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Source: Authors. Stochastic models: As noted, stochastic models give several outputs for one input in the model. These models are used to simulate complex physical processes that appeat to be directed by randomness. The simplest examples of stochastic models are time se- ries in which the variables given at a particular moment are according to their previous values and random error. In this case, the function that unites the values of the variable at different times are deterministic and the error is stochastic. The classical examples are the Markov chains, ARMA (Auto Regressive and Moving Average), etc. Figure A4.1 shows a descriptive picture of the different types of existing models for — Figure 69 Source: Authors. Stochastic models: As noted, stochastic models give several outputs for one input in the model. These models are used to simulate complex physical processes that appeat to be directed by randomness. The simplest examples of stochastic models are time se- ries in which the variables given at a particular moment are according to their previous values and random error. In this case, the function that unites the values of the variable at different times are deterministic and the error is stochastic. The classical examples are the Markov chains, ARMA (Auto Regressive and Moving Average), etc. Figure A4.1 shows a descriptive picture of the different types of existing models for

Related Figures (128)

Source: Figure generated for this study.

Source: Figure generated for this study by Escobar et al. 2008.

Source: Figure generated for this study by IRD 2009.

source: bradley et al. 2UU6. Note: Projected changes in mean annual free-air temperatures between 1990-1999 and 2090-2099 along a transect from Alaska (68°N) to southern Chile (50°S), following the axis of the American Cordillera mountain chain. Results are the mean of eight different general circulation models used in the IPCC AR4, using CO2 levels from Scenario A2 (IPCC 2000; see also Appendix 1). Black triangles denote the highest mountains at each latitude; areas blocked in white have no data (surface or below in the models). In the figure: Blue stars = Quito, Cusco and La Paz, cities that derive water from higher-elevation sources.

Source: Vincent et al. 2005 (c). American Meteorological Society. Reprinted with permission. Note: The numbers in bold indicate that more than 25 percent of the stations have significant trends Votre. Lhe numbers 1n bold inaicate that more than 29 percent OF the stations Nave significant trends. Summer days refer to number of days with daily maximum over 25°C. Warmest day means highest Jaily maximum temperature. Warm days refer to percentage of days with the maximum temperature ibove the 90" percentile. Cold days are the percentage of days with the maximum temperature below the LO percentile. Frost days are the number of days with the daily minimum temperature below 0°C. Cold- est night is the lowest daily minimum temperature. Cold nights are the percentage of days with the daily ninimum temperature below the 10 percentile. Warm nights are the percentage of days with the daily ninimum temperature above the 90' percentile. Tropical nights are the number of days with the daily ninimum temperature above 20°C. Diurnal temperature range is the mean of the difference between the Jaily maximum and minimum temperatures, while extreme temperature range is the difference between he highest daily maximum and lowest daily minimum temperatures during the year.

Source: SPOT and ALOS images collected by the INAP Project in Colombia and stored in IDEAM’s archive. Note: Documented through satellite images (2001-2009).

Source: Ruiz et al. 2010. Note: Paramo starts at around 3,000 m at this location. Annual values (boxes, crosses and circles) anc long-term trends (arrows) observed in the spatial domain 04° 25’N-05° 15’N and 75° 00’W-76° 00’W Gray trends in temperature are expressed in °C/decade.

Source: Figure generated under the Memorandum of Understanding (MOU) between the MRI and th World Bank. Note: Plots correspond to datasets of actual observations and different resolutions for projections. Figure 3.1. Observed and simulated annual mean rainfall (mm d=‘) over Peru for 1979-2003

Figure 3.2. Annual simulated mean precipitation changes (mm) for the a, b) near future (2015-2039) and c, d) end of the 21S century (2075-2099) for 60-km and 20-km resolutions Source: Figure generated under the Memorandum of Understanding (MOU) between the MRI and the World Bank. Note: Areas statistically significant at 95 percent level are hatched. Hatched areas only appear in the 60-km resolution, since only that one could be compared with the ensemble of GCMs. There was only a single run in the 20-km resolution. Therefore, the results obtained from it could not be compared with other results.

