Seminar Ia, 4. letnik, stari program

EFFECTIVE RAINFALL

Application of Effective Rainfall Method for estimation of Soil Water

Content

Author: Ajda Valher

Mentor: Dr. Gregor Gregorič

Comentor: Mag. Andreja Sušnik

Ljubljana, October 2013

ABSTRACT

The seminar describes application of effective rainfall methods in the agrometeorological

practice. Two empirical methods are presented: the Potential Evapotranspiration /

Precipitation Ratio method and the United States Department of Agriculture, Soil

Conservation Service method. Validation is performed with measurements of soil water

content as it is used in the measurement network of the Slovenian Environment Agency.

Calculations of effective rainfall were made for the main Slovenian meteorological station in

Murska Sobota for the period between 2000 and 2012 with an emphasis on the year 2012.

Ajda Valher Effective rainfall

2

CONTENTS

1 INTRODUCTION ........................................................................................................................ 2

2 MATERIALS AND METHODS................................................................................................. 4

2.1 SITE DESCRIPTION ............................................................................................................ 4 2.2 INPUT DATA........................................................................................................................ 4

2.2.1 Meteorological data ......................................................................................................... 4 2.2.2 Soil and crop data............................................................................................................ 5 2.2.3 Potential evapotranspiration .......................................................................................... 5 2.2.4 Water balance .................................................................................................................. 6 2.2.5 Effective rainfall .............................................................................................................. 6

2.2.5.1 Potential Evapotranspiration / Precipitation Ratio Method ...................................... 6 2.2.5.2 United States Department of Agriculture, Soil Conservation Service method......... 6

2.2.6 Measurement of soil water content ................................................................................ 7

3 RESULTS...................................................................................................................................... 7

3.1 ANALISYS OF PRECIPITATION AND EVAPOTRANSPIRATION ................................ 7 3.2 COMPUTING EFFECTIVE RAINFALL ............................................................................. 8 3.3 YEAR 2012............................................................................................................................ 9

4 CONCLUSIONS......................................................................................................................... 12

5 REFERENCES ........................................................................................................................... 12

1 INTRODUCTION

The most important source of water for crop production in agriculture is rainfall. Not all rain

from clouds reaches the ground, and not all the rain which does is useful for plants. That is

why it is so important to know how to estimate the rain which is useful for plants, known as

effective rainfall. Because of numerous interdisciplinary variables, there are many concepts

and definitions of effective precipitation. The definitions also vary according to field of

interests (hydro-electrical engineering, geohydrology, irrigation engineering...). The focus of

this study is on effective rainfall for crop production in agriculture.

There are many definitions of effective rainfall. Two of the simplest definitions are the one

describing the amount of precipitation that is actually added and stored in the soil (Farmwest,

2013) or one defining effective precipitation as useful or utilizable rainfall which does not

include surface run-off or deep percolation losses (Dastane, 1978). According to the Soil

Conservation Service of the United States Department of Agriculture (1967) more complex

definition of effective precipitation is part of precipitation which is received during the

growing period of a crop and is available to meet consumptive water requirements.

Soil has the function of a reservoir for moisture supply to crops. Soil properties influence

effective precipitation, absorption, retention, release and water movement. The infiltration

rate and permeability describe intake and water movement in the soil. This is related to soil

characteristics; texture, structure, and compactness or bulk density. Soils have different rates

of water holding capacity. Soils with a higher water holding capacity are able to store more

rain. The water holding capacity depends upon soil depth, texture, structure and organic

matter content.

Ajda Valher Effective rainfall

3

Effective rainfall depends on meteorological and non-meteorological parameters.

Meteorological parameters are characteristics of rainfall (amount, frequency, intensity and

distribution over the area and in time), air temperature, radiation, relative humidity and wind

velocity. Other, non-meteorological parameters are: land characteristics (topography, slope,

type of use), soil type (depth, texture, structure, bulk density, salt and organic matter content),

management factors (type of tillage, degree of leveling, use of soil conditioners, type of

layout, bunding, terracing, ridging), crops (nature of crops, depth of root system, degree of

ground cover, stage of growth, crop rotations) and characteristics of groundwater and

irrigation channels.

In general, one part of the rain from clouds evaporates in the atmosphere (A), the second

part strikes the soil surface (C), and the third part is intercepted by vegetation (B) (Fig. 1).

