Precipitation forecast over western Himalayas using k-nearest neighbour method

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1 INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 28: (2008) Published online 25 February 2008 in Wiley InterScience ( Precipitation forecast over western Himalayas using k-nearest neighbour method A. P. Dimri, a * P. Joshi b and A. Ganju b a School of Environmental Sciences, Jawaharlal Nehru University, New Delhi, India b Research and Development Center, Snow and Avalanche Study Establishment, HimParisar, Sector 37A, Chandigarh, India ABSTRACT: Knowledge of precipitation over the western Himalayas is of utmost importance during winter season (December, January, February, and March DJFM) due to extreme weather conditions. During winter, eastward moving synoptic weather systems called western disturbances (WDs) yield enormous amount of precipitation over this region. This amount of precipitation by a number of WDs keeps on accumulating and poses an avalanche threat to the habitat. Not only this, low temperature conditions along with precipitation form extremely hostile winter conditions to live with. In the present study, the nearest neighbour (NN) method is used to forecast probability of precipitation (PoP) occurrence/nonoccurrence and its quantity. The method of NN is introduced to visualize the results. The NN forecast technique attempts to compare similar situations in the past with current data and assumes that similar events are likely to occur under similar conditions. At present, only nine important weather variables are considered for generating a 3-day advance forecast of PoP occurrence/non-occurrence and quantity at eight representative observatories in Jammu and Kashmir (J&K), the northmost state of India. This state receives maximum amount of solid precipitation in the form of snow during winter. Past data of 8 14 years (between 1988 and 2003) is considered, from which the nearest days are looked for and tested with data of 2 4 years (between 2003 and 2005). PoP occurrence/non-occurrence is well predicted by k-nearest Neighbour (k-nn) sampling method. It is evident from the results that the model is able to give the projections 3 days in advance, with an accuracy of 71 88%. Probability forecast of occurrence of precipitation is predicted well by the present model setup, but the quantitative precipitation forecast (QPF) is an important issue that still needs improvement, keeping in view the topographical and land-use heterogeneity of the area under study. Copyright 2008 Royal Meteorological Society KEY WORDS precipitation; k-nearest neighbour; probability Received 3 November 2006; Revised 4 December 2007; Accepted 24 December Introduction Northwest India has complex mountain ranges. This region receives high amount of precipitation, in the form of snow, during winter (December, January, February, and March (DJFM). This winter precipitation is mainly attributed to the passage of weather systems called western disturbances (WDs). These are eastward moving low pressure synoptic weather systems that originate over the Mediterranean Sea or mid Atlantic Ocean and travel eastward over Iran, Afghanistan, Pakistan, and India. These weather systems take their southernmost tracks during winter when they pass over northwest India. Further, the strength and vertical extent of these systems are influenced by the position of the mid and upper air tropospheric troughs in the zonal westerlies. A detailed discussion of the synoptic features of the WDs is given by Rao and Srinivasan (1969); Singh (1979) and others. As pointed out by earlier studies (Pisharoty and Desai, 1956; Kalsi, 1980; Kalsi and Haldar, 1992), WDs * Correspondence to: A. P. Dimri, School of Environmental Sciences, Jawaharlal Nehru University, New Delhi, India apdimri@hotmail.com, apdimri@yahoo.com are manifestations of the interaction between the tropics and mid latitude systems, and are associated with extensive sheets of mid- and high-level clouds. Surface weather elements, like precipitation and temperature, associated with these WDs are highly dependent upon local topography and local atmospheric circulations. Also, northern India is composed, in part, of Himalayan mountain ranges having different altitudes and orientations, causing the prevailing weather conditions to be complex. Topography steers atmospheric circulations by thermodynamical and dynamical forcings. Further, the surface heterogeneity of northern India generates numerous meso/microscale circulations in the narrow valleys and rugged hills, which dominate in determining the precipitation and temperature pattern over the region. Topography exerts a strong dynamical forcing on atmospheric circulations, land surface exchanges of momentum, energy, water, and chemical constituents with the atmosphere. In view of these factors, large-scale general circulation models with coarse horizontal resolution cannot properly simulate the horizontal distribution of the precipitation and temperature (Mohanty and Dimri, 2004). In recent years, with the establishment of the National Centre Copyright 2008 Royal Meteorological Society

