# NutSpaFHy—A Distributed Nutrient Balance Model to Predict Nutrient Export from Managed Boreal Headwater Catchments

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Field Data

^{3}ha

^{−1}. The distribution of site fertility classes in peatland and upland sites are presented in Table A1.

#### 2.2. Model Description

#### 2.3. Calibration

^{2}. Initial values for all calibrated immobilization parameters was set to 0.9, and the valid range was for the parameter values was set to [0.5, 1.0]. The optimization was conducted with minimize function in scipy.optimize-package in Python 3.7.

#### 2.4. Model Testing

#### 2.5. Application to Clear-Cut Scenario

^{3}ha

^{−1}. The scenarios contained alternative harvest regimes, where similar size clear-cut area was located close and far away from the water (<35 m, >100 m), where similar total tree volume was harvested from peat and mineral soils (Peat < 100 m, Min < 100 m), and where total volume was harvested from low fertility ($sfc$ 4,5,6) vs. high fertility sites ($sfc$ 1,2,3). In addition, we located clear-cuts extending from stream to 10 ...190 m distance (<10 m ...<190 m), and finally we calculated 10 scenarios, where the clear-cuts with same harvested total volume were randomly located around the catchments (Rand 1 ...10).

## 3. Results

#### 3.1. Model Calibration and Immobilization Parameters

#### 3.2. N and P Concentration and Export Load

^{−1}year

^{−1}, and the P export from 0.1 to 0.25 kg ha

^{−1}year

^{−1}(Figure 5). For the test catchments, NutSpaFHy slightly overestimated the annual export loads both for N and P, whereas the annual N concentrations were remarkably well predicted (Figure 5).

#### 3.3. NutSpaFHy Application

^{−1}year

^{−1}, respectively (Figure 6). Locating a similar size of clear-cut area close to receiving water body (scenario < 35 m) resulted in considerably higher specific N and P export loads than clear-cuts located further away (>100 m) (Figure 6b,d). Harvesting similar tree volume close to the waterbody from peatlands (scenario Peat < 100 m) resulted in higher specific N export, but lower P load than harvesting from mineral soils (Min < 100 m). Clear-cuts in fertile sites ($sfc$ 1,2,3) led to clearly higher specific exports than in lower-fertility sites ($sfc$ 3,4,5). Scenarios <10 m ...<190 m describe a situation where the clear-cut area is extended gradually from close to water body towards further-away locations. The total export load (Figure 6a,c) increased with increasing clear-cut area and harvested volume (Table 2), but the specific export decreased when including harvests from further-away grid cells (Figure 6b,d). Results from Rand 1 ...Rand 10 indicate low variability in export loads when half of the catchment area was clear-cut from randomly selected grid-cells.

## 4. Discussion

#### 4.1. Model Requirements

#### 4.2. Evaluation of Model Structure

_{2}O emissions are considerably smaller fluxes and omitted from NutSpaFHy as they are difficult to describe and parameterize at the relevant spatiotemporal scales using available data. As organic fractions of N and P dominate in the export loads in boreal forested catchments [18,41], we accounted only for total dissolved nutrients that include both inorganic and organic forms of N and P. This considerably simplifies the model structure, and it is the total nutrient export which determines the water quality because organic N and P are eventually mineralized or photochemically degraded in the water courses [42,43].

#### 4.3. Model Performance at Study Catchments

#### 4.4. Nutrient Export from Different Harvesting Scenarios

#### 4.5. Potential for Forest Management Planning

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Sites and stand | |

A | Stand age, years |

${g}_{rel}$ | Relative height growth performance, m m^{−1} |

${A}_{i}$ | Index age, years |

${A}_{obs}$ | Observed stand age in a grid cell, years |

h | Stand height, m |

${h}_{i}$ | h at ${A}_{i}$, m |

${h}_{obs}$ | Observed stand mean height (m) in the grid cell |

${h}_{Motti}$ | Mean stand height predicted by a priori computed parameters |

at age ${A}_{obs}$, m | |

$LA{I}_{obs}$ | Observed leaf area index, m^{2} m^{−2} |

${p}_{0}$ | Height growth parameter, calculated a priori |

${p}_{1}$ | Height growth parameter, calculated a priori |

${p}_{2}$ | Stand yield parameter, calculated a priori |

${p}_{3}$ | Stand yield parameter, calculated a priori |

$smc$ | Site main class, class variable (mineral soil, fen, bog, open peatland) |

$sfc$ | Site fertility class, class variable (fertility dcreases from $sfc1$ to $sfc6$) |

