# Climate Change Impacts on the Water Resources and Vegetation Dynamics of a Forested Sardinian Basin through a Distributed Ecohydrological Model

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. The Rio Fluminimaggiore Basin and the Marganai Forest

^{2}), which is located in the southwest of Sardinia (Italy) (Figure 2), and includes the Marganai Forest, a Long–Term Ecosystem Research (LTER) Italian site and a European Site of Community Importance (Natura 2000).

_{max}and T

_{min}, respectively). We also used wind velocity data from a nearby anemometric station at Capo Frasca, and relative humidity and incoming solar radiation data from the ERA20C (data from 1924 to 1978, [89]) and the ERA5 (data from 1979 to 2021, [90,91] European Centre for Medium-Range Weather Forecasts (ECMWF) atmospheric reanalysis datasets, which we tested successfully using two years of data of incoming solar radiation from two stations (Punta Gennarta and Rio Leni) close to the basin (RMSE = 90.46 W/m

^{2}), and 15 years of data of relative humidity at a Sardinian station in Orroli (distance of 65 km; RMSE = 19.02%).

^{33.06}+ 2.97 for the forest; [93]. Sentinel 2 images, which were characterized by higher spatial resolution (10 m), were also acquired, but they are available from 2016 only.

#### 2.2. The Distributed Ecohydrological Model

_{air}), wind speed (WS), relative humidity (RH), incoming short wave solar radiation (Rsw) and photosynthetically active radiation (PAR). We used the Thiessen method for spatial interpolation of the meteorological model inputs. The parameters of the model are in Table 1.

#### 2.2.1. The Soil Water Balance Model

_{s}) according to the soil depth of the cell, and an underlying active fractured rock depth (d

_{r}) for modeling root zone soil moisture. The model simulates the water balance of the two layers for each cell:

_{s}is the moisture of the upper soil layer, θ

_{r}is the moisture of the underlying rocky layer, P is the precipitation, Q

_{sup}is the surface runoff, E

_{w}is the wet evaporation, which is equal to the rainfall interception, characterized by a storage capacity of 0.2 LAI [94], E

_{bs}is the bare soil evaporation, E

_{g}is the grass transpiration, E

_{t,s}is the tree transpiration from the surface soil layer, E

_{t,r}is the tree transpiration from the fractured rock layer (with tree transpiration, E

_{t}= E

_{t,s}+ (1 − ${\xi}_{t}$) E

_{t,r}), ${\xi}_{t}$ is the percentage of tree root water uptake from the surface soil layer, f

_{d}is the daily hydraulic redistribution flux between the surface soil and the fractured rock through the tree roots, D

_{r}is the vertical drainage, L

_{e}is the leakage, f

_{bs}, f

_{g}and f

_{t}are the fractions of bare soil, grass cover and tree cover in each cell, respectively, with f

_{bs}+ f

_{g}+ f

_{t}= 1. Q

_{sup}is estimated using the Soil Conservation Service Curve Number (SCS-CN) method [81,83,84] from P, and computing the antecedent moisture conditions from the rain in the previous five days (Appendix A). We used the original seasonal rainfall limits of the SCS-CN method for distinguishing the antecedent moisture conditions (Appendix A) and calibrated the CN map (for properly predicting runoff). D

_{r}and L

_{e}are estimated using the unit gradient assumption of gravity drainage [95] and related to soil moisture following Clapp and Hornberger (1978) [96]:

_{sat,s}and k

_{sat,r}are the saturated hydraulic conductivity of the surficial soil layer and the deeper layer, respectively, b

_{s}and b

_{r}are the slopes of the soil retention curve of the two layers, and θ

_{sat,s}and θ

_{sat,r}are the saturated soil moisture of the two layers.