Rain which may be intercepted by vegetation can be absorbed and retained by leaves and it

evaporates in time (B1) or it may drip from the leaves onto the soil surface and drained (B2).

When rain shower is light all the rainfall may be intercepted by crops. So this part of rain

could be treated as effective rainfall. A larger part of effective rainfall represents the rain

which hits the soil surface directly (C) and infiltrates the soil (C2), while some of it may

stagnate on the surface (C3) because of flat areas or may flow over the surface as run-off (C1)

because of field inclination and/or saturation. Of the water which infiltrates into the soil, some

may be stored in the root zone (C2.1) and the rest of it percolates below the root zone (C2.2).

The water stored in the root zone may be retained around the soil particles as a thin film. Of

this stored water, only a part is utilized for crop growing (C2.1.2). The same infiltrated water

can be ineffective if it is received in the dormant season or if it causes harm as a delay of

harvesting, decreasing the quality of the yield. Hence, in view of this current concept, as far as

the water requirement of crops is concerned the annual or seasonal effective rainfall should be

interpreted, from the production point of view, as the share of total annual or seasonal rainfall

which is useful directly and/or indirectly for crop production at the site where it falls without

pumping. It therefore includes the water intercepted by living or dry vegetation (B), the

stagnating water part of which can be lost by evaporation (C3), the retained water which is

utilized for crop during growth (C2.1.2), the fraction which contributes to leaching,

percolation (C2.2.1) or facilitates other cultural operations either before or after sowing

without any harm to yield and quality of the principal crops. Effective rainfall is therefore:

ER = B + C2.1.2 + C2.2.1 + C3 … (1)

As long as a part of rainfall is useful in some way for crop production, it can be treated as

effective rainfall. So, not only the part of precipitation in the growing period is effective, this

also applies to the precipitation during the first tillage operation until the harvest. Crop needs

the majority of water in its growing and flowering periods, while during maturity and

harvesting the demand decreases. It is also important to know that if rain causes any type of

damage it should not be treated as effective, even when the soil is dry. Especially in hot days

during drier periods when the amount of daily precipitation is low it would not be considered

as effective. This amount of precipitation would likely evaporate from the surface before

soaking into the ground.

Ajda Valher Effective rainfall

4

Fig. 1: Pathway of rain water (Dastane, 1978).

2 MATERIALS AND METHODS

2.1 SITE DESCRIPTION

This study was conducted in main agricultural area around Murska Sobota, which is situated

in northeast Slovenia. The average annual (vegetation season) air temperature in the period

1971–2000 was 9.6 °C (16.1 °C), the lowest monthly average air temperature was in January,

-1.2 °C, and the highest in July, 19.7 °C. Annual precipitation amounts are 805 mm, and 502

mm in the vegetation season. The average calculated evapotranspiration (ETP) according to

Penman-Monteith method sums in the vegetation seasons is 599 mm (Sušnik et. al, 2012).

Table 1: Climatic characteristics for Murska Sobota (Sušnik et. al, 2012)

Average air

temperature

[°C]

Precipitation

[mm]

Evapotranspiration

[mm]

Sunshine

duration [h]

Number of

days with

ETP > 5 mm

Annual 9.6 805 741 1913

Vegetation

season 16.1 502 599 1343

Maximum

monthly 19.7 104 148 265

Murska Sobota

46°39' N

16°12' E

188 m. a. s. l. Minimum

monthly –1.2 31 4 57

14.6

2.2 INPUT DATA

2.2.1 Meteorological data

Daily meteorological data (precipitation and potential evapotranspiration calculated by

Penman-Monteith equation; Allen et. al, 1998) for the period 2000-2012 for Murska Sobota

station were retrieved from the archives of the Slovenian National Meteorological Service at

the Slovenian Environment Agency (ARSO).

Ajda Valher Effective rainfall

5

2.2.2 Soil and crop data

Determination of soil type on the Murska Sobota site gives the total available water (TAW) of

46 mm/m. Soil texture is evaluated as silty clay. This soil type is typical for agricultural areas

on alluvial plains of northeast Slovenia, where frequent damage due to agricultural drought is

reported (Sušnik et. al, 2012). Calculations were made for meadows in flat areas.