${t}_{sim}$ | Duration of the simulation, years |

V | Stand volume, m^{3} ha^{−1} |

${V}_{end}$ | Stand volume at the end of simulation, m^{3} ha^{−1} |

y | Stand yield, m^{3} ha^{−1} |

${y}_{i}$ | Stand yield at index age ${A}_{i}$, m^{3} ha^{−1} |

$\Delta {y}_{i}$ | Stand yield between time points, m^{3} ha^{−1} |

Weather data | |

${P}_{r}$ | Precipitation, mm day^{−1}, FMI data |

${P}_{H2O}$ | Vapor pressure, hPa, FMI data |

R | Global radiation, W m^{−2}, FMI data |

T | Air temperature, ${}^{\circ}$C, FMI data |

${T}_{sum}$ | Temperature sum, degree-days |

${T}_{sum\phantom{\rule{4pt}{0ex}}m}$ | Monthly temperature sum, degree-days |

Water and nutrient variables | |

${A}_{catchment}$ | Catchment area, m^{2} |

B | Parameter in peat respiration model |

${c}_{N,P}$ | Content of N, P in the forest stand, kg ha^{−1} |

${c}_{leaf\phantom{\rule{4pt}{0ex}}N,P}$ | N, P concentrations in leaf mass, kg kg^{−1} |

$cg{v}_{N,P}^{i}$ | N, P concentration in ground vegetation component i, mg g^{−1} |

${c}_{obs}$ | Observed monthly mean N,P concentration in runoff water, mg L^{−1} |

${c}_{pred}$ | Predicted monthly mean N,P concentration in runoff water, mg L^{−1} |

${c}_{om\phantom{\rule{4pt}{0ex}}N,P}$ | Concentration of N,P in soil organic matter in mineral soils, kg kg^{−1} |

${c}_{om\phantom{\rule{4pt}{0ex}}C}$ | Concentration of C in soil organic matter in mineral soils, kg kg^{−1} |

${c}_{peat\phantom{\rule{4pt}{0ex}}N,P}$ | Peat N,P concentration, kg kg^{−1} |

$con{v}_{1}$ | Conversion factor from g m^{−2} h^{−1} to kg ha^{−1} day^{−1} |

$con{v}_{CO2toC}$ | Conversion factor from CO_{2} to C |

$con{v}_{to\phantom{\rule{4pt}{0ex}}grid-cell}$ | Conversion factor from kg ha^{−1} month^{−1} to kg grid-cell^{−1} month ^{−1} |

$con{v}_{to\phantom{\rule{4pt}{0ex}}month}$ | Conversion factor from m s^{−1} to m month ^{−1} |

${d}_{peat}$ | Peat depth, m |

$dist$ | Distance to receiving water body, m |

${f}_{ret\phantom{\rule{4pt}{0ex}}N,P}$ | N and P retention factor, kg kg^{−1} |

${f}_{moist}$ | Moisture restriction function for mineal soil respiration |

$g{v}^{i}$ | Biomass in ground vegetation i, kg ha^{−1} |

$G{W}_{N,P}$ | Groundwater N and P storage in catchment, kg |

$G{W}_{sto}$ | Groundwater storage in catchment, m^{3} |

i | Ground vegetation component: dwarf shrub, herbs and sedges, |

mosses, Sphagna | |

$im{m}_{peat\phantom{\rule{4pt}{0ex}}NP}$ | N, P immobilization in decomposition, peatlands, kg kg^{−1} |

$im{m}_{miner\phantom{\rule{4pt}{0ex}}NP}$ | N, P immobilization in decomposition, mineral soil, kg kg^{−1} |

${K}_{sat}$ | Saturated hydraulic conductivity, m s^{−1} |

$llo$ | leaf longevity, years |

$lna$ | b, k, Stand nutrient content parameters from [13] |

$poro$ | Soil porosity, m^{3} m^{−3} |

${\rho}_{b}$ | Peat bulk density, kg m^{−3} |

${r}_{min\phantom{\rule{4pt}{0ex}}0}$ | reference rate of heterotrophic respiration |

kg ha^{−1} month^{−1} | |

${r}_{min\phantom{\rule{4pt}{0ex}}CO2}$ | Heterotrophic respiration from mineral soil, |

kg CO_{2} ha^{−1} month^{−1} | |

${r}_{min\phantom{\rule{4pt}{0ex}}N,P}$ | Release of N,P in the organic matter decomposition, kg ha^{−1} month^{−1} |

${r}_{peat\phantom{\rule{4pt}{0ex}}CO2}$ | Heterotrophic respiration from peat soil, kg CO_{2} ha^{−1} month^{−1} |

${r}_{peat\phantom{\rule{4pt}{0ex}}0}$ | Heterotrophic respiration from peat soil in reference temperature, |

kg CO_{2} ha^{−1} month^{−1} | |

${r}_{peat\phantom{\rule{4pt}{0ex}}N,P}$ | Release of N,P in the peat decomposition, kg ha^{−1} month^{−1} |

$rg{v}_{N,P}^{i}$ | N, P retranslocation before litterfall in ground vegetation |

component i, kg kg^{−1} | |

${n}_{days\phantom{\rule{4pt}{0ex}}in\phantom{\rule{4pt}{0ex}}month}$ | Number of days in month |

$re{t}_{N,P}$ | N, P retranslocation before litterfall, kg kg^{−1} |

s | Slope parameter in the calibration process |

${Q}_{10}$ | Temperature sensitivity parameter |

${Q}_{dr}$ | Water flux down from root layer, m month^{−1} |

${Q}_{dr\phantom{\rule{4pt}{0ex}}N,P}$ | N, P flux down from root layer, kg ha^{−1} month^{−1} |

