Net primary production and light use efficiency in a mixed coniferous forest in Sweden


Fredrik.Lagergren. Fax: +46 46 2220321; e-mail:


Simple light use efficiency (ɛ) models of net primary production (NPP) have recently been given great attention (NPP = ɛ × absorbed photosynthetically active radiation). The underlying relationships have, however, not been much studied on a time step less than a month. In this study daily NPP was estimated as the sum of net ecosystem exchange (NEE) and heterotrophic respiration (Rh) of a mixed pine and spruce forest in Sweden. NEE was measured by eddy correlation technique and Rh was estimated from measurements of forest floor respiration (Rf) and the root share of Rf. The total yearly NPP was on average 810 g C m−2 year−1 for 3 years and yearly ɛ was between 0.58 and 0.71 g C MJ−1, which is high in comparison with other studies. There was a seasonal trend in ɛ with a relatively constant level of approximately 0.90 g C MJ−1 from April to September Daily NPP did not increase for daily intercepted radiation above 6 MJ m−2 d−1, indicating that between-years variation in NPP is not directly dependent on total Qi. The light was most efficiently used at an average daytime temperature of around 15 °C. At daytime vapour pressure deficit above 1400 Pa ɛ was reduced by approximately 50%.


Ecosystem net primary production (NPP) is an important characteristic that distinguishes different biomes and is useful for food and wood production estimates and for carbon budgets. In the past, carbon budgets and estimates of NPP have mostly been calculated on a yearly basis. Recent technological developments in continuous measurements of net ecosystem exchange (NEE), soil carbon fluxes and tree compartment fluxes have made it possible to make NPP estimates with a daily time resolution. The short time responses to environmental variables have to be established in order to model the behaviour of ecosystems in a future changing climate as most processes are non-linear.

The development of remote sensing from satellites has showed potential for estimates of NPP (Ruimy, Saugier & Dedieu 1994; Potter, Klooster & Brooks 1999; Seaquist, Olsson & Ardö 2003). The most commonly used concept is to estimate NPP from the amount of absorbed photosynthetically active radiation (Qa) and a constant light use efficiency, ɛ (Monteith 1972).

NPP = Qa ɛ(1)

It is evolutionarily valid that Qa will be related to NPP, as plants have no benefit of harvesting more light than they have resources to use (Field, Randerson & Malmstrom 1995). Satellite images can be used to derive Qa by the use of a vegetation index (Asrar et al. 1984). The value of ɛ was initially considered as relatively constant but substantial differences have been found that depend on ecosystem type, age, species composition, fertility and stresses (Ruimy et al. 1994; Goetz & Prince 1996; Gower, Kucharik & Norman 1999), ɛ is therefore a crucial parameter to estimate. There have been several attempts to model seasonal variation in ɛ, mainly as a function of air temperature, vapour pressure deficit and soil water deficit (e.g. Waring et al. 1995; Potter et al. 1999) but the relationships have mostly been based on assumptions from the literature and not verified by field studies.

There are three main methods to estimate NPP from field experiments: (1) from measurements of the different constitutions of the biomass produced, namely the above- and below-ground growth and litter production. Continuous measurements are however, difficult to achieve, especially for the below-ground part. (2) From the difference between gross assimilation and total autotrophic respiration measured by gas exchange. The great challenge in this method is to scale up from samples of single branches, roots and stem segments to the entire forest. (3) From the sum of NEE and heterotrophic respiration (Rh). The integrated NEE can be relatively easily and accurately measured by the eddy correlation technique and Rh can be measured by trenching or root exclusion, by isotope technique or indirectly as the difference between soil efflux and root respiration (Hanson et al. 2000). One problem with the method is that the source area of the NEE varies with wind speed and wind direction and that NEE and Rh are not measured on the same scale. A scatter in the results can therefore be expected depending on the heterogeneity of the forest. Another problem is that NEE is small in relation to NPP on an annual basis, especially in old stands where respiration can even exceed assimilation (Lindroth, Grelle & Morén 1998). Consequently, the annual NPP will, to a large extent, depend on Rh and as measurements of soil respiration are generally biased to a various degree (Lund et al. 1999) there will be an uncertainty in the yearly NPP estimates.

