HYDROLOGICAL PROCESSES Hydrol. Process. (2012) Published online in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/hyp.9203

Prediction of temperature variation within a snowpack in open areas and under different canopy covers Abdüsselam Altunkaynak1 and Abdurrahim Aydın2* 1

Faculty of Civil Engineering, Hydraulics Division, Istanbul Technical University, Maslak 34469 Istanbul, Turkey 2 Faculty of Forestry, Düzce University, Konuralp Campus 81620, Düzce, Turkey

Abstract: Snow temperature is a major component of many physical processes in a snowpack. The temperature and the change in temperature across a layer have a dominant effect on physical properties of snow grains as well as its hardness, strength, and failure resistance. In this study, temperature and snow cover thickness were measured during the snow season of 2007–2008 in 11 elevation classes and in three different sampling locations, one in an open area and two under different forest canopy covers for each class along Kartalkaya road, Bolu. Each sampling site was visited 44 times to collect data including snow depth, snow surface temperature, ground temperature, and temperature within snowpack at 20-cm intervals. Seven different models are developed to determine snowpack temperature variations under forest canopy covers and in an open area with different leaf area index values. All models were performed using a multilayer perceptron (MP) method for the Bolu–Kartalkaya area, Turkey. MP approach constitutes a standard form of neural network modeling and can modify two-layer linear perceptron methods using three and more layers. The ability of MP is to handle complex nonlinear interactions, which ease the natural process of modeling. This method can overcome complex computations using neuron networks, and they can easily nonlinearly link input and output variables. The predictive errors are determined on the basis of mean absolute error and mean square error criteria. The Nash–Sutcliffe sufficiency score showing compliance between observed and predicted values is also calculated. According to the mean absolute error, the mean square error, and the Nash–Sutcliffe sufficiency score criteria, the predictive errors are within reasonable error intervals, justifying the use of the developed MP models for engineering applications. Copyright © 2012 John Wiley & Sons, Ltd. KEY WORDS

temperature variation; snowpack; multilayer perceptron; prediction; leaf area index

Received 23 July 2011; Accepted 13 January 2012

INTRODUCTION The properties of snow covers and their effects on the temperature distribution of snowpacks as a result of climate change have received considerable attention in recent years (Whetton et al., 1996; Jaagus, 1997; Arnell, 1999; Vogel and Schneider, 2000; Mourya et al., 2002). Snow is an important water resource and a valuable component of the hydrological cycle (Waring and Schlesinger, 1993). The temperature variations within snowpacks are affected by forest canopy covers (FCC). Under an enclosed forest canopy, smaller air temperature gradients are developed above the snow surface (Frey and Salm, 1990). It is known that the temperature variations within snowpack are crucial for the prediction of snow avalanches. The formation of slab avalanches was found to be closely related to the seasonal features of complex and layered structure of snowpacks (Bader and Salm, 1990). For example, wet snow avalanches develop when the snow temperature in some layers of snowpacks reaches 0
C (Baggi and Schweizer, 2009). The temperature changes between snow layers vary because in each storm event, the amount of snowfall, temperature, temperature trends, new snow density, and associated

*Correspondence to: Abdurrahim Aydın, Faculty of Forestry, Düzce University, Konuralp Campus 81620, Düzce, Turkey. E-mail: [email protected] Copyright © 2012 John Wiley & Sons, Ltd.

wind are different. Because of the temperature variations, a weak snow layer can be formed frequently (Birkeland, 1998). Consequently, the temperature profile within snow covers becomes the main component that affects various physical processes of the formation of weak snow layers (Gray and Male, 1981) and the occurrence of the avalanche hazard (McClung and Schaerer, 1993; Schweizer, 1993; Clarke and McClung, 1999; Birkeland et al., 2006). Also, the temperature variations of snowpacks affect the peak stream flows in the melting season (Hamlet et al., 2005; Stewart et al., 2005) and directly influence basin hydrograph shape (Blöschl et al., 1991). During the temperature increase in melting season (or spring), acceleration in melting and consequent increases in peak stream discharges are seen; therefore, basin hydrograph shape also changes accordingly. Snowpacks are bounded by the atmosphere above and ground surface below. Normally, the combination of ground stored summer heat and geothermal heat from the earth’s center can warm the base layer to 0
C (or close to 0
C). The air temperature also directly affects the snowpack temperature. The duration and intensity of insolation as well as air temperature were found to increase from the winter solstice until the summer solstice (McClung and Schaerer, 1993). Moreover, with an approaching melting season, snow temperatures increase and the snowpack temperature gradient tends to decrease (McClung and Schaerer, 1993; Singh and Gan, 2005).