_{d}contribution is estimated as a function of the soil moisture gradient between the surface and underlying rocky sublayer through [47,97]:

_{f}and b

_{f}are tree root parameters. Evapotranspiration components (E

_{g}, E

_{t,s}, and E

_{t,r}) are estimated by the Penman−Monteith equation ([98] Equation 10.34), with the canopy resistance (r

_{c}) given by [99]:

_{1}, f

_{2}and f

_{3}are stress functions of soil/rock moisture, air temperature and VPD, calculated as [11,68]:

_{wp}is the wilting point, θ

_{lim}is the limiting soil moisture for vegetation, and T

_{min}, T

_{opt}and T

_{max}are the minimum, optimal and maximum temperature for vegetation. Note that θ soil moisture contributors are θ

_{s}for E

_{g}and E

_{t,s}and θ

_{r}for E

_{t,r}.

_{bs}= α PE [100], and PE is the potential evaporation based on (Penman−Monteith [98], Equation 10.15). Total evapotranspiration is given by:

#### 2.2.2. The Vegetation Dynamic Model

_{g}), stem (B

_{s}), living root (B

_{r}), and standing dead (B

_{d}). The biomass (g DM m

^{−2}) components are simulated by ordinary differential equations integrated numerically at a daily time step [52,101,103,104]:

_{g}is the gross photosynthesis, a

_{as}, a

_{ar}, a

_{ss}, a

_{sr}, a

_{rs}, and a

_{rr}are allocation (partitioning) coefficients to leaves, stem and root compartments, R

_{a}, R

_{s}and R

_{r}are the respiration rates from leaves, stem and root biomass, respectively, S

_{a}, S

_{s}and S

_{r}are the senescence rates of leaves, stem and root biomass, respectively, and L

_{a}is the litter fall. The equations of the terms in (11)−(14) are in Table 2. The key term of the VDM, P

_{g}, is computed using the approach of Montaldo et al. (2005) [52], which started from a simplified form of Fick’s law applied to gas exchange in plants [102,105] and the Nouvellon et al. (2000) model [103], deriving a simplified expression that estimates P

_{g}mainly by the photosynthetically active radiation PAR, soil moisture, and other routinely monitored variables (wind velocity, and air humidity and temperature). Note that in Equations (11)−(13), the θ soil moisture contributors are θ

_{s}for P

_{g,s}and θ

_{r}for P

_{g,r}.

_{a}is the specific leaf area of the green biomass. The other VDM equations are reported in Table 2. The SWBM is coupled with the VDM, which provides the LAI values of trees and grass daily, which are then used by the SWBM for computing the evapotranspiration partitioning, and the soil water content. The SWBM provides soil moisture and aerodynamic resistances to the VDM.

#### 2.2.3. The Surface Runoff and Base Flow

_{sup}surface runoff is computed daily by the SWBM, and the total surface runoff at the basin scale is computed by summing the surface runoff contribution of the cells of the basin daily. This model simplification is reasonable for small basins such as the Fluminimaggiore basin, which are characterized by a small time of concentration (<4 h). Following Montaldo et al. (2007) [79], the Q

_{b}subsurface flow at the basin outlet is computed at the j + 1 time step through a lumped conceptual approach, namely a linear reservoir method [107]:

_{b}.

#### 2.3. Other Field Experimental Sites for Testing Model Components

_{2}, and energy fluxes (e.g., [113]).

_{2}exchanges with the standard eddy covariance method. Seven frequency domain reflectometer probes (FDR, Campbell Scientific Model CS-616) were inserted in the soil close to the tower (3.3−5.5 m away) to estimate moisture at half-hourly intervals in the thin soil layer. FDR calibration and the other instrumentation of the field site are described in Montaldo et al. (2020) [109].

#### 2.4. IPCC Future Projections

#### 2.5. Comparisons and Statistical Data Analysis

_{μ}).

## 3. Results

#### 3.1. The Ecohydrological Model Testing and Its Predictions for the Past Period

^{2}= 0.73 and p < 0.05; Figure 6a,b). The model well predicted the seasonal variability of ET, which reached 4 mm/d in summer (Figure 6a). Soil moisture and f

_{d}(a

_{f}= 169.83, b

_{f}= 8.61 in Equation (6); ξ

_{t}= 0.3 if θ

_{s}> = 0.2, otherwise ξ

_{t}= 0.1) are successfully tested using the long data base (15 years) of the Orroli site (RMSE = 0.067 R

^{2}= 0.78 and p <0.05 for soil moisture prediction; RMSE = 0.48; R

^{2}= 0.74 and p <0.05 for seasonal f

_{d}; Figure 6c,d). The model well predicted the strong seasonal variability of soil moisture, ranging from dry (~0.1 in summer) to saturated (~0.5 in winter) conditions (Figure 6c).