Daily values of gross primary production (GPP) can be estimated directly from eddy correlation measurements of NEE by subtracting the total ecosystem respiration, estimated from the night-time flux relationship to temperature. This method has been used to evaluate daily variation in GPP and GPP light use efficiency (Turner et al. 2003). To our knowledge, daily variation in ecosystem NPP and the corresponding ɛ has not been analysed before.

In the present study NPP and ɛ were estimated according to method (3) as described above. NEE, Qa, soil efflux and the fraction of root respiration to the total soil efflux were measured over the course of a season in a forest in central Sweden. The aim of the study was to evaluate how NPP and ɛ varied over the year in relation to seasonal trends and meteorological variables. A simple model of ɛ was developed and used to estimate daily NPP. The model was calibrated on data from 1999 and tested on the two preceding years.


General methodology

The light extinction coefficient was estimated in seven different stands from leaf area index and measurements of radiation above and below the canopy. The mean extinction coefficient was used to calculate the amount of absorbed radiation for the forest within 300 m radius from the flux tower where NEE was measured. NPP was estimated from NEE and heterotrophic respiration (Rh, positive values of NEE and NPP represent an uptake of C by the vegetation).

NEE = NPP − Rh(2)

Rh was estimated from measurement of forest-floor respiration (Rf), for which a relationship was established with soil temperature (Widén 2001), and the fraction of soil CO2 efflux from roots (Fr) (Widén & Majdi 2001) [Rh = Rf (1 − Fr)].

Measurement site

The measurements were made in the forest around the Norunda flux tower in central Sweden (60°5′ N, 17°29′ E, 45 m a.s.l). Scots pine (Pinus sylvestris L.) and Norway spruce [Picea abies (L.) Karst.] are the dominant tree species with a small fraction of deciduous trees, mainly Betula pubescens Ehrh., B. pendula Ehrh. and Alnus glutinosa (L.) Gaertn. The soil is a sandy glacial till with moderate to high occurrence of large boulders. Stands of varying species composition and age can be found within 1 km from the tower. The leaf area index (LAI) is between 3 and 6 with the higher values for stands dominated by spruce. The stands within 300 m from the tower are about 100 years old-but differ in soil properties and species composition in both the tree and forest floor vegetation (Table 1). More details about the site can be found in Lundin et al. (1999).

Table 1.  Stand description and measurements accomplished for the six satellite stands (Lundblad & Lindroth 2002), the plot measured in 2001 and the mean for the area within 300 m from the flux tower
(m2 ha−1)
Tree density
(trees ha−1)
(m2 m−2)
  1. Stand description: age; BA, basal area at 1.3 m height; P/S/D, fraction of BA for pine, spruce and deciduous trees; tree density; and LAI, leaf area index from LAI-2000. Measurements: light interception (Qi), net ecosystem exchange (NEE), soil CO2 efflux (Rf) and root share of Rf (Fr).

North-east (NE) 9027.190/1/9 9063.99x   
North (N) 3418.771/27/2 9713.84x xx
North-west (NW)11048.666/32/2 6695.41x xx
South-west (SW) 5028.653/47/0 7945.02x x 
South (S)10535.859/38/4 7005.17x xx
South-east (SE) 6024.1 7/93/010425.59x   
Plot A 9540.547/53/0 7895.61x   
300 m radius10039.363/33/5 8704.34 x  

