CARBON OFFSET POTENTIALS OF FOUR ALTERNATIVE FOREST MANAGEMENT STRATEGIES IN CANADA:A SIMULATION STUDY WENJUN CHEN1,?,JING M.CHEN1,DA VID T.PRICE2,JOSEF CIHLAR1and
JANE LIU1
1Applications Division,Canada Centre for Remote Sensing,Canada
2Northern Forestry Centre,Canadian Forest Service,Canada
(?Author for correspondence:588Booth St.,Ottawa,ON,Canada,K1A0Y7;Tel.:(613)947-1286;
Fax:(613)947-1406;E-mail:wenjun.chen@geocan.nrcan.gc.ca)
(Received11May1999;accepted in?nal form20October1999)
https://www.doczj.com/doc/2e14359219.html,ing an Integrated Terrestrial Ecosystem C-budget model(InTEC),we simulated the carbon(C)offset potentials of four alternative forest management strategies in Canada:afforestation, reforestation,nitrogen(N)fertilization,and substitution of fossil fuel with wood,under different climatic and disturbance scenarios.C offset potential is de?ned as additional C uptake by forest ecosystems or reduced fossil C emissions when a strategy is implemented to the theoretical max-imum possible extent.The simulations provided the following estimated gains from management: (1)Afforesting all the estimated～7.2Mha of marginal agricultural land and urban areas in1999 would create an average C offset potential of～8Tg C y?1during1999–2100,at a cost of3.4Tg fossil C emission in1999.(2)Prompt reforestation of all forest lands disturbed in the previous year during1999–2100would produce an average C offset potential of～57Tg C y?1for this period, at a cost of1.33Tg C y?1.(3)Application of N fertilization(at the low rate of5kg N ha?1 y?1)to the～125Mha of semi-mature forest during1999–2100would create an average C offset of～58Tg C y?1for this period,at a cost of～0.24Tg C y?1.(4)Increasing forest harvesting by 20%above current average rates during1999–2100,and using the extra wood products to substitute for fossil energy would reduce average emissions by～11Tg C y?1,at a cost of0.54Tg C y?1.If implemented to the maximum extent,the combined C offset potential of all four strategies would be 2–7times the GHG emission reductions projected for the National Action Plan for Climate Change (NAPCC)initiatives during2000–2020,and an order of magnitude larger than the projected increase in C uptake by Canada’s agricultural soils due to improved agricultural practices during2000–2010. Keywords:afforestation,Canada,C cost,C offset potential,climate change mitigation,forest man-agement,fossil fuel substitution,low-rate N fertilization,reforestation
1.Introduction
Global climate change may be the most critical and complex environmental issue facing humanity over the next century.Global temperatures have increased0.3–0.6?C over the last100years and are expected to rise by a further1–3.5?C by2100, accompanied by changes in precipitation,storm patterns,and drought frequency and intensity(Santer et al.1996;Kattenberg et al.1996).These changes in global climate could signi?cantly affect agricultural production,water supplies,human health,and terrestrial and aquatic ecosystems(Dixon1997).The1995assessment Mitigation and Adaptation Strategies for Global Change5:143–169,2000.
?2000Kluwer Academic Publishers.Printed in the Netherlands.
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of the Intergovernmental Panel on Climate Change(IPCC)concluded that observed global climate changes can be at least partially attributed to recent increases in atmospheric concentrations of greenhouse gases(GHGs)including CO2,CH4,and N2O(Houghton et al.1996).
Canada’s forests occupy approximately417.6million hectares of the land sur-face,about one tenth of global forest cover(Canadian National Forestry Database, http://www.nrcan.gc.ca/cfs).These forest ecosystems contain about13Pg C in aboveground biomass(Kurz et al.1992),and38.6Pg C in soil excluding peaty organic soils(Siltanen et al.1997).Peaty organic soils contain an estimated addi-tional168Pg C(Tarnocai1997).Even using the lower value for soil C content, a mean annual increase in the C pools of these forest ecosystems of only0.1% would remove～52Tg C y?1(1Tg=1012g)from the atmosphere.Several altern-ative forest management strategies could conceivably be followed to increase C storage in Canada’s forest ecosystems.These include:(1)afforestation;(2)prompt reforestation following natural disturbance and harvesting;(3)N fertilization to increase forest productivity;and(4)increased harvesting for direct and indirect substitution of fossil fuel(Price and Apps1996;Matthews et al.1996;Brown et al. 1996).
Implementation of these different management strategies would likely cause a large number of interacting effects on forest C pools(including biomass,soils,and wood products),and?uxes(including photosynthesis,plant respiration,soil and lit-ter decomposition,C emission during forest?res and oxidation of forest products). The C biomass pools include wood,foliage,?ne roots,and coarse roots,while soil C pools include coarse and?ne structural detritus,metabolic detritus,and microbial biomass as well as,slow and passive humus pools.The forest product C pools include construction and other lumber,pulp and paper products,and land?lls. Hence,evaluating the C offset potentials and associated C costs of these different management strategies requires a comprehensive analysis.In addition,the effects of anticipated environmental changes,including temperature,precipitation regime and atmospheric CO2concentration,must also be considered.An Integrated Ter-restrial Ecosystem C-budget model(InTEC)has been developed for this purpose (Chen et al.1999a).In this study,we used the InTEC model to quantify the C offset potentials of the four alternative management strategies for the next century under different climatic and disturbance scenarios.Following the suggestions of Mat-thews et al.(1996),we?rst calculate the baseline C balance without implementing any of these alternatives,and then estimate C offset potential as the difference between the baseline value and that when an alternative strategy is implemented at full scale,under speci?ed climatic and disturbance scenarios.We also compare the projected C offset potentials of these strategies with other proposed GHG reduction programs in Canada.
CARBON OFFSET POTENTIALS OF ALTERNATIVE FOREST MANAGEMENT STRATEGIES145
2.The InTEC Model
The InTEC model is a regional scale C budget model,which calculates the annual C balance of a region in year i,dC(i),as the sum of changes in size of all relevant forest C pools including biomass,dC biomass(i),soil,dC soil(i),and forest products, dC products(i),i.e.,
dC(i)=dC biomass(i)+dC soil(i)+dC products(i).(1) The changes in C pool sizes are caused by C?uxes among these pools and between the pools and the atmosphere.Because the inter-pool?uxes cancel when summed, dC(i)is calculated as the net of all?uxes between the forest C pools and the atmo-sphere,including net primary productivity(NPP(i)),soil respiration,and oxidation of forest products(R(i)),and C emission from forest?res(ξA f(i),whereξis an assumed constant value of C loss per unit burned forest area and A f(i)is the total area burned in year i)i.e.,
dC(i)=NP P(i)?R(i)?ξA f(i).(2) Because the value of dC(i)is usually an order of magnitude smaller than that of NPP(i),R(i),andξA f(i),a10%error in estimates of NPP(i),R(i),andξA f(i) could easily result in a more than100%uncertainty in dC(i).To avoid this type of uncertainty,InTEC adopts a relative change approach which consists of the following three steps:
(1)We assume that exchanges of C and N between terrestrial ecosystems and the atmosphere were in equilibrium under the mean pre-industrial conditions of climate(e.g.temperature and precipitation),atmosphere(e.g.,CO2concentration and N deposition),and disturbance(e.g.,?re,insect-induced mortality,harvest), such that
dC(0)=NP P(0)?R(0)?ξA f(0)=0.(3)
(2)We convert the problem of calculating the net difference between NPP(i), R(i),andξA f(i)in equation(2)to a problem of estimating interannual variations in NPP,R,andξA f.Subtracting equation(3)from equation(2)and rearranging the result,gives
dC(i)=[NP P(i)?NP P(0)]?[R(i)?R(0)]?[ξA f(i)?ξA f(0)](4) =[ NP P(i)+...+ NP P(1)]?[ R(i)+...+ R(1)]
?[ξ A f(i)+...+ξ A f(1)],
where NPP(i)(=NPP(i)–NPP(i-1)), R(i)(=R(i)–R(i-1)),andξ A f(i)
(=ξ A f(i)–ξ A f(i-1))are,respectively,the interannual variations of NPP,R,and ξA f in year i.
(3)We determine NPP(i), R(i),andξ A f(i).A new spatial and temporal scaling algorithm is used to determine NPP(i)(Chen et al.1999a).The algorithm
146WENJUN CHEN ET AL.
is based on the Farquhar leaf photosynthesis model (Farquhar et al.1980;Bonan,1995;Luo et al.1996),which is ?rst scaled up to stand level with a canopy radiation and sunlit/shade leaf separation.We then integrate the instantaneous,relative vari-ations in stand-level photosynthesis,d NPP /NPP ,temporally and spatially to obtain NPP (i )over a region.Detailed data for photosynthesis and all other variables are required in the integration,but such detailed data are not available for the historical period.To overcome this dif?culty,we use the concept of a correlation coef?cient,r ,between any two variables x (j )and y (j ) i .e .,n j =i
x(j)y(j)=n ˉx ˉy(1+r σx σy n ˉx ˉy ,where n is the number of data points,and σis the standard deviation).In this way,we convert the integration problem to a problem of calculating statistics of mean,correlation coef?cient,and standard deviation.These statistics are derived from tower ?ux measurements of the BOReal Ecosystem-Atmosphere Study (BOREAS,Chen et al.1999b;Goulden et al.1998).Using this scaling algorithm, NPP (i )can be estimated from annual mean atmospheric CO 2concentration,N depos-ition,precipitation,disturbance rates,growing season mean temperature and length (determined from mean spring temperature),and NPP determined for a single cal-ibration year.The effect of disturbances on NPP is described through their impacts on forest age class distribution.We estimated the average NPP of Canada’s forests in 1994,using the Boreal Ecosystems Productivity Simulator (BEPS)(Liu et al.1997;Chen et al.1999c).Inputs required by BEPS include land cover and leaf area index maps derived from 1-km resolution A VHRR data at 10-day intervals,soil texture,and daily meteorological data.We calculate R (i )using a modi?ed version of the Century model (Parton et al.1987;Schimel et al.1996),with NPP inputs obtained from the above procedures.The climatic effects on decomposition rate are estimated using a modi?ed Arrhenius-type equation (Lloyd and Taylor 1994).The value of R (0)is determined using Equation (3).At an annual time step,the net N mineralization associated with decomposition is also estimated and provides a negative feedback to NPP;hence decomposition and photosynthesis processes are closely coupled in the InTEC model.
