Sunshine duration

The course of annual sunshine duration is depicted in Figure 4.10a. The moving average over 6 years shows a local minimum during the sixties and one at the end of the seventies. At the beginning of the seventies sunshine duration has been high and the moving average is above the mean sunshine duration of 1565 h per year. Since 1985 the sunshine duration is higher than average, except for a local minimum between 1998 and 2002. During the year 2003 the highest sunshine duration has been measured since 1950, although it was also exceptionally high during 1959 and 1976.

50 Chapter 4. Observed climate of the Upper Moselle region 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 Sunshine duration [h] mean value movav(6y)

(a) Annual sunshine duration

0 100 200 300 400 500 600 700 800 900 195019551960196519701975198019851990199520002005 Sunshine duration [h] DJF 0 100 200 300 400 500 600 700 800 900 195019551960196519701975198019851990199520002005 Sunshine duration [h] MAM 0 100 200 300 400 500 600 700 800 900 195019551960196519701975198019851990199520002005 Sunshine duration [h] JJA 0 100 200 300 400 500 600 700 800 900 195019551960196519701975198019851990199520002005 Sunshine duration [h] SON mean value movav(6y)

(b) Seasonal sunshine duration

Figure 4.10: Time series of annual and seasonal sunshine duration (1951-2006). The solid line is a moving average over 6 years and the dashed line is the average over the whole period. (Station: Trier-Petrisberg)

51 Even though annual sunshine duration is highly variable from year to year, an increasing trend of 22 hours per decade is significant on the 90 % level.

The lowest sunshine duration is observed in winter with an average of 150 hours over 3 months (Figure 4.10b). In spring the sun shines on average almost 500 hours and in summer about 630 hours. The sunshine duration in autumn is between spring and winter with 295 hours from September until November.

Sunshine duration has increased significantly (93 % level) by 4.3 hours per decade in winter. A much more important increase is observed during summer. Here, sun- shine duration has augmented by 15.5 hours per decade and this trend is significant on the 96 % level. During spring and autumn, however, no significant trend can be detected.

4.3.4 Short summary

Annual mean screen-level temperature has increased significantly since 1951 by 0.26 ℃ per decade. Maximum temperature had a minimum during the seven- ties, while annual minimum and mean temperature are steadily increasing. This behaviour is less pronounced on the seasonal scale. Significant trends are only ob- served during spring and summer. These trends are also higher during the period 1979-2005 as for 1951-1979.

Precipitation has not changed significantly during the investigated period. There are high fluctuations on annual and seasonal scale, but on average it is quite equally distributed during the whole year, thus there are no especially dry nor wet intra- annual periods, on average. The division of precipitation into classes shows also no important changes.

Annual sunshine duration has increased by 22 hours per decade since 1951. Dur- ing winter and summer sunshine duration has significantly increased but during spring and autumn no trend has been detected.

The climate conditions at the Upper Moselle meet the minimum requirements for profitable viticulture according to the criterions from Stock et al. (2007), Huglin and Schneider (1998) and Blaich (2000c) shown in Table 4.5. Sunshine duration and precipitation are sufficiently high. The minimum value of precipitation is below the suggested limit, but water deficit may be compensated by irrigation with water taken from the Moselle. In general, temperature requirements are also fulfilled, although summer temperatures are close to the lower required limit; the Huglin Index actually advises for half of the years against commercial viticulture. On average, however, there is enough heat available for vine-growing especially for Rivaner. The highest Huglin index measured in the region is 2103, which indicates a climate even suitable for Ugni blanc, Grenache and Syrah to become mature. The Huglin index has a highly significant trend of 4.4/year between 1951-2005 and even 15.4/year since 1985.

52 Chapter 4. Observed climate of the Upper Moselle region

Table 4.5: Required climate conditions (assembled from Stock et al. (2007), Huglin and Schneider (1998), Blaich (2000c)) and measured mean climate conditions for 1951-2005 in the Upper Moselle region.