2 1922 A. P. DIMRI ET AL. for Medium Range Weather Forecasting (NCMRWF) in New Delhi, India, a direct numerical model output operationally provides precipitation forecasts over the western Himalayas with a horizontal model resolution of 1.5 latitude 1.5 longitude. The performance of numerical weather (NWP) models over this region is severely constrained due to complex topography as well as lack of adequate observations. In view of this; large-scale general circulation models with coarse horizontal resolution cannot properly simulate the quantity of precipitation and its horizontal distribution. Hence it is very difficult to predict/simulate such surface weather elements over complex mountainous region by even sophisticated state-of-the-art NWP models. Forecast of probability of precipitation (PoP) and Quantitative Precipitation Forecast (QPF) at a specific site and time provide important guidance for human activity, preparedness for natural hazards (such as avalanches and floods), and forecast management. Various statistical techniques are available to predict PoP and QPF. Glahn and Lowry (1969, 1972) used outputs from NWP models to develop regression models to forecast PoP over different parts of the USA. Paegle (1974) compared the forecast of PoP over different parts of the USA derived from equations stratified with respect to the synoptic weather patterns and equations that were not stratified. It was found that the stratified methods were more accurate. Kriplani and Singh (1986) developed composite charts of probabilities of 24-h rainfall amounts exceeding 2.5 mm and 65 mm, when there is a monsoon depression over India. Upadhyay et al. (1986) developed a method to forecast precipitation by considering the fact that the precipitation rates are directly proportional to the large-scale vertical velocity. Using this method, precipitation rates were computed for specific monsoon depression situations over central parts of India. Kruzinga (1989) compared the forecasting of PoP over the Netherlands using an analogue technique and logistic regression. For a 1 3 days lead time, the regression method performed better than the analogue technique. Kumar and Ram (1995) developed a technique for QPF over the Rapti catchment region in Uttar Pradesh, India. This is a synoptic-analogue method in which synoptic systems are classified according to the observed rainfall rates in the ranges 11 25, and >50 mm. Mohanty et al. (2001) developed objective methods to forecast PoP and QPF at Delhi using classical multivariate regression and discriminant analysis. Maini et al. (2002) employed the perfect prognostic method for precipitation and temperature forecasts during monsoon season. Mohanty and Dimri (2004) and Dimri and Mohanty (2007) have presented performance of statistical downscaling on numerical model outputs of various models and shown enhanced skills by implementing statistical techniques over the complex Himalayan region. Thus, the use of objective techniques to forecast precipitation for a specific location in the mountainous region of northwest India is limited. It may be noted that in mountainous region mainly synoptic, persistence, climatological methods are used to predict the occurrence of the precipitation. Forecasts based on persistence show very poor results, as precipitation has a strong temporal and spatial variability over the region. Therefore, there is a need for more skilful objective methods to predict precipitation over mountains. It is also desirable to introduce statistical relations between precipitation and other observed meteorological parameters using the Nearest Neighbour (NN) method to produce PoP and QPF guidance over the region. Development of NN models for PoP and QPF is a difficult task over rugged mountainous regions like the western Himalayas. This is mainly due to highly heterogeneous terrain and non-availability of adequate observational data sets. Thus, the of occurrence/non occurrence of precipitation is a challenging task over the western Himalayas. Hence, the objective of the present study is to generate PoP occurrence/nonoccurrence and its quantity (QPF) for day 1, day 2 and day 3. In the present study, the k-nearest Neighbour (k-nn) technique is used, which is a flexible approach, developed here based on past observations. Nonetheless, performance of k-nn with historical data sets will depend upon the quality of the observations. In the present work, siteand time- specific of precipitation is carried out by developing an analogue model over the western Himalayas using the k-nn concept. Section 2 describes the methodology of k-nn technique for formulation of the precipitation forecast model. The data source, quality control, and data preparation for the model development over Jammu and Kashmir (J&K), the northernmost region of India (Figure 1), are presented in Section 3. Results and discussion based on this are given in Section 4. Finally, Section 5 presents the main conclusions of the study. 