In this study,the original InTEC model was expanded to simulate C cycling in forest products by including the following components:land?lls,recycling of lumber and pulp products,and use of wood products as energy substitutes for fossil fuels (Figure 1).We also divide lumber into construction lumber and other lumber,and burned wood into bioenergy and waste components,following Kurz et al.(1992).The partitioning coef?cients for initial forest products (i.e.,sawlogs,pulpwood,and fuelwood)and secondary products (i.e.,recycled lumber and pulp materials)are given in Table I,based on statistics obtained from the Canadian Na-tional Forestry Database Program (www.nrcan.gc.ca/cfs)and Kurz et al.(1992).Recycling is de?ned as the fraction of each pool which is transferred to itself at the end of each accounting period.Table II lists turnover rates and fossil fuel substitution coef?cients,following Kurz et al.(1992),Houghton (1993),and Sch-lamadinger and Marland (1996).Land?lled material is further divided into 80%
CARBON OFFSET POTENTIALS OF ALTERNATIVE FOREST MANAGEMENT STRATEGIES147
Figure1.Flow chart of the integrated terrestrial ecosystem C-budget model(InTEC),which syn-thesizes the interacting effects of ecosystem disturbances,N deposition,climate change,and CO2 fertilization on the C budget of boreal forests.Dashed arrows indicate in?uences,and solid arrows show C and N?ows.
short-lived and20%long-lived C pools(Kurz et al.1992),with their turnover rates also listed in Table II.
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TABLE I
Initial and secondary(includes recycling)partitioning coef?cients for forest products in Canada(Kurz et al.1992;Canadian National Forestry Database).
Initial partition Secondary partition
Construction Lumber to Other Lumber to Pulp to
Construction Lumber0.2360.05//
Other Lumber0.090/0.05/
Pulp0.225//0.05
Bioenergy0.1150.020.020.025
Burned as Waste0.1740.030.030.03
Oxidation0.0600.050.050.005
Land?ll0.1000.850.850.90
TABLE II
Turnover rate and fossil fuel substitution ef?ciency of forest products in Canada(Kurz
et al.1992;Houghton1993;Schlamadinger and Marland1996).
Turnover Rate(y?1)Fossil Fuel Substitution ef?ciency
Construction Lumber1/1000.6
Other Lumber1/400.6
Pulp1/10/
Short-lived Land?ll1/66.67/
Long-lived Land?ll1/3000/
Bioenergy/0.5
3.Simulation Experiments
3.1.M ANAGEMENT S CENARIOS
Nagle(1990)estimated that approximately7.2Mha of marginal agricultural land and urban areas are available for afforestation in Canada.Although this estimate is disputable due to the vague de?nition of marginal agricultural land,we use the value because no other more credible estimate currently exists.The maximum area available for prompt reforestation following natural disturbance and harvesting will be the total area disturbed in the previous year.
The maximum acceptable N fertilization rate is considered to be that at which no N saturation may occur(i.e.,annual N input should be below the critical N load).Measurements and modeling results(Dise and Wright1995;Baron et al.
CARBON OFFSET POTENTIALS OF ALTERNATIVE FOREST MANAGEMENT STRATEGIES149
Figure2.Measured(1895–1996,solid line)and predicted(1997–2100,dotted line)annual air temperature and precipitation departures from1961–90normals.Predicted values are simulation results from the?rst version of Canada’s Coupled Global Model(CCGM1)using measured CO2 concentration before present and1%increase compounded annually afterwards(upper panel). 1994;Houle et al.1997)suggest that the critical load is10–19kg N ha?1y?1for Canada’s forest ecosystems.In comparison,the average atmospheric N deposition rate for Canada’s forested area is 2.5kg N ha?1y?1(Ro et al.1995).These measurements indicate that an appropriate maximum N fertilization rate would be～7.5kg N ha?1y?1.To be conservative,we use two thirds of the latter value as the maximum N application rate in this study.Forest fertilization trials have shown that not all forest stands are suitable for N fertilization;semi-mature stands in the age range20–90years are generally more responsive(Foster and Morrison 1983;Weetman et al.1987).About40%of Canada’s forests were within this age group in1990and～60%in1920(Kurz and Apps1998).Anticipating a possible ?uctuation in the proportions of semi-mature stands in Canada’s forests due to changes in disturbance rates,we therefore assumed that30%of Canada’s forests will be suitable for N application.Therefore,the maximum possible(‘full-scale’) implementation of low-rate N fertilization would be5kg N ha?1y?1to～125Mha semi-mature forests.
Forest harvest rates in recent years have been20–30%below the annual allow-able cut(Canadian National Forestry Database,www.nrcan.gc.ca/cfs).To assure long-term sustainability,the maximum allowable increase in harvesting level was therefore assumed to be20%.
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3.2.C LIMATIC AND D ISTURBANCE S CENARIOS
The Canadian Centre for Climate Modelling and Analysis(CCCMA)has recently developed its?rst coupled ocean–atmosphere GCM(the Canadian Global Coupled Model,CGCM1)(Flato et al.1997).Under the IPCC IS92A‘business-as-usual’scenario,an increase of CO2at a rate of1%per year(compounded)from the present until2100is used.The direct forcing effect of sulphate aerosols is also included(Boer et al.1997).Figure2shows the simulation results of the CGCM1 for key Canadian annual climate statistics over the next century.Although CGCM1 reproduces present-day mean climate and its historical variation reasonably well, changes in future climate predicted by any GCM are clearly dependent upon the speci?cation of GHG and aerosol forcing.Uncertainties in the future atmospheric concentrations of GHGs and aerosols lead to uncertainties in the projection of future climate.To circumvent this dif?culty,a scenario approach is taken in this study.Since the CGCM1results have not taken into account possible increases in C uptake by ecosystems and possible reductions in GHG emissions by the energy and end-use sectors,the actual radiative forcing due to atmospheric GHGs during the next century could be smaller than the‘business as usual’scenario.Therefore, we selected the CGCM1simulation as the upper bound for the future(1997–2100) climate(dubbed‘scenario c1’).On the other hand,all GCMs predict that sur-face temperatures will increase at greater rates in the21st century.Consequently, we selected climate data extrapolated using linear relationships derived from the historical period1895–1996as the lower bound for the future climate(dubbed ‘scenario c2’).
It has been suggested frequently that future disturbance rates due to wild?re and insect-induced mortality will increase under a warmer climate(Flannigan and Van Wagner1991;V olney1996;but see also Flannigan et al.1998).Flannigan and Van Wagner(1991)predicted a possible46%increase in seasonal?re severity rating for Canada under a2×CO2climate,indicating a similar projected increase in area burned.Bergeron and Flannigan(1995)found that mean?re intensity would likely decrease in eastern Canada,but increase in western Canada under a2×CO2 climate.Yet,as with future climate,there is large uncertainty in these projections of future disturbance rates.As a result,a scenario approach is taken for future disturbance rates in this study.The average rate from pre-industrial times to the present(1996)is set as the lower bound(‘scenario d1’),and double this average rate is set as the upper bound(‘scenario d2’).We further assumed that in the baseline scenario,annual rates of harvesting and N-deposition would remain at current levels,as obtained from statistics for the period1980–1996.
CARBON OFFSET POTENTIALS OF ALTERNATIVE FOREST MANAGEMENT STRATEGIES151
Figure3.Baseline annual C balance projections for Canada’s forests under four different scenarios: (1)low climate change rate and low disturbance rate(c1d1);(2)low climate change rate and high disturbance rate(c1d2);(3)high climate change rate and low disturbance rate(c2d1);and(4)high climate change rate and high disturbance rate(c2d2).Also included are historical annual C balance and Canada’s observed and projected greenhouse gas(GHG)emissions from1895to2020.
4.Results and Discussion
4.1.B ASELINE C B ALANCE
Figure3shows estimated historical(1895–1996)and projected future(1997–2100) annual C balances of Canada’s forests,respectively.Data sources of historical climate,N deposition,atmospheric CO2concentration,and disturbance rates(in-cluding forest?re,insect induced forest mortality,and harvesting)have been de-scribed previously(Chen et al.1999d).According to the model,during the past 100years,the country’s forests underwent a period(1895–1905)as a small C source(～30Tg C y?1)due to large areas disturbed by?res and/or insects near the end of the19th century,a period(1930–1970)as a large C sink(～170Tg C y?1)due to forest regrowth in previously disturbed areas,and a recent period (1980–1996)as a moderate C sink(～50Tg C y?1)(Chen et al.1999d).The sink estimated for1980–1996is the net balance of the negative effects of increased disturbances and the positive effects of other non-disturbance factors.Analysis of the model output showed these non-disturbance factors,in order of importance, are(1)atmospheric N deposition estimated from data measured by the national monitoring network;(2)increased net N mineralization and?xation estimated from temperature and precipitation records;(3)CO2fertilization estimated from CO2 records using the leaf-level photosynthesis model,and(4)increased growing sea-son length,estimated from spring air temperature records.Increased disturbances
152WENJUN CHEN ET AL.
(mostly?res and insects)in recent decades caused a loss of about60Tg C y?1from the forests in1980–1996.If disturbance rates had remained approximately constant during the period1895–1996,Canada’s forests in1980–1996would have been a sink of～150Tg C y?1.The large amount of C accumulated during1930–1970 with relatively low disturbance rates contributed to larger than normal accumu-lations of decomposable organic material during and immediately following the period of disturbance–resulting in additional losses of～40Tg C y?1through decomposition in1980–1996.