Source: Figure generated under the Memorandum of Understanding (MOU) between the MRI and the World Bank. Note: Hatched areas show consistency in ensemble results at 60-km resolution. Figure 3.3. Changes in maximum annual five-day precipitation (total in mm) for the a, b) near future (2015-2039) and c, d) end of the century (2075—2099), for 60- km and 20-km resolutions

Figure 3.4. Changes in maximum annual consecutive dry days for the a, b) near future and c, d) end of the century, for 60 km and 20 km Source: Figure generated under the Memorandum of Understanding (MOU) between the MRI and the World Bank. Note: The scale is in days.

Figure 3.5. Change in wetness index of top layer of soil for the a, b) near future and c, d) end of the century, for 60 km and 20 km Source: Figure generated under the Memorandum of Understanding (MOU) between the MRI and the World Bank. Note: The wetness index WSLN is defined as average change in moisture content of the top 10 cm of surface soil.

Figure 3.6. Potential changes in temperature and precipitation in the Santa River Basin (Collota, Huaraz, Par6én, and Caraz meteorological stations) Source: Figure generated for this study by SEI, 2009. Note: Outputs are from a set of 16 GCMs. The numbers on the Y axis indicate the values of the variable that would fall within one standard deviation in each direction.

Source: Figure generated for this study by SEI, 2009. Figure 3.7. Precipitation and temperature time series associated with two sets of conditions in the Santa River Basin

Source: Figure generated for this study by SEI, 2009. Note: Annual average precipitation for the historical time period (1960-1999), mid-century (2000-2050) and late century (2050-2099) for 16 models from the WCRP CMIP3 multi-model database project (www. earthsystemgrid.org) for scenarios Alb and B1. Boxplots include data for stations Collota, Huaraz, Parén, and Caraz. The 16 GCMs used in this figure are Model 01: bem2, Model 02: cccma_cgcem3, Model 03: cnrm_ cm3, Model 04: csiro_mk3_0, Model 05: gfdl_cm2_1, Model 06: giss_aom, Model 07: lap_fgoals1_0_g, Model 08: inmcm3_0, Model 09: ipsl_cm4, Model 10: miroc3_2_hires, Model 11: miub_echo_g, Model 12: mpi_echam5, Model 13: mri_cgcm2_3_2a, Model 14: ncar_ccsm3_0, Model 15: ncar_pcm1 and Model 16: ukmo_hadcm3. For the historical time period (1960-1999), the distribution of the observations and a horizontal line are added at 556.65 mm, which is the median annual precipitation of the observations for all four stations.

Source: Ghan and Shippert 2009.

Source: Ghan and Shippert 2009.

Table 3.1. Observed annual precipitation trends in the Mantaro River Basin (mm/period) Source: Authors.

Source: Authors. Note: This figure shows the distribution of the stations in the Mantaro Basin.

Source: Figure generated for this study by SENAMHI.

Source: Authors, based on SENAMHI’s data.

Source: SENAMHI 2009b.

Table 3.3. Statistically significant observed and estimated precipitation trends for 1979-2008 VUHICE, SAULLTLOLS. Note: * Definition of Small, Medium and Large for annual values correspond to the following ranges (1-3, 3-10, >10). For monthly/seasonal estimates the ranges are: 0-1, 1-5, >5, respectively.

Source: Authors.

Source: Authors, based on SENAMHI data.

Source: Authors, based on SENAMHI data.

Source: Authors, based on SENAMHI data.

Source: Authors. Note: More results are presented in the appendixes.

Table 4.1. Principal selection criteria for glacier modeling Source: Table generated for the report by IRD, 2009.

Source: Figure generated for the report by IRD, 2009.

Source: Figure generated for the report by SEI, 2009.

Source: Figure generated for the report by SEI, 2009. Note: Q = average flow in selected glaciated sub-basins.

Table 5.1. Calibration and validation statistics for the Santa River source: Figure generated for the report by SEI, 2009. Vote: Root Mean Square Error (RMSE) is a good measure of precision or repeatability, which is the degree to which repeated measurements under unct how the same results. Bias: perceptual bias; and Ef: Nash-Sutcliffe efficiency coefficient is used to assess the predictive power of hydrological models. I neasures the fraction of the variance of observed values explained by the model. It ranges from minus infinity to 1.0. An efficiency of 1 corresponds to. nodeled discharge to the observed data. Therefore, large positive values close to 1.0 are sought.