Required Measured

Yearly sunshine duration >1250 h 1461 h

Days without frost

>180 d 221 d

(vegetation period) Mean temperature:

Annual >8℃ 9.9℃

Winter (DJF) around 0℃ 2.4℃

Summer (JJA) around 20℃ 17.5℃

April-October >13℃ 14.3℃ July-October >16℃ 15.2℃ or hottest month >18℃ 18.3℃ May-June >15℃ 15.0℃ Tolerable extremes: Winter (DJF) temperature -25℃ (-15℃)* -21℃

Summer (JJA) temperature around 45℃ 40℃

Precipitation during vegetation period:

Minimum 300 mm 232 mm Optimum/mean 420 mm 451 mm Maximum 700 mm 651 mm Huglin Index: Minimum 1500**) 1183 Mean / 1515 Median / 1500 Maximum / 2103

*) depending on duration, and health of the vine plants

**) threshold depends on vine variety, under 1500 no commercial wine cultivation is suggested

5

Statistical modelling of

phenological events and

must quality

During the last 40 years budburst and flowering in the Upper Moselle region re- cessed to earlier days, must density has increased, and acidity decreased. Annual mean temperature has increased significantly as well as spring and summer temper- atures. Precipitation did not change substantially, but annual sunshine duration shows a significant positive trend. It is known that the growing cycle of grapevine is influenced by the environment, especially climate. The goal of this chapter is to find the important climate signals which are responsible for the trends in phenology and must quality.

In order to find an answer to this issue, the statistical relations between a com- prehensive pool of potential predictors and climate variables is analysed in the following. Regression models are developed in order to link phenology and must quality to climate conditions and to estimate phenology and must quality from meteorological parameters.

5.1 Stepwise regression model

A commonly used procedure in the statistical modelling is the stepwise regression, which can be performed using a forward selection method, a backward elimination method or a combination of both (Wilks, 2006; Bortz , 1993; Sachs, 1978). In this study, the combination method is applied.

Regression method Forward selection starts with the predictor, which has max- imum correlation with the predictand. In a step-wise fashion further predictors x_i are added from the pool of potential predictors based on maximum positive impact (i.e. increase of explained variance) on the regression. The chosen measure is the regression sum of squares (SSR) defined by the difference between the total 53

54 Chapter 5. Statistical modelling of phenological events and must quality sum of squares (SST) and the error sum of squares (SSE):

SSR = SST − SSE (5.1) = n  i=1 (y_{i− ¯y)}2₋n i=1 (y_{i− ˆyi})2 _(5.2) = n  i=1 ( ˆy_i− ¯y)2 (5.3)

where ˆy_iestimated predictand for the ith year and ¯y mean of n observations y. With ˆyk _{is the estimated predictand based on k predictors, the corresponding regression}

sum of squares, SSRk is given by

SSRk= n  i=1 (ˆyk i − ¯y)2 (5.4)

The model scheme is shown in Figure 5.1, with the forward selection method marked by the green boxes. In the first step SSR1 is computed for all predictors, and the predictor with the highest SSR1 is kept. Then a second predictor is added to compute SSR2; again the predictor leading to the highest SSR2is kept, but only if the increase in SSR, i.e. SSR2 >> SSR1 is significant on 95% level according to the F-test (Wilks, 2006). Then, a further predictor is tested in the same way, and the procedure is continued, computing at each step the F parameter via

F = SSR

k+1_{− SSR}k 1

n−(k+1)SSEk+1

(5.5) where SSRk+1 _{is the SSR for the tested enhanced regression equation with k + 1}

predictors and sample size n, while SSRk _{is the SSR of the previous step with k}

predictors.

