Using hybrid modelling to predict basal area and evaluate effects of climate change on growth of Norway spruce and Scots pine stands

Figures & data

Figure 1. Functions for calculating modifiers used to adjust incoming radiation (PAR) values according to the following monthly variables. a) vapour pressure deficit (VPD). b) mean monthly temperature (°C) by species. c) soil water ratio (soil water balance (mm) (S) divided by the potentially available soil water (mm) (Φ) (see equation 10). d) number of frost days in a month.

Figure 2. Residuals of the fitted mensurational time-based model (a) and the hybrid model (Hybrid-TFDW) (b) for Scots pine. Residuals from the validation of the mensurational time-based model (c) and the hybrid model (Hybrid-TFDW) (d). The thick lines show the trend in the residuals.

Figure 3. Residuals of the fitted mensurational time-based model (a) and the hybrid model (Hybrid-TFDW) (b) for Norway spruce. Residuals from the validation of the mensurational time-based model (c) and the hybrid model (Hybrid-TFDW) (d). The thick lines show the trend in the residuals.

Table 1. Variables and parameters used in the climate modifier calculations.

Parameter or variable	Symbol	Unit	Value	Reference
Monthly mean daytime vapour pressure deficit	VPD	mbar
Canopy response to VPD	kg	mbar	0.05	(Sand 2004)
Monthly average of the daily temperature	Ta	°C
Monthly average of the daily minimum temperature	Ta-min	°C
Monthly average of the daily maximum temperature	Ta-max	°C
Monthly average daytime temperature	Tec	°C
Species-specific maximum, minimum, and optimum temperatures for photosynthesis:
Pinus sylvestris	Tmax, Tmin and Topt	°C	40, −2, 20	(Kolari et al. 2007)
Picea abies	Tmax, Tmin and Topt	°C	42, −3, 15	(Bergh et al. 1998)
Soil water modifier coefficient for clay, clay loam, sandy loam, and sandy soils	cθ		0.4, 0.5, 0.6, 0.7	(Landsberg and Waring 1997)
Soil water modifier exponent for clay, clay loam, sandy loam, and sandy soils	nθ		3, 5, 7, 9	(Landsberg and Waring 1997)
Atmospheric pressure	Pa	kPa
Slope of the saturation vapour pressure curve	Δ	kPa°C^−1
Psychrometric parameter	γ	kPa°C^−1
Net radiation	Rn	kWh m^−2
Total shortwave radiation	GHI	kWh m^−2
Intercept and slope of the relationship between Rn and GHI	qa, qb	Wm^−2	−90, 0.8	(Landsberg and Sands 2011)
Photosynthetically active radiation	PAR	MJm^−2
Monthly precipitation	P	mm
Interception	I	mm
Potential evapotranspiration	E0	mm
Actual evapotranspiration	E	mm
Plant available soil water balance in the root zone at the end of the month	S	mm
Soil water balance previous month	St-1	mm
Potentially plant-available soil water in the root zone	Φ	mm
Soil water ratio between S and Φ	rw

Table 2. Estimated parameters for the fitted basal area models and their standard errors (SE) and model fit and validation RMSE (m² ha⁻¹). Time-based (Equation 1) = mensurational model using time as driving variable. Hybrid (Equation 2) = unmodified PULS, Hybrid-D = modified by VPD, Hybrid-W = modified by soil water, Hybrid-T= modified by temperature, Hybrid-F= modified by frost, and Hybrid-TFDW= all four modifiers included. All estimated parameters were significant (p-value < 0.05).