Light interception

The flux density of photosynthetic active radiation (PAR) above the canopy (Q) was measured in the Norunda central tower at a height of 98 m with a Li-190SZ (Li-Cor Inc., Lincoln, NE, USA) sensor. Other meteorological variables were also measured in the tower (Lundin et al. 1999). PAR below the canopy (Qb) was measured in six satellite stands with different characteristics within 1 km from the tower (Table 1). Measurements were conducted in a plot of 40 m × 40 m or 40 m × 30 m within each stand. The measurements were made between 8 July and 21 September 1998. A 1-m-long ramp with three PAR sensors (Li-190SZ) placed approximately 50 cm above the ground was moved between the stands; each stand was measured during two periods of 3 to 8 days. Data were logged every 30 s and 5 min mean values were stored in a Campbell CR10 data logger (Campbell Scientific Inc., Logan, UT, USA). The LAI was estimated with a LAI-2000 plant canopy analyser (Li-Cor Inc.). In each of the six stands LAI was measured on two to six occasions between 24 July and 15 September in 1998, on 10 points in each stand. As no significant trend over time was found, the arithmetic means of the measured values were used (Table 1).

In addition, Qb was measured in a stand 150 m south-west from the tower (Plot A, Table 1) in 2001 between 15 August and 25 October. Twenty-four sensors (JYP 1000; SDEC France, Reignac Sur Indre, France) were placed randomly over an area of about 40 m × 40 m. The sensors were logged every 20 s, and 5 min mean values were stored with a MiniCube VV data logger (Environmental Measuring Systems, Brno, Czech Republic). LAI in Plot A and in 12 additional plots within 300 m from the tower was measured in year 2001, also with the LAI-2000. Each plot was measured once, on approximately 25 points, and an average for the plots was calculated. All LAI-2000 measurements in this paper were corrected for clumping of needles with a correction factor of 1.65 (LAI-2000 Instruction Manual; Li-Cor Inc.).

For each day the quotient of the sum of the average PAR below (Qb) and the summed PAR above (Q) the canopy was calculated. This quotient and LAI for the measured stand were used in the Beer–Lambert law to calculate the light extinction coefficient (k) for each day.

k = ln(Qb/Q)/ − LAI(3)

These values of k are therefore based on intercepted PAR (Qi) and not absorbed PAR. The difference is however, small for LAI above 1 (Prince 1991). Measurement of reflected PAR in the tower showed that it was fairly constant at around 2.5% of Q on a daily basis. As reflected PAR was not measured above the satellite stands and can be expected to vary, Qi was used. There is also a small fraction (< 1% of Q) of the light penetrating the canopy that is reflected in the ground vegetation and thereafter absorbed by the canopy, which was neglected. As this effect slightly compensates for the light that is reflected in the canopy the total difference between Qa and Qi was around 2%. To obtain Qi for the area that represented the NEE flux, an average value of k was computed which was used with the LAI for the stands within 300 m from the tower and Q to calculate Qi for each day in 1997–1999:

Qi = Q[1 − exp( − LAI k)](4)

Net primary production (NPP)

Net ecosystem exchange (NEE) was measured at a height of 35 m in the Norunda tower with a SOLENT three-dimensional sonic anemometer (Gill Instruments, Lymington, UK) and a LI-6262 infrared gas analyser (Li-Cor Inc.). The sampling rate was 10 Hz and the fluxes were calculated based on 30 min averages. A detailed description of the system can be found in Grelle & Lindroth (1996). The eddy fluxes were corrected for sensor inclination, signal time lag caused by the length of the tube, frequency loss caused by tube attenuation and sensor response time (Leuning & Moncrieff 1990) and air density fluctuations because of sensible heat fluxes (Webb, Pearman & Leuning 1980). Data coverage was over 90% for all the years that are considered here. Soil temperature (Ts) at 5 cm depth was measured in the six stands by thermocouples (105T: Campbell Scientific, Ltd. Shepshed, UK); the average of the six stands was used in Eqn 5 below. Soil CO2 efflux was measured in the six stands from September 1997 to August 1999 with a transparent open path chamber system (Iritz, Lindroth & Gärdenäs 1997; Morén & Lindroth 1999) that was moved between the stands (Widén 2001). The nocturnal mean values were used to obtain a relationship between forest-floor respiration (Rf) and Ts for the four stands with mineral soil (excluding stands North-east and South-east that had peat soil):