${Q}_{dr\phantom{\rule{4pt}{0ex}}N,P\phantom{\rule{4pt}{0ex}}delayed}$ | N, P flux down from root layer, delayed with ${t}_{delay}$ |

${Q}_{ex}$ | Water flux from soil to surface runoff, m month^{−1} |

${Q}_{ex\phantom{\rule{4pt}{0ex}}N,P}$ | N, P flux from soil to surface runoff, kg ha^{−1} month^{−1} |

${Q}_{gwout\phantom{\rule{4pt}{0ex}}N,P}$ | N, P outflux from catchment with groundwater, kg month^{−1} |

${Q}_{out\phantom{\rule{4pt}{0ex}}N,P}$ | Outflux of N and P from the catchment, kg month^{−1} |

${Q}_{runoff}$ | Runoff from catchment, m month^{−1} |

${Q}_{runoff\phantom{\rule{4pt}{0ex}}N,P}$ | N, P flux with runoff from catchment, kg ha^{−1} month^{−1} |

${Q}_{s\phantom{\rule{4pt}{0ex}}runoff}$ | Runoff from catchment, m month^{−1} |

${Q}_{s\phantom{\rule{4pt}{0ex}}runoffN,P}$ | N, P flux with surface runoff, kg ha^{−1} month^{−1} |

$sla$ | Specific leaf area, m^{2} kg^{−1} |

$slope$ | Mean water flow path slope, m m^{−1} |

${\tau}^{i}$ | Turnover rate in ground vegetation component i, years^{−1} |

${T}_{soil}$ | Soil temperature, ${}^{\circ}$C |

${T}_{soil\phantom{\rule{4pt}{0ex}}0}$ | Soil temperature where ${r}_{peat\phantom{\rule{4pt}{0ex}}CO2}$ = 0, ${}^{\circ}$C |

${T}_{soil\phantom{\rule{4pt}{0ex}}ref}$ | Reference soil temperature, ${}^{\circ}$C |

${t}_{delay}$ | Time delay from ${Q}_{dr}$ to stream, months |

${U}_{N,P\phantom{\rule{4pt}{0ex}}m}$ | Monthly uptake of N,P, kg ha^{−1} month^{−1} |

${U}_{N,P}$ | Total N, P uptake of stand and ground vegetation, kg ha^{−1} |

${U}_{comp\phantom{\rule{4pt}{0ex}}N,P}$ | Uptake of N, P to compensate the nutrient lost in litterfall, kg ha^{−1} |

${U}_{gr\phantom{\rule{4pt}{0ex}}N,P}$ | N, P uptake by ground vegetation, kg ha ^{−1} |

${U}_{net\phantom{\rule{4pt}{0ex}}N,P}$ | Stand net uptake of N, P, kg ha^{−1} |

$Ugvlitte{r}_{N,P}^{i}$ | Ground vegetation uptake of N, P to compensate the nutrient |

lost in litterfall, kg ha^{−1} year^{−1} | |

$Ugvne{t}_{N,P}^{i}$ | Ground vegetation N,P net uptake, kg ha^{−1} |

${W}_{m}$ | Monthly mean water content in root layer, m^{3} m^{−3} |

$W{T}_{m}$ | Monthly mean water table, m |

## Appendix A. Catchment Properties

**Table A1.**Volume fraction of coniferous trees (${f}_{conif}$), areal share of fens, bogs and open peatlands ($fen$, $bog$, $open$), and peatlands in different fertility classes (${p}_{rich}$, ${p}_{medium}$, ${p}_{poor}$), and upland mineral soil sites in different fertility classes (${m}_{rich}$, ${m}_{medium}$, ${m}_{poor}$) in the catchments.

$\mathit{id}$ | ${\mathit{f}}_{\mathit{conif}}$ | $\mathit{fen}$ | $\mathit{bog}$ | $\mathit{open}$ | ${\mathit{p}}_{\mathit{rich}}$ | ${\mathit{p}}_{\mathit{medium}}$ | ${\mathit{p}}_{\mathit{poor}}$ | ${\mathit{m}}_{\mathit{rich}}$ | ${\mathit{m}}_{\mathit{medium}}$ | ${\mathit{m}}_{\mathit{poor}}$ |
---|---|---|---|---|---|---|---|---|---|---|

