (data provided by the German weather service), Cherry
Blossom Russia (from http://www.biodat.ru/) and the Marsham oak
time series from the UK . The correlations are the
maximum correlations for the month previous to the day of leaf out,
the month concurrent with the day of leaf out, or the month after the
day of leaf out. The frequency distributions showed more significant
(larger negative) correlations for the CCVI in the German oak and
cherry bloom cases than for RVI. RVI and CCVI correlations were
similar for the lilac data. The Marsham oak correlation 1901–1958 was
-0.41 fore CCVI vs. -0.78 for the RVI
. Overall the CCVI captured interannual variation
in the phenology data better than the RVI.
Extreme events
Over the course of the 20th century extreme events occurred that had
a severe negative impact on vegetation. Two well-known examples are
the drought in and around the Great Plains in North America, referred
to as the dust bowls of the 1930s and 1950s, and the drought of the
century in the Sahel in 1984. Figure a shows the
mean annual RVI and CCVI times series for an area in the Great
Plains. Both time series show a decrease in values during the 1930s
and the CCVI also shows a decrease during the 1950s. The NPP
calculated by the CENTURY model by
comparison does not show any significant decrease during these periods
(Fig. b). The CENTURY model uses a different leaf
phenology model that, for this case, fails to capture the effects of
drought on vegetation. The precipitation data for the same area
indicate a decrease during the 1930s and a smaller decrease during the
1950s similar to the decrease in the CCVI.
The time series of RVI and CCVI for an area in the Sahel, the second
drought example, are shown in Fig. c. Both time
series show a decrease in values during 1984 and both match the NDVI
data from 1982–2010 well. Correlations between RVI and precipitation
are higher than correlations between CCVI and precipitation (Fig. ).
Comparison CCVI with leaf area index from climate change
scenarios
The CCVI was calculated for three climate change scenarios to explore
differences with current implementations of leaf seasonality
models. The three climate change scenarios were obtained for the
representative concentration pathway RCP4.5 for 2006–2100
and were from the MPI-ESM
coupled to the JSBACH/BETHY land-surface
parameterisation , the Hadgem-CC model
coupled to MOSES TRIFFID
and the CESM model coupled to the
BioGeochemical Cycles model (CESM1-BGC) . The
scenarios form part of the coupled model intercomparison project
phase 5 . Precipitation and surface air
surface temperature from 2046–2075 were used to calculate the KT
classes, and CCVICO2 was calculated for 2006–2100 using
precipitation surface air temperature and the RCP4.5 mid-year
greenhouse gas concentrations for 2006–2100
. The comparison with leaf area index was
made for the last 30 years of the simulations; during this
period the CO2 concentrations have stabilised for RCP4.5 which
excludes trend effects from the analysis.
Figure a shows the change in LAI between two
15 year periods calculated as the average for 2086–2100 minus
the average for 2071–2085 for the CESM1-BGC
model. Figure b and c show the partial correlation
between leaf area index and temperature and precipitation
respectively. Temperature shows large negative correlations for most
of the tropics and positive correlations for high northern
latitudes. Partial correlations with precipitation are low in
general. Figure d shows the difference between the
last two 15 year periods in CCVI. Differences tend to be
smaller in the tropics, but larger in mid to high latitudes compared
to the change in LAI. Correlations with temperature are negative in
the tropics and appear of similar magnitude as correlations for LAI;
however, positive correlations with temperature appear high throughout
most of the mid-to-high latitudes. Correlations with precipitation are
higher across the globe compared to correlations with LAI. Results for
the other two climate models, provided in the Supplement, show
substantially higher partial correlations between CCVI precipitation
than for LAI and precipitation for mid latitudes as well. As an aside,
notice that the UK Met Office model shows no change in the LAI over
the Amazon and that correlations between LAI and both temperature and
precipitation are low. Overall, the CCVI appears more sensitive to
variations in precipitation in mid latitudes than current
implementations of leaf seasonality models.