2. The k-nn sampling methodology A continuous NN query retrieves the NN at every point on a line segment (Tao et al., 2002). The basic assumption of NN technique is as follows: if a day like today can be found in the past, we will have a similar precipitation distribution pattern. Certainly, such a likeness must be based on parameters related to the precipitation occurrence and its quantity. In principle, this method makes forecast based on the assumption that for the same weather conditions precipitation occurrence and its quantity will be similar and therefore the method seeks to identify similar situations in the past. Accadia et al. (2003) have used a simple NN average method, also known as remapping of budge interpolation, which maintains total precipitation to a desired degree of accuracy. Buser (1989) and Martin et al. (2000) have extensively used the NN techniques for formulating site specific avalanche forecasting. An annotated algorithm for sampling precipitation value considered with day-to-day dependence on the (nine) variables is presented below. In the present work, the k-nn model is developed, in which nine daily weather elements are considered

3 PRECIPITATION FORECAST OVER WESTERN HIMALAYAS 1923 Figure 1. Schematic representation of geography and topography (m) of the region under study. This figure is available in colour online at as members of the daily weather vector, which is represented by the vector time series of weather variables x t,t = 1,...,n (n = 9 in the present study), as listed in Table I. This weather vector synoptically defines the future state of the precipitation for that particular day. Being a dependent structure, it explains which and how many lags the future state of precipitation will depend on and the number of NN k touse. A vector x t 1 is then defined. This vector of the (nine) variables of interest of the previous day is considered to assess the next day s precipitation (say ppt t ). Now the current day s vector, x i, is used to Table I. Meteorological parameters considered for the study. SNo Parameter Time of observation 1200 UTC (previous day) 0300 UTC 1 Maximum temperature (T x ) 2 Minimum temperature (T n ) 3 Dry bulb 0300 UTC temperature (T ) 4 Av wind speed (ws avg ) 5 Wind direction (wd) 0300 UTC 6 Wind speed (ws) 0300 UTC 7 Surface Pressure (P) 0300 UTC 8 Cloud amount (cla) 0300 UTC 9 Cloud type (clt) 0300 UTC Average of last 24 h determine/select the k-nns among the historical state vectors (x 1,x 2,...,x m,...,x i,...,x t ) using the weighted Hamming distance. To determine this, the distance between individual parameters is calculated and one threshold value is set for each parameter. If the distance is less than this threshold value, then that particular day would be considered as a nearest day. This method is described in greater detail below. N(x) = (y 1,y 2,...,y 9 )/(x 1 θ 1 y 1 x 1 + θ 1 ), (x 2 θ 2 y 2 x 2 + θ 2 ),...,(x 9 θ 9 y 9 x 9 + θ 9 ) (1) where N(x) is the overall vector distance; y 1,y 2,...,y 9 are the vector distances corresponding to variables(say) x 1,x 2,...,x 9 and θ 1, θ 2,...,θ 9 are the threshold values for each variable. These threshold values are chosen in such a way that variability in each variable is accounted for and is schematically described by Figure 2, in which the dependency is shown with two variables. Threshold value is considered in a way that significant contribution of both the variables is looked into. Therefore, ±θ i is considered within the limits of the shaded portion, where simultaneous contribution of both the variables is seen. Similarly, other threshold values are considered in the study. To elaborate further, say, n is the total number of data points, m is the number of actual days for validation and p is the number of days to be tested and θ 1,θ 2,...,θ 9

4 1924 A. P. DIMRI ET AL. +θ 2 is taken into account for the forecast. The number of NNs selected is based on the criteria that evaluate the mean square forecast error (corrected for degree of freedom of the model) to choose model parameters of time series simulation models. e i = x i x f i (5) k x f 1 i = xi,j k j=1 1m (6) x 2 -θ 2 -θ 1 +θ 1 m=1 x 1 Figure 2. A schematic representation of selection of threshold values for individual parameters. ±θ 1 or ±θ 2 represents the most suitable limits of variables, such as relative humidity and temperature, under which maximum occurrence of precipitation is likely (the shaded portion represents the most suitable region of variables). are the threshold values corresponding to each of the parameters. The differences between parameters of an actual day with the same parameters of the past years, i.e. p days, are calculated. Below is shown the distance, y 1 (k) and y 2 (k), calculated