2.2.3 Potential evapotranspiration

Potential evapotranspiration is the amount of water which evaporates from soil and the

reference crop (grass). Many methods are in use to calculate evapotranspiration, but the

Penman-Monteith method is recommended as a standard method according to the Food and

Agriculture Organization (FAO). Derivation of evapotranspiration is based on energy balance

with mass transfer method. Energy balance is described with net radiation (Rn), latent heat

flux (λE), soil heat flux (G) and sensible heat flux (H), as presented in Fig. 2 (during the day).

Fig. 2: Energy balance during the

day (Vodna bilanca ..., 2013).

Fig. 3: Simplified representation of the (bulk) surface and aerodynamic

resistances for water vapour flow (Allen et al., 1998).

There is an exchange of sensible heat flux between the crop canopy and the surrounding air,

which is what the term aerodynamic resistance (ra) implies, describing the resistance from the

vegetation upward and involving friction from air flowing over vegetative surfaces. Another

steady state can be assumed for the exchange of vapour, latent heat, between the crop and the

surrounding air. This is known as surface resistance (rs), which describes the resistance of the

vapour flow through stomata openings. Net radiation can be measured or estimated from solar

radiation and air temperature. The soil heat flux can be neglected for many applications (on

daily or larger scale). Taking into account all this and some approximations, we get the

Penman-Monteith equation with radiation and aerodynamic part.

( )

( )a

c

a

p

r

r

r

VDPC

n GRE

++∆

+−∆=

1γλ

ρ

… (2)

whereas: Eλ … latent heat flux [ ]daym

MJ2

nR … net radiation [ ]daym

MJ2

G … soil heat flux [ ]daym

MJ2

ρ … atmospheric density [ ]3m

kg

pC … specific heat capacity [ ]CkgMJ

°

Ajda Valher Effective rainfall

6

VDP … vapour pressure deficit [ ]kPa

ar … aerodynamic resistance [ ]mday

sr … canopy resistance [ ]mday

2.2.4 Water balance

Simple surface water balance accumulation (denoted as WB and calculated as precipitation

minus evapotranspiration) is used as one of the parameters to link precipitation with soil water

content.

2.2.5 Effective rainfall

All of the methods to calculate effective rainfall are empirical. Two methods are used for our

analysis:

- the Potential Evapotranspiration / Precipitation Ratio method;

- the United States Department of Agriculture (USDA), Soil Conservation Service

(SCS) method.

2.2.5.1 Potential Evapotranspiration / Precipitation Ratio Method

The Potential Evapotranspiration / Precipitation Ratio method (hereafter the Ratio method) is

a simple semi-empirical method based on the ratio of potential evapotranspiration to total

rainfall over a certain period of time. The length of the period depends on soil type or soil

moisture properties, weather conditions or evapotranspiration values (Table 2). The maximum

number of computed days is 15 in warm weather, and 30 during cool weather for all crops

with the exception of rice. The expressed ratio cannot exceed 100 %. Mean monthly ratio is

computed from period ratios, and mean seasonal ratio from monthly ratios. Periods with no

rain are eliminated from calculations.

Table 2: Number of days in period for different soil types and climatic conditions (Dastane, 1978).

Soil texture and water storage capacity [mm/m]

Crop

Mean monthly

ETP [mm/day]

Light

(< 40)

Medium

(40-80)

Heavy

(80-120)

Very heavy

(> 120)

Rice 3-12 2 3 4 7

Other >6 4 7 10 15

Crops < 6 7 10 15 30

The soil in the area around Murska Sobota can be classified as medium according to its water

holding capacity. Calculations were made for periods of 7, 10 and 15 days.

2.2.5.2 United States Department of Agriculture, Soil Conservation Service method

The USDA, SCS method combines various data in calculations; land use or cover, treatment

or practice, hydrological soil class (A, B, C, D), hydrological conditions (good, poor, fair),

and precipitation during 5 days before the day in question (growing or dormant season). On

this basis, the curve number and the antecedent moisture condition (I, II, III) are defined. This

method does not include evapotranspiration data at any point of the calculation procedure.

The USDA, SCS method for calculation of effective rainfall is described in a FAO

publication (Dastane, 1978). The method is implemented in models for planning and

management of irrigation as the CROPWAT model, where the USDA, SCS method is the

default method for calculation of effective rainfall among four methods (Marica, 2013).