Source: Figure generated for the report by SEI, 2009.

Figure 5.4. Comparison of streamflow at La Balsa with and without glaciers (Seasonal flows) Source: Figure generated for the report by SEI, 2009.

Source: Figure generated for the report by IRD, 2009.

Figure 5.7. Observed (Qo) and simulated (Qs) monthly average streamflows for the Mantaro River Basin during the 1970-1981 calibration period Source: Figure generated for the report by IRD, 2009.

Source: Figure generated for the report by IRD, 2009.

Source: Figure generated for the report by IRD, 2009. Table 5.3. Criteria for the calibration and validation periods in the Mantaro Sub-basins

Source: Figure generated for the report by IRD, 2009.

Source: Figure generated for the report by IRD, 2009.

Source: Figure generated for the report by IRD, 2009.

Source: Figure generated for the report by IRD, 2009. Figure 5.12. Observed (Qo) and simulated (Qs) streamflows at the Surco station in the Rimac River Basin that calculated by the model. This validation yielded reasonable results. However, for the Rimac-Mantaro system, future simulations would need to reproduce the reservoirs’ operation and management: 16 reservoirs were operational from 1995 to 2000, and 28 reservoirs are planned for the future.

Figure 6.1. Changes in river flows: a) current annual flows (mm) and b) change between the present and the end of the century (%) Source: Figure generated under the Memorandum of Understanding (MOU) between the MRI and the World Bank. Note: Picture a) presents the absolute annual flow, and therefore the scale is in mm. Picture b) presents the change, and the scale is in percentage.

Table 6.1. Simulated reductions in glaciated area between 2006 and 2036 under two climate projections

Source: Figure generated for the report by SEI, 2009.

Figure 6.4. Observed (blue line) and simulated (red line) discharges using trend analysis at selected sites on the Santa River, 1966-1996 Source: Figure generated for the report by IRD and SEI.

Figure 6.3. Flow through Canon del Pato for historical conditions, marginally warmer and much warmer scenarios Source: Figure generated for the report by SEI, 2009.

Source: Figure generated for the report by IRD and SEI. In terms of projected impact, the expected discharges by mid-century are lower than the historical record (Figure 6.5 displays the results of the hydrological response in the 2050s), which summarizes the expected changes in the average monthly discharges at the selected sites.

Figure 6.6. Comparison of average monthly discharges in the Santa River between observed historical (blue line) and projected mid-century (red line) values (m/s), based on trend analysis Source: Figure generated for the report by IRD and SEI.

Figure 6.7. Observed (blue line) and projected (red line) discharges using trend analysis at selected sites on the Rimac and Mantaro Rivers, 1966-1996 Source: Figure generated for the report by IRD and SEI.

Source: Figure generated for the report by IRD and SEI.

Source: Figure generated for the report by IRD and SEI.

Source: Figure generated for the report by IRD and SEI.

Figure 6.12. Hydrological response by mid-century: Rimac River Basin monthly discharges (mcs) February and March, while there will be little or no reduction in the dry months from June to November. More water is welcome, especially for hydropower production, ag- riculture, and water supply to Lima. On the other hand, excessive runoff might lead to flooding, which could affect the most vulnerable inhabitants of Lima. Higher discharges imply increased sediment transport capacity in the stream. Such changes in sediment balances could enhance climate risks (Figure 6.12).

Source: IPCC 2000, modified. re a © aa © aes As an underlying feature of all emissions scenarios, the IPCC developed four dif- ferent narrative storylines to describe the relationships between emission-driving forces and their evolution over time (Figure Al.1). Each storyline represents different demo- graphic, social, economic, technological, and environmental developments. Each emis- sions scenario represents a specific quantitative interpretation of one of the four story- lines. All the scenarios based on the same storyline constitute a scenario “family.”! The SRES scenarios cover a wide range of the main driving forces of future emis- sions, from demographic to technological and economic developments. None of the sce- narios includes any future policies that explicitly address climate change, although all scenarios necessarily encompass various policies of other types and for other sectors. The set of SRES emissions scenarios is based on an extensive literature assessment, six alternative modeling approaches, and an “open process” that solicited wide participa- tion and feedback from many scientific groups and individuals. The SRES scenarios in- clude a range of emissions of all relevant greenhouse gases and sulfur, as well as their underlying driving forces.

