2.1. The IVINE Model
The numerical model IVINE is a crop growth model created to simulate physiological and phenological vineyard conditions. The model requires a set of meteorological data and vineyard and soil information. It runs on daily steps, and phenological phases dictate the timing of different model routines.
The required boundary conditions, provided during the simulation, are hourly data: Air temperature and relative humidity, solar global radiation, photosynthetically active radiation, soil temperature, soil water content, wind speed and direction, and atmospheric pressure.
Other data required as inputs (about vineyard and soil characteristics) are geographic information (latitude, longitude, and elevation), soil hydrology, variety characteristics, and vineyard management information. Soil parameters (the b-power parameter [
35], hydraulic conductivity, soil porosity, wilting point, field capacity, saturated soil water potential, and soil thermal capacity) are required and can be evaluated according to empirical equations [
35] by means of organic matter and sand and clay soil percentages, if available, or according to the U.S. Department of Agriculture soil textural classes [
36,
37,
38]. We are aware of the approximations introduced by such kind of parameterizations, but we think that an even larger error could be produced by the large variations in soil parameters within the same soil class. Unfortunately, in the absence of specific measurements at a local scale, we think that this kind of error cannot be reduced. The presence of a steep slope on terrain has [
32] a direct effect on air temperature, solar radiation, and soil status (temperature and moisture [
39]). IVINE does not consider explicitly this parameter in its equations, but terrain slope information can be implicitly given to IVINE by selecting an accurate set of boundary conditions.
The IVINE model also requires the setting of some experimental parameters that depend on the cultivar (plant density, thermal thresholds, sugar content threshold at harvest, mean number of clusters per plant, and mean number of berries per cluster) and the site (soil layers number, texture, and depth). The following data about vineyard management are also required: The date and the severity of trimming and thinning (in case they are not available, IVINE prescribes fixed values at fixed dates). At present, the model is optimized for cv. Nebbiolo, since in Piedmont the most famous wines are produced from this cultivar.
The main model outputs are timing of the main phenological stages, leaf development, yield, and berry sugar concentration.
The occurrence of main simulated phenological stages (expressed in Julian days (JDs), used instead of calendar dates to represent the latter by integer values, starting from 1 on January 1st and ending with 365 or 366 on December 31st, and restarting the count at the beginning of each year) are dormancy break, bud-burst, flowering, fruit-set, beginning of ripening, veraison, and harvest: Their simulations use some thermal thresholds and the berry sugar concentration.
The phenological phase of dormancy break is simulated by means of chilling units (
Cu) [
28,
40,
41]: Its calculation starts on August 1st (a date close to the period in which the highest annual temperature is usually observed), and the phenological stage occurs when a critical amount of chilling units (100
Cu) is reached. Chilling units (Equation (1)) are calculated by means of maximum and minimum daily temperatures (
Tx and
Tn) and a parameter
Q, set equal to 2.17 [
28], while
n refers to days [
28]:
The postdormancy time period is calculated from the dormancy break using a sum of hourly temperatures
Tr(
h,
n), called growing degree hours or
GDH, defined in Equation (2) and obtained by the method of Richardson [
42,
43], used in the BRIN model [
28]. If not available, hourly temperatures are derived as in
Section S1. The calculation stops when a threshold value equal to 8050
GDH (derived from the IVINE calibration) is reached:
The phenological phase of flowering (fruit-set) is simulated by means of growing degree-days
GDD (Equation (3)) [
44]: Its calculation starts from zero at bud-burst (flowering) and stops when an appropriate critical amount of
GDD is reached (370
GDD and 50
GDD, respectively).
GDDs are calculated through mean daily air temperature and a base temperature (set to 10 °C for cv. Nebbiolo):
with the assumption that, when the mean daily temperature
Tav(n) is lower than
Tbase,
GDDn is set equal to 0 for that day.
The calculation of the beginning of ripening, veraison, and harvest occurs by means of amounts of GDDs (Equation (3)) and critical thresholds of berry sugar content. These thresholds were set in the calibration to 10 °Bx for the beginning of ripening, 12.5 °Bx for veraison, and 25 °Bx for the harvest, which are specific to cv. Nebbiolo.
The leaf area index (
LAI, m
2 m
−2) is calculated as a measure of plant development [
45,
46],
using some functions and coefficients detailed in
Supplementary Materials, Section S2 (Equations (S3)–(S5)). In more detail, leaf expansion is simulated by IVINE in terms of
LAI modulating its value according to the phenological phases: The simulation of leaf development starts at bud-burst and stops at veraison and, from October 1st, leaf senescence is considered by IVINE by imposing a decreasing linear trend. Additional corrections are performed by taking into account the eventual vine trimming carried out in the vineyard.
The value of berry sugar content
BSC (°Bx), considered a good indicator of maturity and quality, is evaluated by
in which
BSCmax is the maximum berry sugar content (e.g., its value at the harvest), imposed equal to 25.5 °Bx for cv. Nebbiolo. The function
σBrix is a normalized number, lower than 1, which is parameterized by means of a double sigmoid curve, a function of thermal time and of cultivar sugar content value at harvest [
47,
48], whose calculation starts from the phenological stage of flowering (see
Supplementary Materials, Section S3).
The yield (kg vine
−1) is simulated by means of a photosynthetic process, starting from the flowering stage with the following equation [
22],
where
DMcluster is the dry matter accumulation into vine clusters (see
Supplementary Materials, Section S4),
D_P the plant density, and 5.5 an empirical coefficient [
22].