Ajda Valher Effective rainfall

7

The soil moisture condition is classified in three antecedent moisture condition classes. The

classes are based on 5-day antecedent rainfall. To allow a difference in evapotranspiration, a

distinction was made between the dormant and the growing season. If the curve number value

is classified as the antecedent moisture condition class I or III, it is necessary to convert it into

class II. This is the right value to continue computations.

Potential water retention (S) by the soil over the drainage at the time of start of rainfall, is

computed from the curve number (CN), which is determined by land use or cover, treatment

or practice, state and hydrological soil class:

−⋅= 1

100254

CNS … (3)

Runoff (Q) over the drainage is determined by condition: SRR 2.0> , where RR is the rainfall

over the drainage area, and the equation is calculated as follows:

( )SRR

SRRQ

8.0

2.02

+

−= … (4)

Finally, there is an approximation for effective rainfall (ER):

QRRER −= … (5)

Computations were made for different soil groups, defined by SCS soil scientists, from group

A which includes soils with high infiltration rates even when thoroughly wetted and a high

rate of water transmission, to group D which includes soils with very low infiltration rates

when thoroughly wetted and a very low rate of water transmission (Dastane, 1978).

Flat areas can cause calculation problems because of standing water. The soil in the area

around Murska Sobota can be sorted as soil type B according to its water holding capacity.

Calculations were made on a daily scale for meadows (permanent).

Using the Ratio method it is possible to calculate effective rainfall values for periods (e. g. 7-,

10-, 15-days). But the SCS method is the only one allowing calculation of daily values of

effective rainfall.

2.2.6 Measurement of soil water content

The best known and oldest method to determine the soil water content is the gravitational

method, which based on extraction of water from a collapsed soil sample in a laboratory.

More suitable methods for continuous, non-destructive and in situ monitoring of volumetric

moisture in soil are indirect methods. Indirect methods determine the soil water content based

on measuring of various variables such as electrical resistance, emitted heat heated probe,

reducing gamma and neutron radiation and electrical constants. The ARSO measurement

network uses sensors IMKO TRIME EZ, which are based on Time Domain Reflectometry.

This method gives the volumetric soil water content of the measured area.

3 RESULTS

3.1 ANALISYS OF PRECIPITATION AND EVAPOTRANSPIRATION

Analysis was made for the period from 2000 to 2012. Cumulative precipitation and

evapotranspiration in the vegetative season were compared. The difference between these two

variables gives the first assessment of the drought situation. The years which stand out are

Ajda Valher Effective rainfall

8

2003 (with water deficit, 416.4 mm), 2000 (368.8 mm), 2012 (190.4 mm), 2001 (189.9 mm),

2011 (184.4 mm), 2008 (180.1) and 2007 (145.0 mm). All these years, with the exception of

2008 and 2011, are archived as dry years.

If we take a closer look at events in the years 2011 and 2012, it can be said that the

cumulative rainfall and evapotranspiration is what hides the realistic scenario. The amount of

precipitation in the vegetative season 2011 was 509 mm, evapotranspiration 693 mm, and in

the season 2012, precipitation was 540 mm and evpotranspiration 730 mm. Monthly amounts

of precipitation in the vegetative season 2011 were lower than the long-term average, with the

exception of July (when the amount exceed the long-term average by 140 %). But

precipitation was well distributed over time. The situation in the season 2012 was much

different. The spring of 2012 had already been extremely dry, so the entry into the vegetation

season was already disturbed. Water deficit was present for the entire period when crops need

water for growing and development. Summer amounts of precipitation (June, July and

August) were lower than in 2011 by 45 %, with only 10 mm in August. The rainiest month

was September with 150 mm of precipitation but at the end of the vegetation season crops no

longer need water. Evapotranspiration values in April, June, July and August 2012 were

higher than in 2011. The major difference was July 2012, when the monthly amount of

evapotranspiration exceeded that from 2011 by more than 34 mm.

Fig. 4: Cumulative precipitation and evapotranspiration in vegetative seasons from 2000 to 2012.

3.2 COMPUTING EFFECTIVE RAINFALL

Effective rainfall was computed using two different methods: the USDA, SCS method and the

Ratio method. Fig. 5 and Fig. 6 show absolute values of cumulative precipitation and

effective rainfall in vegetative seasons from 2000 to 2012.