Rf = 0.0085(Ts + 7.14)2.3(5)

The root respiration share of Rf (Fr) was estimated on five occasions (17–19 May, 5–7 July, 8–10 August, 25–27 August and 5–7 October) in three of the six stands in 1999 (Widén & Majdi 2001). Root respiration was measured on excised roots in a chamber at ambient root temperature and soil CO2 concentration, which is important for correct measurements (Hanson et al. 2000). Measurements were started within 30 min after excision; no decreasing trend was observed over time (B. Alstad (former Widén) personal comm. 2004) and cannot be expected during this time interval as the starch reserves can support root respiration for several weeks (Högberg et al. 2001). Before the roots were dug up, Rf was measured with a closed dark chamber system (Li-Cor 6000-09 chamber connected to a Li-Cor 6200 gas analyser; Li-Cor Inc.) on the same spots. At each occasion six spots were measured in each stand and the root respiration was scaled to area-based unit from root density that was measured in September 1998. Root biomass can vary over the season, which could have caused a systematic error in the Fr estimates. The measured Fr was on average 47% in the middle of May decreasing to 15% at the beginning of October (Fig. 1, symbols). It is a difficult task to measure Fr and the value varies over a wide range (10–90%) in different studies (Hanson et al. 2000). In a relatively poor pine forest in Northern Sweden, Högberg et al. (2001) found an average Fr value of 54% in a tree girdling experiment. A linear decrease of Fr from approximately 55% in the middle of May to 27% in the beginning of September can be interpreted from the results in a cool-temperate deciduous forest (Lee et al. 2003).

Figure 1.

Fraction of total soil CO2 efflux emerging from roots (Fr) in 1999, measured values (diamonds, from Widén & Majdi 2001) and modelled (solid line).

Fr was modelled as a function of a cumulative temperature sum based on daytime average temperature, with a threshold of 0 °C. The accumulation of the temperature sum started on the first day of each year. When 350 day-degrees had been reached Fr was considered to be at the measured value in May (Fig. 1). Temperature sums are generally good predictors for triggering of biological cycles (Begon, Harper & Townsend 1990). The recovery of the photosynthetic capacity in the spring, which can be assumed to be related to the activity of the roots, has been successfully modelled with a temperature sum concept (Bergh, McMurtrie & Linder 1998). For best fit a half sine wave was adjusted from the date of 350 day-degrees to the date of the first autumn frost, to reach the measured value in October This was followed by a constant value until next spring. The peak in May–June is associated with maximum rates of root growth and turnover in the annual cycle (Hanson et al. 1993).

Knowing the seasonal variation in Fr, NPP could be calculated as:

NPP = NEE + Rf(1 − Fr)(6)

The daily value of the light use efficiency (ɛ) was then calculated as the quotient between the corresponding values of NPP and Qi. NPP calculated this way is hereafter referred to as ‘measured’ although it depends on empirical relationships for the estimate of Rh. The seasonal variation in Fr is hard to interpolate from the measured occasions to the entire year, especially during winter and spring. However, since as much as 87–91% of the total NPP was produced between 18 May and 6 October the yearly totals were not sensitive to the exact level of Fr during winter and spring. Additionally, as the heterotrophic respiration is Rf(1 − Fr), the estimate of NPP is not either too sensitive to Fr at low fractions; for example a value of 10 or 30% means just a 29% difference in heterotrophic respiration.

Modelling the seasonal variation in ɛ

In general, variation in ɛ over time for an ecosystem depends mainly on temperature and soil water deficit (Potter et al. 1999). For cold climates, temperature is the dominant factor, reducing the photosynthesis and growth, especially in spring, far below the level that could be expected from the radiation (Bergh et al. 1998). A simple model that was based mainly on temperature sums and frost events was developed to describe the variation in ɛ with separate functions for the spring recovery and the autumn decline. A seasonal factor (f) was calculated for each day (index d). In the spring f was modelled as a function of a cumulative temperature sum (Sspring) with a threshold of 0 °C:


where Tday is the average daytime temperature and Pfrost is a reduction factor for frost events:


and Tmin is the daily minimum temperature.