The projected C budgets for the next century suggest that for the approximate period1997–2020,Canada’s forests will remain a small sink,although the mag-nitude varies substantially under different scenarios.Under low disturbance rate scenarios(c1d1and c2d1),the forests become a larger sink,but with a high disturb-ance rate and low climate change(c1d2),they could become a small C source.After the initial period ending～2020,Canada’s forests could become an increasingly large C sink under all scenarios.This is due mainly to the relatively large fraction of the total forest area burned in the1980s and1990s entering a period of vigor-ous growth,combined with the positive effects on NPP of projected increases in growing season length and atmospheric CO2concentration,while the disturbance rate stabilizes.Such an outcome is,of course,dependent upon the stabilization of the disturbance regime.Figure3,however,suggests that the long-term impacts of the disturbance regime are small compared to the effects of climate on NPP. Kurz and Apps(1995)found a similar trend in the annual C budget for Canadian boreal forests based on observed and projected changes in age-class distribution. The wide range in the magnitude of the projected sink,particularly beyond2050, is a direct consequence of the uncertainties associated with the different scenarios. Hence it must be emphasized that any projection for Canada’s future forest C-balance is subject to considerable uncertainty.The outcomes of these alternative scenarios should instead be treated as a range of possible baselines for comparing the C offset potentials of the different management strategies.
4.2.C O FFSET P OTENTIAL OF A FFORESTATION IN C ANADA
To estimate the C offset potential of afforestation in Canada,we made the following assumptions:(1)the～7.2Mha urban and marginal agricultural lands available for afforestation(Nagel1990)were carbon-neutral in the past and would remain so if not afforested(i.e.,baseline projection in C balance is zero);(2)these lands have soil C densities similar to agricultural soils which on average contain～50% of that typically found in forest soils(Tarnocai1997)and no signi?cant woody biomass;(3)these lands will be planted with locally dominant tree species with similar success rate(71%using seedlings and53%when grown from seed(Kuhnke and Brace1986),causing established stands to grow at rates comparable to those of other forests in the same regions;(4)disturbances affect the afforested areas as they do all other forests,and the disturbed areas will be naturally regenerated.If these
CARBON OFFSET POTENTIALS OF ALTERNATIVE FOREST MANAGEMENT STRATEGIES153
Figure4.Estimated C offset potential of afforestation in Canada if all7.2Mha of available marginal agricultural land and urban areas are planted in1999,under the four climatic and disturbance scen-arios shown in Figure3.Also plotted is an independent estimate of Guy and Benowicz(1998)for the same area.
lands were planted in1999,they would release C in the initial3years,and then gradually increase C uptake to～7Tg C y?1by2030under the low climate change and high disturbance scenario(c1d2),or to～15Tg C y?1under the high climate change and low disturbance scenario(c2d1)(Figure4).Increases in C uptake under the remaining scenarios(c1d1and c2d2)are intermediate to these two values.The simulation shows a larger increase in C uptake under the c2scenarios,because average growth rates are projected to be higher than those under c1scenarios.On the other hand,a smaller increase in C uptake under higher disturbance conditions (d2scenarios)is projected during the next century,except for the last20years when the higher disturbance rate would result in a younger and more productive age class.
These results are consistent with an independent estimate of Guy and Benowicz (1998)for the same available afforestation area,although the implementation de-tails are somewhat different(Figure4).They assumed that28%of the area would be planted with hybrid poplars,and the remainder planted with species typical for the regions in which planting will occur.Cumulative C uptake includes above and below ground biomass plus increases in soil C for those areas where planting would occur on marginal agricultural land.For other regions,Guy and Benowicz assumed that soil C pools would not increase beyond the levels observed prior to afforest-ation.The effects of planting success,longer growing seasons,and disturbances were also not considered in their estimates.
154WENJUN CHEN ET AL.
Figure5.Estimated changes in the wood,root+foliage,and soil C pools resulting from full-scale afforestation in1999(i.e.,of all7.2Mha of available marginal agricultural and urban land).
When averaged over the period1999–2100for all4climatic and disturbance scenarios,the approximate allocations of the increased C uptake to wood,roots+ foliage and soil were36%,11%and53%,respectively,(Figure5).These partition-ing coef?cients are,however,not constant.For example,in the initial decade after afforestation,the soil C pool would undergo a net loss,whereas in the late21st century,it would actually increase faster as the new forest approached maturity. 4.3.C O FFSET P OTENTIAL OF P ROMPT R EFORESTATION IN C ANADA
Figure6shows the projected C offset potential of prompt reforestation in Canada when carried out for the period1999–2100.The area planted for the high dis-turbance scenarios(c1d2)and(c2d2)is about1.8times that planted under the low disturbance scenarios(c1d1)and(c2d1).The proportions of areas planted with seedlings and by direct seeding are assumed to remain at93%and7%,re-spectively(Canadian National Forestry Database,www.nrcan.gc.ca/cfs).While the typical delay period for natural regeneration in Canada’s forests is in the range1–10years and has an average of～5years(Bunce1989),accelerated regeneration through planting and direct seeding can generally be carried out within a year of disturbance.Assuming all disturbed areas are planted,the additional C uptake maximizes around2040,to90–120Tg C y?1if disturbances occur at a high rate, or to60–80Tg C y?1if disturbances occur at a low rate.The effects of climatic and disturbance scenarios on the C bene?t of reforestation are similar to those of afforestation discussed above.
CARBON OFFSET POTENTIALS OF ALTERNATIVE FOREST MANAGEMENT STRATEGIES155
Figure6.Estimated C offset potential resulting from prompt reforestation of all recently disturbed forest areas for the period1999-2100,under the four climatic and disturbance scenarios of Figure3.
Figure7.Estimated impacts of prompt reforestation on the relationship between net primary productivity and years following disturbance.
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Figure8.Same as Figure5except applied to the reforestation strategy.
When the full life cycle of a forest stand is considered,the increase in C up-take due to prompt reforestation can be viewed as the result of eliminating the 5-year natural regeneration delay period during which annual NPP was not con-tributing signi?cantly to C sequestration(Auclair and Carter1993),while soil respiration remains high(Burke and Zepp1997).Yet,the duration of this natural regeneration delay may vary signi?cantly depending on location,species and,site conditions.Consequently,different natural regeneration delay lengths have been reported and used(Kurz and Apps1995;DesRochers and Gagnon1997).Kurz and Apps(1995)used a10-year natural regeneration delay,whereas DesRochers and Gagnon(1997)reported that major boreal forest species may be naturally regenerated in1–3years.Hence,the5-year delay assumed for this study appears to be a reasonable estimate of the median value.An additional effect of prompt regeneration is a forward shift of the stand growth curve,which also in?uences the C offset potential(Figure7).Over the decades following reforestation,the early arrival of higher growth rates as the stand matures will increase mean annual C uptake,although this advantage could be reversed if stands are allowed to become overmature.This age-related dynamic explains the relatively rapid projected in-crease in C uptake due to reforestation during1999–2040,and the decrease in subsequent decades.
For the projected increases in C uptake created by reforestation,the additional accumulations in the wood,roots+foliage and soil C pools,were about22%, 8%and70%respectively,when averaged over the period1999–2100for the four climatic and disturbance scenarios(Figure8).
CARBON OFFSET POTENTIALS OF ALTERNATIVE FOREST MANAGEMENT STRATEGIES157
Figure9.Estimated C offset potential of low-rate N fertilization in Canada when5kg N ha?1y?1is applied to～125Mha of semi-mature forest stands(i.e.,the maximum area considered possible for this strategy)during1999–2100,under four different climatic and disturbance scenarios.
Figure10.Same as Figure5except applied to the low-rate N fertilization strategy.
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4.4.P OTENTIAL OF L OW-RATE N F ERTILIZATION TO I NCREASE C U PTAKE
BY C ANADA’S F ORESTS
Application of5kg N ha?1y?1during1999–2100to the125Mha of semi-mature
forests(～30%of Canada’s forest area)would increase C uptake to～60Tg C
y?1by2010and beyond(Figure9).The differences in response to this treatment
among the different climatic and disturbance scenarios are small.Averaging over
the whole period1999–2100,the estimated N fertilization ef?ciency is～80kg C
(kg N)?1.About25%of increased C uptake ends up in the wood C pool,～9%goes
to roots+foliage,and the remaining66%accumulates in the soil pool(Figure10).
This partitioning is almost identical to that reported by Kurz and Apps(1998),who
found that total biomass C in Canada’s forests increased from11.0Pg to14.5Pg
from1920to1989,while the soil C pool increased from61.2Pg to71.4Pg;i.e.,～34%of the total increase accumulated in forest biomass.Since only～25%of the increase in C uptake accumulates in wood,the N fertilization ef?ciency for wood
alone is thus～20kg C(kg N)?1.
One question that then arises is whether there is experimental evidence to sup-
port this projection.A number of fertilization trials were conducted in Canada
during1960s–80s,and their results can be used as a validation(Weetman et al.