Discussion
The aim of the present study was to develop a model that predicts
global spatial, seasonal and interannual variations in the normalised
difference vegetation index for a range of climates. The resulting
model, referred to as the climate constrained vegetation index (CCVI)
required only atmospheric CO2 concentrations, precipitation
and temperature as input; climate vs. NDVI relationship depended on
a stratification of the globe into the 6 Köppen–Trewartha classes
A–F, but other eco-climatic classification systems could be used in
lieu of the KT classification. Biophysical parameters such as LAI or
the fraction of photosynthetically active radiation absorbed by green
parts of the vegetation canopy can be estimated similar to the
approach adopted for the CCVI or can be estimated from the CCVI
. Implementation of the CCVI
using a hydrological model was not considered since in a previous
study only a minor improvement was found for one land-surface model
and worse performance for two others .
Constraints on the NDVI were calculated for each of the KT classes as
the minimum of 7 precipitation functions at different lags and 5
temperature functions at different lags; separate functions were
derived for increasing and decreasing NDVI. The constraint functions
provided evidence of adaptations of vegetation to different climate
regimes. The adaptations of vegetation to colder climates were
particularly prominent. NDVI values around freezing point increased
with decreasing average temperature for a KT zone; thus NDVI at
freezing for class F > class E > class D > class C. This
differentiation according to climate zone is not found in the Miami
model which uses one equation to calculate temperature constraints on
annual NPP across the globe. The higher NDVI values at low
temperatures for colder climates will result in more realistic, lower
albedo estimates which is of importance for the calculation of the
energy budget and of land-surface
temperatures . Other
processes will also be affected by higher NDVI values at low
temperatures, such as photosynthesis, net primary productivity and the
interception of precipitation.
The CCVI model captured spatial, seasonal and interannual variations
well; spatial correlations were lower than for the previously
developed RVI. Some of the seasonal and spatial variability captured
in the RVI may not be present in the source data (precipitation and
temperature), and therefore the RVI may underestimate errors. Further
evidence of this is that the CCVI picks up residual BRDF errors in the
FASIR NDVI, which the RVI does not.
Compared to other land-surface schemes the CCVI had higher spatial
correlation; monthly spatial correlations globally between CCVI and
NDVI varied between 0.8 and 0.87; for latitudes above 30∘ N
average spatial correlation varied around 0.75; which is higher than
spatial correlations for current leaf seasonality models which vary
between 0.2–0.66 .
Seasonal variations were similarly high for both RVI and CCVI in areas
with large vegetation seasonality. The CCVI did not capture seasonal
variations in NDVI as well as the RVI over areas with small seasonal
amplitudes such as deserts and tropical forests. However, NDVI
seasonality in these areas is not always linked to variability in
vegetation and deviations from observed values were often small.
Interannual variations outside the period used for model development
were overall better captured by the CCVI than the RVI. The global
median correlation for CCVI interannual variability was around 0.24;
this number includes areas with low temporal variability (but not
deserts or tropical forests). Since the interannual signal in NDVI is
small, in the order of 0.1 NDVI, and residual errors can be in the
range of 0.05 NDVI and r value of at best 0.7 can be expected. Very
few studies provide tests of interannual variability for leaf area
index or associated parameters. The study by
using the Interactions between Soil, Biosphere and Atmosphere (ISBA)
calibrated interannual variability in LAI to
observations. Correlations of interannual variability in ISBA LAI were
similar to those found in the the present study (see
, Fig. 3). The analysis of two extreme events,
the dust bowl and Sahel, shows that the CCVI captures the effects of
droughts.
The CCVI resulted in larger interannual variability in vegetation in
response to climate variability than implementations in (at least
three) current earth system/general circulation models. In particular,
the greater sensitivity of vegetation towards drought and temperature
is important to capture in land-surface parameterisations. A recent
analysis of a range of climate change scenarios indicated possible
drying or more frequent droughts . The present
analysis indicates that current land-surface parameterisations
underestimate the response of vegetation to drought and therefore
underestimate the implications for, e.g. agriculture. A recent study
presents observational evidence that the relationship between NDVI and
temperature switched from a positive to a negative relationship for
a large region around the Ural mountains, this switch could possibly
be linked to increased drought stress .
