200 R. Schulze Agriculture, Ecosystems and Environment 82 2000 185–212
explain both the signal and the variances of the re- sponse. If the dis-aggregation is too coarse, one has
to assume that the “dominance” principle applies, viz. that each HLRU responds similarly to that of the dom-
inant land use or soil within it, in which case many of the variances resulting from interacting non-linear
responses of important, but non-dominant, processes cannot be explained.
At the other end of the scale, the dis-aggregation may become so detailed that there can be dis-aggrega-
tion “overkill”, primarily because of the ease with which HLRUs can nowadays be created from GIS
overlays by using just a few commands. Scientists may then become intrigued by detail rather than by
the actual scaling problem they are trying to resolve. With the resultant multitude of disconnected HLRUs
they may have created, a number of pertinent ques- tions arise:
•
Are the many HLRUs identified actually all res- ponding differently which is, after all, the purpose
of dis-aggregation or do many of them display sim- ilar behaviour?
• Does the high degree of dis-aggregation actually
improve simulation results, or is a point reached in dis-aggregation at which goodness-of-fit statistics
between simulated and observed no longer improve and, in fact, may be regressing?
• Is noise beyond signal eventually being created with
further dis-aggregation? This leads to the concept of re-aggregation,
whereby a re-lumping of equi-response units is un- dertaken, with due consideration given to lateral and
subsurface processes occurring in a landscape, into what have been termed “hydrotopes” in an hydrolo-
gical context Becker, 1995; Becker and Braun, 1999. The procedure adopted in Becker and Braun 1999 is
an excellent example of hydrological re-aggregation, viz. to apply a sensitivity analysis between simulated
and observed values according to pre-selected fit- ting criteria e.g. r
2
, coefficient of efficiency. They then combine HLRUs which are similar in behaviour
until the goodness-of-fit criteria either drop below a predetermined limit, or any further re-aggregation
displays a natural break in goodness-of-fit. What has to be borne in mind when re-aggregating is that
one should distinguish, when combining HLRUs, between elements of the natural landscape e.g. to-
pography, wetlands, climate, soils and the “human” landscape e.g. land use and land management
practices. A question frequently posed is whether there is a
preferred scale at which to model. Considerable theo- retical work has been undertaken in scaling theory,
resulting in concepts such as the representative ele- mentary area or applications of fractals or rescaling.
These concepts are important in improving our un- derstanding of scaling, and such scientific approaches
may be applicable in a relatively unperturbed natural landscape. However, most real landscapes in which
scaling issues occur are human-modified landscapes in which theoretical scaling concepts are not always
any longer valid, in hydrology for example because of river abstractions, return flows, construction of dams
or canalisation, all of which alter considerably the nat- ural flow regimes, and hence, scaling laws.
The question of dis-aggregation and preferred scale in real world situations thus often becomes a
problem-determined one which changes from case to case.
11. Space and time scaling: examples from southern Africa
Following on the discussions on types of scale and up- and downscaling, examples of the application of
scaling issues are presented from a southern African perspective, at both country level and local level.
11.1. Mesoscale representation of a country-level sensitivity analysis of hydrological responses to
climate change forcing over southern Africa
Sensitivity analysis can be undertaken to establish the extent to which a driving variable in a system is
sensitive to change, in which direction the sensitivity tends and whether the sensitivity is spatially uniform
or heterogeneous. Such analysis is particularly impor- tant where uncertainty exists as to the importance of
change to that variable in a system.
Climate change can impact runoff generation by changes to three variables:
• An increase in atmospheric CO
2
concentration can cause a feedback through enhanced stomatal resis-
tance which suppresses transpiration. The degree of suppression varies between C3 and C4 plants, the
R. Schulze Agriculture, Ecosystems and Environment 82 2000 185–212 201
actively photosynthesising biomass LAI and soil water availability. Hydrologically, the hypothesis is
that through say a doubling of CO
2
levels, transpi- ration would be reduced, the soil profile would thus
be relatively moister and runoff would increase. •
Increases in temperature result in a higher atmo- spheric demand, and hence, potential evaporation.