A. ALTUNKAYNAK AND A. AYDIN

Diurnal fluctuations of the air temperature are very important in influencing the temperature of the first 30–40 cm of snowpack (Armstrong and Williams, 1992; Fukuzawa and Akitaya, 1993; McClung and Schaerer, 1993; Birkeland, 1998; Birkeland et al., 1998; Ingolfsson and Grimsdottir, 2008). Therefore, the temperature profile within the snowpack is not linear (Koivusalo and Heikinheimo, 1999). Various studies also show that snowpack temperature and vertical temperature variations are affected by the thickness of snow cover (McClung and Schaerer, 1993; Arons et al., 1998) and melt–freeze cycle (Singh and Gan, 2005). It is known that the FCC affects snow temperatures and temperature gradients. As canopy cover controls incoming short-wave radiation and outgoing long-wave radiation (McClung and Schaerer, 1993; Koivusalo and Heikinheimo, 1999; Weir, 2002), it affects the transfer of energy from above the canopy to the forest floor (Hardy et al., 2001). It also decreases energy loss (Frey and Salm, 1990) and prevents extreme changes in snow surface temperatures (Frey and Salm, 1990; McClung and Schaerer, 1993). In the present study, snowpack temperatures are predicted using a multilayer perceptron (MP) approach with input parameters of leaf area index (LAI), ground temperature (Tg), snow surface temperature (Ts), and snow thickness (d0). It is aimed to establish a predictive model without using any restrictive assumptions such as linearity, normality (Gaussian distribution), variance constancy (homoscedasticity), and stationary. The MP approach, which does not include any of these restrictive assumptions, is used for the development of predictive models. Seven different models are developed using MP in this study. Models 1–3 are established for the condition of FCC. Also, the effects of LAI, ground temperature, snow surface temperature, and snow thickness on the prediction of snowpack temperature for snow thickness varying from 20 to 60 cm (TH20, TH40, and TH60 cm) are examined in these modeling studies. Models 4–7 are developed for open areas by using ground temperature, snow surface temperature, and snow thickness to predict snowpack temperature within the snow thickness ranging from 20 to 80 cm (TH20, TH40, TH60, and TH80 cm). The aims of the present study were (i) to predict snow temperatures within snowpacks using the new MP approach with the following input parameters and variables: LAI, ground temperature (Tg), snow surface temperature (Ts), and snow thickness (d0); and (ii) to provide an assessment of the prediction performance of this approach to other researchers involved in snowpack studies.

factors. The ANN provides an opportunity to make computation with a large amount of data because of its parallel process mechanism (Lippmann, 1987). Input and output layers are connected to each other through a net of transition matrix weights. In case of absence of hidden layer, this system is called perceptron (Holland, 1975). MP models have been used in different study areas since their first introduction by Rumelhart et al. (1986). A MP is a feed-forward ANN model that relates the input variables to output variables using optimum weighting coefficients (Figure 1). In Figure 1, “I” corresponds to input, “a” is the optimum weighting coefficient providing connection between input layer and hidden layer, “h” is the neuron in hidden layer, “b” is the weighting coefficient connecting hidden layer to output layer, “m” is the bias coefficient for hidden layer, “c” is the bias coefficient for output layer, and “o” is the output. MP approach constitutes a standard form of neural network modeling and can modify two-layer linear perceptron methods using three and more layers. The ability of MP is to handle complex nonlinear interactions that ease natural process of modeling. This method can overcome complex computations using neuron networks. Also, they can easily nonlinearly link input and output variables (Altunkaynak and Strom, 2009). Different from a standard linear perceptron, the MP uses three or more layers of neurons (nodes) with nonlinear activation functions (Haykin, 1998). The MP consists of layers, computational units (neurons), and activation functions. Each neuron contains an activation function and has an ability to generate weighting coefficients and convey it to the layer followed. The number of neurons in the hidden layer should be between 3 and 7 for the application of MP models (Altunkaynak, 2007; Altunkaynak and Strom, 2009). In many applications, the units of these networks apply a “tansig” or “pureline” function as an activation function. The back-propagation training algorithm (Rumelhart et al., 1986) is the most preferred technique in the learning process of multilayer networks. Output values of Input I1

a13

b11

h

b12

a22

a21

O1

a23

I2

MP approach

Copyright © 2012 John Wiley & Sons, Ltd.

Output

h

a12

.

An artificial neural network (ANN) is a system that imitates the biological neural system and its internal operation processes. The smallest unit in the neural nets is called neuron. The ANN has a capability to function as a unified system with parallel interconnections of simple neurons. Neurons can receive information inputs either from other neurons or from external sources such as bias

Hidden a11

a2r

a1r

.

. .

anr

In

h O2

br1

b1p

hr

brp

mr m1

.

br2

. Op

c1 cp

Bias Bias

Figure 1. Architecture of MP Hydrol. Process. (2012) DOI: 10.1002/hyp

PREDICTION OF TEMPERATURE VARIATION WITHIN A SNOWPACK

the network are compared with the observed values to find the optimum weighting coefficients. The algorithm determines the optimum weighting coefficients by using back-propagated error information. After a certain number of repetitions of the abovementioned procedure, the network becomes stable in terms of its weighting coefficients. Once the fixed weighting coefficients are obtained, one can use this network to make estimations. Back-propagation training algorithms

Back propagation is a method that is widely used algorithm for any number of neurons in the hidden layer. After training process, the results obtained from the trained (calibrated) network are compared with the measured data, which were not used in the training process, to test the network (prediction). Once the network architecture is configured, the learning process, which is the adjustment of the weights, takes place as a subsequent step. The error can be represented in the output node j at the nth data point by ej(n) = tj(n)  Oj(n), where t is the target value and O is the value yielded by the MP. The final aim is to minimize the error function, which is expressed as hðnÞ ¼

1X 2 e ðnÞ 2 j j

(1)

