Maria Jo20 SANTOS & Antonio GONCALVES HENRIQUES Instituto da Agua (INAG) - Av. Almirante Gago Coutinho 30
1000 Lisboa - Portugal
FAX +35 1 1 84092 18 PHONE +351 1 8430347 e-mail mariaj @inag.pt ABSTRACT
Droughts are extreme hydrological events characterised by lack of precipitation affecting large area1 extensions and with long duration periods. Appropriate methodologies for drought evaluation can be used to identify the area1 drought distribution within a region.
A regional model was developed for drought analysis and it has been applied to several regions in Portugal, being used at present for drought detection and monitoring. Its generalised application to the characterisation of droughts in Europe is actually being worked out in a specific European project, ARIDE-Assessment of the Regional Impact of Droughts in Europe. The application of this methodology for the characterisation of meteorological drought in Mozambique is presented in this paper.
The results obtained for Mozambique using the regional model in the period 1930/31-1980/81 suggests drought events in the whole area in 22% of the analysed years.
Nevertheless this kind of drought events do not persist in time.
The most severe droughts, in the hydrological years 1940/41 and 1948/49, have an associated return period of 100 years in 50% of the total area and a return period of about 50 years in the total area of the country. Droughts observed in 1943/44, 1950/51, 1953/54, 1963/64, 1965/66, 1967168 and 1972/73 have associated return periods greater than 10 years.
1 - REGIONAL DROUGHT DISTRIBUTION MODEL
Meteorological drought occurs when precipitation is below a threshold level and an important area of the region is affected (figure 1). The definition of threshold values related to precipitation and drought affected areas (the critical area) are not universal. However the drought threshold can be related to a given probability of non-exceedance. The critical area, as a significant area of the studied region to be considered, should include at least a given part (say, half) of the total area of the region.
The regional drought distribution model developed elsewhere [l] [2] is used to characterise regional droughts. This model relates elemental areas of the region with recorded data series of precipitation. The regional drought area is obtained through weighting adjacent areas using a given selection criteria, that enables to discriminate relevant drought areas from disperse ones. Model outputs are drought severity in the affected areas, the area1 evolution of drought and drought persistence in subsequent periods.
I ,+1 i+2 a+3 I+4 1+5 i+6 ,+7 I+8 i+9 i+10 t+11 i+12 i+13 time
Figure l-Evaluation of meteorological drought events.
The standard precipitation variate used in the model is given by the following formulae:
Pijk -1 wi,j = (
h
zi,j =
wi,j -Pi Oi
(2)
where Pij is the precipitation in period j and in location i, h is the parameter of the Box- Cox model for correcting skewness and pi and Cri are the mean and the standard variation of the data series Wij. One assumes that the parameter h is constant throughout the study region.
The regional model in a applied period by period basis. Several calculation steps are performed in each period (figure 2):
1) In a first step the region’s elementary area where the standardised precipitation Zi,j is smaller is selected, being Z,j lesser than a drought threshold defined. Drought area As’“’
and standard deviation stk) are the ones verified in the first area selected (AS’k’=Aick),
Stk) = f&(k))+
2) For the second and sequent up to k+l drought calculation steps another area is selected, adjacent to the initial one, where the standard variable Z (k) in the total area As’“’ is smaller:
z’k’ =
,/(As(‘-‘))~ (sck-:;
(k-‘k(k-‘)Z(k-‘) + Aick,~ickjZick,,j
(3)
+ Aitk,2si(k,2 + 2p’k-‘*i’k”As’k-‘~Ai~k~~(k-‘~~i~k~
The correlation coefficient p and standard deviation in several k drought areas (sCk)) are obtained per:
N V
c Z. ;‘-I’ - (2 Zik-” /N) Zi(k),j - (2 Zick,,j / N)
j=l j=l j=l
P (k-IAk)) = h (4)
2
zlk-” -(~Z:k-“/N) Zi(k),j -($Zi,kj,j /N)
j=l j=l
100
S(k) _ J(As”-” )’ (~‘~-‘))2 + Ai(k,2~i(k,2 + 2p’k-1.i)As’k-“Ai~k)SoSi(l;)
As(‘-‘) + Aick) (5)
The average drought area and the average drought severity of the drought initiated in period j, with duration Dj, are defined as: being drought severity represented by the absolute value of the standardised precipitation in the whole drought area. series is used to construct severity-area-frequency curves. Historical drought severity in the affected areas is compared to the severity-area-frequency curves and the drought return period is evaluated. The drought return period is a measure of the risk of droughts occurrence associated to the spatial distribution.