Figure A1.2. Scenarios for GHG emissions from 2000 to 2100 (in the absence of additional climate policies) and projections of surface temperatures DIU ee AAR Nee SU 8 Notes: Left Panel: Global greenhouse gas emissions (in GtCO,-eq) in the absence of climate policies: six illustrative SRES marker scenarios (colored lines) and the 80th percentile range of recent scenarios published since SRES (post-SRES) (gray-shaded area). Dashed lines show the full range of post-SRES scenarios. The emissions include CO,, CH,, N,O and F gases.

Source: IPCC 2005. perspective, and the reason for their use should be carefully explained. Notes

Source: SENAMHI 2009b. sample location as a point for comparison with observed data. SENAMHI’s analysis of future climate scenarios is summarized in Figure A2.1, which describes the expected percentage change in annual precipitation by 2030 based on the observed early trends in the past. The map covers the entire country.

Source: SENAMHI 2009b Note: Highlighted values show maximum precipitation months in the left columns; trends are highlighted in the right columns.

lated based on the grid cell mean variables. Model output is written for each elevation band during the simulation and then spatially distributed in postprocessing according to the elevation of the subgrid band and the high-resolution surface elevation data. This method has been implemented and evaluated in a regional climate model (Leung and Ghan 1998; 1999) and a global climate model (Ghan et al. 2004).

Figure A3.3 compares the simulated and observed distribution of surface air tem-

Source: Observations are from New et al. (2002).

Source: Authors.

Source: Authors.

Source: Authors.

Figure A3.9 shows the distribution of the change in precipitation for Peru for each decade. The distributions of the change are remarkably complex and consistent from decade to decade, amplifying in time. Precipitation increases exceeding 2 mm/day are simulated along the eastern side of the Andes. Decreases are less than 0.5 mm/day except in one small region.

Source: Authors.

Source: Authors.

Source: Authors.

Source: Authors.

Figure A3.13. Change in snowfall (mm/day) (2090s—1990s) versus surfac« elevation for Peru

Source: Authors.

Figure A3.14. Snowfall for Bolivia during the 1990s (left) and the change in snowfall for each decade (right) In summary, these simulations produce remarkably consistent but spatially com- plex distributions of changes in surface air temperature, total precipitation, and snow- fall that amplify with time. Total precipitation increases in most locations, but snowfall decreases. These changes are likely to produce strong effects on estimates of impacts of global warming on surface water resources in Peru and Bolivia. ia aR DS aaa However, large biases are evident in the distribution of precipitation. The immedi- ate solution would be to apply empirical corrections for these biases. Longer-term solu- tions would be to improve the subgrid orography scheme to account for subgrid rain shadows, or to employ explicit regional modeling for Peru and Bolivia. A treatment of rain shadows might be applied to this problem. Saved daily history from other global simulations could also be used to drive simulations with the regional climate model.

Figure A4.2. Information measured by a complete station located on the Swedish glacier Storglacien (Hock 2005) for an energy balance model and glacier station

Degree-Day Models ae eS CS as The study of the physical basis of this model emphasizes the role of long-wave radi- ation: Usually this is by far the largest source of heat for melting; along with the sensible heat flux, it provides nearly three-quarters of the energy for melting. Both heat fluxes are strongly affected by air temperature, which is the main reason for the close relationship between the melting and the air temperature. Moreover, the temperature is inside the affected parties because of global radiation, which is the second source for the melting. These models can be used at different time steps: hourly, daily and monthly.

Source: Authors. Table A4.1. Different values of DDF for snow and ice in different parts of the world The difference between the term degree-days is attributable to the relative difference (significance) of the energy balance components that provide energy for the melting, considering that the energy balance may change in space and in time; the environmental conditions (altitude, climate) will not be the same in a glacier in Greenland as in an- other one situated in an intermediate or low latitude. Because of the important relative turbulence of flows, including condensation and marine environment, the areas with continental regimes probably have a lower “degree-days” factor. Tahle A4 1 chowe that the valiee af DIE are lower than thoce nf IDE. Thicie

Figure A4.3. Results simulation conducted by Bernard Pouyaud on different sub- basins of the Santa River Figure A4.4. Re-analysis of temperature (500 hPa) versus depth of runoff in the Llanganuco Sub-basin

Source: Pouyaud et al. 2005.