Each weighting coefficients can be determined by differentiating with respect to the desired weight: @hðnÞ Δaji ðnÞ ¼ a (2) Oi ð n Þ @Ij ðnÞ where Oi is the outcome of the previous neuron and a is the learning rate, which is carefully assigned to ensure the convergence of the weights toward a response that should be neither too specific nor too general. In practical applications, typically it ranges from 0.2 to 0.8. The derivative at the right-hand side of Equation (2) depends on the input node sum Ij. It is easy to prove that an output node derivative can be simplified to 

  @hðnÞ ¼ ei ðnÞd’ Ij ðnÞ @Ij ðnÞ

(3)

where d’is the derivative of the activation function described earlier, which is constant. The analysis is more difficult for the change in weights of a hidden node, but it can be shown that the relevant derivative is   X @hðnÞ @hðnÞ   ¼ d’ Ij ðnÞ akj ðnÞ @Ij ðnÞ @Ik ðnÞ k

(4)

The accuracy of the MP approach is evaluated by using the mean absolute error (MAE), the mean square error (MSE), the and Nash–Sutcliffe sufficiency score (NSSS), which are defined as n   1X THpi  THoi  (5) MAE ¼ n i¼1 Copyright © 2012 John Wiley & Sons, Ltd.

MSE ¼ 2

n  2 1X THpi  THoi n i¼1

2 3 6 7 i¼1 7 NSSS ¼ 6 n 41  P 5 2 ðTHoi  THm Þ n  P

(6)

THpi  THoi

(7)

i¼1

where n is total number of observations and THpi, THoi, and THm are the model predictions, observed data, and the mean of the observed data, respectively. For all models (models 1–7), the values of MAE, MSE, and NSSS are obtained from Equations (5)–(7), respectively. Study area and data

To measure snowpack temperature, we performed a study along Kartalkaya road, Bolu (which is the only accessible route in the region during snow season), Northwestern Turkey (31
46′E–40
45′N and 31
48′E– 40
35′) (Figure 2) during winter of 2007–2008. Sampling points are located in 11 elevation classes, which range from 930 to 1930 m and totally 33 sampling points with three different covers (one in an open area and two in different FCCs) were selected. At each sampling point, a total of 33 sticks were placed to manually measure the snow depth on the ground. The study area is affected by the maritime climate regimes with cool winters. No previous snowpack data have been ever collected. There is only one meteorological station in Bolu city center (elevation 742 m a.s.l.), at a horizontal distance of approximately 16 km from the study area. The annual average precipitation is 542 mm, and it is covered with snow during 44 days of the year. The measured average maximum snow depth is 64 cm, occurring in February. The temperature and the snow cover thickness were measured in 2007–2008 winter season using thermometers with an accuracy of 0.1
C. Each sampling site was visited 44 times (approximately three times per week) to collect data that include snow depth, snow surface temperature, ground temperature, and snowpack temperature at 20-cm intervals (TH20, TH40, TH60, and TH80) (Figure 3). The snow surface temperature was instantaneously measured by putting thermometer manually on snowpack surface. Leaf area index

LAI is a dimensionless parameter and is defined as the one-sided leaf area per ground surface area (Chen and Black, 1991, 1992). LAI plays important roles in many ecological applications because of the vegetation– atmosphere processes of the canopy cover (Running and Coughlan, 1988; Running and Gower, 1991; Schleppi et al., 2006; Visscher von Arx et al., 2007; Thimonier et al., 2010). Because canopy cover is the first barrier against fallen snow from air to the ground surface, the determination of the values of LAI is of particular importance. Hydrol. Process. (2012) DOI: 10.1002/hyp

A. ALTUNKAYNAK AND A. AYDIN

Figure 2. Map of study area

Figure 3. Snow profile temperature measurement (following McClung and Schaerer, 1993)

In the present study, the canopy cover in forest was determined on the basis of the values of LAI. The values of LAI from sample pictures were calculated according to the hemispherical photograph analysis. Hemispherical photographs were collected using a Canon EOS 5D digital camera with a fisheye lens. All photographs were taken looking upward by keeping the lens horizontal. A total of 33 photographs were taken and analyzed with the Hemisfer software (version1.4), developed by Copyright © 2012 John Wiley & Sons, Ltd.

the Swiss federal Institute for Forest, Snow and Landscape research (WSL) (Schleppi et al., 2006). Model description

In the present study, we developed seven different models (models 1–7) in 11 elevation classes ranging between 930 and 1930 m and in three different sampling locations (one in an open area and two in different FCCs) for each elevation classes along Kartalkaya road, Bolu, for the prediction of Hydrol. Process. (2012) DOI: 10.1002/hyp

PREDICTION OF TEMPERATURE VARIATION WITHIN A SNOWPACK

snowpack temperature in a depth with 20-cm interval. Inputs and outputs of training and testing data are given in detail in Table I. Models 1–3 are developed for predictions of snowpack temperature under different FCC where model 1 is based on the inputs of LAI, ground temperature, snow depth, snow surface temperature, and output of snowpack temperature for the 20-cm depth (TH20). Model 2 includes the same inputs and snowpack temperature for the 20- and 40-cm depths (TH20 and TH40 cm). Model 3 consists of the same inputs and outputs of snowpack temperature for the depths of 20, 40, and 60 cm (TH20, TH40, and TH60 cm). Model 1 is developed for shallow snow depths (d0 < 20 cm), model 2 for medium snow depths (20 cm < d0 < 40 cm), and model 3 for deep snow depths (d0 > 40 cm) to predict snowpack temperatures. Models 4–7 are developed for predictions of snowpack temperature in an open area. Model 4 is established from inputs of ground temperature, snow surface temperature, and output of snowpack temperature for the 20-cm depth (TH20). Similarly, models 5–7 include