^{2}= 0.94 and p < 0.001 in calibration, and RMSE = 17.76 mm/month and R

^{2}= 0.84 and p < 0.001 in validation; for yearly runoff: RMSE = 36.38 mm/year and R

^{2}= 0.98 and p < 0.001 in calibration, and RMSE = 48.51 mm/year and R

^{2}= 0.90 and p < 0.001 in validation), and the total predicted runoff of the whole observed period (~28 m) matched well to the total observed runoff (difference of 0.02%; Figure 7c). A sensitivity analysis of the model to the soil depths was also performed. We varied the basin soil depths uniformly with respect to the reference soil depth map (made by AGRIS) in a wide range (increasing up to +80% and decreasing up to −80%). The runoff predictions were mainly sensitive to the decrease in the soil depths (for values lower than −40%), due to the high increase in predicted runoff (which increased up to 58%, and RMSE increased up to 210 mm/y). Using more realistic scenarios of soil depths (variations from −40% to 40% respect to the reference soil depth map), the model results have low sensitivity to the soil depth variations (RMSE always lower than 53 mm/y), confirming the robustness of the model results.

^{2}= 0.69, mean ratio = 0.99), and the mean LAI predictions of the forest (RMSE = 0.18, R

^{2}= 0.72, mean ratio = 0.99, Figure 8c).

^{2}= 0.98, p = <0.05), confirming the model’s reliability at the basin scale.

^{−3}, Theil−Sen β of −0.005, Figure 8c)

#### 3.2. Future Ecohydrological Scenarios

## 4. Discussion

_{t}) for properly predicting tree transpiration in semi-arid ecosystems [47,48,49]. The proposed ecohydrological model proved to be an effective tool for predicting climate change effects, which needed to be evaluated with long data series to avoid erroneous evaluations due to the limitation of the data extension [62,132].

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

_{a}is the initial abstraction before ponding and is equal to cS with c constant (=0.2; see Ponce, 1989), and S is the maximum soil potential retention given by

_{5d}) preceding a storm (Soil Conservation Service, 1972 and 1986). The SCS-CN method distinguishes three levels of antecedent moisture condition (AMC I, AMC II, and AMC III), depending on the total rainfall in the 5 days (P5d) preceding a storm (Soil Conservation Service, 1972 and 1986). We used the original seasonal rainfall limits of the SCS-CN method for the three antecedent moisture conditions (Ponce, 1989), distinguishing between dormant season (AMC I if P5d < 12.7 mm, AMCIII if P5d > 28 mm) and growing season (AMC I if P5d < 35.5 mm, AMCIII if P5d > 53.3 mm). The values of CN for the AMC II condition are tabulated by the Soil Conservation Service on the basis of the soil type and land use. Then, the values of CN for AMC I and AMC III are expressed in terms of CN for AMC II through the following relationships (Ponce, 1989):

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**Figure 1.**Comparison of the state of the Marganai forest in summer 2017 with that in the previous summer: (

**a**,

**b**) pictures of the forest from the VP sight point shown in panels (

**c**,

**d**) in summer 2016 and summer 2017, respectively; (

**c**,

**d**) images of Sentinel 2 satellite at 10 m spatial resolution (VP is the view point of the pictures in (

**a**,

**b**)); (

**e**,

**f**) NDVI maps from MODIS images at 250 m spatial resolution; (

**g**) time series of the forest average NDVI (~16−day temporal resolution) from MODIS data.

**Figure 2.**The Rio Fluminimaggiore river: (

**a**) basin with the river network and the position of the meteorological stations and hydrometer; (

**b**) digital elevation model (DEM) of the basin; (

**c**) model scheme of the soil layers and vegetation for each basin cell.

**Figure 4.**For the Fluminimaggiore basin, historical annual time series of: (

**a**) precipitation (P

_{y}), (

**b**) air temperature (T

_{y}), and (

**c**) runoff (Q

_{y}). The slopes of the trend lines (red dashed) are estimated using the Theil−Sen method.