Hydrologically, it is then hypothesised that soil water evaporation between rainfall events would
increase, as would transpiration demand, with the relative importance of the two processes dependent
on biomass cover. The resultant drier soil should thus generate less runoff, conditional upon precip-
itation and CO
2
levels being held constant. •
Any changes in precipitation would change both antecedent soil moisture conditions and the indi-
vidual event’s magnitude, thereby changing the runoff response.
To assess the respective mesoscale spatial sensitivi-
ties of these three forcing variables, the ACRU model was run for a 45-year daily rainfall record on each of
the 1946 QCs covering southern Africa, in each case changing a single variable at a time while holding
the other two constant at present values Schulze and Perks, 2000. Fig. 9 top shows that transpiration sup-
pression in a 2 × CO
2
atmosphere is, by itself, hydro- logically relatively insensitive according to the ACRU
model, with MAR generally increasing by only 2, except in wetter regions with longer periods of active
plant growth, where it can increase the MAR by up to 8. A 2
◦
C temperature increase, on the other hand, reduces MAR by 5 to 0.95 of the present runoff
over most regions Fig. 9, middle. However, in cooler high-altitude areas and particularly in the winter
rainfall regions of the southwest, an increase in tem- perature by itself can become a critical variable in the
impact of climate change, with the enhanced evap- otranspiration changing soil moisture regimes to the
extent that MAR could be reduced by up to 50 in places. Runoff responses in southern Africa remain
most sensitive by far to changes in precipitation, how- ever, with a unit 1P e.g. by 10 generally resulting
in a two to four times unit change in runoff i.e. 20–40. This response increases to five times in the
winter rainfall regions where antecedent soil moisture conditions remain wet in the inter-rainfall event pe-
riods because of low winter-time evapotranspiration Fig. 9, bottom.
This analysis shows clearly the considerable spa- tial differences in sensitivity which can exist in a
complex, interactive hydrological system, and hence, stresses the value of such analyses being undertaken
at mesoscale level.
11.2. Mesoscale representation of a country-level sensitivity study of maize yield change to the CO
2
fertilisation effect with climate change over southern Africa
A great deal of uncertainty exists as to whether the laboratory-determined CO
2
“fertilisation effect” influences on plant growth through changes in photo-
synthetic responses and water use efficiency partially by the transpiration suppression described above will
actually manifest themselves under large field con- ditions. Equally, uncertainty, therefore, exists as to
whether the algorithms imbedded in agrohydrological models such as ACRU represent this “fertilisation
effect” realistically. To assess the mesoscale sensi- tivity of this uncertainty, the differences in QC level
maize yields between a “future” and present climate were assessed with the CO
2
feedback switched on versus switched off, using the ACRU maize yield
module Schulze, 1995 with a plant date of 1 Novem- ber Fig. 10. For the “future” climate, the region-
alised monthly changes in maximum and minimum temperatures as well as precipitation for a 2 × CO
2
scenario from the 1998 version of the Hadley GCM excluding sulphate feedbacks was used to perturb
the 45-year present day daily rainfall and temperature series for each QC with MAP 300 mm.
The significant mesoscale regional differences be- tween changes in maize yield when just one uncertain
feedback variable is either switched on or off Fig. 10 highlights again the value of sensitivity analysis in
spacetime scale studies.
11.3. Inverting the time scale in a country-level threshold analysis of critical change in runoff with
climate change, mapped at mesoscale
It is the norm to express the potential impact of greenhouse gas induced climate change in terms of
the magnitude of change of the response variable e.g. runoff, either in absolute e.g. mm or in relative
terms, assuming climatic conditions under doubled
202 R. Schulze Agriculture, Ecosystems and Environment 82 2000 185–212
Fig. 9. Mesoscale sensitivity of simulated runoff over southern Africa to three climate change forcing variables after Schulze and Perks, 2000.