the same input (Tg and Ts) and output variables as (TH20, TH40), (TH20, TH40, and TH60), and (TH20, TH40, TH60, and TH80), respectively. RESULTS AND DISCUSSION The application of the MP approach is carried out along the Kartalkaya road, Bolu, located in the Northwestern Turkey. In the context of MP approach, seven different models (models 1–7) are developed using a data set obtained by measurements in the study area. Input and output variables of the models are given in Table I. In this study, variables including LAI, ground temperature (Tg), snow surface temperature (Ts), snow thickness (d0), and snowpack temperature for the depth of 20 cm (TH20) were analyzed in terms of linearity, normality (Gaussian distribution), and variance constancy (homoscedasticity), as shown in Figures 4 and 5. Figure 4 indicates that the variables do not have normality distribution. It is noted

Table I. Various scenarios to predict temperature variations of snowpack in open areas and under different canopy covers Model no. 1 2 3 4 5 6 7

Input

Output

No. training (calibration) data

No. testing (prediction) data

LAI, d0, Tg, and Ts LAI, d0, Tg, and Ts LAI, d0, Tg, and Ts, d0, Tg, and Ts d0, Tg, and Ts d0, Tg, and Ts d0, Tg, and Ts

TH20 TH20 and TH40 TH20, TH40, and TH60 TH20 TH20 and TH40 TH20, TH40, and TH60 TH20, TH40,TH60, and TH80

236 115 31 232 115 70 40

100 50 15 50 60 40 21

Normal Probability Plot

Probability

Probability

Normal Probability Plot 0.999 0.997 0.99 0.98 0.95 0.90 0.75 0.50 0.25 0.10 0.05 0.02 0.01 0.003 0.001 20

40

60

80

100

120

0.999 0.997 0.99 0.98 0.95 0.90 0.75 0.50 0.25 0.10 0.05 0.02 0.01 0.003 0.001 -16

-14

-8

-6

-4

-2

0

(a)

(c)

Normal Probability Plot

2

Normal Probability Plot 0.999 0.997 0.99 0.98 0.95 0.90

Probability

Probability

-10

Snow surface temperature (oC)

0.999 0.997 0.99 0.98 0.95 0.90 0.75 0.50 0.25 0.10 0.05 0.02 0.01 0.003 0.001

-12

Snow thickness (cm)

0.75 0.50 0.25 0.10 0.05 0.02 0.01 0.003 0.001

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1

1.5

2

2.5

Ground temperature (oC)

Leaf area index

(b)

(d)

3

Figure 4. Normal probability plots for (a) snow thickness, (b) ground temperature, (c) snow surface temperature, and (d) LAI. Copyright © 2012 John Wiley & Sons, Ltd.

Hydrol. Process. (2012) DOI: 10.1002/hyp

2 0 -2 -4 -6 -8 -10 0

20

40

60

80

100

120

140

0 -2 -4 -6 -8 -10 -16 -14 -12 -10

-8

-6

-4

-2

0

2

(a)

(c)

0 -2 -4 -6 -8 -2.5

2

Snow surface temperature (oC)

2

-3

4

Snow thickness (cm)

4

-10 -3.5

Snowpack temperature (TH20)

4

Snowpack temperature (TH20)

Snowpack temperature (TH20)

Snowpack temperature (TH20)

A. ALTUNKAYNAK AND A. AYDIN

-2

-1.5

-1

-0.5

0

Ground temperature (oC)

0.5

1

1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 0.5

1

1.5

2

2.5

3

4

3.5

Leaf area index

(b)

(d)

Figure 5. Scatter diagrams for the (a) snow thickness versus snowpack temperature (TH20), (b) ground temperature versus snowpack temperature (TH20), (c) snow surface temperature versus snowpack temperature (TH20), (d) LAI versus snowpack temperature (TH20)

Table II. Prediction errors of MP for model 3 Observation

MP model Prediction

LAI d0 Tg (m2/m2) (cm) (
C) 1.19 2.38 2.38 2.38 1.27 1.27 1.27 1.27 1.19 1.19 1.19 1.19 1.19 1.19 1.19

57 68.5 94 81 74 60 82 69.5 65 60.5 87 80 41 43 65

Ts (
C)

TH20 (
C)

T H 4 0 T H 6 0 TH20 (
C) (
C) (
C)

1.2 0.7 1.9 2.8 0.9 2.3 3.9 4.3 5.7 5.8 3.1 6.2 5.6 6.2 6.3 1.2 0.8 1.2 1.2 1 2.6 4.9 4 5.1 4.9 1.9 4.5 2.8 3.1 4 1 0.9 0.6 1 0.7 0.9 0.7 0.9 0.8 0.8 1.9 4.5 2.7 3.9 4.6 2.4 6.3 4.5 5 5.9 3.3 7.2 4.8 5.9 6.3 1.2 0.9 1.3 1.2 1 0.9 0.9 0.9 0.8 0.9 1 0.7 1.1 0.8 1.1 1 3.4 0.9 1 1.7 Average of test (prediction) TH20,TH40, NSSS = R2

TH40 (
C)