1987).One of the most comprehensive N fertilization experiments in Canada was
the Interprovincial Forest Fertilization Program(IFFP)(Weetman et al.1987).The
IFFP?eld trials were designed to test the effect of N when applied as urea at rates
of112and224kg ha?1on the growth of pole-size and semi-mature stands.All
provinces except Newfoundland,British Columbia,and Prince Edward Island par-
ticipated in the program.The IFFP comprised81standard trials in stands of jack
pine(Pinus banksiana Lamb.),black spruce(Picea mariana[Mill.]B.S.P),red
spruce(Picea rubens Sarg.),white spruce(Picea glauca[Moench]V oss),balsam ?r(Abies balsamea[L.]Mill),and trembling aspen(Populus tremuloides Michx.) from1969to1972.Seventy-?ve installations were remeasured after10years. Figure11shows the N fertilization ef?ciency expressed in units of kg wood C increment per kg N applied.A conversion factor of200kg C m?3wood is used here to convert the results of these?eld trials from volume to C mass terms.The trial results indicate N fertilization ef?ciencies in the range3.4–18kg wood C(kg N)?1 at an application rate of224kg N ha?1,compared to7.6–18kg wood C(kg N)?1 when applied at112kg N ha?1.In another experiment,where56kg N ha?1were applied six times over12years,with stand remeasurement after22years,Weetman et al.(1995)reported N fertilization ef?ciency of39.4kg wood C(kg N)?1.With single application and remeasurement after5years,Morrison et al.(1976)observed an N fertilization ef?ciency of8.2kg wood C(kg N)?1for an application rate of56 kg N ha?1,compared to2.2kg wood C(kg N)?1at448kg N ha?1.All these results show greater N fertilization ef?ciency at lower application rates,as predicted by the InTEC model.Ballard(1984)developed a simple empirical model for predicting
CARBON OFFSET POTENTIALS OF ALTERNATIVE FOREST MANAGEMENT STRATEGIES159 stand volume growth response to fertilization which estimates cumulative stand volume growth response(V)from:
V=KT ACZQ,(5) where K is a constant(=52.76m3ha?1for N application to coastal Douglas-?r),T is a dimensionless factor accounting for the period after application(=0.97 after10years),A is the application rate factor(=1-exp(–0.0089r),where r is the application rate in kg N ha?1),C is a stand composition factor accounting for the fraction of responding species(=1for virtually pure stands),Z is a stocking factor(=0.02417s–0.0001778s2,where s is stocking in unit of percentage of the normal),and Q is a site factor(=1.9877–0.0394q,where q is the50-year site index in metres).This simple empirical model described measured responses of Douglas-?r to N fertilization(Anonymous1982;Barclay and Brix1985),which are much greater than most other species(Figure11).Overall,despite the fact that forest growth responses to N fertilization are extremely variable,these results provide some experimental evidence that N fertilization could signi?cantly increase aver-age C storage in forest biomass.The responses calculated by InTEC lie well within the range of N fertilization ef?ciencies obtained in these fertilization trials.
It must be emphasised,however,that the general application of these exper-imental results on a wide scale is extremely dubious:the response of particular sites to applications of N fertiliser are generally not well-understood,and hence the predictions of increased productivity at other sites are subject to considerable uncertainty.
4.5.C O FFSET P OTENTIAL OF THE S UBSTITUTING F OSSIL F UEL WITH
W OOD S TRATEGY
Figure12shows the C offset potential of increasing forest harvesting and using the extra harvested material as a substitute for fossil fuels,both directly and indirectly from1999–2100.With full-scale application,harvesting would be increased by 20%compared to current annual average rates.Direct substitution of fossil fuel implies conversion to bioenergy of90%of wood currently burned as waste(i.e., with no energy capture),and100%of the pulp fraction of the extra harvested products(Table I).Table I shows that the percentage of wood burned-as-waste is substantial(17.4%).If90%of this material was instead substituted for fossil fuels,with an ef?ciency of0.5(i.e.,1mg wood C replaces0.5mg fossil C), fossil C emissions would be reduced by～3.27Tg C y?1.Indirect substitution assumes that the lumber fraction of the extra harvested products is used to replace steel,aluminum,plastics and concrete,whose production would have released a large amount of fossil carbon.The ef?ciencies of these indirect substitutions vary with the types and lifespans of wood products and the materials for which they are substituted(Nabuurs1996).For example,substituting concrete sleepers with oak,carpet(polyamide)with oak parquet,and plastic(polythylene)palettes by
160WENJUN CHEN ET AL.
Figure11.N fertilization ef?ciency estimated10years after N fertilizer application in the Inter-provincial Forest Fertilization Program(Weetman et al.1987).Stands of jack pine,black spruce,mixed conifers(mainly black spruce and jack pine),white spruce,red spruce,and balsam ?r,were treated at81sites across Canada with application rates of112and224kg N ha?1.To supplement these data,we also include jack pine results remeasured after5years for application rates of56and448kg N ha?1(Morrison et al.1976),jack pine results remeasured after22years at an application rate of56kg N ha?1repeated six times over12years(Weetman et al.1995), and Douglas-?r results remeasured after12years at application rates of224and448kg N ha?1 (Anonymous1982;Barclay and Brix1985).Simulation results from InTEC and a simple empirical model of Ballard(1984)are also presented for comparison.
spruce,reduces C emission by0.6,1.0,and0.3mg per mg C of wood,respectively (Nabuurs1996).On average,the fossil fuel substitution ef?ciency for construction and other lumbers is assumed to be0.6(Table II),following Nabuurs(1996)and Schlamadinger and Marland(1996).Because fossil fuel substitutions at current levels have been incorporated in the national GHG emission statistics,we account only for these simulated extra replacements and the resultant reductions in fossil C emissions.This strategy creates an almost steady C offset potential of～10Tg C y?1during1999–2100,when the impact of the strategy on ecosystem C pools is excluded(i.e.,only fossil fuel substitution,forest product C pool,and land?ll C pools are considered).The increased harvesting would reduce both the forest ecosystem C pools and forest productivity in the initial decades.Consequently, when all C pools and the fossil fuel substitution bene?t are considered in total, this strategy would have little bene?t in the initial decades(Figure12).As the harvested areas regenerate and regrowth increases,however,a relatively large C bene?t would be expected to accrue in the second half of the21st century.
CARBON OFFSET POTENTIALS OF ALTERNATIVE FOREST MANAGEMENT STRATEGIES161
Figure12.Estimated C offset potential of increasing annual forest harvesting by20%above current levels for the period1999–2100and using the extra wood products as biofuels to substitute for fossil fuels,under the four climatic and disturbance scenarios of Figure3.
4.6.C ARBON C OST OF T HESE F OREST M ANAGEMENT O PTIONS
The C costs associated with afforestation and reforestation(mainly fossil fuel con-sumed in transporting seedlings,personnel and equipment)are typically much lower than those for harvesting.Schlamadinger and Marland(1996)reported that the typical C cost for harvesting is0.01Mg C of fossil fuel per Mg C of wood harvested,which corresponds to an average release of approximately0.47Mg C y?1per hectare of harvested area.To be conservative,we made the assumption that afforestation and reforestation(including seed collection,seedling cultivation,and site preparation)would release as much as50%of the fossil C emissions due to harvesting a similar area.Hence,carrying out afforestation of7.2Mha would incur an estimated total C cost of～3.38Tg C,or～0.4%of the cumulative C bene?t from 1999–2100under the c1scenarios.The C cost of implementing the reforestation strategy at full scale would be～0.96Tg C y?1,or～2.0%of the mean additional
C uptake of47.9Tg C y?1under the d1scenarios(i.e.,prompt reforestation of
4.07Mha y?1).Under the d2scenarios(i.e.,prompt reforestation of7.25Mha y?1),the cost would increase to1.7Tg C y?1,or～2.6%of the mean additional C uptake of66.3Tg y?1.
For the N fertilization program,the major C costs are caused by N fertilizer production and its repeated application to the vast area of forest.In1993,about 2.6Tg nitrogen fertilizer,0.32Tg P2O5phosphate fertilizer,and6.67Tg K2O potassium fertilizer were produced in Canada(Korol and Girard1994).Total fossil fuel C emission for producing these fertilizer was approximately0.72Tg(Nyboer and Bailie1997;Natural Resources Canada1997).Clearly less fossil fuel would
162WENJUN CHEN ET AL.
be consumed if only N fertilization were carried out.On the other hand,to balance the nutrition requirements of some forest sites,sulphur and potassium fertilizers
may also need to be applied.Therefore,to be conservative,we estimate the C cost of N fertilizer production to be0.72Tg C fossil fuel for the2.6Tg N nitrogen fertilizer produced,i.e.,0.28Tg C(Tg N)?1.The fuel consumption rates of a small ?xed-wing aircraft or a helicopter range from0.1to5km?ight distance per1kg aviation fuel,with a mean value of～1km per1kg aviation https://www.doczj.com/doc/2e14359219.html,ing the mean fuel consumption rate and assuming a spread width of30m,we calculate that to apply5kg N fertilizer over1ha forest area would require?ying0.333km,and consume0.5kg aviation https://www.doczj.com/doc/2e14359219.html,bustion of1kg aviation fuel emits0.76kg C, including the CO2equivalents of methane(CH4)and nitrous oxide(N2O)(Natural Resources Canada1997).Therefore,the C cost of applying N fertilizer would be ～0.333×0.76kg C per5kg N of nitrogen fertilizer,i.e.,0.05Mg C(Mg N)?1. Considering the extra fuel consumption needed to?y to the application site,the possible need for applying other supplemental fertilizers,and the C cost of ground transportation of fertilizer,we allow a doubling of the total C cost of N fertilizer
application to0.10kg C(kg N)?1.The estimated C cost of N fertilization(i.e., including production,transport,and application)is then0.38kg C per1kg N applied,and a total of0.24Tg C y?1for applying5kg N ha?1y?1over the125Mha forest area.As discussed in section4.4,applying1kg N fertilizer would increase uptake by～80kg C y?1.Therefore,the estimated C cost of low-rate N fertilization would be0.38kg C fossil fuel per80kg increase in C uptake,or～0.5%.
The C costs of harvesting and processing bioenergy products are assumed to be0.01Mg C of fossil fuel(Mg C of wood harvested)?1,and0.05Mg C of fossil fuel(Mg C of wood processed)?1,respectively,based on data for the USA (Schlamadinger and Marland,1996).The C cost for increasing the harvest rate by 20%to substitute fossil fuel would be0.54Tg C y?1,or5.3%of the mean C bene?t created by increasing the harvest to substitute for fossil fuels during1999–2100.