for maximum (T x ) and minimum (T n ) temperature respectively. y 1 (k) = T x (j) T x (k) (2) y 2 (k) = T n (j) T n (k) (3) where j varies from m, m + 1,...,n and k is varying from 1, 2,...,p. Similarly, distances y 3 (k), y 4 (k),...,y 9 (k) are calculated for rest of the parameters considered in this study. Now if the distance y 1 (k) is less than θ 1, threshold value for the first parameter, the value is set to be 0 otherwise 1. Let this value be z 1 (k). Thus if y 1 (k) < θ 1 then z 1 (k) = 0otherwisez 1 (k) = 1 Similarly, If y 2 (k) < θ 2 then z 2 (k) = 0otherwisez 2 (k) = 1, and so on. Then the final Hamming distance is calculated as D = z 1 (k) + z 2 (k) + z 3 (k) z 9 (k) (4) Among these days, the days with zero distance will be nearest to the conditioning day and it will be assumed that the synoptic situations of that particular nearest day will be closest and hence corresponding precipitation state of next 24 h can be estimated as that of the nearest days. Finally, a set of k-nn states is selected in which an element of this set records the time t associated with closest historical state with the current vector (x i ). In this manner, sampling is continued to achieve the similar state and hence corresponding precipitation state where, e i is the error vector of the ith vector x i ; x i is the recorded value that is to be forecast; x f i is the k-nn forecast vector corresponding to x i ; xi,j s is the vector corresponding to the j th nearest neighbor of the vector on which we are conditioning to sample a vector corresponding to x i. 3. Model application and performance measure In general, in most of the statistical methods, a statistical dependence or correlation of daily sequence of weather variables with each other on the same day or on the previous day, persistence, is considered. For example, on rainy days, solar radiation and maximum temperature are likely to be lower, whereas wind speed and minimum temperature may be higher than on dry days. Here, precipitation is chosen as the driving variable to be predicted, as it is one of the requirements over the western Himalayas, which has complex variability within it. A precipitation occurrence model based on NN is developed to generate the sequence of dry and wet days and precipitation amount. The precipitation amount on a rainy day may also depend on the wind, the humidity, and the temperature. Consequently, there is a reason to consider dependence of the daily weather processes on more than just precipitation, as has traditionally being done. Typically, daily precipitation is generated independently, and the other variables are generated by conditioning on precipitation events, i.e. whether a day is wet or dry (Jones et al., 1972). Serial dependence of weather variables is defined by fitting auto regression models of order 1 (AR-1) independently to each variable for each period (Nicks and Harp, 1980). Further, a multivariate autoregressive model of order 1 (MAR-1), adds the consideration of dependence across variables (Richardson, 1981). Mohanty and Dimri (2004) have also shown such dependence using multivariate statistical models. The nine important weather variables considered for the study are maximum temperature (T x ), minimum temperature (T n ), dry bulb temperature (T ), 24 h average wind speed (ws avg ), wind direction (wd), wind speed (ws), surface pressure (P), cloud amount (cla) and cloud type (clt) (Table I). Though these variables are recorded twice a day at 0300 UTC and 1200 UTC, in the present study, the variables observed at the time shown in Table I

5 PRECIPITATION FORECAST OVER WESTERN HIMALAYAS 1925 are considered, whereas for 24 h observations, average of these two records are calculated and used. All these parameters are assessed to determine the state of the precipitation in the next 24 h. Therefore, cumulative precipitation amount recorded in 24 h is considered for study. Precipitation is treated as a binary variable here. If measurable precipitation is observed, the binary value of precipitation is set to 1; if no measurable precipitation is observed, the value is set to 0. The threshold value of precipitation is taken as 0.1 cm, which is the least measurable snow depth. The 24-h accumulated snow depths are found to be highly variable. The precipitation reported on a particular day is the accumulated snow depth in the 24 h ending at the reporting time i.e UTC. A schematic diagram pertaining to observation and forecast time is depicted in Figure 3. Snowfall depths are classified firstly into two classes: non-occurrence and occurrence. Further the occurrence class is classified into four categories: Category I: cm; Category II: cm; Category III: cm and Category IV: 48.1 cm. Snow depth (in cm) is used to verify the results in this method because they are the only observations available. Eight representative observatories (road axes/sectors) considered for study are Kanzalwan (Bandipur Gurez axis/bg), Haddantaj (Nogaon Kaiyan axis/nk), Drass (Srinagar Leh axis/sl), StageII (Chowkibal Tangdhar axis/ct), Banihal (National Highway No. IA/NHIA), Pharkian (Keran sector), Gulmarg (Gulmarg sector), and ZGali (Macchal sector) (Figure 4). These observatories are considered since they represent the climatic and weather conditions of the region in which they fall and are also nodal centres for assessing/disseminating warnings of any natural hazards in time. Further, these sectors are considered because they represent different geographical and climatic conditions of the J&K, the northmost state of India. Data from December 1988 to March 2005 is considered for the present study for predicting probability of occurrence/non-occurrence and category of the precipitation for 3 days in advance. Out of this, December 1988 March 2003 data is used as the historical data set from which nearest days are selected Observation Time N-1 N day N+1 Variable considered Precipitation occurrence/ nonoccurrence and amount Figure 3. Reference time, in UTC, for the variables considered in the study. for the current days which are from December 2003 to March Experimental design The PoP occurrence/non-occurrence model is initiated at 0300 UTC to generate a forecast for the next 3 days. The probability of quantity of precipitation model is initiated at the same time only if the first model indicates the precipitation occurrence as yes. The algorithm defined in Section 2 is applied to data from the eight observatories and selected statistics of the simulated state of precipitation are computed. The statistics of interest, as described in Section 3.2, is computed for each simulation and compared with the actual observation Performance measure The following statistics are considered to be of interest in comparing historical record and the simulated record of precipitation state. None of these statistical measures are explicitly specified in fitting the k-nn model. Consequently, their successful reproduction can be considered a sign of success for the method. For the purpose of verification of categorical forecast, contingency tables are prepared and the verification parameters and skill scores are evaluated as defined in the appendices (Wilks, 1995). 4. Results and discussion PoP occurrence/non-occurrence and probability of occurrence of certain category are assessed. Various statistical scores and skill scores are computed on the basis of simulation. Comprehensive analysis of these scores is carried out for day 1, day 2 and day 3 projections Performance of PoP occurrence/non-occurrence model The model for forecasting performance of probability of occurrence/non-occurrence of precipitation at the eight sites is evaluated using a 2 2 contingency table (Wilks, 1995). For the purpose of verification, measures and skill scores are computed (Appendix A). Table II illustrates that the probability of detection (POD) of occurrence of precipitation is higher in case of day 1 as compared to day 2 and day 3 at all the eight stations. This is attributed to the fact that the relation of precipitation events with synoptic situations decreases as the time lag increases. This also occurs because over the western Himalayas, precipitation has large variability owing to topographic variation. False alarm rate (FAR) for all these stations does not exceed 0.56 for day 1, whereas for day 2 and day 3, its value is less than 0.74 and 0.73, respectively. These extreme values are at Drass, which is situated in Great Himalayan range. Drass, as per the geographic location (Figure 4) receives lot of modified weather as WDs which travel eastward first interact/cross Pir Panjal range and then reach the Drass region. By virtue of this, precipitation patterns over Drass

6 1926 A. P. DIMRI ET AL. Figure 4. Observatory and sector network in Jammu and Kashmir. This figure is available in colour online at region are very different from that at the rest of the stations, which are mostly located in the Pir Panjal range. These values of FAR also illustrate that the model has better POD for non-occurrence of precipitation (C-NON) for all the 3 days (ranging from 0.70 to 0.94; and for day 1, day 2, and day 3, respectively) than it does for occurrence of precipitation (POD ranging from 0.50 to 0.92; and for day 1, day 2, and day 3, respectively). This may be attributed to the fact that the number of no-precipitation days is generally higher compared to the number of days with precipitation (Table III). The model bias shows the stability in the model performance with values ranging from 0.90 to 1.23; , and for day 1, day 2 and day 3, respectively at all the stations except at Banihal, where it shows low values. Also, the model performance is degraded as the lead time increases. Now, this clearly shows the fact that the model was not able to capture the synoptic weather observations satisfactorily for the forecast for day 3. Nonetheless, the model