The effect of CO2 fertilisation appeared of similar magnitude
as an earlier estimate. The magnitude of the effect increased linearly
with simple ratio; a transformation of the NDVI. This allows for
a straightforward implementation in models and provides an estimate
valid at regional to continental scale.
Conclusions
(1) The constraint analysis showed higher low temperature tolerance in
vegetation of colder climatic zones – at freezing, the NDVI of class
E was about 0.2 NDVI higher than of Class C; this adaptation is not
implemented in some vegetation models. (2) Realistic spatial and
temporal estimates of NDVI, here referred to as CCVI, were obtained
from precipitation and temperature constraints. The previously
developed RVI exhibited more realistic spatial
variability, however, the CCVI demonstrated greater skill in
predicting interannual variability. Moreover, the CCVI can be applied
to a wider range of climates than the RVI. (3) Implementation of the
CCVI in land-surface parameterisations and ecosystem models is
straightforwards since only temperature, precipitation and atmospheric
CO2 concentrations are required as inputs. Inclusion of
a water balance model was not considered given the relatively poor
performance of hydrological schemes in land-surface parameterisations
. (4) The CCVI showed greater sensitivity towards
variations in climate, in particular to change in precipitation in
continental interiors, than leaf seasonality schemes implemented in
land-surface parameterisations investigated. The ability to reproduce
the manifestation of drought in vegetation is of great importance for
estimation of the effects of climate variability on vegetation, and is
particularly important to assess risks for crop productivity. (5) The
magnitude of CO2 the fertilisation effect on global NDVI found
in an earlier study was confirmed; the magnitude
of the effect was found to change linearly with simple ratio.
Code availability
The code is written in the R language (http://www.r-project.org)
and is available upon request from the author
(s.o.los@swansea.ac.uk). An implementation of the model in
Fortran is under development.
The Supplement related to this article is available online at doi:10.5194/gmdd-8-4781-2015-supplement.
Acknowledgements
CRU TS version 3.21 precipitation data and temperature data and the
Hadgem-CC, CESM1-BGC and MPI-ESM-MR RCP4.5 realisation 1
precipitation, temperature and leaf area index simulations were
obtained from the British Atmospheric Data Centre (BADC;
http://badc.nerc.ac.uk/). The RCP4.5 atmospheric CO2
concentrations were obtained from the Potsdam institute for Climate
Impact Research (http://www.pik-potsdam.de/). The
Deutscher Wetterdienst (German Meteorological Service) provided the
German oak data; M. Schwartz and J. Caprio provided the North
American lilac phenology data through the NOAA NCDC Paleoclimatology
Program; T. Sparks (CEH) and I. Robertson (Swansea University)
provided the Marsham oak data; A. Andreevitch provided the Russian
Bird Cherry data (http://www.biodat.ru/); and P. Tans and
C. Keeling provided the Mauna Loa CO2 data through the NOAA
ESRL.
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Köppen–Trewartha classification rules with Tmin the minimum average monthly temperature over 30 years; R=2.3Tavg-0.64Pw+41. Tavg the average annual surface air temperature over 30 years, Pw is the winter precipitation, here taken as November until April (inclusive) for the Northern Hemisphere and April until September (inclusive) for the Southern Hemisphere; NT>10=∑i=1360(Ti>10)/30 is the total number of months mean temperature above 10 ∘C during a 30 year period divided by 30. NT>10 is used as a continuous variable, rather than an integer variable as is the case in the KT classification. Thresholds based on NT>10 that identify class boundaries have been revised as well.
Matrix comparing agreement between Köppen–Trewartha classes and USGS-EDC SiB Classes . Numbers indicate percentage of total land surface between 60∘ S and 80∘ N; percentages >1 % are in bold face. Wetlands (EDC SiB class 13) are excluded, permanent snow and ice (EDC SiB class 14) is considered bare soil.