Species	Model		Parameter			RMSE (m^2 ha^−1)
			a	b	c	Model fitting	Validation
Scots pine	Time-Based	Estimate	4.822	0.151	0.224	1.404	1.471
		SE	0.017	0.006	0.006
	Hybrid	Estimate	4.816	0.156	0.224	1.393	1.470
		SE	0.017	0.007	0.006
	Hybrid-D	Estimate	4.816	0.151	0.228	1.398	1.473
		SE	0.017	0.007	0.006
	Hybrid-T	Estimate	4.806	0.139	0.238	1.394	1.475
		SE	0.016	0.006	0.006
	Hybrid-W	Estimate	4.760	0.108	0.276	1.396	1.481
		SE	0.016	0.005	0.007
	Hybrid-F	Estimate	4.806	0.139	0.238	1.394	1.475
		SE	0.016	0.006	0.006
	Hybrid-TFDW	Estimate	4.728	0.076	0.324	1.396	1.485
		SE	0.016	0.006	0.007
Norway spruce	Time-Based	Estimate	5.113	0.328	0.119	2.507	2.279
		SE	0.018	0.022	0.009
	Hybrid	Estimate	5.089	0.303	0.137	2.472	2.242
		SE	0.017	0.020	0.009
	Hybrid-D	Estimate	5.082	0.281	0.148	2.465	2.238
		SE	0.017	0.018	0.009
	Hybrid-T	Estimate	5.098	0.287	0.143	2.483	2.252
		SE	0.018	0.019	0.009
	Hybrid-W	Estimate	5.092	0.195	0.192	2.476	2.194
		SE	0.018	0.013	0.009
	Hybrid-F	Estimate	5.097	0.259	0.156	2.476	2.262
		SE	0.017	0.017	0.009
	Hybrid-TFDW	Estimate	5.082	0.144	0.231	2.485	2.267
			0.018	0.010	0.009

Figure 4. 140 randomly selected NFI plots, a) yearly radiation sum (MJ m⁻²) over the measurement period for unmodified PULS (MJ m⁻²; blue line), and PULS modified by temperature (PULSf_T; red line). b) yearly mean temperature (°C) at the same sites. The black lines show linear trends.

Figure 5. Average effect for July of temperature and precipitation changes on the soil water modifier (f_W) during a 20-year simulation with altered input climate data. The dots represent randomly selected permanent sample plots from the Swedish NFI. The panels show scenarios of: (a) current climate, (b) temperature increased by 4 °C, (c) precipitation increased by 20%, and (d) precipitation increased by 20% and temperature increased by 4 °C.

Figure 6. Relative change of basal area (%) after a 20-year simulation with altered input climate data compared with current climate. The different scenarios tested were increased monthly precipitation by either 10% or 20%, increased monthly temperatures by either 2 °C or 4 °C, and all four combinations of increased temperature and precipitation. All scenarios, except for the 2 °C warming scenario at current precipitation for Norway spruce, were significantly different (p-value < 0.05) from the unaltered climate scenario.

Figure 7. Relative change in basal area change (%) after a 20-year simulation with altered input climate data compared with current climate using the hybrid Scots pine model containing all modifiers (Hybrid-TFDW). The dots represent 140 randomly selected permanent sample plots from the Swedish NFI. Scenarios: (a) = increased temperature increased by 2 °C, (b) = increased precipitation increased by 10%, and (c) = increased precipitation increased by 10% and increased temperature increased by 2 °C.

Figure 8. Relative change in basal area change (%) after a 20-year simulation with altered input climate data compared with current climate using the hybrid Norway spruce model containing all modifiers (Hybrid-TFDW). The dots represent 140 randomly selected permanent sample plots from the Swedish NFI. Scenarios: (a) = increased temperature increased by 2 °C, (b) = increased precipitation increased by 10%, and (c) = increased precipitation increased by 10% and increased temperature increased by 2 °C.

Sand P. 2004. Adaptation of 3-PG to novel species: guidelines for data collection and parameter assignment (Technical Report 141). Cooperative Research Centre for Sustainable Production Forestry.

 Google Scholar

Kolari P, Lappalainen HK, Hanninen H, Hari P. 2007. Relationship between temperature and the seasonal course of photosynthesis in Scots pine at northern timberline and in southern boreal zone. Tellus Ser B: Chem. Phys. Meteorol. 59:542–552. doi:https://doi.org/10.1111/j.1600-0889.2007.00262.x.

 Web of Science ®Google Scholar

Bergh J, McMurtrie RE, Linder S. 1998. Climatic factors controlling the productivity of Norway spruce: A model-based analysis. For Ecol Manag. 110:127–139. doi:https://doi.org/10.1016/S0378-1127(98)00280-1.

 Web of Science ®Google Scholar

Landsberg JJ, Waring RH. 1997. A generalised model of forest productivity using simplified concepts of radiation-use efficiency, carbon balance and partitioning. For Ecol Manag. 95:209–228. doi:https://doi.org/10.1016/S0378-1127(97)00026-1.

 Web of Science ®Google Scholar

Landsberg J, Sands P. 2011. Physiological ecology of forest production, 1st ed, Terrestrial Ecology Series. San Diego, USA: Elsevier.

 Google Scholar