In the autumn the photosynthetic capacity is reduced by long-night-induced winter hardiness and frost events (Dormling 1993; Hollinger et al. 1999). Hence, during autumn f was calculated for each day as a combination of a negative temperature sum (Saut) with a threshold of 0 °C down to −50 day-degrees and an additive function of days from a starting date set to 10 August (Dsum) as:


where DDOY is the day number of the year. A linear regression between f and ɛ was fitted to establish the relationship used in the final model. The ɛ-values were calculated for periods which lengths were varied to have a total Qi of 25 MJ m−2.

As Fr measurements were made in 1999 this year was used to establish the seasonal variation in ɛ, and 1997 and 1998 were used for testing.


Light extinction coefficient (k)

Plotting k over the measured period generated a large scatter. By splitting the data into ‘clear’ and ‘cloudy’ days, two more distinct sets of k-values were obtained (Fig. 2). Separating ‘clear’ and ‘cloudy’ days was done by fitting a line to the envelope of daily total radiation and setting a limit at 73% of the maximum. The limit was set after visual inspection of daily courses and setting a value above which clear conditions dominated. The mean k was 0.44 and 0.52 for the cloudy and clear days, respectively, with a significant difference (P < 0.001). The difference between the data sets is most likely a result of different proportions of direct and diffuse radiation, which are absorbed at different ratios (Jarvis & Leverenz 1983). There were weak trends over the season for the two data sets that went in opposite directions. A decreasing trend for cloudy days could be a result of decreasing LAI. However, in 1998 no trend in LAI was found in the measurements that were ongoing until 15 September In 2001 the light interception measurements continued until 21 October whereas LAI was only measured once. It is likely that some needle shedding occurred during this period. An increasing trend for clear days is expected as a lower sun angle means a longer passage through the canopy for the direct radiation.

Figure 2.

The light extinction coefficient (k) calculated for single days for seven different stands (see Table 1) with stand name as symbol. Plot A was measured in 2001 whereas the other stands were measured in 1998. The days were separated into clear and cloudy. To the right are box-plots of the distribution of k, showing the 5, 10, 25, 75, 90 and 95% percentiles and the median.

There was some variation in k between the stands (Table 2), but no relationship to the stand variables (Table 1) was found. The average k-values are within the range of earlier reports (Jarvis & Leverenz 1983), for example, 0.43 by Morén et al. (2000) (70-year-old Norway spruce and Scots pine mixture) and 0.69 by Sampson & Allen (1998) (14-year-old loblolly pine). An uncertainty in the estimated k-values lies in the correction for clumping of needles in the LAI estimate. The correction factor varies in relation to species and stand structure (Stenberg 1996). The aim was, however, not to obtain exact values of k but rather to use k as an effective parameter to estimate Qi for the stand around the tower. This estimate is insensitive to the correction factor as the stand around the tower had similar species composition as the average of the satellite stands for which k was estimated (Table 1). In the satellite stands there were only three sensors used, which is a small number, but as the variation in k was not larger than for stand A, where 24 sensors were used, the daily totals seem to have been sufficiently sampled.

Table 2.  The mean light extinction coefficient (k) for the different stands divided into cloudy and clear days and the number of observed days (n)
North-east0.4510 00.45 10
North0.44 50.44 20.44  7
North-west0.49 60.56 40.52 10
South-west0.46 90.50 30.47 12
South0.50 60.55 60.52 12
South-east0.46 9 00.46  9
Plot A0.41460.51220.44 68
Average all plots0.46 70.51 50.47  7
Average all days0.44910.52370.46128

Net primary production (NPP) and intercepted radiation (Qi)

Plotting 7-d running means of NEE, NPP and Qi shows that Qi and NPP are related (Fig. 3). The coefficient of determination (r2) between NEE and Qi was 0.43 and it was 0.70 between NPP and Qi(Fig. 4). As the heterotrophic respiration (Rh), that depends on soil temperature, is added to NEE and as Q and soil temperature are related (r2 = 0.35) there is some degree of multicollinearity, which partly explains the stronger relationship to NPP. The maximum NPP was about 16 g C m−2 d−1, which was reached in the middle of July Of this maximum value NEE contributed to 66%, and 34% was added from the estimate of Rh.