4.7.C OMPARISON WITH O THER GHG E MISSION R EDUCTION OR C U PTAKE
E NHANCEMENT P ROGRAMS
The National Action Program on Climate Change(NAPCC)is Canada’s response to the United Nations Framework Convention on Climate Change(FCCC)(Envir-onment Canada1997).The NAPCC program includes GHG emission reduction initiatives announced or planned by the fossil fuel,electricity,non-energy,and end-use(i.e.,residential,commercial,industry,and transportation)sectors(Envir-onment Canada1997;Natural Resources Canada1997).If all NAPCC initiatives were adopted,it is estimated that they would reduce GHG emissions by10–29Tg C y?1during the period2000–2020(Figure13).In comparison,the combination of the four alternative forest management strategies studied here could have a net C offset potential(i.e.,C offset potential–C cost)between23±8and129±59Tg C y?1in the same period.The uncertainties shown here are estimated from two error
INDEX和MATCH函数嵌套应用 主讲老师：简单老师 第一部分：INDEX和MATCH函数用法介绍 第一，MATCH函数用法介绍 MATCH函数也是一个查找函数。MATCH 函数会返回匹配值的位置而不是匹配值本身。在使用时，MATCH函数在众多的数字中只查找第一次出现的，后来出现的它返回的也是第一次出现的位置。 MATCH函数语法：MATCH(查找值，查找区域，查找模式) 可以通过下图来认识MATCH函数的用法： =MATCH(41,B2:B5,0)，得到结果为4，返回数据区域B2:B5 中41 的位置。 =MATCH(39,B2:B5,1)，得到结果为2，由于此处无正确匹配，所以返回数据区域B2: B5 中(38) 的位置。注：匹配的查找值，MATCH 函数会查找小于或等于(39)的最大值。 =MATCH(40,B2:B5,-1)，得到结果为#N/A，由于数据区域B2:B5 不是按降序排列，所以返回错误值。 第二，INDEX函数用法介绍 INDEX函数的功能就是返回指定单元格区域或数组常量。如果同时使用参数行号和列号，函数INDEX返回行号和列号交叉处的单元格中的值。
INDEX函数语法：INDEX(单元格区域，行号，列号) 可以通过下图来认识INDEX函数的用法： =INDEX(A1:C6,2,3)，意思就是返回A1:C6中行号是2 列号是3 ,即第二行与第三列的交叉处，也就是C2单元格的值，为84。 第二部分：INDEX和MATCH函数应用案例介绍 下图工作表所示的是一个产品的型号和规格的价格明细表。通过这个表的数据，进行一些对应的查询操作。
第一，单击B5单元格下拉按钮，选择型号，然后在B6单元格完成型号所在行号的查询。如下图所示： 随意选择一个型号，比如A0110，然后在B6单元格输入公式：=MATCH($B$5,$D$4: $D$12,0)，得到结果1。 公式解释：用MATCH函数查找B5单元格这个型号在D4:D12区域中对应的位置。其中的0参数可以省略不写。MATCH函数中0代表精确查找，1是模糊查找。 第二，单击B9单元格下拉按钮，选择规格，然后在B10单元格完成规格所在列号的查询。如下图所示： 随意选择一个规格，比如101，然后在B10单元格输入公式：=MATCH(B9,E3:G3,0)，得到结果1。 第三，查询B6和B10单元格所对应的价格。 价格的查询，可以使用index函数完成，输入公式：=INDEX(E4:G12,B6,B10)可以得到结果为78。嵌套上面的match函数，可以将公式改为：=INDEX(E4:G12,MATCH(B5,D4: D12,0),MATCH(B9,E3:G3,0))。大家可以变化C3中的型号来看看结果是否正确。 通过下面工作表的源数据，利用index函数实现行列汇总查询。
首先，认识一下OFFSET函数。 从下图说明来认识一下excel中OFFSET函数的用法。 在C7单元格，输入公式：=SUM(OFFSET(C2,1,2,3,1))，得到结果为18。这个公式是什么意思呢?就是计算C2单元格靠下1 行并靠右2 列的3 行 1 列的区域的和。 可以在公式编辑栏，选中OFFSET(C2,1,2,3,1) 部分，按F9键抹黑，得到运算结果为：{3;8;7}，此时公式变为：=SUM({3;8;7})。从上图可以得知，就是利用OFFSET 函数来得到一个新的区域，然后使用SUM函数求出这个新区域的和。 下面，介绍OFFSET函数的用法。 Offset函数主要应用在单元格区域的定位和统计方面，一般做数据透视表定义名称都需要用到Offset函数。Offset函数属于查找与引用类的函数。 OFFSET函数以指定的引用为参照系，通过给定偏移量得到新的引用。返回的引用可以为一个单元格或单元格区域，并可以指定返回的行数或列数。 OFFSET函数的语法是：OFFSET(reference,rows,cols,height,width)，按照中文的说法即是：OFFSET(引用区域,行数,列数,[高度],[宽度]) 其中的参数意义如下： Reference：作为偏移量参照系的引用区域。Reference必须为对单元格或相连单元格区域的引用;否则，函数OFFSET 返回错误值#VALUE!。 Rows：相对于偏移量参照系的左上角单元格，上(下)偏移的行数。如果使用 5 作为参数Rows，则说明目标引用区域的左上角单元格比reference 低5 行。行数可为正数(代表在起始引用的下方)或负数(代表在起始引用的上方)。 Cols：相对于偏移量参照系的左上角单元格，左(右)偏移的列数。如果使用 5 作为参数Cols，则说明目标引用区域的左上角的单元格比reference 靠右 5 列。列数可为正数(代表在起始引用的右边)或负数(代表在起始引用的左边)。 Height：高度，即所要返回的引用区域的行数。Height 必须为正数。 Width：宽度，即所要返回的引用区域的列数。Width 必须为正数。 学习使用OFFSET函数需要注意以下几点： 第一，如果行数和列数偏移量超出工作表边缘，函数OFFSET 返回错误值 #REF!。
Excel中index和match函数的应用实例 原文出处https://www.doczj.com/doc/2e14359219.html,/50281/400990 查询函数一直是Excel中常被用到的一种函数，本篇来介绍一下index与match在实际工作中的应用实例。先看一下这个Excel工作簿。要求：将“用户分析”工作表中机房名称列中输入函数，向下拖动使其自动选择对应“号段检索”工作表中备注的机房名称。
其中故障号码为“号段检索”表中起始、结束号段中的码号。因此这里需要利用index 与match函数来完成检索号段归属机房查询工作。 想到了index与match函数了吧，可以先回顾一下。 -------------------------------------INDEX------------------------------------ index函数的意义：返回指定行列交叉处引用的单元格。 公式：=index(reference,row_num,column_num,area_num) reference指的是要检索的范围； row_num指的是指定返回的行序号，如超出指定检索范围，返回错误值#REF!; column_num指的是指定返回的列序号，如超出指定检索范围，返回错误值#REF!; area_num指的是返回该区域中行和列的交叉域。可省略，默认1。如小于1时返回错误值#VALUE! -------------------------------------MATCH------------------------------------ match函数的意义：返回指定方式下查找指定查找值（可以是数字、文本或逻辑值）在查找范围1行或1列的位置。 公式：=match(lookup_value,lookup_array,match_type) lookup_value指指定查找值； lookup_array指的是1行或1列的被查找连续单元格区域。 match_type指的是查找方式，1或省略指查找小于或等于lookup_value的最大值，lookup_array必须为升序排列，否则无法得到正确结果。 0指查找等于lookup_value的第一个数值，如果不是第一个数值则返回#N/A -1指查找大于或等于lookup_value的最小值，lookup_array必须为降序，否则无法得到正确结果。 ------------------------------------------------------------------------------- 那么在这里是用match函数来定位“用户分析”表中故障号码在“号段检索”起始号段或结束号段的所在行序号。 如下图：=MATCH(用户分析!K2,号段检索!B:B,1)。但是为什么检索出来的行号会是错误值呢？
6. 相关函数的估计（循环相关） 6.1. 相关函数与协方差函数 6.1.1. 自相关函数和自协方差函数 1、 自相关和自协方差函数的定义 相关函数是随机信号的二阶统计特征，它表示随机信号不同时刻取值的关联程度。 设随机信号)(t x 在时刻j i t t ,的取值是j i x x ,，则自相关函数的定义为 j i j i j i j i N n n j n i N j i j i x dx dx t t x x f x x x x N x x E t t R ??∑= ===∞ →),;,(1lim ] [),(1 ) ()( 式中，上角标“（n ）”是样本的序号。 自协方差函数的定义与自相关函数的定义相似，只是先要减掉样本的均值函数再求乘积的数学期望。亦即： j i j i j i x j x i N n x n j x n i N x j x i j i x dx dx t t x x f m x m x m x m x N m x m x E t t C j i j i j i ??∑--= --=--==∞ →),;,())(() )((1lim )] )([(),(1 ) ()( 当过程平稳时，);,(),;,(τj i j i j i x x f t t x x f =。这时自相关函数和自协方差函数只是i j t t -=τ的函数，与j i t t ,的具体取值无关，因此可以记作)(τx R 和)(τx C 。 对于平稳且各态历经的随机信号，又可以取单一样本从时间意义上来求这些统计特性： 时间自相关函数为：