1.0 1.7 4.2 5.6 5.5 6.5 1.8 2.1 3.4 4.7 2.8 4.3 0.6 0.1 0.5 0.1 2.8 4.2 3.3 4.8 4.4 5.6 0.7 0.3 1.0 1.3 1.0 1.3 1.4 1.9 and TH60

Square errors

Absolute errors

TH60 (
C)

TH20 (
C)

TH40 (
C)

TH60 (
C)

TH20 (
C)

TH40 (
C)

TH40 (
C)

1.7 6.0 7.9 1.9 4.8 3.7 1.5 1.4 3.7 4.6 6.8 1.5 1.2 1.4 2.1

0.84 0.01 0.01 0.35 0.40 0.00 0.00 0.12 0.00 1.36 0.14 0.41 0.00 0.01 0.30 0.26 0.91

1.14 0.01 0.11 0.82 0.16 1.47 0.77 0.44 0.09 0.06 0.09 0.80 0.26 0.27 0.88 0.49 0.89

0.70 0.06 2.51 0.87 0.00 0.10 0.56 0.36 0.86 1.60 0.28 0.30 0.08 0.06 0.20 0.57 0.90

0.92 0.11 0.08 0.59 0.63 0.03 0.04 0.35 0.07 1.17 0.38 0.64 0.06 0.10 0.54 0.38

1.07 0.10 0.34 0.90 0.40 1.21 0.88 0.66 0.30 0.25 0.30 0.90 0.51 0.52 0.94 0.62

0.84 0.24 1.58 0.93 0.06 0.32 0.75 0.60 0.93 1.26 0.53 0.55 0.27 0.25 0.44 0.64

TH20, TH40, and TH60, snow profile temperature for each 20 cm.

that there is no linear relation between input and output variables as depicted in Figure 5. Also, as can be seen from Figure 5, independent variables change with dependent variable. Therefore, the variables do not have Copyright © 2012 John Wiley & Sons, Ltd.

variance constancy (homoscedasticity). Consequently, our results suggest that the variables in this study do not satisfy the restrictive assumptions such as linearity, normality distribution, and variance constancy. The MP Hydrol. Process. (2012) DOI: 10.1002/hyp

PREDICTION OF TEMPERATURE VARIATION WITHIN A SNOWPACK

approach is trained in three steps: (i) feed-forward of the input training pattern, (ii) associated error calculation and back propagation, and (iii) optimization of weighting coefficients. For all models (models 1–7), the data set is separated as calibration (training) and testing (prediction) data. The number of data used for the calibration and test phases is given in Table I. Because of the limitation of showing all results in tables, only the results of model 3 are shown in Table II to represent the predictions of snowpack temperature for cases with different FCC (models 1–3). Similarly, the results of model 6 are shown in Table III to show the model predictions for open area (models 4–7). The predicted snowpack temperatures as time series using models 1–3 under different FCCs are given in Figures 6, 7a and 7b, and , 8a–8d, respectively.

For the cases of open area, the snowpack temperatures obtained from models 4 to 7 are plotted in time series in Figures 9, 10a and 10b, 11a–11c, and , 12a–12d, respectively. In addition, perfect model line (1:1 line) plots using results from models 1 to 3 are shown in Figures 13, 14a and 14b, and , 15a–15c, whereas the perfect model line plots for the results of models 4–7 are given in Figures 16, 17a and 17b, 18a–18c, and , 19a–19d. The test (prediction) results of model 3 for FCC are given in Table II, and the test (prediction) values of model 6 are given in Table III. Tables II and III show the computed values of MAE, MSE, and NSSS for the predicted data of models 3 and 6, respectively. Examining the performance of developed models (models 1–7), the calculated MAE, MSE, and NSSS

Table III. Prediction errors of MP for model 6 Observation

MP model Prediction

d 0 (mm)

T g (
C)

T s (
C)

80.0 69.0 68.0 74.0 68.0 75.0 67.5 71.0 61.5 84.0 80.0 83.0 82.5 69.0 70.0 67.0 71.3 123.0 100.0 86.5 84.0 85.0 81.0 86.3 117.0 122.0 114.0 107.0 119.0 116.0 105.0 104.0 69.0 120.0 102.0 115.0 109.0 111.0 110.0 109.0

0.7 0.6 0.6 0.7 0.7 0.7 0.6 0.8 0.8 0.8 0.3 5.1 0.3 2.6 0.8 6.9 0.6 7.7 1.0 9.8 0.3 0.5 0.3 5.7 0.2 9.8 1.3 5.5 2.6 3.9 1.7 4.4 1.9 15.0 1.4 12.8 1.9 5.9 1.3 5.1 1.7 4.7 2.1 6.1 3.1 6.4 2.6 5.4 2.1 14.0 1.6 7.3 1.6 8.4 1.1 0.7 0.9 0.8 0.8 0.7 0.8 0.7 0.7 0.8 0.7 1.2 0.7 1.0 0.7 0.6 0.7 0.9 0.6 0.6 0.7 0.8 0.8 0.6 0.7 0.7 Average of

TH20 (
C)

TH40 (
C)

TH60 (
C)