**Figure 5.**Historical climate at the Fluminimaggiore basin: (

**a**) monthly precipitation (P

_{m}) and air temperature (T

_{m}) regimes (in each estimation box, the statistics of the 1924−2021 period are shown: filled circles indicate the means, the horizontal lines the median, the box and whiskers represent quartiles, and outliers are depicted individually); (

**b**) the Theil−Sen β of the seasonal mean precipitation and air temperature trends; (

**c**) the Mann−Kendall τ of the seasonal mean precipitation and air temperature trends (thicker arrows when p < 0.05).

**Figure 6.**Model results at the two further experimental sites: (

**a**,

**b**) comparison of observed and predicted evapotranspiration (ET) at the Castelporziano site; (

**c**) comparison between observed and predicted soil moisture (q) at the Orroli site in Sardinia; (

**d**) comparison between seasonal predicted and observed hydraulic redistribution flux between the surface soil and the underlying fractured rock through the tree roots (f

_{d}) at the Orroli site.

**Figure 7.**For the historical period, the comparison between observed and modeled runoff of the Rio Fluminimaggiore basin at (

**a**) monthly timescale (regression line in red with slope of 1.08; R

^{2}= 0.83; p-value = < 10

^{5}) and (

**b**) yearly time scale (regression line in red with slope of 0.99; R

^{2}= 0.90; p value = < 10

^{5}) (

**c**) cumulative runoff (Q

_{cum}, missing observed values are also not considered in the model time series; values are expressed in millions of cubic meters (Mm

^{3})).

**Figure 8.**(

**a**) Evapotranspiration (ET), (

**b**) tree transpiration (E

_{t}), and (

**c**) tree LAI (LAI

_{t}) predictions using the meteorological observations of the Sardinian meteorological network (up to 2021), and the future climate scenarios of the HadGEM2-AO model (up to 2100). The slopes of the trend lines (red dashed) are estimated by the Theil−Sen method. For the future period, blue dots represent the mean of the four representative concentration pathways (RCP 26, RCP 45, RCP 60, RCP 85), and the shaded light blue areas around the mean bound the minimum and maximum values of the scenarios. For LAI

_{t}, green asterisks are the estimated values from NDVI of the MODIS remote sensor.

**Figure 9.**In the Rio Fluminimaggiore basin, mean predicted changes in the future with respect to the historical 2000−2020 period of: (

**a**) annual precipitation (ΔP

_{y}), (

**b**) annual air temperature (ΔT

_{y}), (

**c**) annual vapor pressure deficit (ΔVPD

_{y}) and (

**d**) annual runoff (ΔR

_{y}).

**Figure 10.**In the Rio Fluminimaggiore basin, the changes of daily runoff extremes under climate change: runoff values corresponding to different return periods estimated using the Generalized Extreme Event (GEV) distribution fits to historical observed data (1924–2021), and future climate scenario predictions (2022–2100, using HAdGEM2-AO predictions under RCP 85 concentration pathway).

Parameter | Description | Grass | Forest |
---|---|---|---|

r_{s,min} (s m^{−1}) | Minimum stomatal resistance | 150 | 290 |

θ_{wp} (-) | Wilting point | 0.08 | 0.05 |

θ_{lim} (-) | Limiting soil moisture for vegetation | 0.20 | 0.18 |

T_{min} (°K) | Minimum temperature | 279.15 | 268.15 |

T_{opt} (°K) | Optimal temperature | 293.15 | 288.15 |

T_{max} (°K) | Maximum temperature | 299.15 | 304.15 |

c_{a} (m^{2} gDM^{−1}) | Specific leaf areas of the green biomass | 0.01 | 0.0065 |

c_{d} (m^{2} gDM^{−1}) | Specific leaf areas of the dead biomass | 0.01 | 0.0062 |