The forward selection method would continue until SSRk+1 is not significantly greater than SSRk_{, meaning that no further contributing predictor can be found.}

However, an already selected predictor may become insignificant, if a new one is added (Efroymson, 1960). This complication is resolved by the backward method (blue boxes in Figure 5.1). Obviously the backward scheme is used if three or more predictors have already been selected by the forward scheme. In the backward scheme, each of the selected predictors is removed once while keeping all the others. This leads to k−1 new values of SSRk−1_{. If the highest SSR}k−1_{is not significantly}

lower than SSRk _{this predictor is removed. The remaining selected predictors are}

tested again whether one of them becomes insignificant. If, however, SSRk  SSRk−1_{, the omitted predictor is kept and the forward selection method proceeds}

55

Take the predictor with the highest SSR

Calculation of SSR with the selected predictor(s) plus each non selected

Calculation of SSR with each predictor

Take the combination of the predictors with the highest SSR

All significant predictors have been found

significant increase of the new

SSR ?

Leave out one of the selected predictors. Calculation of SSR of the remaining ones

# selected predictors > 3 Keep the combina- tion of the selected predictors

Take the combination of the predictors with the highest SSR significant

decrease of the new SSR ?

Delete the predic- tor left out from the selected ones lation of or est Ca_wit R ed us Ta of the on ith en found i ifi ctors out one se Ca the on with Ta of the SSR ? h non s i ifi elected g ant the new ?

Delete the predic tor left out from th selected ones d se selected ones YES NO YES NO YES NO SSR ? p the co YES Ke tio pr c- he START END

Figure 5.1: Scheme of the stepwise regression model procedure containing the for- ward selection method (green boxes) and the backward elimination method (blue boxes).

Reduction of the predictor pool For an independent evaluation, the whole data set is usually split into: a training data set based on which the model is developed, and an independent data set, on which the model is tested. In this study, the observational data is too small for separating it into two sufficiently long parts. Instead a bootstrap method is used by repeating the regression model derivation n-times each time omitting one year of the dataset. Only those predictors, which are selected at least once in the n regression models are finally kept in the pool of predictors. The final regression equation is calculated by the forward-backward combination using the reduced pool of predictors.

56 Chapter 5. Statistical modelling of phenological events and must quality Cross validation control The interaction of forward and backward regression steps generally prevents model overfitting. Nevertheless controlling the optimum number of predictors is of advantage. In some cases one predictor is very powerful and inhibits the addition of other predictors. In such a case the approximation found would have a high explained variance, but a model with a similar one using more predictors and with a higher biological meaning could also exist.

Cross validation can be used to clarify this aspect (Wilks, 2006): Such a situation may exist, when the optimum number of predictors identified by cross validation disagrees considerably with the number of significant predictors found by the re- gression method. In this study, cross validation often suggested a model with only one predictor, usually a temperature accumulating predictor. Such a model is, however, not very meaningful (Due et al., 1993) and e.g., does not explain delay of phenological events. The responsible, i.e. the dominant, predictor is then isolated and a new regression equation is calculated.

In order to obtain the optimum number of predictors (i.e., more than one and less than 10), the cross validation based on the leave-one-out method is used. The number of predictors k is increasing from one to the number of available predictors. Here, the cross validation iteration is stopped at the 10th predictor. For every fixed k the regression model is applied n times using n− 1 observations, i.e. the ith year is left out. The regression algorithm still contains forward and backward steps, but now it stops when the given number k of predictors is reached.

For every k, n − 1 equations are obtained and the corresponding dependent variables {y_m|m ∈ [1, n], m = i} are called developmental data. These equations are applied on the respective omitted ith year and the dependent variables yi are

called cross validation data. For every k, the average of the mean squared error of the developmental data (MSE_m) and the cross validation data (MSE_i) is computed. The MSEi gives an indication of the expected prediction error for other independent

data; MSE_m gives the model error (i.e., for dependant data) and is decreasing with increasing k. The optimum number of predictors k_optis where the prediction error is smallest, i.e. kopt = min(MSEi). Following Wilks (2006) it is not always necessary

to strictly limit the number of predictors according the lowest prediction error if the predictors contribute to scientific understanding. However, the prediction error should be low and close to the minimum.

5.2 Results of phenology and must quality