? + - ∞ →+=22 )()(1lim )(T T T x dt t x t x T R ττ 时间自协方差函数为： ? + - ∞ →-+-=22 ])(][)([1lim )(T T x x T x dt m t x m t x T C ττ 在信号处理过程中，有时会人为地引入复数信号。此时相应的定义变成 ][),(* j i j i x x x E t t R = )]()[(),(* j i x j x i j i x m x m x E t t C --= 式中，上角标*代表取共轭。 2、 自相关和自协方差函数的性质 自相关和自协方差函数的主要性质如下： （1） 对称性 当)(t x 时实函数时，)(τx R 和)(τx C 是实偶函数。即 ) ()(), ()()()(),()(* * ττττττττx x x x x x x x C C R R C C R R =-=-== 当)(t x 时复值函数时，)(τx R 和)(τx C 具有共轭对称性。即 )()(), ()(* * ττττx x x x C C R R =-=- （2） 极限值 )(, )()0(,)0(2=∞=∞==x x x x x x x C m R C D R σ （3） 不等式 当0≠τ时， )()0(), ()0(ττx x x x C C R R ≥≥ 因此， )0()()(x x x R R ττρ=
目录 一、IF函数——————————————————————————————————2 二、ASC函数—————————————————————————————————4 三、SEARCH函数——————————————————————————————4 四、CONCATENATE函数———————————————————————————4 五、EXACT函数———————————————————————————————5 六、find函数—————————————————————————————————5 七、PROPER函数——————————————————————————————7 八、LEFT函数————————————————————————————————7 九、LOWER函数———————————————————————————————7 十、MID函数————————————————————————————————8 十一、REPT函数———————————————————————————————8 十二、Replace函数——————————————————————————————9 十三、Right函数———————————————————————————————10 十四、UPPER函数——————————————————————————————10 十五、SUBSTITUTE函数———————————————————————————10 十六、VALUE函数——————————————————————————————12 十七、WIDECHAR函数———————————————————————————12 十八、AND函数———————————————————————————————12 十九、NOT函数———————————————————————————————13 二十、OR函数————————————————————————————————13 二十一、COUNT函数—————————————————————————————14 二十二、MAX函数——————————————————————————————15 二十三、MIN函数——————————————————————————————15 二十四、SUMIF函数—————————————————————————————16 二十五、OFFSET函数————————————————————————————17 二十六、ROW函数——————————————————————————————20 二十七、INDEX 函数————————————————————————————21 二十八、LARGE函数—————————————————————————————22 二十九、ADDRESS函数————————————————————————————23 三十、Choose函数——————————————————————————————24 三十一、HLOOKUP函数———————————————————————————24 三十二、VLOOKUP函数———————————————————————————26 三十三、LOOKUP函数————————————————————————————29 三十四、MATCH函数————————————————————————————29 三十五、HYPERLINK函数——————————————————————————30 三十六、ROUND函数————————————————————————————31 三十七、TREND函数—————————————————————————————32
match函数的使用方法 match函数的实例我相信许多人对Excel表应该很熟悉吧，那么你们知道“match”函数的用法吗?下面是我为大家整理的“match函数的使用方法及实例”，欢迎参阅。想要了解更多关于函数实用方法的内容，实用资料栏目。 match函数的使用方法 match函数的实例 match函数的使用方法： MATCH函数是EXCEL主要的查找函数之一，该函数通常有以下几方面用途： (1)确定列表中某个值的位置; (2)对某个输入值进行检验，确定这个值是否存在某个列表中; (3)判断某列表中是否存在重复数据; (4)定位某一列表中最后一个非空单元格的位置。 查找文本值时，函数 MATCH 不区分大小写字母。 match函数的含义：返回目标值在查找区域中的位置。 match函数的语法格式： =match(lookup_value, lookup_array, match_type) =Match(目标值，查找区域，0/1/-1) 方法详解： 1.MATCH函数语法解析及基础用法 MATCH用于返回要查找的数据在区域中的相对位置。下面介绍她的语法和参数用法。 语法 MATCH(lookup_value,lookup_array, [match_type]) 用通俗易懂的方式可以表示为
MATCH(要查找的数据, 查找区域, 查找方式) MATCH 函数语法具有下列参数： 第一参数：要在lookup_array中匹配的值。例如，如果要在电话簿中查找某人的电话号码，则应该将姓名作为查找值，但实际上需要的是电话号码。 第一参数可以为值(数字、文本或逻辑值)或对数字、文本或逻辑值的单元格引用。 第二参数：要搜索的单元格区域。 第三参数：可选。数字 -1、0 或 1。match_type参数指定 Excel 如何将lookup_value与lookup_array中的值匹配。此参数的默认值为1。 下表介绍该函数如何根据 match_type参数的设置查找值。 对于非高级用户可以略过这部分直接看后面的示例，因为99%的情况下，第三参数只用0就足以应付日常工作需求啦! 2.MATCH函数根据模糊条件查找 上一节中咱们学习了MATCH函数最基础的用法(按条件完全匹配查询)，但在工作中很多时候会遇到查询条件并不那么明确，只能根据部分已知条件模糊查询。 MATCH函数查找特殊符号的方法 上一节教程中，我们学习了MATCH函数按照模糊条件查询的方法，但其只适用于普通字符的字符串，当要查找的数据包含一些特殊字符(比如星号*问号?波浪符~)时，原公式结果就会出错了。 3. MATCH函数提取最后一个文本数据的行号 之前几节的学习中，我们掌握了MATCH的基本查找方法，根据模糊条件查找的方法以及查找内容包含特殊符号的处理方法。
用OFFSET函数定义一个动态区域 我们可以给一个单元格或区域定义一个名称，以便在公式中引用。如果区域不是固定的而是一个动态的范围，我们也可以给它定义名称，以后在公式中引用的就是一个动态区域。例如我们可以在A列中定义一个动态区域，是从A1单元格开始的动态连续区域，其包含的行数不固定，操作步骤如下： 1.单击菜单“插入→名称→定义”，打开“定义名称”对话框。 2.在“在当前工作簿中的名称”下的文本框中输入要定义的名称，如“数据A”，在“引用位置”下的文本框中输入 “=OFFSET(Sheet1!$A$1,0,0,COUNTA(Sheet1!$A:$A),1)”，单击“确定”。
公式说明：用OFFSET()函数定义一个动态区域，其参数分别是 Sheet1!$A$1：为作为参照系的引用单元格，是Sheet1表中的A1单元格； 第一个0：偏移的行数； 第二个0：偏移的列数； COUNTA(Sheet1!$A:$A)：区域高度，即区域中包含的行数，用COUNTA()函数计算A列中非空单元格个数，由这个公式可以看出，如果A列中有多个数据且不连续，将会返回错误结果； 最后一个参数1：区域宽度，即区域中包含的列数；
动态数据展示的实现 在工作表Sheet1中的单元格A1、A2、A3中分别输入“月份”、“销售额”、“销售汇总”，及相应的月份和销售额数据，请按以下步骤完成余下操作。 编辑推荐阅读 ● Excel函数应用之数学和三角函数 ● Excel函数应用之函数简介 1.单击主选单“插入/名称/定义”命令，弹出“定义名称”对话框，在“在当前工作簿中的名称”文本框中输入“Month”，在“引用位置”文本框中输入公式： “=offset($A$2,0,0,count($A:$A),1)”，单击“添加”按钮；重复上述步骤，在“在当前工作簿中的名称”文本框中输入“Sales”，在“引用位置”文本框中输入公式： “=offset($B$2,0,0,count($B:$B),1)”，单击“确定”按钮。 2.在C2单元格输入公式“=SUM(Sales)”，本文充分利用了“名称”的作用。 3.鼠标单击A2，再单击工具栏中的“图表向导”按钮，在“图表向导—4步骤之1—图表类型”对话框中，选择“XY散点图”的第二个图表子类型，单击“下一步”按钮。 4.在“图表向导—4步骤之2—图表源数据”对话框中，单击“系列”标签，修改“X值(X)：”文本框里的内容为“=Sheet1!Month”，修改“Y值(Y)：”文本框里的内容为 “=Sheet1!Sales”。单击“完成”按钮。 5.单击图表，清除图表的“网格线”、“绘图区背景格式”，至此完成。 现在，不管你怎样修改区域A3、B3以下两列的数据，添加/删除，销售汇总和图表都将随着你输入的数据集的变化而动态变化（注：不能删除A2、B2单元格中的数据）。 几点说明 对步骤1中所使用的函数，主要有两个：OFFSET函数和COUNT函数，就是这两个函数的配合实现了动态数据的展示。 COUNT函数的参数是一个单元格区域引用。此时，它只统计引用中的数字，引用的空单元格将被忽略。利用函数 COUNT 可以计算单元格区域引用中数字项的个数，作为OFFSET函数的相对偏移量参数使用。 OFFSET函数实现动态区域的扩展。此函数的功能是以指定的引用为参照系，通过给定偏移量得到新的引用。返回的引用可以为一个单元格或单元格区域，并可以指定返回的行数或列数。 OFFSET函数的语法是：OFFSET（reference，rows，cols，height，width），这里参数“Reference”代表作为偏移量参照系的引用区域，Reference 必须是对单元格或相连单元格区域的引用。否则，函数 OFFSET 返回错误值 #VALUE!。参数“Rows”表示相对于偏移量