2 - PRECIPITATION OVER MOZAMBIQUE
The monthly precipitation data series were obtained from the Global Historical Climatology Network-GHCI version 1 (:1998), produced jointly by the U.S. Department of Energy’s Carbon Dioxide Information Center CDIAC - Oak Ridge National Laboratory
Data Center. This database includes 109 monthly data series in the area (including the border with Tanzania, Zimbabwe and South Africa), with data from 1900 to 1988 and with important lack of information before 1925 and after 1980 (figure 3). The variable chosen for drought analysis in Mozambique is the total precipitation from 1” October to 30th September.
Figure 3 - Annual precipitation series availability (%) from 1900/01 to 1987/88 (88 years), in the total data set (109 series).
To test the randomness of the precipitation data series, non-parametric tests were applied.
Trends, changes on average, variance and values distribution were checked using several non-parametric tests:
- Spearman, Mann-Kendall, number of local extremes and autocorrelation coefficient tests (evaluation of trends);
- Wald-Wolfowitz test (changes in the distribution of values);
- Test on the homogeneity of the variance;
- Mann-Whitney and order tests (analysis of the homogeneity of the mean).
Considering the confidence level of 0.95 most of the data series analysed are homogeneous (72% of the total). Non homogeneity of the mean and trends are the most common problems in 13% and 14% of the series. The data series that were not homogeneous are not considered for drought analysis.
The period with similar length for drought analysis was defined from 1930/31 to 1980/81.
Based on the results obtained of the non-parametric tests and considering this reference period, 50 data series were selected for the drought study for the period of 51 years considered.
Missing values were calculated considering the linear regression between the precipitation serie with missing data and the precipitation data series with best correlation coefficient for each year. For this a minimum correlation coefficient of 0.35 and at least 10 years of common data periods were considered.
The annual precipitation series mean, standard deviation, coefficient of skewness and coefficient of variation are presented in figure 4. The annual precipitation average is less than loo0 mm in 46% of the series. Most of the data series (86%) have positive skewness.
The influence area of each station is obtained through the Thiessen method. The stations’
location and influence areas are represented in figure 5. The two more representative 102
polygons, located in Montepuez (North) and Mabote (South), have an area of about 5-6%
of the total area.
0 0 oa”,”
o8 ?, ’ 0 . boo0 O 0 o”0 ‘ 0
ooo..o* o* 0
9. O 0
I 0 o
0 0
300 500 700 9fM 1100 1300 1500 1700 1900 2’00
---- c,=o.23 average (mm)
0.0 I .o 2.0 3.0 4.0
Coef. of skewness
Figure 4 - Statistical parameters of the annual precipitation series in Mozambique:
relationship between the average and the standard deviation (a) and the coefficient of skewness and the coefficient of variation (b).
MASS INGA
INHPUUUSSUA
Average annual precipitation (mm):
<600 600 - 600 I 600-1000 I lOOO- 1400 1 1400 - 1600
Figure 5 - Representation of the stations’ location, influence areas and the classification of the average annual precipitation in the elemental areas.
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3 - APPLICATION OF THE REGIONAL DROUGHT DISTRIBUTION MODEL Normal distribution can be used to represent annual precipitation in Mozambique considering the regional Box-Cox parameter A~0.38.
k(fi& TIM
Q-3)\ i=l /
The Box-Cox parameter hi is calculated by maximum likelihood for each data series i. The use of the regional transformation reduces the skewness in the whole dataset (figure 6). The normal distribution does not fit to 24% of the data series of transformed annual precipitation, against 40% if the distribution is fit to the non-transformed precipitation, with a confidence level of 0.95. The results obtained for the normal distribution goodness- of-fit tests (Chi-squared and Kuiper) are presented in figure 7.
0 non-transformed precipitation + transformed precipitation
precipitation serie
b
Figure 6 - Coefficient of skewness of non-transformed and transformed data series.
Figure 7 - Number of data series (%) where the normal distribution hypothesis is rejected in the Kuiper and Chi-squared tests (confidence level 0.95).