Calibration | ||||||||||

2 | 0.88 | 0.17 | 0.22 | 0.03 | 0.03 | 0.46 | 0.09 | 0.03 | 0.55 | 0.00 |

10 | 0.94 | 0.02 | 0.35 | 0.11 | 0.00 | 0.23 | 0.25 | 0.00 | 0.48 | 0.02 |

13 | 0.83 | 0.02 | 0.03 | 0.00 | 0.01 | 0.03 | 0.02 | 0.19 | 0.55 | 0.01 |

14 | 0.82 | 0.05 | 0.04 | 0.00 | 0.01 | 0.12 | 0.01 | 0.25 | 0.63 | 0.00 |

21 | 0.82 | 0.06 | 0.22 | 0.00 | 0.02 | 0.24 | 0.06 | 0.02 | 0.67 | 0.00 |

22 | 0.89 | 0.02 | 0.17 | 0.06 | 0.02 | 0.16 | 0.08 | 0.01 | 0.73 | 0.00 |

24 | 0.84 | 0.05 | 0.39 | 0.09 | 0.04 | 0.30 | 0.16 | 0.00 | 0.45 | 0.00 |

25 | 0.81 | 0.10 | 0.13 | 0.00 | 0.02 | 0.19 | 0.04 | 0.25 | 0.43 | 0.00 |

27 | 0.89 | 0.00 | 0.02 | 0.02 | 0.02 | 0.03 | 0.00 | 0.00 | 0.09 | 0.17 |

31 | 0.85 | 0.00 | 0.05 | 0.00 | 0.00 | 0.03 | 0.02 | 0.12 | 0.77 | 0.03 |

32 | 0.90 | 0.00 | 0.08 | 0.00 | 0.00 | 0.03 | 0.05 | 0.06 | 0.65 | 0.06 |

33 | 0.84 | 0.06 | 0.24 | 0.00 | 0.01 | 0.28 | 0.05 | 0.06 | 0.64 | 0.00 |

Test | ||||||||||

3 | 0.89 | 0.03 | 0.14 | 0.00 | 0.02 | 0.15 | 0.02 | 0.06 | 0.76 | 0.01 |

6 | 0.88 | 0.01 | 0.33 | 0.04 | 0.01 | 0.27 | 0.09 | 0.00 | 0.62 | 0.00 |

9 | 0.85 | 0.01 | 0.15 | 0.15 | 0.00 | 0.22 | 0.08 | 0.00 | 0.69 | 0.00 |

15 | 0.88 | 0.01 | 0.32 | 0.02 | 0.00 | 0.17 | 0.19 | 0.02 | 0.48 | 0.11 |

16 | 0.88 | 0.03 | 0.39 | 0.00 | 0.02 | 0.33 | 0.09 | 0.05 | 0.51 | 0.00 |

17 | 0.83 | 0.13 | 0.19 | 0.00 | 0.03 | 0.31 | 0.02 | 0.19 | 0.45 | 0.01 |

## Appendix B. Description of NutSpaFHy

#### Appendix B.1. Regional Scale Growth and Yield

^{3}ha

^{−1}) from each simulation. The development of h and y follows Schumacher equation [64,65], whose shape parameters were defined through a curve-fitting procedure to the Motti-simulated results (Equation (A1)).

^{3}ha

^{−1}) is yield at age A (years), ${y}_{i}$ (m

^{3}ha

^{−1}) is the yield at index age ${A}_{i}$, ${p}_{2}$ and ${p}_{3}$ are fitted parameters. Parameters ${p}_{0}$, ${p}_{1}$, ${p}_{2}$ and ${p}_{3}$ were indexed by grid point coordinates, site main class (upland, peatland) and tree species and saved into a database.

#### Appendix B.2. Grid-Cell Water and Nutrient Balance

#### Appendix B.2.1. Soil Moisture and Water Flux from Rooting Zone to Groundwater

^{3}m

^{−3}) and local soil moisture deficit at grid scale to be used as an input for the nutrient balance modelling. SpaFHy also accounts for daily water flux from the rooting zone down to groundwater (${Q}_{dr}$, m day

^{−1}), daily return flow from groundwater to rooting zone (${Q}_{ex}$) in grid scale, and the daily volume of runoff (${Q}_{runoff}$, m

^{3}day

^{−1}) in catchment scale. For NutSpaFHy, the water fluxes and state variables were aggregated to monthly timescale.

#### Appendix B.2.2. Nutrient Uptake

^{3}ha

^{−1}) during the simulation period (${t}_{sim}$) was computed as:

^{3}ha

^{−1}) in the end of the simulation period is:

^{3}ha

^{−1}), and $y\left({t}_{sim}\right)$ is the projected yield during the simulation period (m

^{3}ha

^{−1}).

^{−1}), V is stand volume (m

^{3}ha

^{−1}), $lna$, b, and k are species-specific parameters provided by Palviainen and Finér [13]. The net N and P uptake (${U}_{net\phantom{\rule{4pt}{0ex}}N,P}$, kg ha

^{−1}) resulting from stand volume growth during the simulation period can now be calculated as:

^{−1}). It is calculated accounting for the nutrient retranslocation from senescing leaf mass:

^{2}m

^{−2}), ${c}_{leaf\phantom{\rule{4pt}{0ex}}N,P}$ is concentration of N, P in leaf (kg kg

^{−1}), $re{t}_{N,P}$ is share of nutrient re-translocation in litterfall, $sla$ is specific leaf area (kg m

^{−2}), $llo$ is leaf longevity (yrs), and ${t}_{sim}$ is length of simulation (years).