MATCH 函数 全部显示本文介绍Microsoft Office Excel 中MATCH 函数的 公式语法和用法。 说明 MATCH 函数可在单元格区域中搜索指定项，然后返回该项在单元格区域中的相对位置。例如，如果单元格区域A1:A3 包含值5、25 和38，则以下公式： =MATCH(25,A1:A3,0) 会返回数字2，因为值25 是单元格区域中的第二项。如果需要获得单元格区域中某个项目的位置而不是项目本身，则应该使用MATCH 函数而不是某个LOOKUP 函数。例如，可以使用MATCH 函数为INDEX 函数的row_num 参数提供值。 语法 MATCH(lookup_value, lookup_array, [match_type]) MATCH 函数语法具有以下参数：
?lookup_value必需。需要在lookup_array 中查找的值。例如，如果要在电话簿中查找某人的电话号码，则应该将姓名作为查找值，但实际上需要的是电话号码。 lookup_value 参数可以为值（数字、文本或逻辑 值）或对数字、文本或逻辑值的单元格引用。 ?lookup_array必需。要搜索的单元格区域。 ?match_type可选。数字-1、0 或1。match_type 参数指定Excel 如何在lookup_array 中查找 lookup_value 的值。此参数的默认值为1。 下表介绍该函数如何根据match_type 参数的设 置查找值。 MATCH_TYPE 行为 1 或被省略MATCH 函数会查找小于或等于 lookup_value 的最大值。lookup_array 参 数中的值必须按升序排列，例如：...-2, -1, 0, 1, 2, ..., A-Z, FALSE, TRUE。 0 MATCH 函数会查找等于lookup_value 的第一个值。lookup_array 参数中的值可
电子表格常用函数公式及用法 1、求和公式： =SUM(A2:A50) ——对A2到A50这一区域进行求和； 2、平均数公式： =AVERAGE(A2:A56) ——对A2到A56这一区域求平均数； 3、最高分： =MAX(A2:A56) ——求A2到A56区域（55名学生）的最高分；4、最低分： =MIN(A2:A56) ——求A2到A56区域（55名学生）的最低分； 5、等级： =IF(A2>=90,"优",IF(A2>=80,"良",IF(A2>=60,"及格","不及格"))) 6、男女人数统计： =COUNTIF(D1:D15,"男") ——统计男生人数 =COUNTIF(D1:D15,"女") ——统计女生人数 7、分数段人数统计： 方法一： 求A2到A56区域100分人数：=COUNTIF(A2:A56,"100") 求A2到A56区域60分以下的人数；=COUNTIF(A2:A56,"<60") 求A2到A56区域大于等于90分的人数；=COUNTIF(A2:A56,">=90") 求A2到A56区域大于等于80分而小于90分的人数； =COUNTIF(A1:A29,">=80")-COUNTIF(A1:A29," =90")
求A2到A56区域大于等于60分而小于80分的人数； =COUNTIF(A1:A29,">=80")-COUNTIF(A1:A29," =90") 方法二： （1）=COUNTIF(A2:A56,"100") ——求A2到A56区域100分的人数；假设把结果存放于A57单元格； （2）=COUNTIF(A2:A56,">=95")－A57 ——求A2到A56区域大于等于95而小于100分的人数；假设把结果存放于A58单元格；（3）=COUNTIF(A2:A56,">=90")－SUM(A57:A58) ——求A2到A56区域大于等于90而小于95分的人数；假设把结果存放于A59单元格； （4）=COUNTIF(A2:A56,">=85")－SUM(A57:A59) ——求A2到A56区域大于等于85而小于90分的人数； …… 8、求A2到A56区域优秀率：=(COUNTIF(A2:A56,">=90"))/55*100 9、求A2到A56区域及格率：=(COUNTIF(A2:A56,">=60"))/55*100 10、排名公式： =RANK(A2，A$2:A$56) ——对55名学生的成绩进行排名； 11、标准差：=STDEV(A2:A56) ——求A2到A56区域(55人)的成绩波动情况（数值越小，说明该班学生间的成绩差异较小，反之，说明该班存在两极分化）； 12、条件求和：=SUMIF(B2:B56,"男"，K2:K56) ——假设B列存放学生的性别，K列存放学生的分数，则此函数返回的结果表示求该班
上海立信会计学院 班级：学号: 姓名：指导教师: 专业: 习题六p150 -、简述子过程与函数过程的共同点和不同之处。 答：相同之处：都是功能相对独立的一种子程序结构，它们有各自的过程头、变量声明和过程体，在程序的设计过程中可以提高效率。 不同之处: (1)声明的关键字不同。子过程为Sub,而函数过程为 Funct ion。 (2)了过程无值就无类型说明，函数过程有值因此有类型的说明 (3)函数的过程名称同时是结果变量，因此在函数过程体 内至少要对函数的过程名赋值一次数据，而子过程内不能赋 值。
(4)调用的方式不同，子过程是一条独立的语句，可以用 Cal I子过程名或省略Call直接以子过程名调用；函数的过 程不是一条独立的语句，是一个函数值，必须参与表达式运算。(5)通常，函数过程可以被子过程代替，只需要在调用的 过程中改变一下过程调用的形式，并在子过程的形参表中增加一个地址传递的形参来传递结果。 二、什么是形参，实参？什么是值引用？地址引用？地址应用 对实参有什么限制？ 答：形参：在定义过程时的一种假设的参数，只代表该过程的参数的个数、类型，它的名字不重要，没有任何的值, 只表示在过程体内将进行的一种操作。 实参：在调用子过程时提供过程形参的初始值，或通过过程体处理后的结果。 值引用：系统将实际参数的值传到形参之后，实参与形参断开联系，过程中对于形参的修改不会影响到实际参数的变化。 地址引用：实参与形参共同使用一个存储单元，在过程中对形参进行修改，则对应的实际参数也同时变化。
在地址引用时，实参只能是变量，不能是常量或表达式。
三、指出下面过程语句说明中的错误: Sub f1 (n%) as Integer Function f1%(f1%) Sub fl (ByVa I n% 0) Sub fl(X(i) as Integer) 答：(1) Sub子过程名没有返回值，因此就没有数据的类型 (2)函数名与形参名称相同 (3)形参n为数组，不允许声明为By Vai值传递 (4)形参x(i)不允许为数组元素 四、已知有如下求两个平方数和的fsum子过程: Publ ic Sub fsum (sum%, ByVaI a%, ByVaI b%) sum =a*a+b*b End Sub 在事件过程中若有如下变量声明: Pr ivate Sub Commandl Cl ick()
在Excel中，我们经常会需要从某些工作表中查询有关的数据复制到另一个工作表中。比如我们需要把学生几次考试成绩从不同的工作表中汇总到一个新的工作表中，而这几个工作表中的参考人数及排列顺序是不完全相同的，并不能直接复制粘贴。此时，如果使用Excel的VLOOKUP、INDEX或者OFFSET函数就可以使这个问题变得非常简单。我们以Excel 2007为例。 图1 假定各成绩工作表如图 1所示。B列为，需要汇总的项目“总分”及“名次”位于H列和I列（即从B列开始的第7列和第8列）。而汇总表则如图2所示，A列为列，C、D两列分别为要汇总过来的第一次考试成绩的总分和名次。其它各次成绩依次向后排列。
图2 一、 VLOOKUP函数 我们可以在“综合”工作表的C3单元格输入公式“=VLOOKUP($B3,第1次!$B$1:$I$92,7,FALSE)”，回车后就可以将第一位同学第一次考试的总分汇总过来了。 把C3单元格公式复制到D3单元格，并将公式中第三个参数“7”改成“8”，回车后，就可以得到该同学第一次考试名次。 选中C3:D3这两个单元格，向下拖动填充句柄到最后就可以得到全部同学的总分及名次了。是不是很简单呀？如图3所示。
VLOOKUP函数的用法是这样的：VLOOKUP(参数1,参数2,参数3,参数4)。“参数1”是“要查找谁？”本例中B3单元格，那就是要查找B3单元格中显示的人名。“参数2”是“在哪里查找？”本例中“第1次!$B$1:$I$92”就是告诉Excel在“第1次”工作表的B1:I92单元格区域进行查找。“参数3”是“找第几列的数据？”本例中的“7”就是指从“第1次”工作表的B列开始起，第7列的数据，即H列。本例中“参数4”即“FALSE”是指查询方式为只查询精确匹配值。 该公式先在“第1次”工作表的B!:I92单元格区域的第一列（即B1:B92单元格区域）查找B3单元格数据，找到后，返回该数据所在行从B列起第7列（H列）的数据。所以，将参数3改成“8”以后，则可以返回I列的数据。 由此可以看出，使用VLOOKUP函数时，参数1的数据必须在参数2区域的第一列中。否则是不可以查找的。 二、INDEX函数 某些情况下，VLOOKUP函数可能会无用武之地，如图4所示。“综合”工作表中，列放到了A 列，而B列要求返回该同学所在的班级。但我们看前面的工作表就知道了，“班级”列是位于“”列前面的。所以，此时我们不可能使用VLOOKUP函数来查找该同学的班级。而INDEX函数就正可以一试身手。