k_{e} (-) | PAR extinction coefficient | 0.5 | 0.5 |

ξ_{a} (-) | Parameter controlling allocation to leaves | 0.6 | 0.55 |

ξ_{s} (-) | Parameter controlling allocation to stem | 0.1 | 0.1 |

ξ_{r} (-) | Parameter controlling allocation to roots | 0.4 | 0.35 |

Ω (-) | Allocation parameter | 0.8 | 0.1 |

m_{a} (d^{−1}) | Maintenance respiration coefficients for aboveground biomass | 0.032 | 0.0001 |

g_{a} (-) | Growth respiration coefficients for aboveground biomass | 0.32 | 0.85 |

m_{r} (d^{−1}) | Maintenance respiration coefficients for root biomass | 0.007 | 0.0003 |

g_{r} (-) | Growth respiration coefficients for root biomass | 0.1 | 0.1 |

Q_{10} (-) | Temperature coefficient in the respiration process | 2.5 | 3 |

d_{a} (d^{−1}) | Death rate of aboveground biomass | 0.023 | 0.0019 |

d_{r} (d^{−1}) | Death rate of root biomass | 0.005 | 0.0001 |

k_{a} (d^{−1}) | Rate of standing biomass pushed down | 0.23 | 0.35 |

Q_{N} (-) | Soil respiration coefficient related to temperature | 1.2 | |

R_{10}(mmol CO _{2}/m^{2}s) | Reference respiration at 10 °C | 2.54 | |

z_{om,v} (m) | Vegetation momentum roughness length | 0.05 | 0.5 |

z_{ov,v} (m) | Vegetation water vapor roughness length | z_{om}/7.4 | z_{om}/2.5 |

z_{om,bs} (m) | Bare soil momentum roughness length | 0.015 | |

z_{ov,bs} (m) | Bare soil water vapor roughness length | z_{om}/10 |

**Table 2.**Equations of the vegetation dynamic model components. Parameters are defined in Table 1.

Ecophysiological Term | Equation |
---|---|

Photosynthesis | ${P}_{g}={\epsilon}_{P}\left(PAR\right){f}_{PAR}PAR\frac{1.37{r}_{a}+1.6{r}_{c,min}}{1.37{r}_{a}+1.6{r}_{c}}$ ${\epsilon}_{P}\left(PAR\right)={a}_{0}PAR/\left(1+{a}_{1}PAR\right)$ ${f}_{PAR}=1-{e}^{-{k}_{e}\mathrm{LAI}}$ |

Allocation | For woody vegetation |

${a}_{aj}=\frac{{\xi}_{a}}{1+\mathrm{\Omega}[2-\lambda -{f}_{1}\left({\theta}_{j}\right)]}$ | |

${a}_{sj}=\frac{{\xi}_{s}+\mathrm{\Omega}\lambda}{1+\mathrm{\Omega}[2-\lambda -{f}_{1}\left({\theta}_{j}\right)]}$ | |

${a}_{rj}=\frac{{\xi}_{r}+\mathrm{\Omega}(1-{f}_{1}\left({\theta}_{j}\right)}{1+\mathrm{\Omega}[2-\lambda -{f}_{1}\left({\theta}_{j}\right)]}$ $\lambda ={e}^{-{k}_{e}LAI}$ ${\xi}_{a}+{\xi}_{s}+{\xi}_{r}=1$ | |

For grass | |

${a}_{a}=\frac{{\xi}_{a}+\mathrm{\Omega}\lambda}{1+\mathrm{\Omega}[1+\lambda -{f}_{1}\left({\theta}_{s}\right)]}$ | |

${a}_{r}=\frac{{\xi}_{s}+\mathrm{\Omega}(1-{f}_{1}\left({\theta}_{s}\right)}{1+\mathrm{\Omega}[1+\lambda -{f}_{1}\left({\theta}_{s}\right)]}$ | |

${\xi}_{a}+{\xi}_{r}=1$ | |

Respiration | ${R}_{a}={m}_{a}{f}_{4}(T){B}_{a}+{g}_{a}\left[{a}_{as}{P}_{g,s}{\xi}_{t}+{a}_{ar}{P}_{g,r}\left(1-{\xi}_{t}\right)\right]$ |

${R}_{s}={m}_{s}{f}_{4}(T){B}_{s}+{g}_{s}[{a}_{ss}{P}_{g,s}{\xi}_{t}+{a}_{sr}{P}_{g,r}(1-{\xi}_{t})]$ | |