As we assumed, light soil with a lower water infiltration and transmission rate gives lower

values of effective rainfall.

Because soil determinations in both methods are a lot different it is hard to compare computed

values across methods.

The USDA, SCS method (Fig. 5) gives results for cumulated values for soil type A, which

represents deep soil with a high water infiltration and transmission rate, almost the same as

cumulative precipitation in the vegetative season. That means all the precipitation would be

effective. The biggest differences in the proportion of precipitation to effective rainfall are for

Ajda Valher Effective rainfall

9

soil type D, which has very low infiltration rates when thoroughly wetted and a very low rate

of water transmission. Differences are in range from around 8 % to 24 % for soil type D.

Fig. 5: Cumulative precipitation and effective rainfall for USDA, SCS method in vegetation seasons from 2000

to 2012.

The Ratio method (Fig. 6) gives lower values as the USDA, SCS method. Differences

between dry (e. g. 2000, 2003, 2007…) and wet (2005, 2006) years are evident. Differences

are larger in wet years for medium soil: in the year 2005 by 20 %, and in 2006 by 25 %; while

in dry years values are in the rage from 4 % to 16 %.

Fig. 6: Cumulative precipitation and effective rainfall for Ratio method in vegetation seasons from 2000 to 2012.

3.3 YEAR 2012

The year 2012 was archived as a dry year. Fig. 8 presents daily values of precipitation,

effective rainfall (USDA, SCS method) and averaged value of soil water content (TRIME).

Until the end of May, precipitation events were almost all lower than 15 mm (Fig. 8) and all

rain was effective. Differences between precipitation and effective rainfall are noticeable in

values of precipitation which are approximately more than 20 mm. Also the very dry period

from June 25 to September 6 is clearly visible.

It is very difficult to compare the response of TRIME measurements with a single rain event

because in many cases the TRIME response for one daily precipitation event could last for

two days. Because of this, the analysis was made for decades and results are shown in Fig. 9.

Ajda Valher Effective rainfall

10

But first of all, we can look at the differences between precipitation and effective rainfall (Fig.

7), which are clearly noticeable in the 3rd

decade of May, 1st decade of June, 2

nd and 3

rd

decades of July, and in 1st and 2

nd decades of September. In these decades values are much

lower for the Ratio method than for the USDA, SCS method. Absolute accumulate values of

the vegetation season for the Ratio method are 124 mm lower compared with seasonal

precipitation, which is 540 mm, and 37 mm lower for the USDA, SCS method.

Cumulative water balances, which are calculated for precipitation and effective rainfall

according to both methods and average values for TRIME for a 30 cm deep soil layer, are

presented in Fig. 9. The initial value is set to 42 mm, which presents only 42 % of the total

available water. The start of the vegetation season in 2012 was dry, because of the lack of

precipitation since autumn 2011. Soil water reservoir supplies were reduced.

Fig. 7: Decade precipitation and effective rainfall for both methods in 2012.

In Fig. 9 it is evident that effective rainfall is equal to precipitation until the 3rd

decade of

May, where separation happens (as daily values also show). Until the 1st decade of July the

difference is rather negligible. Larger differences occur in July and September. Losses of crop

available water are the largest with the Ratio method. Values of WB at the end of the season

are quite different. Deficit of simple water balance is 148 mm, for water balance with the

USDA, SCS method 185 mm, and for the Ratio method 272 mm. The TRIME curve is in line

with the cumulative water balance all season, except at the beginning.

Although water balance is negative until the 3rd

decade of May, there is some ascending of

TRIME values in April and May. The cause can be found in a very dry start of the vegetation

season, low precipitation events and reduced vegetation cover, which could cause higher

infiltration.

Unfortunately changes of decade values of water balance and TRIME can not be connected to

some kind of coefficient, especially because the average TRIME value depends also on

previous soil moisture conditions, which can vary from layer to layer. Crops need enough

effective precipitation at the beginning of the season (sowing) and in growing phases. This is

why larger amounts of rain in September did not improve the damage already done to crops.

Crops can take water from soil when the soil reservoir is at least half full, which in our case is

at approximately 61 mm. As already said the vegetation season started with only 24 % of

TAW and finished at the end of August with an even lower value at 22 %.

Ajda Valher Effective rainfall

11

Fig. 8: Graph of daily precipitation, effective rainfall (USDA, SCS method) and averaged value of soil water

content (TRIME) for year 2012.