上海立信会计学院 班级：学号：姓名：指导教师： 系部：专业： 习题六p150 一、简述子过程与函数过程的共同点和不同之处。 答：相同之处：都是功能相对独立的一种子程序结构，它们有各自的过程头、变量声明和过程体，在程序的设计过程中可以提高效率。 不同之处： （1）声明的关键字不同。子过程为Sub，而函数过程为Function。 （2）了过程无值就无类型说明，函数过程有值因此有类型的说明 （3）函数的过程名称同时是结果变量，因此在函数过程体内至少要对函数的过程名赋值一次数据，而子过程内不能赋值。 （4）调用的方式不同，子过程是一条独立的语句，可以用Call子过程名或省略Call直接以子过程名调用；函数的过程不是一条独立的语句，是一个函数值，必须参与表达式运算。 （5）通常，函数过程可以被子过程代替，只需要在调用的过程中改变一下过程调用的形式，并在子过程的形参表中增加一个地址传递的形参来传递结果。 二、什么是形参，实参？什么是值引用？地址引用？地址应用对实参有什么限制？ 答：形参：在定义过程时的一种假设的参数，只代表该过程的参数的个数、类型，它的名字不重要，没有任何的值，只表示在过程体内将进行的一种操作。 实参：在调用子过程时提供过程形参的初始值，或通过过程体处理后的结果。 值引用：系统将实际参数的值传到形参之后，实参与形参断开联系，过程中对于形参的修改不会影响到实际参数的变化。 地址引用：实参与形参共同使用一个存储单元，在过程中对形参进行修改，则对应的实际参数也同时变化。 在地址引用时，实参只能是变量，不能是常量或表达式。 三、指出下面过程语句说明中的错误：
（1）Sub f1(n%) as Integer （2）Function f1%(f1%) （3）Sub f1(ByVal n%()) （4）Sub f1(x(i) as Integer) 答：（1）Sub子过程名没有返回值，因此就没有数据的类型 （2）函数名与形参名称相同 （3）形参n为数组，不允许声明为ByVal值传递 （4）形参x(i)不允许为数组元素 四、已知有如下求两个平方数和的fsum子过程： Public Sub fsum(sum%, ByVal a%, ByVal b%) sum = a * a + b * b End Sub 在事件过程中若有如下变量声明： Private Sub Command1_Click() Dim a%, b%, c! a = 10: b = 20 则指出如下过程调用语句的错误所在： （1）fusum 3, 4, 5 （2）fsum c, a, b （3）fsum a + b, a, b （4）Call fsum(Sqr(c), Sqr(a), Sqr(b)) （5）Call fsum c,a,b 答：（1）furm子过程的第一个形参是地址传递，因此对应的实参3不能是常量 （2）furm的第一个形参是整型而且是地址传递，对应的实参c是单精度，数据类型不匹配（3）furm的第一个形参是地址传递，因此对应的实参a+b不应当是表达式 （4）furm的第一个形参是地址传递，因此对应的实参Sqr(c)不应当是表达式 （5）用Call语句调用furm子过程时，必须用圆括号来描述实参 六、要使变量在某事件过程中保留值，有哪几种变量声明的方法？ 答：声明为static或者全局变量 七、为了使某变量在所有的窗体中都能使用，应在何处声明该变量？ 答：应在窗体\模块的通用声明段用Public关键字声明为全局变量。
显示满足条件的所有数据—VLookup函数、IF函数、Row函数、Small函数、Index函数、Match函数、IFERROR函数、表结构的组合使用 2009年03月20日, 1:26 下午 (4人投票, 平均: 5.00 out of 5) 一个简单的示例：查找Excel工作表中的重复数据 记得一位网友曾问：要求找出Excel工作表中的重复数据并显示在工作表相应的单元格中。我给出了一个数组公式供参考，但不是太符合要求，因为这个数组公式虽然找出了重复数据，但是如果将数组公式向下复制时超出了出现重复数据的数量，会在相应单元格中显示错误。不久，这位朋友获得了更好的一个公式。这个公式非常好，完美地解决了这类问题，因此，我将其转贴于此，供有兴趣的朋友参考。 先看看下图： 在列A和列B中存在一系列数据（表中只是示例，可能还有更多的数据），要求找出某人（即列A中的姓名）所对应的所有培训记录（即列B中的数据）。也就是说，在单元格E1中输入某人的姓名后，下面会自动显示这个人所有的培训记录。 我们知道，Excel的LOOKUP系列函数能够很方便地实现查找，但是对于查找后返回一系列的结果，这类函数无能为力，因此只能联合其它函数来实现。 这里，在方法一中使用了INDEX函数、SMALL函数、IF函数和ROW函数，在方法二中还使用了Excel 2007中新增的IFERROR函数。 方法一： ?选择单元格E3； ?输入公式： =INDEX(B:B,SMALL(IF($A$2:$A$25=$E$1,ROW($A$2:$A$25),65536),ROW( 1:1))) & “” 然后同时按下Ctrl+Shift+Enter键，即输入数组公式。
第六章函数 二、选择题 1．C语言程序由函数组成。正确的说法是____B______。 A）主函数写在必须写在其他函数之前，函数内可以嵌套定义函数 B）主函数可以写在其他函数之后，函数内不可以嵌套定义函数 C）主函数必须写在其他函数之前，函数内不可以嵌套定义函数 D）主函数必须在写其他函数之后，函数内可以嵌套定义函数 2．一个C语言程序的基本组成单位是_____C_____。 A）主程序B）子程序C）函数D）过程 3．以下说法正确的是____ C ______。 A）C语言程序总是从第一个定义的函数开始执行 B）C语言程序中，被调用的函数必须在main（）函数中定义 C）C语言程序总是从主函数main（）开始执行。 D）C程序中的main（）函数必须放在程序的开始处 4．已知函数fun类型为void，则void的含义是____ A ______。 A）执行函数fun后，函数没有返回值B）执行函数fun后，可以返回任意类型的值 C）执行函数fun后，函数不再返回D）以上三个答案都是错误的 5．下列对C语言函数的描述中，正确的是____ A ______。 A）在C语言中，调用函数时只能将实参的值传递给形参，形参的值不能传递给实参B）函数必须有返回值 C）C语言函数既可以嵌套定义又可以递归调用 D）C程序中有调用关系的所有函数都必须放在同一源程序文件中 6．以下叙述中错误的是_____ B _____。 A）函数形参是存储类型为自动类型的局部变量 B）外部变量的缺省存储类别是自动的。 C）在调用函数时，实参和对应形参在类型上只需赋值兼容 D）函数中的自动变量可以赋初值，每调用一次赋一次初值 7．C语言中的函数____D______。 A）不可以嵌套调用B）可以嵌套调用，但不能递归调用 C）可以嵌套定义D）嵌套调用和递归调用均可 8．C语言中函数返回值类型由____D_____决定。 A）调用该函数的主调函数类型B）函数参数类型 C）return语句中的表达式类型D）定义函数时指定的函数类型 9．C语言规定，调用一个函数，实参与形参之间的数据传递方式是___D_____。 A）由实参传给形参，并由形参传回来给实参B）按地址传递 C）由用户指定方式传递D）按值传递 10．下列叙述错误的是____C______。 A）形参是局部变量 B）复合语句中定义的变量只在该复合语句中有效 C）主函数中定义的变量在整个程序中都有效 D）其他函数中定义的变量在主函数中不能使用 11．若函数类型和return语句中的表达式类型不一致，则____B______。
§6.1 函数 教学目标： 1、初步掌握函数概念，能判断两个变量间的关系是否可看做函数。 2、根据两个变量间的关系式，给定其中一个量，相应地会求出另一个量的值。 3、会对一个具体实例进行概括抽象成为数学问题。 教学重点 1、掌握函数概念。 2、判断两个变量之间的关系是否可看做函数。 3、能把实际问题抽象概括为函数问题。 教学难点 1、理解函数的概念。 2、能把实际问题抽象概括为函数问题。教学过程 一、导入新课 你坐过摩天轮？你坐在摩天轮上时，人的高度随时在变化，那么变化是否有规律呢？ 摩天轮上一点的高度h与旋转时间t之间有一定的关系，请看图6—1进行填表。 当t为0时，h约为3米， 当t为1分时，h约为11米， 当t为2分时，h约为37米， 当t为3分时，h约为45米， 当t为4分时，h约为37米， 当t为5分时，h约为11米.…… 二、讲授新课 做一做 1、按如图所示画圆圈，并填写下表。 层数n 1 2 3 4 5 … 圆圈总 1 3 6 10 15 … 数 随着层数的增加，物体的总算是如何变化？
2、在平整的路面上，某型号汽车紧急刹车后仍将滑行S 米， 一般地有经验公式S =300 2 V ，其中V 表示刹车前汽车的速度(单位： 千米/时)。 (1)计算当V 分别为50，60，100时，相应的滑行距离S 是多少？ (2)给定一个V 值，你能求出相应的S 值吗？ 议一议 在上面我们共研究了三个问题，下面大家探讨一下，在这三个问题中的共同点是什么？相异点又是什么呢？ 函数的概念 一般地，在某个变化过程中，有两个变量x 和y ，如果给定一个x 值，相应地就确定了一个y 值，那么我们称y 是x 的函数，其中x 是自变量，y 是因变量。 三、随堂练习 课本随堂练习 第1、2题。 四、小结 1、初步掌握函数概念，能判断两个变量间的关系是否可看做函数。 2、在一个函数关系式中，能识别自变量与因变量，给定自变量的值，相应地会求出函数的值。 3、函数的三种表达形式。 五、作业 课本习题6.1 第1题。
函数 教学目标： 【知识目标】1、初步掌握函数概念，能判断两个变量间的关系是否可看作函数。 2、根据两个变量间的关系式，给定其中一个量，相应地会求出另一个量的值。 3、会对一个具体实例进行概括抽象成为数学问题。 【能力目标】1、通过函数概念，初步形成学生利用函数的观点认识现实世界的意识和能力。 2、经历具体实例的抽象概括过程，进一步发展学生的抽象思维能力。 教学过程设计： 一、创设问题情境，导入新课 下图像车轮状的物体是什么 图6-1，每过6分钟摩天轮就转一圈，而且图中反映了给定的时间t 与所对应的高度h 之间的关系。下面根据图6－1进行填表： 对于给定的时间t ，相应的高度h 确定吗 这个问题中的变量有几个 ，分别是什么 二、新课学习 1、 做一做 （1）瓶子或罐子盒等圆柱形的物体，常常如下图那样堆放，随着层数的增加，物体的总数是如何变化的 t/分 0 1 2 3 4 5 …… h/米 ……
填写下表： 层数n 1 2 3 4 5 … 物体总数y … （2）在平整的路面上，某型号汽车紧急刹车后仍将滑 行S 米，一般地有经验公式300 2 V S ,其中V 表示刹车前汽 车的速度（单位：千米/时） ①计算当V 为50，60，100时，相应的滑行距离S 是多少 ②给定一个V 值，你能求出相应的S 值吗 结论： 1. 上面三个问题。每个问题都研究了 个变量。 2. 函数的概念 一般地，在某个变化过程中，有两个变量 和 ，如果给定一个x 值，相应地就确定了一个y 值，那么我们称y 是x 的 ，其中x 是 ，y 是 。 三、随堂练习 书100页 随堂练习 习题 四、本课小结 1、 初步掌握函数的概念，能判断两个变量间的关系是否可看作函数。 2、 在一个函数关系式中，能识别自变量与因变量，给定自变量的值，相应地会求出函数的值。 3、 函数的三种表达式： （1） 图象；（2）表格；（3）关系式。 五探究活动 为了加强公民的节水意识，某市制定了如下用水收费标准： 每户每月的用水不超过10吨时，水价为每吨元；超过10吨时，超过的部分按每吨元收费，该市某户居民5月份用水x 吨（x >10），应交水费y 元，请用方程的知识来求有关x 和y 的关系式，并判断其中一个变量是否为另一个变量的函数