Figure 3.

Seven-day running means of NEE (dashed line), NPP (dotted line) and Qi (solid line) in 1999.

Figure 4.

The relationship between NEE (above) and NPP (below) to intercepted PAR in 1999.

Light use efficiency (ɛ)

The plot of ɛ over time showed a considerable scatter, especially during winter-time when it is the quotient between two small numbers. By calculating ɛ for periods with a total Qi of 25 MJ m−2 much of the scatter was reduced. The fit for the regression between the ɛ-values and the seasonal factor f (Eqn 7 and 10) was:

ɛmodelled = 3.29f − 2.37; r2 = 0.75.

This gives a maximum ɛmodelled of 0.92 g C MJ−1(Fig. 5). During winter-time ɛ becomes negative as a result of negative NPP. Negative NPP values in the winter are a consequence of higher autotrophic respiration than photosynthesis. There is, however, no reason for NPP to be negatively correlated to Qi and a negative ɛ has consequently no physical meaning. Actually NPP and Qi have no relationship during this period and the model is only capable of giving a mean NPP for the period with negative ɛ.

Figure 5.

Measured (dots) light use efficiency (ɛ) calculated for periods with a total of 25 MJ m−2 of intercepted PAR and the modelled ɛ (line) in 1999.

An annual value of ɛ was also calculated from the yearly total of Qi and NPP, respectively, which was 0.71 g C MJ−1 for 1999. The NPP value was replaced by the one estimated from the light use efficiency model for the days when NEE was missing, so that a yearly total could be estimated. The value is high, but within the range of values in other studies of similar ecosystems. Ruimy, Dedieu & Saugier (1996) have calculated a value of 0.44 for temperate evergreen needle-leaf forests. Higher values for high latitudes with relatively low amounts of yearly Qi, as the present studied forest, can however, theoretically be expected (Medlyn 1998). With the assumption that 50% of the dry matter production is carbon, the value would be 1.42 g dry matter MJ−1 (ɛtotal). The value for the above ground production (ɛabove) would be 0.99 g dry matter MJ−1 if 70% of the total NPP was above ground. Goetz & Prince (1996) reported ɛabove values between 0.17 and 0.89 for boreal black spruce (Picea mariana). In various conifer forests in Oregon, Runyon et al. (1994) reported ɛabove values between 0.18 and 0.92.

One reason for the difference between different estimates is that forest floor vegetation NPP may or may not be included. In the present approach the forest floor vegetation is included in NPP but since Qi was estimated for the canopy only, ɛ is overestimated. The assimilation of the forest floor has been estimated to be 19% of the total gross assimilation for a stand in the same forest (Morén 1999). With the assumption that the forest floor vegetation intercepts 80% of the light below the canopy the ɛ-values are overestimated by approximately 12%.

Between-year variation in annual NPP and ɛ

The total measured NPP for the 3 years varied between 712 and 938 g C m−2 year−1(Table 3) and ɛ calculated from the yearly totals varied between 0.57 and 0.71. A better relationship with yearly NPP was found for the length of the growing season than for total Qi. As the relationship between Qi and NPP is relatively weak (Fig. 4) it is reasonable that the number of days that contribute to the yearly NPP is of importance. NPP calculated from a variable ɛ was not closer to the measured yearly totals than NPP calculated from a constant ɛ.