2.3. Model Validation
A comparison between IVINE outputs and measurements collected during some field experiments carried out in some Piedmontese vineyards was performed. The variables measured were the timing of some phenological stages, the vine LAI, the berry weight, and the sugar content.
Measurements were carried out from 2004 to 2010 on the cv. Nebbiolo in three different experimental vineyards located within the most famous wine regions in Piedmont (Langhe, Roero, and Monferrato): Castiglione Falletto (44°37′ N; 7°59′ E; 275 m a.s.l.), Fubine (44°58′ N; 8°26′ E; 200 m a.s.l.), and Castagnito (44°45′ N; 8°01′ E, 300 m a.s.l.). For the first two sites, input data required by IVINE were collected from sensors installed within the vineyards and from regional meteorological stations of Quargnento and Serralunga d’Alba. For the Castagnito site, input data were collected from the regional meteorological station of Castellinaldo and from the global archive GLDAS2.0.
Regarding phenological phases, observations performed in the experimental sites reported the BBCH stage (BBCH means Bundesanstalt, Bundessortenamt and CHemical industry; it is the German scale used to identify the phenological development stages of a plant) achieved at the date of the survey, based on the complete list of BBCH stages [
55]. Surveys were performed during the 2008–2010 vegetative seasons at Castiglione Falletto, and during the 2008–2009 seasons at Fubine. IVINE simulations instead returned the dates (in Julian days) in which some BBCH stages occurred (to be precise, the beginning of bud break, BBCH 7; flowering, BBCH 65; fruit set, BBCH 71; veraison, BBCH 83 and °Bx ≥ 12.5; harvest, BBCH 89 and °Bx ≥ 25; Reference [
55]). Despite the attempt to make the surveys in proximity to the beginning of the IVINE calculated stages, sometimes the achieved stage was not in the list of those evaluated by IVINE, making a direct comparison difficult.
Regarding the seasonal evolution of the leaf area index (
LAI: m
2leaf area m
−2soil area), available measurements performed every 15–20 days refer to the period May–October 2009 in Castiglione Falletto and Fubine.
LAI was estimated by comparing the radiation above the top of the vegetation to the one intercepted by the canopy using a solarimeter bar placed within the canopy, selecting the minimum value of radiation of the bar and comparing it to the radiation above the vegetation (see more details in Reference [
56]). The vines were generally about 0.5 m thick, and measurements were carried out mostly during the central hours of the day.
Berry weight and sugar content measurements were measured at Castagnito approximately every 10 days in the periods July–harvest of 2004–2005 and July–September of 2006–2007. For each measurement, 200 berries were collected and weighed, and the juice obtained by their pressing was analyzed to determine their sugar concentration (°Bx).
2.4. Sensitivity Analysis
To understand the importance of the input data and their role in determining the IVINE output values, a sensitivity analysis test was carried out on main input variables.
Among input data, air temperature and soil water potential were chosen as the primary parameters to be investigated, in order to assess their relevance to model behavior. The impact of input variability was evaluated on the following output variables: Phenological phases, berry sugar content, leaf development, and yield.
One year of input data was the period selected for carrying out this kind of analysis: Since the choice of period and site were meaningless, we arbitrarily chose the last year of the selected time period (1950–2009) and one specific grid point (the one labeled as 03_01, whose details are listed in
Table 1). The reason for choosing 2009 was to have the simulation output data in the same temporal period in which the IVINE model was calibrated for cv. Nebbiolo, while the reason for selecting the 03_01 grid point was that it was located at an intermediate elevation and its soil type (loam) was more common in the area.
The values of input temperature were varied in nine scenarios of simulation by summing to all air input temperatures a fixed value ΔTair respectively equal to −2.0, −1.5, −1.0, −0.5, 0.0, +0.5, +1.0, +1.5, +2.0, where the value ΔTair = 0 °C corresponds to no change in input temperature (control run). The values of soil water potential were varied in seven scenarios of simulation by summing to all input values a fixed value ΔΨ respectively equal to −3.0, −2.0, −1.0, 0.0, 1.0, 2.0, 3.0 m (note that 1 m of hydraulic head roughly corresponds to 0.01 MPa of suction), where the value ΔΨ = 0 m corresponds to no change in input soil water potential (control run). Since this variable has two realistic limiting thresholds, e.g., the wilting point and the field capacity, at each step it was checked that the modified values stayed between those thresholds.
2.5. Long-Term Simulations and Statistical Analysis
The time trend of each variable and dependence of phenological phases and physiological variables on elevation and soil type were examined for each grid point. Then, results of simulations performed in grid points with different values of soil type and elevation were analyzed and compared, in order to highlight the effects of such variables.
As a general premise in evaluating the results, it is necessary to consider, in the following analysis, that the IVINE model was calibrated for cv. Nebbiolo through comparisons with data recorded in the last 10 years, and thus this calibration (see details in
Section S6) is representative of the standard practices currently performed. When current values are compared to those referring to the beginning of the simulation, the latter should be interpreted as the values of a plant raised similarly to the current plants, but 60 years before. Thus, the output variations can be considered to be the consequence of changes in the input data, e.g., they can highlight more efficiently the effects of climate change. For the same reason, this approach could not take into account the evolution of the change of vineyard methodologies in the analyzed time, in which vine grower standards have certainly changed.
A statistical test related to the significance of linear regression slopes over the whole period was performed on all IVINE output variables. In the paper, only those for the phenological phases, berry sugar content, maximum annual value of leaf area index, and yield are shown. In all cases, the selected test was the Cox–Stuart test, and the significance level was chosen at 95% (p-values ≤ 0.05).