KT Class/SiB Class ABSBCDEF1Evergreen broad leaf trees8.7900.0890.0020.9560.1860.0890.0162Broad leaf deciduous trees0.0350.0040.0020.1441.0501.1700.0163Deciduous and evergreen trees0.1580.0490.0000.7341.5300.7550.0014Evergreen needle leaf trees0.2090.0590.0000.5021.8303.3100.0225Deciduous needle leaf trees0.0000.0000.0000.0000.2862.5000.0086Trees with ground cover5.3005.9401.6003.1200.4880.3390.0077Ground cover0.0070.5381.2300.3182.2000.4060.0398Shrubs with ground cover0.0180.4161.5800.3230.2810.5470.1229Shrubs and bare soil0.0001.1004.0500.1672.5300.2810.68310Tundra0.0280.1180.13300.0370.6934.2002.64011Bare soil0.0020.3109.7600.0241.2700.1682.36312Agriculture2.1302.4600.5493.8709.1000.7220.636
Variables for which climate constraints on NDVI were derived. P is total precipitation, T is mean monthly temperature, V is CCVI during calculations or NDVI for initial estimates, t is month for which end-of-month CCVI values were estimated.
Lag (month)PrecipitationTemperatureNDVI (min constraint)010log{Pt+1}Tt110log{Pt-1+1}Tt-1210log{Pt-2+1}Tt-20–110log{Pt+Pt-1+1}∑i=01Tt-i/20–210log{Pt+Pt-1+Pt-2+1}∑i=02Tt-i/30–310log{Pt+Pt-1+Pt-2+Pt-3+1}0–1110log{∑i=011Pt-i+1}0.05∑i=112Vt-i
Climate (mean annual temperature – x axis at the bottom,
continuous line – and total annual precipitation – x axis at the
top, dashed line) constraints on potential annual net primary
productivity (NPP) according to the Miami model . The temperature constraint on NPP is given by
NPPT=3000/(1+exp(1.315-0.199T)) with T the mean
annual temperature (∘C), and the precipitation constrain is
given by NPPP=3000×(1-exp(-0.000664P)) with P
the total annual precipitation
(mmyr-1).
Example derivations of temperature and precipitation
constraints on monthly NDVI; relationships are for ascending
NDVI. (a) End-of-month NDVI as a function of monthly
precipitation for KT class A; the dots show the 95th percentile for
each of 64 intervals and the green line shows the fit through these
dots as estimated with segmented regression
. (b)
End of month NDVI as a function of annual precipitation for
KT class B. (c and d) End of month NDVI as
a function of monthly temperature for KT class B and C,
respectively. (e) End of month NDVI (KT class D) as
a function of mean temperature for the current and past two
months. (f) As (c and d); but for KT
class E.
Bias adjustment of the CCVI. Dots indicate median observed
NDVI per interval of CCVI (the CCVI was divided in 64 equidistant
intervals). The green line shows the function obtained with
segmented regression through the median points. (a)
Relationship between modelled CCVI and observed NDVI for KT Region
A for precipitation constraints and ascending NDVI. (b)
Same as (a) but for class B and temperature
constraints. (c) Same as a but for KT class D and
descending NDVI. (d) Same as (b) but for KT class
E.
(a) Mean January CCVI 1982–1989. (b)
Difference between observations and (a). (c) Mean
July CCVI 1982–1989. (d) Difference between observations
and (c). (e) Mean annual CCVI
1982–1989. (f) Difference between observations and
(e).
Change in CO2 fertilisation effect as a function of
mean SR per KT climate zone; the intercept and slope vary linearly
with simple ratio (SR) (see Eqs. and
).
Time series of mean global annual CCVI with and without
CO2 fertilisation from 1901–2010. FASIR NDVI is shown from
1982–2010.