0.9 0.8 0.7 0.6 0.8 0.8 0.8 0.9 0.8 1.0 0.8 1.1 1.0 0.9 0.6 0.1 0.6 2.2 1.1 2.2 3.6 3.0 4.6 5.6 0.7 2.4 6.2 2.2 2.7 4.8 2.2 3.3 3.8 1.8 3.1 3.7 5.5 3.8 4.1 2.3 3.5 4.0 3.3 4.2 4.6 1.9 2.8 3.8 3.4 5.0 8.0 3.0 3.8 5.0 6.2 3.5 4.8 2.4 3.2 4.2 2.7 3.3 4.7 3.5 4.2 4.7 5.4 6.3 7.7 4.1 4.9 6.2 8.1 8.4 4.9 2.8 4.4 5.5 2.9 4.0 4.8 1.4 2.1 2.6 1.2 1.2 1.8 1.0 1.2 1.3 0.5 0.9 0.9 1.0 1.0 1.0 1.2 1.2 1.2 1.2 0.7 1.0 0.6 0.7 0.8 1.0 1.2 1.0 0.9 1.1 0.9 0.9 0.9 0.9 0.7 0.8 0.6 0.7 0.7 0.7 test (prediction) TH20,TH40, NSSS = R2

Copyright © 2012 John Wiley & Sons, Ltd.

TH20

Square error

Absolute errors

TH40

TH60

TH20

TH40

TH60

TH20

TH40

TH60

1.5 2.1 1.5 2.4 1.7 2.6 1.4 2.2 1.9 2.8 0.9 0.2 0.6 1.6 0.7 2.8 1.3 2.8 3.2 4.8 1.1 2.6 1.0 2.1 2.5 4.0 3.1 4.6 3.6 5.0 3.3 4.7 3.6 5.6 3.4 5.0 3.3 4.4 2.9 4.1 3.2 4.2 3.4 4.6 3.6 4.9 3.5 4.6 3.6 6.2 3.1 4.6 3.2 4.8 1.7 2.2 1.3 2.0 1.2 1.7 1.2 1.7 1.1 1.6 1.8 2.7 1.1 1.7 1.1 1.6 1.0 1.6 0.9 1.4 1.1 1.6 1.2 1.7 1.1 1.6 and TH60

1.8 1.5 1.8 1.6 2.1 3.2 2.6 4.3 4.1 5.8 2.2 1.9 4.7 4.6 4.9 4.5 6.3 6.3 5.7 4.9 5.0 5.5 5.3 5.4 6.6 5.8 6.0 2.6 2.3 1.9 1.9 1.7 2.0 1.9 1.7 1.8 1.4 1.7 1.8 1.7

0.31 0.84 0.79 0.20 0.74 0.61 0.23 5.34 0.35 0.98 1.16 0.67 1.66 0.70 0.08 1.98 0.06 0.14 0.05 0.27 0.23 0.00 3.12 0.33 1.79 0.11 0.12 0.08 0.02 0.02 0.12 0.02 0.33 0.02 0.27 0.00 0.00 0.02 0.22 0.12 0.60 0.65

1.57 2.50 2.96 1.90 3.75 0.20 0.37 3.09 0.13 4.39 0.46 1.02 0.02 1.14 0.71 3.64 0.36 1.34 0.14 0.73 0.87 0.14 2.00 0.10 3.69 0.04 0.57 0.00 0.58 0.27 1.51 0.39 2.26 1.09 0.75 0.20 0.09 0.49 0.75 0.75 1.17 0.66

1.21 0.54 0.94 0.27 2.11 0.91 1.06 1.63 4.29 1.05 2.69 3.16 0.67 0.39 0.07 0.55 2.77 1.74 0.28 0.47 0.11 0.63 5.65 0.59 3.10 0.12 1.52 0.00 0.28 0.40 1.04 0.55 0.64 0.83 0.75 0.58 0.24 0.64 1.54 0.92 1.17 0.79

0.55 0.92 0.89 0.45 0.86 0.78 0.48 2.31 0.59 0.99 1.08 0.82 1.29 0.84 0.28 1.41 0.24 0.38 0.23 0.52 0.48 0.07 1.77 0.57 1.34 0.33 0.34 0.28 0.15 0.16 0.35 0.13 0.58 0.14 0.52 0.04 0.01 0.15 0.47 0.35 0.60

1.25 1.58 1.72 1.38 1.94 0.44 0.61 1.76 0.36 2.10 0.68 1.01 0.13 1.07 0.84 1.91 0.60 1.16 0.38 0.86 0.93 0.38 1.42 0.32 1.92 0.20 0.75 0.07 0.76 0.52 1.23 0.63 1.50 1.05 0.87 0.45 0.29 0.70 0.87 0.87 0.94

1.10 0.74 0.97 0.52 1.45 0.96 1.03 1.28 2.07 1.02 1.64 1.78 0.82 0.62 0.26 0.74 1.67 1.32 0.52 0.68 0.32 0.79 2.38 0.77 1.76 0.34 1.23 0.03 0.53 0.63 1.02 0.74 0.80 0.91 0.87 0.76 0.49 0.80 1.24 0.96 0.96

Hydrol. Process. (2012) DOI: 10.1002/hyp

A. ALTUNKAYNAK AND A. AYDIN 1 0

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(c) Figure 8. Predicted and measured time series for snow profile temperature for model 3: (a) TH20, (b) TH40, and (c) TH60