Severity-area-frequency curves are obtained from the drought severity computed for the simulated precipitation replicates of Mozambique. Ten replicates of transformed precipitation over Mozambique, 100 years length each, were obtained using the multivariate simulation model. Simulated series replicate the mean (maximum deviation from the historical mean is 17%) the variance (maximum deviation from the historical variance is 6%) and the spatial correlation coefficients similar to the historical ones.
Coefficients of skewness are simulated between -0.2 and 0.9.
104
The drought threshold represented by the exceedance probability of 0.20 &.2e=-0.842) is considered. For the development of the severity-area-frequency curves a critical area of 90% is used.
4 - METEOROLOGICAL DROUGHT IN MOZAMBIQUE
In the period 1930/31-1980181 there are areas affected by drought in Mozambique almost every year (table 1, figure 8). The total area is affected by drought in 1940/41, 1943/44, 1948/49, 1950/51, 1953/54, 1959160, 1963164, 1965166, 1967/68, 1969170 and 1972/73.
Droughts affecting the whole area do not persist more than one hydrological year.
Drought severity is represented by the absolute value of the standardised precipitation.
Considering the critical area of 80% the longest drought is associated to the period 1963/64-1965/66, a three-year drought, with an average drought area of 94% and an average drought severity of 1.18. In this case the occurrence of one-year drought (observed 9 times) is the most common. Only two drought events two years long, starting in 1940/41 and 1958/59, were observed.
The elemental areas located Northeast are more frequently subject to droughts than Northwest areas, that are selected in less than 50% of the years (figure 9). This shows a definition of the dry tropical climate it terms of drought areas, selected less times than the others. Areas where precipitation amounts are usually higher have more sensitiveness to low precipitation, verified more often.
n Ckought affected area (%)
+ Standardised transformed precipitation (absolute value)
Figure 8 - Meteorological drought events in Mozambique.
0.842 EG 3 4 8 Bought r threshold
105
Figure 9 - Number of years (%) that each area was selected for drought calculation.
Calculated droughts in the simulated replicates of Mozambique, considering a critical area of 90% of the total area, are verified between 24% and 31% of the years. By the historical data series droughts are observed with a frequency of 24%.
The extreme-value type 1 distribution is considered in each drought area. The parameters of the extreme-value type 1 distribution are obtained for each area A (figure 10).
4.2 g 8 3.8 8 +Yj 3.4 8
= 3.0 2.6
1.6 1.4 1.0
0.598 0.491
/ loo 0.443 O.Sl6
0 10 20 30 40 50 60 70 80 90 100
area (% of the total)
Figure 10 - Drought severity-area-frequency curves for Mozambique.
In figure 11 historical droughts are compared with the severity-area-curves. The most severe droughts, observed in the hydrological years 1940/41 and 1948/49, have an associated return period of 100 years in 50% of the total area and a return period of about 50 years in the total area of the country. Droughts observed in 1943/44, 1950/51, 1953/54, 1963/64, 1965/66, 1967/68 and 1972173 have associated return periods greater than 10 years.
The use of the drought threshold represented by the exceedance probability of 0.20 can be considered as a high limit for drought occurrence definition in dry/arid climates. The
106
.
generalisation of this threshold, used frequently for in Mediterranean climate, could be considered inappropriate for tropical climates like Mozambique, since drought events are obtained frequently, especially if a low area threshold is considered. However the results obtained comparing the severity-area-curves individualise the most severe droughts, wherefore the use of this level of threshold seams to be adequate, emphasising the characteristics of the climate.
This work gives some clues for future drought studies developments, as follows:
1) Several thresholds should be used in order to verify the significance of the threshold represented by the exceedance probability of 0.20.
2) By its total area Mozambique should probably be splited into regions for analysis of common climate, and the new droughts and severity curves compared with the ones calculated for the whole area.
3) More information must be incorporated for a detailed drought analysis in the area. A better spatial precipitation distribution is to be considered.
4) Different types of spatial distribution of precipitation are to be tested and its outputs used in the drought model.
4.3 E 3.8 'E
8 g 3.3 j 2.8 -U 2.3 1.8 - 1.3 - 0.8
0 10 20 30 40 50 60 70 80 90 100
area (%) 4.3
30 40 50 60 70 80 90 100
area (%)
Figure 11 - Return period of droughts classified with return period greater than 5 years.
Drought severity is represented by the absolute value of the standardised transformed
Hydrological Drought area Precipitation over the Difference between the Standardised precipitation European Water Resources and Climate Change Processes, European Geophysical Society, Vo1.24, n”1/2, pp.19-22.