Fig. 9: Cumulative water balance for precipitation, water balance for both methods and averaged soil water

content for vegetation season 2012.

Drought in the year 2012 had dimensions of a natural disaster. Its great impact included

uneven precipitation distribution and also frequent events of high air temperature and wind,

which both caused high evapotranspiration. The meteorological summer of 2012 was the

second warmest in the last 160 years (only the summer of 2003 was hotter). Drought hit

106,540.02 ha of Slovenian farmland covered in various crops, and caused a € 56,510,351.55

damage. The biggest damage was recorded on first quality apples, maize for grain, and

permanent grassland, hops, grapes (white and red for processing) and maize for silage (RS

MKO. 2013).

Ajda Valher Effective rainfall

12

4 CONCLUSIONS

For optimal agricultural management accurate input data is needed. Understanding the

pathway of rain water, it is obvious that the soil water content correlates with effective rainfall

and not with total precipitation. The two methods used and presented have different

requirements and therefore give different results. The Ratio method requires less input data

than the USDA, SCS method. Results for the Ratio method are accumulated amounts of

effective precipitation on different time scales (at least 7 days for crops) and the method is

rather quick. On the other hand, the USDA, SCS method is more time-consuming and

requires a larger amount of data, but results are on a daily scale. There is also one drawback to

this method; it fails to take into account evapotranspiration. This means that all low

precipitation will infiltrate in soil even on a hot day (e. g. on a day with 8.6 mm of rain with 5

mm evapotranspiration, 8.6 mm would be infiltrated, but logically if 5 mm evaporate only 3.6

mm remain). Furthermore, the Ratio method gives lower values of effective rainfall.

According to the USDA, SCS method, effective rainfall is lower than the total measured

precipitation at approximately 20 mm of rain in one precipitation event. Neither of the

methods has a mechanism to stop infiltration in soil when the field capacity is reached.

5 REFERENCES [1] Absoulute Monitoring Technologies. 2013. Trime-EZ soil Sensor:

http://www.absolutemonitoringtechnologies.com.au/trimeez.shtml (22. 3. 2013)

[2] Allen, R. G.; Pereira, L. S.; Raes, D., Smith, M. 1998. Crop evapotranspiration – Guidelines for

computing crop water requirements. Irrigation and drainage paper 56, FAO, Rome, Italy.

http://www.fao.org/docrep/X0490E/x0490e06.htm#TopOfPage (22. 3. 2013)

[3] Dastane, N. G. 1978. Effective rainfall. Irrigation and drainage paper 25, FAO, Rome, Italy.

http://www.fao.org/docrep/X5560E/X5560E00.htm (22. 3. 2013)

[4] Farmwest. 2013, Effective precipitation:

http://www.farmwest.com/node/934 (22. 3. 2013)

[5] IMKO. 2006. Trime-EZ /-EZC /-IT /-ITC User manual:

http://www.imko.de/images/filebase/Products/TRIME%20EZ%20-%20IT/TRIME-EZ_IT-

manual_WEB.pdf (22 .3. 2013)

[6] Marica, A., 2013. Short description of the CROPWAT model.

http://agromet-cost.bo.ibimet.cnr.it/fileadmin/cost718/repository/cropwat.pdf) (15. 4. 2013)

[7] RS MKO. 2013. Program odprave posledic škode v kmetijstvu zaradi suše leta 2012 – predlog za

obravnavo.

[8] Stöckle, C., Boll J. 2012. Evapotranspiration (ETP), Washington State University, Biological

Systems Engineering Department.

http://www.bsyse.wsu.edu/joan/teaching/bsyse556/W7/L7Joan.pdf (22. 3. 2013)

[9] ARSO. 2013. Drought archive 1961-2012. Ljubljana.

[10] Sušnik, A., Valher, A., Gregorič, G., Trošt, M. 2012. Tools for agricultural drought detection in

the frame of Drought Management Centre for Southeastern Europe – DMCSEE, Acta

Agriculutae Slovenica, Ljubljana, Slovenia.

[11] Vodna bilanca (prezentacija). 2013. Ljubljana, Univerza v Ljubljani, Biotehniška fakulteta.

web.bf.uni-lj.si/agromet/vbilanca.ppt (15.10.2013)