7 PRECIPITATION FORECAST OVER WESTERN HIMALAYAS 1927 Table II. Verification measures (Appendix A) for the probability of precipitation occurrence/non-occurrence model. Measure Day 1 Day 2 Day 3 Kanzalwan POD FAR MR C-NON CSI TSS BIAS PC 74% 54% 44% Haddantaj POD FAR MR C-NON CSI TSS BIAS PC 88% 68% 58% Drass POD FAR MR C-NON CSI TSS BIAS PC 74% 64% 64% Stage2 POD FAR MR C-NON CSI TSS BIAS PC 76% 65% 60% Banihal POD FAR MR C-NON CSI TSS BIAS PC 82% 73% 69% Pharkian POD FAR MR C-NON CSI TSS BIAS PC 71% 59% 52% Table II. (Continued). Measure Day 1 Day 2 Day 3 Gulmarg POD FAR MR C-NON CSI TSS BIAS PC 76% 62% 57% Zgali POD FAR MR C-NON CSI TSS BIAS PC 81% 49% 49% performance is reasonable for day1 and day2 s. The other skill scores/evaluation indices for the model show reasonably high values towards perfect forecast criteria (Appendix A) particularly for day 1 s. It is interesting to note that the overall performance of the model, which is measured by percent correct (PC), is very high for day 1 at all the eight stations ranging from 71 to 88%. All the forecast verification indices estimated from the contingency table clearly demonstrate that at all the eight stations the model provides very satisfactory performances for day 1, whereas definite improvements for day 2 and day 3 are needed. The general deterioration in day 2 and day 3 values may be because the synoptic scale conditions considered in the study are taken at a 24 h interval. However, sometimes it may happen that complex topography play an important role in modifying the mountain weather within the timescale of 24 h. Owing to non-consideration of this variability, occurrence of precipitation events is overlooked. Also, looking into the philosophy of the NN sampling technique, similar synoptic conditions in the past can yield different precipitation states. So, overall, these aspects and variability in the nature of precipitation occurrence will definitely affect model performance Performance of probability of quantitative precipitation forecast We refer to Section 3 for the definition of snowfall categories. This model, is based on the NN sampling method, is sued to predict probability of a categorical quantity of precipitation. The skill scores and the other verification measures are calculated using 4 4 contingency (Table BI, Wilks, 1995). The skill scores/evaluation indices and other verification measures of this model are illustrated in Table IV for day 1, day 2 and day 3 for the eight stations.

8 1928 A. P. DIMRI ET AL. Table III. Comparison of the number of days with no precipitation with the number of days with precipitation at each station. Station Total no of days considered for study No of days with no precipitation No of days with precipitation Kanzalwan 1715 ( ) Haddantaj 1647 ( ) Drass 1399 ( ) Stage ( ) Banihal 763 ( ) Pharkian 1313 ( ) Gulmarg 2111 ( ) Zgali 1107 ( ) Table IV. Verification measures (Appendix B) for the probability of Quantitative Precipitation Forecast (QPF) model. Measure Day 1 Day 2 Day 3 Kanzalwan CSI I II III IV HSS Percentage Correct 47% 55% 55% % for non-occurrence 72% 62% 62% Haddantaj CSI I II III IV HSS Percentage Correct 79% 49% 49% % for non-occurrence 77% 75% 75% Drass CSI I II III IV HSS Percentage Correct 70% 63% 84% % for non-occurrence 79% 78% 80% Stage2 CSI I II III IV HSS Percentage Correct 45% 35% 55% % for non-occurrence 76% 74% 76% Banihal CSI I II III IV Table IV. (Continued). Measure Day 1 Day 2 Day 3 HSS Percentage Correct 76% 62% 57% % for non-occurrence 94% 91% 85% Pharkian CSI I II III IV HSS Percentage Correct 49% 46% 37% % for non-occurrence 70% 68% 61% Gulmarg CSI I II III IV HSS Percentage Correct 49% 41% 56% % for non-occurrence 83% 76% 78% Zgali CSI I II III IV HSS Percentage Correct 39% 54% 40% % for non-occurrence 77% 51% 52% The Critical Success Index (CSI) of the model in assessing the PoP is higher in category I as compared to other categories for all three days at all the eight stations. This illustrates the fact that the model could capture the precipitation amounts in lower snowfall categories better than the higher categories. In the present model, some of the cases show higher CSI for day 2 and day 3 as compared to day 1. This is attributed to the fact that once

9 PRECIPITATION FORECAST OVER WESTERN HIMALAYAS 1929 the same synoptic situations are found correctly in the past, a category forecast upto 3 days in advance can be made with satisfactory results. Heidke skill score (HSS) ranges from 0.07 to 0.52; and for day 1, day 2 and day 3 respectively at all the eight stations. It is interesting to note that the overall performance in terms of PC ranges from 39 to 79%; 35 79% and 37 84% for day 1, day 2 and day 3, respectively, at all the stations. All the forecasts estimated from NN sampling method for of probability of category of precipitation amount at all the eight stations are able to provide reasonable performance over this data-sparse region. The complexity associated with accurate precipitation