${R}_{r}={m}_{r}{f}_{4}(T){B}_{r}+{g}_{r}[{a}_{rs}{P}_{g,r}{\xi}_{t}+{a}_{rr}{P}_{g,r}(1-{\xi}_{t})]$ ${f}_{4}(T)={Q}_{10}^{Ta/10}$ | |

Senescence | ${S}_{a}={\delta}_{a}{B}_{a}$ |

${S}_{s}={\delta}_{S}{B}_{S}$ | |

${S}_{r}={\delta}_{r}{B}_{r}$ | |

Litterfall | ${L}_{a}={k}_{a}{B}_{d}$ |

Parameter | Description | Mean | Range |
---|---|---|---|

CN | Curve Number of the Soil Conservation Service method | 89.7 | 80–99 |

θ_{sat,s} (-) | Saturated soil moisture | 0.44 | 0.41−0.46 |

b_{s} (-) | Slope of the retention curve in the surface soil | 10.28 | 7.75−11.40 |

k_{sat,s} (m/s) | Saturated hydraulic conductivity | 2.82 × 10^{−7} | 10^{−8}−10^{−6} |

d_{s} (m) | Soil layer depth | 0.36 | 0.20−0.85 |

q_{sat,r} (-) | Saturated rock moisture | 0.48 | 0.45−0.50 |

b_{r} (-) | Slope of the retention curve in the fracture rock layer | 7 | |

k_{sat,r} (m/s) | Saturated hydraulic conductivity in the fracture rock layer | 1.41 × 10^{−7} | 5 × 10^{−9}−5 × 10^{−7} |

d_{r} (m) | Fractured rock depth | 1.5 |

**Table 4.**Past mean changes (1976−2000 with 1951−1975) of annual precipitation (P

_{y}), air temperature (T

_{y}), and predicted annual runoff (Q

_{y}), evapotranspiration (ET

_{y}), and tree LAI (LAI

_{t,y}) using observations of the Sardinian meteorological network and the HadGEM2-AO meteorological data as model input.

ΔP_{y} (%) | ΔT_{y} (%) | ΔQ_{y} (%) | ΔET_{y} (%) | ΔLAI_{t,y} (%) | |
---|---|---|---|---|---|

From land-observations | −8.47 | 1.36 | −20.73 | −1.85 | −1.39 |

HadGEM2-AO | −9.42 | 1.67 | −16.18 | −2.57 | −2.07 |

**Table 5.**Results of the statistical tests (Chi-square and Kolmogorov−Smirnov tests) of the Generalized Extreme Value distribution fitting to the annual maximum daily runoff time series of the Fluminimaggiore basin for the past (1924–2021) and the future climate scenario (2022–2100), predicted using HadGEM2-AO data in the RCP 85 configuration. Statistics of the Chi-square and Kolmogorov−Smirnov tests for normality, applied to the series, have 5% significance level.

Period | Kolmogorov–Smirnov | Χ^{2} |
---|---|---|

1924−2021 | 0.0721 (0.1354) | 4.2951 (5.991) |

2022−2100 | 0.0783 (0.1505) | 5.1175 (5.991) |

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## Share and Cite

**MDPI and ACS Style**

Sirigu, S.; Montaldo, N. Climate Change Impacts on the Water Resources and Vegetation Dynamics of a Forested Sardinian Basin through a Distributed Ecohydrological Model. *Water* **2022**, *14*, 3078.
https://doi.org/10.3390/w14193078

**AMA Style**

Sirigu S, Montaldo N. Climate Change Impacts on the Water Resources and Vegetation Dynamics of a Forested Sardinian Basin through a Distributed Ecohydrological Model. *Water*. 2022; 14(19):3078.
https://doi.org/10.3390/w14193078

**Chicago/Turabian Style**

Sirigu, Serena, and Nicola Montaldo. 2022. "Climate Change Impacts on the Water Resources and Vegetation Dynamics of a Forested Sardinian Basin through a Distributed Ecohydrological Model" *Water* 14, no. 19: 3078.
https://doi.org/10.3390/w14193078