Time series of monthly spatial correlation between
CCVICad and FASIR NDVI (solid line). Shown for
comparison are the spatial correlations for RVI (dashed line) and
CCVIcontrol (dotted line). RVI has the highest spatial
correlations with FASIR NDVI but shows a decrease from about
r=0.97 to about r=0.93 after 2000. A smaller downward deviation
from about r=0.84 to about r=0.82 occurs in the CCVI
correlations. The average monthly spatial correlation for latitudes
above 30∘ N (not shown) is r=0.75.
(a) Spatial distribution of temporal correlations
between RVI and FASIR NDVI for 1982–1999
(training period). (b) Same as (a) but for
2001–2006. (c) Temporal correlations between CCVI and
FASIR NDVI for 1982–1999; (d) same as (c) but for
2001–2006.
(a) Spatial distribution of temporal correlations
between RVI and FASIR NDVI anomalies for 1982–1999 (training
period). (b) Same as (a) but for 2001–2006
(outside training period; mean r=0.188. (c) Temporal
correlations between CCVI and FASIR NDVI anomalies for
1982–1999. (d) Same as (c) but for 2001–2006,
mean r=0.255 – significantly higher at p<2.210-16 than
r=0.188 for the RVI under
(b).
Temporal correlations between RVI (control) and CCVI
(control) monthly anomalies for (a)
1901–1981, (b) 1982–1999, (c) 2001–2006, and
(d) 1982–2006.
Frequency distributions of maximum correlations between day
of leaf out (or first day of bloom) and CCVI of previous, concurrent
or next month. Black indicates correlations significant at p<0.1; white bars show correlations that are not significant.
(a) Correlations for day of lilac leaf out. (b)
For day of lilac blossom. (c) For German oak leaf
out. (d) Cherry blossom in former Soviet Union. CCVI
correlations were significantly more negative (larger absolute
value) than RVI correlations for German oak (mean r=-0.34 vs. mean
r=-0.29 respectively with p≪0.01) and for cherry blossom
(r=-0.38 vs. r=-0.22; P<0.01). RVI and CCVI correlations
with cherry blossom were not significantly different. Correlation of
CCVI with Marsham Oak data for 1901–1958 is
-0.41 compared to -0.78 for the RVI data
.
Impact of extreme drought on the CCVI. (a) CCVI and
RVI time series for the northern US Plains between
40.5–45.5∘ N and 99–101.5∘ W, both showing
severely depressed vegetation during the 1930s dust bowl; the CCVI
also shows negative excursions during the 1950s. (b) As
(a) but for CRU precipitation and CENTURY NPP
. Precipitation shows negative
anomalies similar to the CCVI whereas the CENTURY NPP does not show
negative anomalies. Coefficient of correlations between
precipitation (1901–1993) and CCVI: r=0.83; RVI r=0.60 and
CENTURY NPP r=0.17. (c) CCVI and RVI time series for the
Sahel in Sudan between 12.5–15∘ N and 23–34∘ E
with FASIR NDVI data added for comparison. Both CCVI and RVI
indicate a drought in 1984. Correlations for precipitation
1901–2006 with CCVI r=0.71; and with RVI r=0.80; for
1982–2006: correlation of precipitation with CCVI r=0.64; with
RVI r=0.70 and with FASIR NDVI r=0.74. Correlation between FASIR
NDVI and RVI (r=0.89) and between FASIR NDVI and CCVI
(r=0.80).
Comparison of the response of CCVI and CESM LAI to changes in
CESM precipitation and temperature between 2071–2100. (a)
Difference mean LAI 2086–2100 and mean LAI 2071–2085. (b)
Partial correlations between mean annual temperature and mean annual
LAI for 2071–2100. (c) Partial correlations between annual
precipitation and mean annual LAI for 2071–2100. (d–f) Same as (a–c)
but for CCVI. Both CCVI and LAI have negative correlations with
temperature in (semi-arid) tropical regions. Partial correlations
between CCVI and precipitation are higher than partial correlations
between LAI and precipitation in mid-to-high northern latitude. The
MPI and HadGEM analyses are provided in the
Supplement.