^{−1}). Ground vegetation was considered in i components, where i = [dwarf shrubs, herbs and sedges, mosses]. Field layer consists of dwarf shrubs and herbs and sedges, whereas the ground layer consists of mosses only. In upland mineral soil sites, the share of dwarf shrubs and herbs from the total field layer biomass was assumed to be 91%, 9%; 71%, 29%; 38%, 62% in Scots pine, Norway spruce and broad leaved stands, respectively (Figure 1 in [34]). Parameterization of peatland sites is presented in details in [35]. Ground vegetation nutrient contents ($cg{v}_{N,P}$, mg g

^{−1}), turnover rate ($\tau $, years

^{−1}), and nutrient retranslocation fractions ($rg{v}_{N,P}$, kg kg

^{−1}) (Table A2) were derived from [14,67,68].

**Table A2.**Ground vegetation nutrient contents ($cg{v}_{N,P}$, mg g

^{−1}), turnover time ($\tau $, years

^{−1}), and nutrient retranslocation fractions ($rg{v}_{N,P}$, kg kg

^{−1}).

i | ${\mathit{cgv}}_{\mathit{N}}$ | ${\mathit{cgv}}_{\mathit{P}}$ | $\mathit{\tau}$ | ${\mathit{rgv}}_{\mathit{N}}$ | ${\mathit{rgv}}_{\mathit{P}}$ |
---|---|---|---|---|---|

Dwarf shrubs | 12.0 | 1.0 | 0.2 | 0.5 | 0.5 |

Herbs, sedges | 18.0 | 2.0 | 1.0 | 0.5 | 0.5 |

Upland mosses | 12.5 | 1.4 | 0.3 | 0 | 0 |

Sphagna | 6.0 | 1.4 | 0.3 | 0 | 0 |

^{−1}) during the whole simulation period, $\Delta g{v}^{i}$ is the ground vegetation biomass change from the beginning to the end of the simulation (kg ha

^{−1}), $cg{v}_{N,P}^{i}$ is the nutrient concentration in the ground vegetation component i (mg g

^{−1}). Change in $g{v}^{i}$ occurs when the stand volume, stem number, basal area and stand age change from the beginning and the end of the simulation. In some cases with increasing stand volume $\Delta g{v}^{i}$ may become negative, and then $Ugvne{t}_{N,P}^{i}$ is set to zero.

^{−1}year

^{−1}), ${\tau}^{i}$ is the turnover rate of ground vegetation component i (year

^{−1}), and $rg{v}_{N,P}^{i}$ is the fraction of N, P retranslocated back to living tissues before the litterfall (kg kg

^{−1}). Total ground vegetation nutrient uptake (${U}_{gr\phantom{\rule{4pt}{0ex}}N,P}$ kg ha

^{−1}) was obtained by:

^{−1}) of the stand and ground vegetation was calculated as a sum of stand and ground vegetation uptake:

^{−1}month

^{−1}) for month m was derived from ${U}_{N,P\phantom{\rule{4pt}{0ex}}tot}$ using the temperature sum for month m (${T}_{sum\phantom{\rule{4pt}{0ex}}m}$, degree-days), and the long-time temperature sum (${T}_{sum}$, degree-days):

#### Appendix B.2.3. Nutrient Release

_{2}(kg ha

^{−1}month

^{−1}), ${r}_{min\phantom{\rule{4pt}{0ex}}0}$ is reference rate of heterotrophic respiration in CO

_{2}(60.82 kg ha

^{−1}day

^{−1}), ${Q}_{10}$ is temperature sensitivity (value 2.3), and ${T}_{soil}$ is monthly mean soil temperature (${}^{\circ}$C, here ${T}_{soil}$ is assumed to be minimum of monthly mean air temperature and 16.0), ${n}_{days\phantom{\rule{4pt}{0ex}}in\phantom{\rule{4pt}{0ex}}month}$ is number of days in month (days month

^{−1}) and ${f}_{moist}$ is moisture restriction function [69]:

^{3}m

^{−3}), $poro$ is soil porosity in the root zone (m

^{3}m

^{−3}).

^{−1}month

^{−1}) in the organic matter decomposition, we computed:

_{2}to elemental C (12 kg mol

^{−1}/44 kg mol

^{−1}), ${c}_{om\phantom{\rule{4pt}{0ex}}N,P}$ is N,P content in soil organic matter in mineral soils (kg kg

^{−1}). According to Tamminen [60], N content in soil organic matter of $sfc$ 1, 2, 3, 4 and 5 is 0.024, 0.022, 0.018, 0.016 and 0.014 kg kg

^{−1}, respectively. P content of $sfc$ 1, 2, 3, 4 and 5 is 0.0017, 0.0015, 0.0013, 0.0011 and 0.0010 kg kg

^{−1}, respectively. ${c}_{om\phantom{\rule{4pt}{0ex}}C}$ is C content in organic matter (0.55 kg kg

^{−1}), and $im{m}_{miner\phantom{\rule{4pt}{0ex}}N,P}$ is fraction of the released N and P that is immobilized into microbial biomass (kg kg

^{−1}). $im{m}_{miner\phantom{\rule{4pt}{0ex}}N,P}$ was calibrated against measured N and P concentrations in the runoff water (see Section 2.3. Calibration).