R. Schulze Agriculture, Ecosystems and Environment 82 2000 185–212 203
Fig. 10. Mesoscale simulated maize yield changes with climate over southern Africa, with and without CO
2
feedback after Perks, 2000.
204 R. Schulze Agriculture, Ecosystems and Environment 82 2000 185–212
CO
2
conditions in, say, 60 years from the present. In such impact studies, the time scale is fixed, but the
response varies spatially. What conventional analyses, therefore, identify is where, say 60 years from now, the
specific response may be more significant than else- where. However, those studies do not indicate when
over the next 60 years a critical threshold level of change is likely to occur at different locations within
a study region.
Such threshold analyses may be undertaken by ef- fectively “inverting” the timescale. Assuming that a
10 change + or − in MAR was a critical threshold of change, Fig. 11 illustrates, for the 1998 version of
the Hadley GCM output, where such a 10 change is likely to occur with over time, e.g. by the year 2015,
2030, 2045 or only by 2060. Details of the technique are given in Schulze and Perks 2000. Such an inver-
sion of the time scale of a likely climate change im- pact implies that water resources planners could take
Fig. 11. Threshold analysis of assumed critical runoff change with climate change over southern Africa after Schulze and Perks, 2000.
necessary adaptive measures earlier in certain critical regions than in others.
11.4. Downscaling seasonal rainfall forecasts to daily values for country-level modelling of seasonal
runoff forecasts
As an alternative to assessing climate change im- pacts over decadal time scales, climate variability im-
pacts may be more useful in more immediate decision making at inter-annual time scales. An example of this
follows.
Rainfall forecasts based on statistical methods e.g. canonical correlations are made by various institutes
for lead times of several months ahead. These forecasts are frequently of a categorical type, for example, cate-
gorising a seasonal rainfall forecast into above-normal A, near-normal N or below-normal B. With three
categories, a forecast with no skill whatsoever would
R. Schulze Agriculture, Ecosystems and Environment 82 2000 185–212 205
be correct one third of times, and any forecast correct more than 33 would have “skill” to it. In climates
with a high inter-seasonal variability of rainfall, it is hypothesised that, if rainfall season forecasts are of
sufficient skill, that they would be “translatable” into seasonal forecasts of crop yields or streamflows by ap-
propriate models for critical food security or water re- sources decisions to made. Simple downscaling tech-
niques were used in a recent initial study of seasonal streamflow forecastability in South Africa Schulze
et al., 1998.
The summer rainfall zone of South Africa has been classified into six forecast regions. All QCs falling
within a specific forecast region were assumed to have the same seasonal categorical rainfall forecast.
Historical forecasts of rainfall categories A, N or B for the main rainy period December–March were ob-
tained from the Climatology Research Group of the University of the Witwatersrand for the 15 seasons
1981–1982 to 1995–1996 Table 3. When compared with the observed December–March rainfall cate-
gories for those years, the forecast skill was found to be 50, with some regions’ seasonal rainfalls be-
ing more forecastable than those of others, and some years forecast better than others 1981, 1987 and 1990
forecasts were incorrect in all six regions, while 1982 and 1991 were correct in all six regions; Table 3.
In order to undertake an initial evaluation of sea- sonal runoff forecastability, the categorical seasonal
rainfall forecast first had to be downscaled to daily values for use in the ACRU model. This was achieved
in each QC by taking its 45-year daily accumulated observed rainfall record for the December–March pe-
riod and categorising years as A, N or B according to their ranking in the top 15, middle 15 or lower 15 of
the 45 years Schulze et al., 1998. If a forecast was say A, i.e. in the above-normal rainfall category, than
a representative year’s observed December–March rainfall from the A-ranked years was extracted. For a
given year, a runoff simulation with ACRU was then run with observed daily rainfall data until 30 Novem-
ber, and thereafter with the extracted representative year’s daily rainfall for the forecast category. The
simple hypothesis was that, if the seasonal runoff from the forecast rainfall downscaled to daily values
was closer to the seasonal runoff from observed daily rainfall than the long-term median seasonal runoff,
then a hydrological benefit “win” situation in Fig. 12 would have been derived from using the categorical
rainfall forecast; if not, then no benefit was derived “lose” situation in Fig. 12 and if the seasonal runoff
differences were within 5, the rainfall forecast was assumed to have made no difference.