[2] Santos, M.J.J. 1996 - Modelo de distribuicao de secas regionais, MSc Thesis, Universidade TCcnica de Lisboa, Institute Superior Tecnico, Lisbon.
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THE FOUR TIERS OF SEASONAL PREDICTION AT THE SOUTH AFRICAN WEATHER BUREAU
W A J,ANDMAN and W J TENNANT
South African Weather Bureau, Private Bag X097, Pretoria, 0001
INTRODUCTION
Useful skill in predicting southern A&a’s seasonal rainfall may be achieved at lead-times of up to 5 months for certain regions during particular seasons (Mason, 1998). Model skill from purely statistical models is considered to be a baseline skill level (Barnston et al., 1994) that has to be outscored by more elaborate techniques. Before it can be known if there is potential for improvement, the inherent predictability of the ocean-atmosphere system (sea-surface temperatures influencing seasonal rainfall) first has to be determined (Barnston, 1994). If the system contains adequate inherent predictability, dynamical models should be able to outscore models that do not accommodate physical processes or non-linearities (Barnston et al., 1994).
In this paper, it is demonstrated how predictions incorporating different stages, or tiers, by utilizing both statistically and dynamically-based techniques, are incorporated to produce categorized (below-normal, near-normal and above-normal) forecasts for a number of different homogeneous rainfall regions of southern Africa for the December to February (DJF) season.
SETTING A BENCHMARK
Canonical correlation analysis (CCA) (Barnett and Preisendorfer, 1987; Barnston, 1994; and others) is used as the statistically-based prediction technique. Retro-active forecasts for the period 1987/88 to 1996/97 are produced for nine different homogeneous rainfall regions of southern Africa, including South Africa, Botswana and Namibia, to set a minimum skill level. This baseline skill level has to be outscored by the more expensive techniques involving General Circulation Models (GCMs), such as the one described here, in order to justify their greater cost.
TIER 1: PREDICTING SEA-SURFACE TEMPERATURES
A GCM that is used to forecast the atmosphere for a season or longer requires monthly-mean forecast sea- surface temperature anomalies. Near-global anomalies are predictable, using CCA, up to six months in advance. Evolutionary features (warming or cooling) of global-scale sea-surface temperatures are used as predictors and have been used successfully in a CCA model to predict monthly sea-surface temperature anomalies of the equatorial Pacific (Niiio3.4) and Indian Ocean basins over the 1 O-year retro-active period from 1987/88 to 1996/97. Figure 1 shows the predicted versus observed indices for the Niiio3 and
109
Figure 1
equatorial Indian Ocean basin over the 1 O-year period.
Other areas where some skill was found include near-equatorial oceans, the central southern Atlantic and parts of the extra-tropical sea areas. However, equatorial Atlantic Ocean forecasts are poor. Even though sea-surface temperature predictions for non-ENS0 years are satisfactory, most of the predictability of equatorial sea temperatures is associated with ENSO. Often the magnitude of strong events is underestimated in statistically-based predictions.
This may negatively impact on the response of a GCM to the strong sea-surface temperature anomalies. Also, a falsely predicted warm or cold pool may impose an artificial forcing in the GCM leading to undesirable repercussions.
TIER 2: FORCING THE GCM
The T30 version of the COLA (Kirtman et al., 1995) Atmospheric General Circulation Model (AGCM) used here is a spectral model with triangular truncation at wave number 30, corresponding to a resolution of roughly 400 km. The model has 18 unevenly spaced sigma coordinate levels in the vertical. Initial conditions are derived from NCEP reanalysis data fields and lower boundary conditions consist ofmonthly- mean predicted sea-surface temperatures. Each forecast case consists of five forecasts initialized at successive 24-hour intervals and are combined using the lagged average forecast technique. Forecasts fields of mean circulation and moisture for the DJF season are produced.
TIER 3: DOWNSCALING
The large-scale circulation and moisture fields generated by the GCM are downscaled (Von Starch and Navarra, 1995) to specific rainfall regions. The regions are those used in the South African Weather Bureau’s seasonal forecasting operations and are defined as: south-western Cape (region 1); south coast (region 2); Transkei (region 3); KwaZulu-Natal coast (region 4); Lowveld (region 5); north-eastern Highveld (region 6); central interior (region 7); western interior (region 8); northern Namibia/western Botswana (region 9). CCA is used to perform the downscaling process in a “perfect prognosis” approach.