_{2}efflux was calculated as [37]:

^{−1}month

^{−1}), ${r}_{peat\phantom{\rule{4pt}{0ex}}0}$ peat heterotrophic respiration (kg ha

^{−1}day

^{−1}) in reference soil temperature ${T}_{soil\phantom{\rule{4pt}{0ex}}ref}$ (10 ${}^{\circ}$C), ${T}_{soil}$ is monthly mean soil temperature at depth of 0.05 m (${}^{\circ}$C), here represented with monthly mean air temperature ${T}_{soil}$ = min (T, 16.0), ${T}_{soil\phantom{\rule{4pt}{0ex}}0}$ is soil temperature at which soil respiration is zero (−41.02 ${}^{\circ}$C), B is a parameter, and ${n}_{days\phantom{\rule{4pt}{0ex}}in\phantom{\rule{4pt}{0ex}}month}$ is number of days in month. The peat respiration in the reference temperature depends on stand and site properties, and water table [37]:

^{3}ha

^{−1}), ${\rho}_{b}$ is peat bulk density (kg m

^{−3}), and $W{T}_{g}s$ is mean water table during the growing season (here we use monthly mean water table $W{T}_{m}$), and $con{v}_{1}$ is conversion factor from g m

^{−2}h

^{−1}to kg ha

^{−1}day

^{−1}. Parameter B is obtained as:

^{−3}); ${c}_{peat\phantom{\rule{4pt}{0ex}}N}$ was: 0.019, 0.019, 0.016, 0.014, 00012 (kg kg

^{−1}organic matter); and ${c}_{peat\phantom{\rule{4pt}{0ex}}P}$: 0.0010, 0.0010, 0.0008, 0.0006, 0.0005)(kg kg

^{−1}organic matter). These parameters were used to compute the release of N and P from peat (${r}_{peat\phantom{\rule{4pt}{0ex}}N,P}$, kg ha

^{−1}day

^{−1}):

^{−1}), $im{m}_{peat\phantom{\rule{4pt}{0ex}}N,P}$ is fraction of the released N and P that is immobilized into microbial biomass (kg kg

^{−1}). $im{m}_{peat\phantom{\rule{4pt}{0ex}}N,P}$ was calibrated against measured N and P concentrations in the runoff water (see Section 2.3. Calibration).

#### Appendix B.2.4. Nutrient Balance

^{−1}). N and P storage in the rooting zone was obtained as:

^{−1}) at time-steps t and $t-1$, ${r}_{N,P}$ is N and P release from organic matter decomposition (${r}_{min\phantom{\rule{4pt}{0ex}}N,P}$ or ${r}_{peat\phantom{\rule{4pt}{0ex}}N,P}$ depending on the site type), and ${U}_{N,P\phantom{\rule{4pt}{0ex}}m}$ is the monthly nutrient uptake by the stand and ground vegetation. Only positive values for $st{o}_{N,P}$ are allowed. Thereafter, N and P concentration (${c}_{water\phantom{\rule{4pt}{0ex}}N,P}$, kg m

^{−3}) in the rooting zone was calculated as:

^{3}m

^{−3}), ${s}_{depth}$ is the rooting layer depth (m). Thereafter, N and P flux to groundwater (${Q}_{dr\phantom{\rule{4pt}{0ex}}N,P}$, kg ha

^{−1}month

^{−1}) was calculated as:

^{−1}month

^{−1}, ${Q}_{dr}$ is water flux down from root layer (m month

^{−1}). The nutrient flux from soil to surface runoff (${Q}_{ex\phantom{\rule{4pt}{0ex}}N,P}$, kg ha

^{−1}month

^{−1}) was obtained as:

^{−1}). Then, ${Q}_{dr\phantom{\rule{4pt}{0ex}}N,P}$ and ${Q}_{ex\phantom{\rule{4pt}{0ex}}N,P}$ were subtracted from $st{o}_{N,P}$.

#### Appendix B.3. Nutrient Export

^{−1}) of the water flow path was solved accordingly. Using the a macro-scale hydraulic conductivity of ${K}_{sat}$ = 10

^{−4}m s

^{−1}for both mineral soil slopes [53], and for peat soils [71], the time delay (${t}_{delay}$, months) from the generation of ${Q}_{dr\phantom{\rule{4pt}{0ex}}N,P}$ to the visibility in ${Q}_{runoff\phantom{\rule{4pt}{0ex}}N,P}$ was obtained as:

^{−1}to m month

^{−1}, and $poro$ is the soil porosity in the grid-point (m

^{3}m

^{−3}). In the initialization of the Nutrient export module, the three dimensional ${Q}_{dr\phantom{\rule{4pt}{0ex}}N,P}$ matrix (dimensions: time,x,y) was shifted with ${t}_{delay}$ along the time axis for each grid-point to account for the effect of distance and slope to the residence time of groundwater.

