On the Ecology of Mountainous Forests in a Changing Climate: A ...

216 Appendix
PROCEDURE CorrWeatherGenerator( VAR rTVect, rPVect: ARRAY OF REAL );
(*
A weather generator is used which draws samples from the joint distribution
of temperature and precipitation. It takes into account the correlation between the
two variates using the modules "Jacobi" and "MultiNormal" developed by
D. Gyalistras, Systems Ecology, ETHZ
Assumption of normality of T and P: see Botkin et al. (1972), Fliri (1974);
the empirical correction formula for degree-days has been developed by Harald
Bugmann based on SMA data
*)
VAR i: INTEGER;
indx: Month;
valueVect: Vector;
cc: Climate;
BEGIN
GetCurClimate( cc ); (* current climate from ForestBase *)
CalculateWeatherModifiers; (* TableFunctions with climatic change scenario *)
FOR indx := Jan TO Dec DO
i := ORD(indx);
IF (i > 3) AND (i < 10) THEN (* summer *)
tMod := tSuMod; tSDMod := tSDSuMod;
pMod := pSuMod; pSDMod := pSDSuMod;
ELSE (* winter *)
tMod := tWiMod; tSDMod := tSDWiMod;
pMod := pWiMod; pSDMod := pSDWiMod;
END;
MultiN( cc.mnDistr[indx], valueVect );
rTVect[i] := tMod + cc.mTVect[indx] + tSDMod*cc.sdTVect[indx]*valueVect[1];
rPVect[i] := Rmax( 0.0, pMod + cc.mPVect[indx] + pSDMod*cc.sdPVect[indx]*valueVect[2] );
END; (* FOR *)
END CorrWeatherGenerator;
PROCEDURE DegreeDays( VAR uDD: REAL; VAR rTVect: ARRAY OF REAL );
CONST kDTT = 5.5;
VAR
i: INTEGER;
monthlyDD: REAL;
indx: Month;
BEGIN
uDD := 0.0;
FOR indx := Jan TO Dec DO
i := ORD(indx);
monthlyDD := Rmax( (rTVect[i]-kDTT)*kDays, 0.0 ) + Yie(corrDDTab, rTVect[i]);
uDD := uDD + monthlyDD;
END; (* FOR *)
END DegreeDays;
PROCEDURE DeclSoilMoistureParameters;
BEGIN
DeclP( k1, 0.2, 0.0, 1.0, rtc, "k1 (Heat index multiplier)", "k1" , "--" );
DeclP( k2, 1.514, 0.0, 4.0, rtc, "k2 (Heat index exponent)", "k2" , "--" );
DeclP( k3, 6.75E-7, 0.0, 1.0, rtc, "k3 (PET exponent coefficient)", "k3" , "--" );
DeclP( k4, -7.71E-5, -1.0, 0.0, rtc, "k4 (PET exponent coefficient)", "k4" , "--" );
DeclP( k5, 0.01792, 0.0, 1.0, rtc, "k5 (PET exponent coefficient)", "k5" , "--" );
DeclP( k6, 0.49239, 0.0, 1.0, rtc, "k6 (PET exponent coefficient)", "k6" , "--" );
DeclP( k7, 4.61E-4, 0.0, 1.0, rtc, "k7 (Retained water coefficient)", "k7" , "--" );
DeclP( k8, 1.10559, 0.0, 2.0, rtc, "k8 (Retained water coefficient)", "k8" , "--" );
DeclP( kPM, 1.6, 0.0, 3.0, noRtc, 'PET multiplier', 'kPM', '--');
END DeclSoilMoistureParameters;
PROCEDURE SoilMoisture( VAR uDrStr, uAET: REAL; rTVect, rPVect: ARRAY OF REAL );
(* this simple calculation of the soil moisture balance is based on the model by
Thornthwaite & Mather (1957) as modified by Pastor & Post (1984, 1985).
It has been described in detail by Fischlin et al. (1993), including the new
drought stress index which is based on Prentice & Helmisaari (1991).
*)
VAR accPWL, aa, heatIndx, prevWater, currDay, prevDay, PET, pWL,
cSM, latPtr: REAL;
k: Month;
indx: CARDINAL;
BEGIN
uAET := 0.0;
uPET := 0.0;
accPWL := 0.0;
heatIndx := 0.0;
FOR k:= Jan TO Dec DO (* calculate temperature efficiency index *)
heatIndx := heatIndx + Power( k1*Rmax(0.0,rTVect[ORD(k)]), k2);
END; (* FOR *)
aa := k3*Power(heatIndx,3.0) + k4*heatIndx*heatIndx + k5*heatIndx + k6;
prevDay := 0.0;
currDay := 15.0;
FOR k:= Jan TO Dec DO (* main loop for annual water balance calculation *)
indx := ORD(k);
prevWater := currWater; (* help variable for previous month's water *)
latPtr := a[k] + b[k]*site.kLat;
PET := kPMod * kPM * Power( 10.0*Rmax(0.0,rTVect[indx])/heatIndx, aa ) * latPtr;
uPET := uPET + PET;
pWL := rPVect[indx] - PET; (* potential water loss pWL *)
IF pWL < 0.0 THEN (* rain does not satisfy PET, draw on soil water *)
accPWL := accPWL + pWL;
currWater := Rmax( 0.0, site.kFC*( Exp((k7 - k8/10.0/site.kFC)*(-10.0*accPWL)) ) );
cSM := currWater - prevWater; (* change in soil moisture *)
uAET := uAET + rPVect[indx] - cSM;
ELSE (* rain satisfies PET *)
currWater := Rmin( site.kFC, prevWater + pWL);
cSM := currWater - prevWater;
accPWL := accPWL + cSM;
IF currWater >= site.kFC THEN accPWL := 0.0 END;
uAET := uAET + PET;