Source: Juen 2006.

Source: Suarez 2007. “ The last work is the modeling of the glaciers of the Cordillera Blanca belonging to this basin. This modeling was conducted by Wilson Suarez as a part of his doctoral thesis at the University of Montpellier II (France) (2007) under the auspices of IRD. The work used a variation of the degree-day model at monthly time steps and is presented in Suarez et al. (2008). The model was calibrated on the Artesonraju glacier and the available tem- perature data were used as well as the outflow data situated at the front of the glacier. This work modeled 11 subglacial basins of the Santa River with a starting point made on a pilot of the basin (Artesoncocha) that was used to extrapolate the model in a

Source: Suarez 2007. Table A4.2. Results for the modeling of 10 sub-basins g in the Santa River Basin

Source: Authors. The general formulation of glaciers in WEAP will use the standard approach to building a WEAP rainfall-runoff model of a mountainous region as a starting point. In WEAP, rainfall-runoff processes are simulated by first dividing a watershed into subwatersheds, which are the contributing areas above points of streamflow measurement or manage- ment control (Figure A4.7). Furthermore, a subwatershed area above a “pour point” is divided into i elevation bands. Each subwatershed/elevation band is then represented as a unique WEAP catchment object within which temporally variable land cover and temporally variable yet spatially homogeneous climate conditions can be imposed on a time-step by time-step basis. This section describes an approach for adding a represen- tation of evolving glacial contributions to simulate hydrologic processes to be incorpo- rated into the WEAP rainfall-runoff representation by dividing each elevation band, i, into either a glaciated (j=1) or nonglaciated (j=2) portion (Figure A4.8).

where c and b are scaling factors related to the width, slope, side drag and mass balance of a glacier. Analysis of 144 glaciers around the world suggests factor values of b = 1.36 and c = 0.048 (Bahr et al. 1997; Klein and Isacks 1998). The research team decided to use these volume-area correlation factors (Figure 1 in Bahr et al. 1997) despite the fact that no Andean glaciers were included in the correlation due to the lack of studies in the zone. It is expected that similar studies will be developed for Andean glaciers, in which case

The preceding set of equations will be executed during each time step, t, to approxi- mate the contribution of melting snow on the surface of the glacier within a given band to surface flow in the catchment. During time steps, t, when SFree, , ; },-; is non-zero, an additional set of equations will be executed to estimate the contribution of melting gla- cier ice to surface flow in the ith catchment. — OTLOUY ee ee ELS oe T, constitutes a threshold value for conversion of liquid precipitation into snow that is defined by the user and may constitute a calibration parameter. According to (4c), for the first month of each hydrologic year the value of SInitial will be exclusively the value of P..ow,y,t1jcv Siven that at the end of the previous year snow either melted or was con- verted to ice. After the first time step of the water year, each month P.,.,w,,,1-1 18 defined as a function of the current temperature and the threshold temperature for converting water to snow according to (4d). At the end af each monthly time cten the cnow-water eaiivalent accimiu lated on

Source: Authors.

Source: Photo: Bernard Pouyaud.

Figure A4.11. Outflow at Artesoncocha gauge station: comparison between observed and simulated values between September 2001 and August 2005, R2=0.67 ps0.05 Source: Authors.

oource. /\UMNOFS. Note: This is at the lowest pour point before the Cafion del Pato hydroelectric facility, which includes the aggregated response of most glaciated subwatersheds in the Santa River Basin.

(Figure continues on next page)

YUHILE,. SAULLLIUI OS. Note: For each calculated subwatershed, streamflows are indicated the total streamflow (continuous gray line) and the glacial part (dashed line); the subwatersheds presented are Quillcay (highly glaciated), La Balsa (mildly glaciated), and Corongo (lowly glaciated).

Table A4.4. Simulation results in calibration and validation periods using three statistics: (a) Root Mean Square Error (RMSE); (b) BIAS; and (c) Nash-Sutcliffe parameter efficiency (Ef)

Source: Authors.