Table 3.  Total amount of intercepted PAR (Qi, MJ m−2 years−1); total NPP (g C m−2 years−1) from measurements, NPP calculated from Qi, and the light use efficiency (ɛ), either constant from 1999 or modelled and the length of the growing season (GS, number of days with an average temperature above 5 °C between 1 April and 31 October)
YearQiNPP measuredɛNPP const. ɛNPP mod. ɛGS (days)
199713487750.57957 (124%)1006 (130%)173
199810707120.67760 (107%) 729 (102%)160
199913239380.71939 (100%) 918 (98%)181

Comparisons of seasonal NPP estimates

NPP computed from ɛmodelled did not explain more of the variation in measured NPP compared to NPP from using a constant ɛ, but the slope was closer to one and the intercept was closer to zero (Fig. 6). The light interception model performed similarly in explaining NPP for 1997 and 1998 as in the calibration year 1999 (Fig. 7). As expected, NPP is over or underestimated for days with radiation differing from the mean value in the winter and early spring as ɛ is used to calculate NPP, although there is no relationship between NPP and Qi for this period. During spring NPP is systematically over or underestimated for some periods. It has been observed for several boreal sites that the commencement of photosynthesis in spring can be well predicted by a temperature sum whereas this failed for the present stand located just outside the southern limit of the boreal zone (Suni et al. 2003). Obviously, the present stand responds in a quicker way in both positive and negative direction to day-to-day variation in temperature in comparison with the more typical boreal sites. The period in the beginning of June in 1997, which starts with an abrupt change to warm and dry weather, is substantially overestimated.

Figure 6.

Measured NPP against NPP from intercepted light and light use efficiency (ɛ) in 1999, ɛ was either constant (above) or modelled (below). The solid lines are the regression result and the dotted lines are the 1 : 1 relationship.

Figure 7.

Modelled NPP based on light interception estimates for the years 1997–99 (solid line) and the difference between modelled and measured NPP (bars). The dotted lines show a 30-d running mean of the difference. The linear regression parameters with NPP measured as independent and NPP modelled as dependent variables are also given.

Relationships between NPP, ɛ and weather parameters

In Figs 8 and 9 NPP and ɛ for all 3 years are plotted against average daytime temperature (Tday), average daytime vapour pressure deficit (VPDday) and Qi. The plots were divided into three periods: May–June, high light intensity and no water stress; July–August, high soil temperature and occasional soil water deficit; September–October, decreasing light and temperature, and the whole year. The NPP and Qi data were sorted by the evaluated variable and average NPP and ɛ was calculated for ranges that was set to have a total Qi of 50 MJ m−2.

Figure 8.

Average daytime air temperature, intercepted PAR (Qi) and average daytime vapour pressure deficit (VPD) plotted against net primary production (NPP). All three years are included in each plot but the growing season was divided into three periods. Averages were calculated for classes of the x-axis variable that was set to have a total Qi of 50 MJ m−2.

Figure 9.

Average daytime air temperature, intercepted PAR (Qi) and average daytime vapour pressure deficit plotted against light use efficiency (ɛ). All three years are included in each plot but the growing season is divided in three periods. ɛ was calculated for classes of the x-axis variable that were set to have a total Qi of 50 MJ m−2.

The NPP was highest at temperatures of approximately 17–18 °C (Fig. 8) whereas the light was most efficiently used at approximately 14–16 °C (Fig. 9). The relationship was weaker and with a lower optimum temperature in May–June than for the other periods. Seen over the whole year NPP was linearly related to Qi between 1 and 7 MJ m−2 d−1 but from May to August no positive relationship was found above 5 MJ m−2 d−1. The lack in increased NPP above 5–7 MJ m−2 d−1 indicates that the needles begin to be light saturated. Turner et al. (2003) found a similar relationship with gross primary production for a boreal and a temperate forest whereas a tall grass prairie was linearly related to Qi up to the maximum measured Qi levels of 11 MJ m−2 d−1. The maximum photosynthetic capacity of conifers is generally low (Woodward & Smith 1994) and light saturation can be expected especially for stands with fairly low LAI. Another reason for a decreasing trend with increasing radiation is that the proportion of direct radiation increases. Gu et al. (2002) suggested that the diffuse and direct Qi should be treated separately in NPP estimates as the diffuse radiation is more efficiently used. This could not be tested here because direct or diffuse radiation was not measured.