CCA regression equations are trained over the appropriate retro-active training periods of 36,39,42 and 45 years respectively, using observed circulation, moisture and regional rainfall. High cross-validated associations between observed circulation at certain standard pressure levels (850,700,500 and 200 hPa) and moisture at 700 hPa, and DJF rainfall of the region were found, as can be seen in Table 1.
110
Table 1. Cross-validation correlations for each region between observed circulation and moisture at certain standard levels and DJF rainfall, obtained over the different training periods. Correlations that are statistically significant at the 95% level are indicated with an asterisk
1 2 3 4 5
36 yrs 0.09 0.04 0.53* 0.49* 0.79*
6 I 7 I 8 I 9
0.68* 0.81* 0.74* 0.77*
0.69* 0.78* 0.72* 0.79*
0.70* 0.80* 0.71* 0.81*
0.66* 0.80* 0.69* 0.77*
If the GCM has the ability to simulate these quantities related to rainfall accurately, the perfect prognosis scheme has the potential ro produce skilful forecasts. Subsequently, bias-corrected GCM output was used as input to the CCA regression equations. It was found for short leads that the perfect prognosis scheme produces skill levels for most of the regions that are better than the baseline skill level set by the CCA model. Figure 2 is the comparison between the LEPS ((Potts et al., 1996) skill scores of the CCA and perfect prognosis. The circled line is the LEPS produced by the perfect prognosis scheme, and the solid line the LEPS of the CCA. Horizontal lines represent the significant thresholds of the 90%, 95% and 99%
levels respectively.
For longer lead forecasts, the scheme produced skill levels comparable to those set by the CCA model.
Due to some poorly specified predicted sea-surface temperature fields, some of the GCM forecasts during strong ENS0 events in the lo-year retro-active period are not skilful. Given high skill sea-surface temperature forecasts during strong events, the perfect prognosis skill will improve substantially. A number of possibilities may be considered to further improve on the perfect prognosis skill: the forecasts could be variance adjusted or the sea-surface temperature model can be improved to at least capture ENS0 events skilfully. Given high skill sea-surface temperature forecasts, the scheme has the potential to produce high skill forecasts that will outscore the baseline skill level substantially, suggesting that the COLA T30 GCM can be applied successfully for operational rainfall forecasts for the region.GCM simulations using persisted August sea-surface temperature anomalies throughout instead of forecast SSTs produced skill levels similar to those of the baseline for longer leads, indicating the potential for increased skill with more realistic SST forecasts.
Figure 2 111
TIER 4: PROBABILITY FORECAST
Forecasts produced by other models developed at the SAWB and those made available by other institutions are combined to produce a probability forecast for the region. The process to produce probability forecasts follow the same procedure conducted at the yearly meetings of the Southern African Regional Climate Outlook Forum (SARCOF) where seasonal forecasts for the whole of southern Africa are compiled.
REFERENCES
Barnett, T. P. and Preisendorfer, R. W. 1987. ‘Origins and levels of monthly and seasonal forecast skill for United States air temperature determined by canonical correlation analysis’, Mon. Weu.
Rev., 115, 1825-l 850.
Barnston, A. G. 1994. ‘Linear statistical short-term climate predictive skill in the Northern Hemisphere’,J. Clim., 7, 1513-1564.
Barnston, A. G., Van den Dool, H. M., Zebiak, S. E., Bamett, T. P., Ji, M., Rodenhuis, D. R., Cane, M. A., Leetmaa, A., Graham, N. E., Ropelewski, C. R., Kousky, V. E., O’Lenic, E. A.
and Livezey, R. E. 1994. ‘Long-lead seasonal forecasts - where do we stand?‘, Bull. Am. Met.
Sot., 66, 159-l 64.
Kirtman, B. P., Shukla, J., Huang, B., Zhu, Z. And Schneider, E. K. 1995. ‘Multiseasonal predictions with a coupled tropical ocean-global atmosphere system’,Mon. Yea. Rev., 125,789”
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Mason, S. J. 1998. ‘Seasonal forecasting of South At?ican rainfall using a non-linear discriminant
Mason, S. J. 1998. ‘Seasonal forecasting of South At?ican rainfall using a non-linear discriminant