^{3}) was determined as the water located between the $WT$ and the lower boundary of the active groundwater storage. N and P storage in the catchment groundwater storage $G{W}_{N,P}$ (kg) was calculated by considering the outflow with the runoff, and the inflow with the delayed input matrix ${Q}_{dr\phantom{\rule{4pt}{0ex}}N,P\phantom{\rule{4pt}{0ex}}delayed}$ (kg). The inflow was further decreased by N and P retention according to distance to the receiving water body using empirical function [38]. The N and P outflow with the groundwater ${Q}_{gwout\phantom{\rule{4pt}{0ex}}N,P}$ (kg) was calculated as:

^{2}, and ${Q}_{runoff}$ is the monthly runoff (m month

^{−1}). N and P surface runoff flux ${Q}_{srunoff\phantom{\rule{4pt}{0ex}}N,P}$ (kg month

^{−1}) to the receiving water body were calculated as a sum of grid-cell surface runoffs:

^{−1}month

^{−1}) and $con{v}_{to\phantom{\rule{4pt}{0ex}}grid-cell}$ converts the outflux to kg grid-cell

^{−1}month

^{−1}. The new N,P storage in the groundwater was obtained as:

^{−1}) factor. The retention factor was empirically connected to distance to receiving water body ($dist$, m) following the data presented in [38]: ${f}_{ret\phantom{\rule{4pt}{0ex}}N}$ = (15.4 * ln($dist$) − 52.7) * 10

^{−2}and ${f}_{ret\phantom{\rule{4pt}{0ex}}P}$ = (19.1 * ln($dist$) − 61.9) * 10

^{−2}. Finally, the total N and P outflux (${Q}_{out\phantom{\rule{4pt}{0ex}}N,P}$, kg month

^{−1}) from the catchment was obtained as a sum of N P fluxes in groundwater outflow and surface runoff:

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**Figure 2.**NutSpaFHy extends the hydrological model SpaFHy [30] (yellow box). Blue boxes refer to model inputs, orange box to a priori computation of regional forest growth parameters, green boxes are computation modules, grey boxes are variables or data transferred between the modules, and purple box is the model output. Outlines of the boxes describe the frequency of the computation: The box with double solid outline is computed a priori, boxes with a wide dashed outline are calculated only in the beginning of the simulation, and boxes with a square dotted outline are computed in monthly time-step. SpaFHy (yellow box) is calculated in daily time-step. Variable symbols are provided in Abbreviations. Symbols B.1...B.3 refer to Appendix B, where the sub-modules are described in detail.

**Figure 3.**Observed total nitrogen (N) and phosphorus (P) concentration in stream water and export in the calibration catchments (red dots, catchment number as y label). The green and blue lines show mean modeled values with optimized immobilization parameters and those derived from catchment properties, respectively. The green range shows a 95% confidence interval. Units for each figure column are given as a column suptitle.

**Figure 4.**Observed nitrogen (N) and phosphorus (P) stream water concentration and export in the independent test catchments (red dots, catchment number as y label), and modelled values using immobilization parameters derived from catchment properties (blue line).

**Figure 5.**Scatterplots between observed and predicted annual export loads of nitrogen (

**a**) and phosphorus (

**b**), and observed and predicted mean annual nitrogen (

**c**) and phosphorus concentration (

**d**) in calibration (green dots) and test catchments (red dots). The dashed red line is a regression line (equation in the figure) for the test catchments.

**Figure 6.**Mean annual nitrogen (N) and phosphorus (P) export loads (in kg ha

^{−1}year

^{−1}) over 10-year period after clear-cut in Catchment 2. Panels (

**a**) and (

**c**) show the total export load per catchment area. The panels (

**b**) and (

**d**) show the specific export loads (the increase of export load compared to uncut case, normalized by the harvested area). The black lines represent the standard deviation of annual export load. The clear-cut scenarios are summarized in Table 2.

**Table 1.**Characteristics of calibration and test catchments: $id$ denotes catchment identification number, p is pristine and m is managed catchment, $Area$ is catchment area in ha, ${T}_{sum}$ is temperature sum in degree days, ${P}_{r}$ is mean annual precipitation in mm, V is the mean stand volume in m

^{3}ha

^{−1}, ${f}_{conif}$ is the fraction of coniferous trees from the total stand volume in the catchment, $Slope$ is the mean slope in the catchment in %, ${D}_{water}$ is the mean distance to water body in m, and $Peat$ is the share of peatland sites from total area of the catchment.

$\mathit{id}$ | $\mathit{Area}$ | ${\mathit{T}}_{\mathit{sum}}$ | P | V | ${\mathit{f}}_{\mathit{conif}}$ | $\mathit{Slope}$ | ${\mathit{D}}_{\mathit{water}}$ | $\mathit{Peat}$ |
---|---|---|---|---|---|---|---|---|