A light-saturation level for NPP also indicates that inter-annual variation in NPP may be insensitive to yearly total Qi. The total abundant Qi above 6 MJ m−2 d−1 was 17, 11 and 18% of the yearly total for 1997, 1998 and 1999, respectively. If that amount is subtracted from the yearly Qi (Table 3) new values of ɛ can be calculated that would be 0.69, 0.75 and 0.87 g C MJ−1 for the 3 years, respectively. The difference between 1997 and 1998 is thus reduced whereas 1999 is further accentuated. 1999 was a year with high temperatures in July and August leading to higher estimate of Rh than for the other years. The yearly total soil respiration may be insensitive to soil temperature (Giardina & Ryan 2000) and more dependent on substrate quality (Ågren & Bosatta 1996) and production (Janssens et al. 2001).

There is an intercept of the linear part in the Qi–NPP relationship of −2.2 g C m−2 d−1 (Fig. 8) and as a result the Qiɛ relationship deviates from the ideal constant level (Fig. 9). VPDday had strong relationship to NPP with a maximum at approximately 600–800 Pa. The corresponding NPP–ɛ relationships show a very distinct negative correlation in the summer that reduces ɛ to about half of the maximum value at approximately 1400 Pa, above which ɛ reaches a plateau level. At high VPD stomata can be completely closed, which will stop the photosynthesis (Jarvis 1976; Stewart 1988) but with a daily time step a large part of the light can still be utilized as the maximum VPD is normally reached in the afternoon. In a light use efficiency model with an hourly time step a linear decrease in the utilized light (Qu) was assumed between 1.5 and 2.5 kPa and no light utilized above 2.5 kPa (Waring et al. 1995). A similar approach was tested by assuming a linear decrease from 100 to 50% of Qu between 0.5 and 1.5 kPa VPDday and constant levels of 100 and 50% below and above that span. No Qu with Tday below 0 °C was also assumed (Fig. 8 present paper, Waring et al. 1995). Figure 10 shows a positive quadratic relationship between Qu and NPP up to the highest values of Qu but a decreasing slope can still be observed for Qu above 6 MJ m−2 d−1. Yearly total light use efficiency for Qu would be 0.73, 0.79 and 0.89 g C MJ−1 for the 3 years, which is similar to the values found by subtracting the light above 6 MJ m−2 d−1.

Figure 10.

The utilized PAR (Qu, see text), plotted against net primary production (NPP). All three years are included in the plot; ɛ was calculated for classes of Qu that were set to have a total Qu of 50 MJ m−2.


  • 1Using NEE measurements in combination with measurements of Rh is a useful method for assessment of ɛ-models.
  • 2Part of the explanation to the rather high value of ɛ obtained in this study, 1.42 g dry matter MJ−1, can be attributed to the ground vegetation component. Including PAR absorbed by the ground vegetation gives a more reasonable ɛ-value of 1.27 g dry matter MJ−1.
  • 3The lack of correlation between NPP and absorbed PAR at high PAR will have implications for the estimation of annual carbon balances by the linear ɛ-model. It is a risk that such models will overestimate the between-year variation in NPP.
  • 4The yearly total NPP was not better estimated with a seasonal varying ɛ, but the seasonal variation was better described.
  • 5The results indicate that more accurate estimates of NPP can be calculated by including responses of ɛ to low temperatures, high VPD and high light levels, but it could not be confirmed by a better estimate of the yearly total.


This research was supported by EU (within the CARBOEUROFLUX project), the Swedish Energy Agency and the Swedish National Space Board.

Received 25 June 2001; accepted for publication 27 September 2004