Figure 7. Predicted and measured time series for snow profile temperature for model 2: (a) TH20 and (b) TH40

values are listed, respectively, as follows: TH20 (0.6, 0.58, and 0.81); TH20 (0.54, 0.40, and 0.82); TH40 (0.61, 0.6, and 0.84); TH20 (0.38, 0.26, and 0.91); TH40 (0.62, 0.49, and 0.89); TH60 (0.64, 0.57, and 0.90); TH20(0.67, 0.58, and 0.67); TH20 (0.68, 0.76, and 0.63); TH40 (1.00, 1.41, and 0.65); TH20 (0.60, 0.60, and 0.65); TH40 (0.94, 1.17, and 0.66); TH60 (0.96, 1.17, and 0.79); TH20 (0.31, 0.21, and 0.90); TH40 (0.69, 0.89, and 0.81); TH60 (0.95, 1.18, and 0.81); and TH80 (0.88, 0.99, and 0.85). In the brackets (TH20 [MAE, MSE, and NSSS], TH40 [MAE, MSE, and NSSS],. . ., TH80 [MAE, MSE, and NSSS]), the first item is the temperature prediction of TH20 (MAE, MSE, and NSSS), the second item is the temperature prediction of TH40 (MAE, MSE, and NSSS), Copyright © 2012 John Wiley & Sons, Ltd.

and other items indicate the consequent corresponding values. As indicated previously, models 1–3 are developed for different FCCs and models 4–7 are for an open area. The temperature prediction as time series for TH20 of model 1 is shown in Figure 6. It is seen that the predicted results are very close to the observed values. Model 2 is used for the prediction of temperature in two different points (TH20 and TH40) of snowpack. The predicted results of the models are given in Figures 7a and 7b. Figure 7a also shows that prediction results are very close to the observed values. It is clearly seen from the investigation of Figures 7a and 7b (model 2) that the predicted results of TH20 show better performance than those of TH40. It can be noticed that the predictions and Hydrol. Process. (2012) DOI: 10.1002/hyp

PREDICTION OF TEMPERATURE VARIATION WITHIN A SNOWPACK 1

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Figure 9. Predicted and measured time series for snow profile temperature for model 4 (TH20)

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Figure 11. Predicted and measured time series for snow profile temperature for model 6: (a) TH20, (b) TH40, and (c) TH60

Figure 10. Predicted and measured time series for snow profile temperature for model 5: (a) TH20 and (b) TH40

observations are very close in Figure 7b, but they are not as a high coincidence as in Figure 7a. The predicted results of model 3 (TH20, TH40, and TH60) are given in Figures , 8a–8c. It can be seen from the examination of Figures , 8a–8c that the prediction results of model 3 are similar to those of models 1 and 2. In other words, the predictions shown in Figure 8c are slightly more deviated from the observed values when compared with the results presented in Figures 8a and 8b. Prediction results of models 1–3 are close to each other as can be seen from Figures 6–8 as well as from statistical parameters (MAE, MSE, and NSSS). In fact, this is an expected consequence, however, although the inputs for these three models are the same, model 3 can predict the Copyright © 2012 John Wiley & Sons, Ltd.

values of TH20, TH40, and TH60, where model 1 can only predict TH20 and model 2 can predict TH20 and TH40. Therefore, model 2 is superior to model 1, and model 3 is superior to models 1 and 2. We also demonstrated models 1 and 2 in this study to make comparison and to indicate the difference between these two models and model 3. In this study, we suggest that model 3 is useful for the prediction when compared with models 1 and 2 for cases with different FCCs. Models 4–7 for open area are snowpack temperature predictive models for shallow snow depth (TH20), medium snow depth (TH20 and TH40), deep snow depth (TH20, TH40, and TH60), and very deep snow depth (TH20, TH40, TH60, and TH80), respectively. The temperature predictions for TH20 in model 4 are given in Figure 9, whereas those for TH20 and TH40 in model 5 Hydrol. Process. (2012) DOI: 10.1002/hyp

A. ALTUNKAYNAK AND A. AYDIN 1

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are given in Figures 10a and 10b as time series plots, respectively. Figure 10a shows that predicted results are close to the observed values. It can be clearly seen from Figure 10b that the predicted results are found to be with more deviation when compared with the results in Figure 10a. The predicted results of model 6 are given in Figures , 11a–11c. Deviation of the predicted results from the observed data is slightly higher for results in Figure 11b, for those in Figure 11c, and for those in Figure 11a, in a decreasing order. The predicted results for TH20, TH40, TH60, and TH80 of model 7 are given Copyright © 2012 John Wiley & Sons, Ltd.

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(b) Figure 14. Verification of observed and predicted snow profile temperature for model 2: (a) TH20 and (b) TH40 Hydrol. Process. (2012) DOI: 10.1002/hyp

PREDICTION OF TEMPERATURE VARIATION WITHIN A SNOWPACK 1

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Model-3 Standard deviation=2.14 Sample number=15 R=0.94 NSSS=0.89

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(c) Figure 15. Verification of observed and predicted snow profile temperature for model 3: (a) TH20, (b) TH40, and (c) TH60

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in Figures , 12a–12d, respectively. The predicted results of model 7 is better when compared with prediction results of models 4–6 as can be seen from Figures 9–12 and from the statistical values such as MAE, MSE, and NSSS. However, although the inputs for these four models are the same, model 7 can make the prediction of the values for TH20, TH40, TH60, and TH80. Hence, model 7 is found to be superior to models 4–6. In the present study, also the results of model 7 were compared with those of models 4–6. We suggest that model 7 gives more accurate results than models 4–6 for an open area. Copyright © 2012 John Wiley & Sons, Ltd.