Calibration catchments | ||||||||

2 p | 167 | 1118 | 674 | 156 | 0.88 | 1.94 | 70 | 0.42 |

10 p | 74 | 1145 | 668 | 88 | 0.94 | 1.65 | 123 | 0.48 |

13 m | 436 | 1454 | 661 | 148 | 0.83 | 5.50 | 105 | 0.05 |

14 m | 154 | 1283 | 606 | 165 | 0.82 | 2.82 | 86 | 0.09 |

21 m | 1053 | 1043 | 807 | 96 | 0.82 | 3.37 | 86 | 0.28 |

22 m | 1560 | 942 | 600 | 61 | 0.89 | 5.82 | 218 | 0.25 |

24 m | 1719 | 968 | 623 | 51 | 0.84 | 1.49 | 89 | 0.53 |

25 m | 1072 | 1261 | 626 | 142 | 0.81 | 3.00 | 104 | 0.23 |

27 m | 1373 | 942 | 600 | 25 | 0.89 | 3.91 | 235 | 0.04 |

31 m | 31 | 1425 | 574 | 137 | 0.85 | 3.43 | 32 | 0.05 |

32 m | 37 | 1439 | 583 | 145 | 0.90 | 2.45 | 51 | 0.08 |

33 m | 51 | 1118 | 674 | 130 | 0.84 | 2.18 | 215 | 0.30 |

Test catchments | ||||||||

3 p | 72 | 1106 | 731 | 166 | 0.89 | 4.36 | 226 | 0.17 |

6 p | 49 | 878 | 697 | 74 | 0.88 | 3.96 | 351 | 0.37 |

9 p | 75 | 898 | 731 | 62 | 0.85 | 3.02 | 403 | 0.31 |

15 m | 1455 | 1287 | 667 | 108 | 0.88 | 1.53 | 126 | 0.34 |

16 m | 505 | 1366 | 646 | 152 | 0.88 | 2.05 | 49 | 0.42 |

17 m | 1966 | 1275 | 665 | 140 | 0.83 | 1.97 | 52 | 0.33 |

**Table 2.**Clear-cut scenarios calculated for Catchment 2 (area 166 ha). In all scenarios, clear-cut was only conducted to grid where stand volume exceeded 100 m

^{3}ha

^{−1}.

Scenario | Distance, m | Clear-Cut Area, ha | Harvested V, m^{3} | Mean Harvested V, m^{3} ha ^{−1} |
---|---|---|---|---|

Uncut | - | - | - | - |

>100 m | >100 | 41 | 9066 | 211 |

<35 m | <35 | 43 | 6955 | 168 |

Peat <100 m | <100 | 30 | 4977 | 168 |

Min <100 m | <100 | 27 | 4979 | 184 |

sfc 4,5,6 | no limit | 21 | 3032 | 144 |

sfc 1,2,3 | no limit | 15 | 3035 | 196 |

<10 m | <10 | 34 | 5582 | 166 |

<50 m | <50 | 60 | 10,298 | 174 |

<70 m | <70 | 73 | 12,775 | 174 |

<90 m | <90 | 82 | 14,445 | 175 |

<110 m | <110 | 91 | 16,118 | 177 |

<130 m | <130 | 99 | 17,802 | 179 |

<150 m | <150 | 105 | 19,154 | 181 |

<170 m | <170 | 112 | 20,471 | 183 |

<190 m | <190 | 118 | 21,692 | 184 |

Rand 1 ...10 | no limit | 80 | 15,000 | 188 |

Variable | ${\mathit{imm}}_{\mathit{N}\phantom{\rule{4pt}{0ex}}\mathit{peat}}$ | ${\mathit{imm}}_{\mathit{N}\phantom{\rule{4pt}{0ex}}\mathit{miner}}$ | ${\mathit{imm}}_{\mathit{P}\phantom{\rule{4pt}{0ex}}\mathit{peat}}$ | ${\mathit{imm}}_{\mathit{P}\phantom{\rule{4pt}{0ex}}\mathit{miner}}$ |
---|---|---|---|---|

$Intercept$ | 0.652 ($p<0.001$) | 0.894 ($p<0.001$) | 0.846 ($p<0.001$) | 0.882 ($p<0.001$) |

${f}_{conif}$ | 0.282 (p 0.013) | - | - | - |

$bog$ | −0.150 (p 0.009) | - | - | - |

${m}_{poor}$ | - | 0.284 (p 0.038) | - | - |

$Adjusted\phantom{\rule{4pt}{0ex}}{R}^{2}$ | 0.607 | 0.301 | 0.031 | 0.0 |

$RMSE$ | 0.019 | 0.019 | 0.070 | 0.054 |

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## Share and Cite

**MDPI and ACS Style**

Lauren, A.; Guan, M.; Salmivaara, A.; Leinonen, A.; Palviainen, M.; Launiainen, S. NutSpaFHy—A Distributed Nutrient Balance Model to Predict Nutrient Export from Managed Boreal Headwater Catchments. *Forests* **2021**, *12*, 808.
https://doi.org/10.3390/f12060808

**AMA Style**

Lauren A, Guan M, Salmivaara A, Leinonen A, Palviainen M, Launiainen S. NutSpaFHy—A Distributed Nutrient Balance Model to Predict Nutrient Export from Managed Boreal Headwater Catchments. *Forests*. 2021; 12(6):808.
https://doi.org/10.3390/f12060808

**Chicago/Turabian Style**

Lauren, Annamari (Ari), Mingfu Guan, Aura Salmivaara, Antti Leinonen, Marjo Palviainen, and Samuli Launiainen. 2021. "NutSpaFHy—A Distributed Nutrient Balance Model to Predict Nutrient Export from Managed Boreal Headwater Catchments" *Forests* 12, no. 6: 808.
https://doi.org/10.3390/f12060808