Fig. 12 shows that the application of the above simple temporal downscaling techniques, particularly
under conditions when the seasonal rainfall skill may be considered to be reasonably accurate e.g. when
totally incorrect forecasts for years 1981, 1987, 1990 are removed, can be potentially beneficial for sea-
sonal runoff forecasts and that such information is thus potentially useful to water resources operators.
Similar scaling methodologies could be used to assess the benefits of crop yield forecasts.
11.5. Spatial scaling in mountainous terrain: the case of crop yield variations with altitude, aspect
and gradient
Mountainous terrain at hillslope and valley levels present special challenges to spatial scaling for, in ad-
dition to having to contend with more conventional downscaling procedures, the local climate assumes
more complex dimensions through influences of alti- tude, aspect and slope gradient.
Solar radiation loadings in mountainous terrain, for example, can vary markedly at different altitudes,
slopes and aspects as a function of latitude, time of year, time of day, atmospheric conditions of turbidity,
degree and type of cloud, topographic shading from surrounding hills and re-radiation from surrounding
hills. Numerous models exist to quantify these ef- fects on solar radiation, and one which can account
for all the factors listed above is the Radslope model Schulze and Lambson, 1986. Solar radiation, in turn,
is a major forcing variable of temperature as well as radiation-driven potential evaporation equations such
as that by Penman 1948, which can also be simu- lated on sloping terrain with the Radslope model. In
addition, temperature lapse rates with altitude vary in mountainous terrain by region, season and tempera-
ture parameter Schulze, 1997a. Solar radiation, tem- perature and potential evaporation are all important
input variables in more crop-detailed yield models.
Using the Radslope model to provide input on solar radiation loadings, temperature and potential evapo-
ration in the Central Drakensberg Mountain range of
206 R. Schulze Agriculture, Ecosystems and Environment 82 2000 185–212
R. Schulze Agriculture, Ecosystems and Environment 82 2000 185–212 207
Fig. 12. Simple benefit analysis of applying downscaled seasonal categorical rainfall forecasts to forecasts of runoff in South Africa after Schulze et al., 1998.
South Africa 29
◦
05
′
S, 29
◦
27
′
E at altitudes ranging from 1000 to 3000 m, together with locally obtained
daily rainfall, the influence of mountainous terrain on maize yield Zea mais was simulated using the
CERES 3.0 maize yield model Jones et al., 1998. Model runs were performed at three altitudes, viz.
1000, 2000 and 3000 m, in each case for a warm aspect i.e. north facing in the southern hemisphere
and a cool aspect at respective slope gradients of 0, 10 and 30
◦
. From Fig. 13 top, it may be seen how simulated maize yield varies under present climate
conditions from zero yield at high altitude where temperature andor solar radiation thresholds are too
low for plant physiological requirements to be met to 8.4 tha at hotter, lower altitudes. For the climate
change scenario which is indicated in Fig. 13 bot- tom, it is significant to note that, at the lower al-
titudes, there is a yield reduction temperatures too high, while at 2000 m, where present temperatures
are too low for high yields, yields may increase by over 6 tha, particularly on warm aspects.
This case study has illustrated clearly how differ- ent spatial scale considerations become important in
mountainous terrain under present, but particularly under possible future climates, when new thresh-
olds for response not reached under present climatic conditions may be met. It is for this reason that
mountainous regions are highly sensitive to climate change and deserve special attention at the appropriate
scale.
12. Types of errors associated with scale issues