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(b) Figure 17. Verification of observed and predicted snow profile temperature for model 5: (a) TH20 and (b) TH40

Furthermore, the results of models 1–3 (under different canopy covers) have good prediction performance when compared with the results of models 4–7 (under open area). The main reason is that the canopy cover controls Hydrol. Process. (2012) DOI: 10.1002/hyp

A. ALTUNKAYNAK AND A. AYDIN 1 Model-6

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(c) Figure 18. Verification of observed and predicted snow profile temperature for model 6: (a) TH20, (b) TH40, and (c) TH60

incoming short-wave and outgoing long-wave radiations (McClung and Schaerer, 1993; Koivusalo and Heikinheimo, 1999; Weir, 2002), which affects the energy transfer from canopy to the forest floor (Hardy et al., 2001), decreases energy loss (Frey and Salm, 1990), and prevents snow surface temperatures fluctuations (Frey and Salm, 1990; McClung and Schaerer, 1993). Therefore, using LAI as an input parameter has increased the prediction performance of the models. Copyright © 2012 John Wiley & Sons, Ltd.

In details, TH20 in models 1 and 4, for thinner snowpack (i.e. 50 cm), Tg has a greater effect compared with Ts. By adding parameter d0 to the model as an input, the model takes into account TH20 if this was affected from d0. In models 2 and 5, the lowest d0 value is 41 cm; thus, many exemplars in TH20 are mainly affected from Tg. In contrary, effect of Tg on TH40 decreases in a thinner d0 value (in range of 41–70 cm). For snowpack thicker than 70 cm, TH40 is affected by both Tg and Ts but with lower power. In models 3 and 6, the lowest d0 value is 61 cm. As the same with model 2, the exemplars in TH20 are mainly affected from Tg, many exemplars in TH60 are affected from Ts, and many exemplars in TH40 are affected from both Tg and Ts but with lower power. In model 7, the lowest d0 value is 81 cm (max d0 is 123 cm). Thus, TH20 was affected by Tg and TH80 by Ts. TH40 and TH60 are affected by both Tg and Ts but with lower power. Prediction performance of model 3 is better than models 1 and 2 (for under different canopy covers) and that of model 7 is better than models 4–6 (for open area). The reason is that for thick snowpack (i.e. 1 m), Ts influences the first 30 cm temperatures and Tg influences the first 20–30 cm aboveground (McClung and Schaerer, 1993). Because TH40 and TH60 remain in boundary of Tg and Ts, the prediction reveals a better performance. The perfect model line of model 1 is shown in Figure 13. The observed data and predicted model results are scattered around a 1:1 line (diagonal line). The perfect line of model 2 is shown in Figures 14a and 14b. In Figures 14a and 14b, observations and predicted values are also shown to be scattered around a 1:1 line. Good agreements between observed data and predicted values of model 3 are shown in Figures , 15a–15c. Similar perfect model line plot of model 4 is shown in Figure 16. It can be clearly seen that observations and predicted model results are scattered around the 1:1 line. A perfect model line plot of model 5 with results scattered around a 1:1 line is shown in Figures 17a and 17b. The comparisons between observed data and model predictions using model 6 are shown in Figures , 18a–18c. It is noted that the predicted values and observed data had good consistency. The comparison plots for model 7 are presented in Figures , 19a–19d. Here, there is a good agreement between predicted values and observed data. In this study, for all models described earlier, the investigation of predicted snowpack temperature using the MP approach is carried out with results presented in time series plots and along the perfect model line. It can be seen that the predictive models show good performance in producing results that match reasonably well with the observed data. The results suggest that the MP approach shows good performance in predicting the snowpack temperature. Also, models 3 and 7 are found to be useful to make prediction for cases with different FCCs and for an open area, respectively. Hydrol. Process. (2012) DOI: 10.1002/hyp

PREDICTION OF TEMPERATURE VARIATION WITHIN A SNOWPACK 0

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Figure 19. Verification of observed and predicted snow profile temperature for model 7: (a) TH20, (b) TH40, (c) TH60, and (d) TH80

CONCLUSIONS The temperature variations of snowpack are strongly affected from the snow surface temperature compared with air temperature above and ground temperature below. Temperature gradient–caused metamorphic processes in a snowpack have profound effects on the time of the occurrence of avalanches. In addition, snow is an important resource of freshwater that dominates the hydrology in mountain catchments. Thus, the prediction of snowpack temperature is important to understand metamorphic process in a snow pack for prediction and evaluation of avalanche formation, snow melting, and hydrological processes. Because canopy cover influences snow surface and temperature fluctuations, LAI parameter is an important input parameter in the prediction of snow profile temperature. Our results suggest that in thinner snow pack, both Tg and Ts affects the snow profile temperature. In thicker snowpack, Ts has decreasing effects on downward in the snowpack, and Tg has decreasing effect of upward of snowpack so that in thicker snowpack, the model has a better prediction performance. In the present study, seven different models are developed for FCCs and open areas to predict the snowpack temperatures. These models are developed using the MP approach. The MP method allows generating models with multi-inputs and multi-outputs. Copyright © 2012 John Wiley & Sons, Ltd.

The predictive models show good performance in producing results that match reasonably well with the observed data.

ACKNOWLEDGEMENTS

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Hydrol. Process. (2012) DOI: 10.1002/hyp