Figure A5.1. Change in discharge and storage over time according to the linear reservoir approach Source: Authors. —e—e——ee eee ee ee ae The linear reservoir approach presents challenges to represent the discharge from paramos. For instance, storage is not a function of discharge alone, but also varies as a function of inflows (precipitation) and other potential outflows (evapotranspiration). Moreover, hydrographs do not typically have this smoothly decaying structure. Rather, the structure of the hydrograph changes over time (Figure A5.2). Linear portions of the hydrograph can be analyzed to estimate different values of 1/T, or k.

Buytaert hypothesized that the hydrograph structure of paramos (Figure A5.2) is formed by three potential reservoirs: 1) water stored on the soil surface, 2) water stored in the upper soil H-horizon, and 3) water stored in the lower soil A-horizon. Each of these reservoirs can be represented with the linear reservoir equation (Eq.1) where k=1/T is different for each reservoir. The representation of these three reservoirs is shown in Figure A5.3.

Source: Authors.

Source: Authors.

Figure A5.6. Implementation of paramo hydrology algorithm in WEAP Source: Authors. The test focused on 1) adjusting the parameters of the four-parameter in WEAP, and 2) adjusting the parameters of the existing two-bucket hydrologic model in WEAP to see if these routines approximated observed hydrology to any significant degree. For this exercise, two rivers were created in WEAP, one for each test (Figure A5.7).

Parameterization of Four-Parameter Model

Source: Authors.

Figure A5.9. Two-bucket model schematic and parameters Figure A5.10 shows the final results after calibration. The six degrees of freedom provided by the two-bucket model provide a better representation of the hydrology of this particular paramo watershed. With this test, the model well represents the peak flows and provides a good approximation of baseflows.

Source: Authors. The existing WEAP model in the Rio Paute watershed was implemented using a monthly time step. Consequently, it will be necessary to coordinate modeling paramo hydrology using the daily time step to track soil moisture, with the reality of modeling for planning purposes using the monthly time step to observe management and climate change scenarios.

Source: Authors. Table A6.1. Calibration parameters

Table A6.2. Statistics of correspondence between observed volume and simulated volume in the Tablachaca and Corongo sub-basins Figure A6.1. Calibration and validation

Source: Authors.

Source: Authors. Note: The spacing of altitude is accurate for the higher zone (300m) in order to correctly report the glacier behavior. Table A7.1. Altitude bands for the different subcatchments and notification of the presence or absence of glacier for each band

Source: Authors. Table A7.2. Land cover classification from ATA-INADE (2002) and simplification in the WEAP model

Source: Authors.

Source: Authors. Note: Pearson correlation of observed and simulated values: R?=0.7 ps0.01.

Source: Authors.

Source: The results are given for the principal subwatersheds. Table A7.4. Criteria for the calibration and validation periods

YVUHILE,. LAULLLUILO. Note: This is the lowest pour point before the Cafién del Pato hydroelectric facility, which includes the aggregated response of most glaciated subwatersheds in the Santa River Basin. Pearson correlation of observed and simulated values: R?=0.74 ps0.01.

Figure A7.3b Interannual variability of simulated and observed streamflow at La Balsa gauge station between hydrologic years 1969-1970 and 1996-1997 Source: Smith et al. 2000. Note: Distribution of El Nifo and La Nifia events.

YVUHILE, FAULLIUIO. Note: For each calculated subwatershed streamflow, the total streamflow (continuous gray line), the gla- cial part (dashed line) and the groundwater part (black dashed lines) are indicated.

ible A7.5. Results for simulated and observed runoff, groundwater part, and glacier part for the calibration and the validation periods Note: Stations on the Santa River are shaded in gray. DJF (December, January, February)-wet season; JJA (June, July, August)—-dry season. Groundwater outflow is the sum of simulated interflow and baseflow.

* Observed data error +- 25 km?

Figure A7.5. Scatter plot graph with observed versus simulated glacial areas fo the two periods (1987 and 1998)

Related topics:

Climate Change Hydrology Conservation Ecology Agriculture Agricultural Water Management Climate modeling Water Cycle Extreme Weather Events SURFACE RUNOFF PREDICTION

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