occurs mainly for the following reasons. First, the difference may lie in the fact that topography and vegetation cover is very fast changing within a kilometres over the Himalayan region. This variability may be attributed to the fact that although in general topographically induced cold season precipitation maxima are well captured by the model, but the corresponding peak precipitation values are somewhat overestimated. This is evidently a problem in the analogue model relative to numerical models where resolution over the complex topographical Himalayan region does come into play. Secondly, spatial variability of precipitation increases substantially with the effect of land surface heterogeneity due to temperature. Therefore, precipitation can be in the form of snowfall over the higher peaks and rainfall over the valleys. As a result, snow tends to accumulate over the high resolution peaks and melt more effectively over the corresponding valleys over complex Himalayan topography. This can be attributed to the inherent nonlinear nature of snow forming processes. As the temperature threshold for snow formation is reached, say at the high elevation of a peak, snow starts accumulating. Because snow has a higher albedo than a bare soil or vegetation, the overall surface albedo increases and this causes a decrease in absorption of solar radiation at the surface, further bringing down temperatures and allowing for an increase in snow accumulation. 5. Conclusions In this article a k-nn method is used and tested for precipitation forecast over the Himalayan region where both topography and land-use variability is large. In the present multivariate setting, neighbours of the conditioning point correspond to data patterns that are similar to the patterns at the conditioning point. And it was found that for a day with no rain, which is warm, with little wind, and no humidity, neighbours established by calculating the vector distance between the observations will be similar days. The values for the precipitation for the next day are sampled as a vector from a historically similar day. Clearly, this method has shown strong utility in giving a probability forecast to a day that is more similar to the conditioning day than the other neighbours. Using a weighted Hamming distance function, sensitivity in the developed model has increased for selecting the number of NNs for precipitation. The model could reproduce the day 1 forecast with reasonable accuracy as a short range statistical tool. This technique mainly focuses on short range statistical properties and suffers from the drawback of assuming the data to be normally distributed. Therefore, only linear dependence between surface variables and precipitation states from one day to the next is reproduced. Also this model is unlikely to reproduce the variance and related attributes at longer periods (e.g. the inter-annual variance and dependence of seasonal precipitation). In this article, only a winter (DJFM) is considered for study. The results might depend on the specific simulated year, which are not considered in the study. In addition to this, fine-scale heterogeneity of topography and land use strongly affect the large-scale circulations and surface features, and hence suitable interpolations schemes are necessarily to be considered in the study to obtain data over the data-sparse region. Therefore, some of these aspects are proposed for introduction into the k-nn model for future study. Also, considering more variables like wind fields, vorticity, and divergence from the numerical model output will be more helpful to assess larger variability of the method. Apart from this, suitable assumption and selection of threshold values for each parameter will take care of regional and geographical precipitation distribution. Keeping in view the operational use of NWP models over the Himalayan region, the k-nn technique can potentially be used for integration on to the NWP numerical model outputs for statistical downscaling. Since the Himalayan region has a large topographical and land-use variability, simulating NWP models with very fine resolution needs extensive computational power and data assimilation in initial and boundary conditions. This integration will be able to consider effects of local meso/microscale circultation that can be considered as future study. Acknowledgements The authors acknowledge Dr R.N. Sarwade, Director, SASE, for encouraging the study. Thanks are also due to various persons of Avalanche Forecasting Group (AFG), SASE, who have done a tremendous job in the complex Himalayan region during winter. Appendix A The values in the contingency table are defined as follows, 1. When an event is predicted to occur (forecast occurrence) and in reality it does occur (observed occurrence), then it is classified as A, otherwise (observed non-occurrence) it is classified as C.

10 1930 A. P. DIMRI ET AL. Table AI. Verification measures used for forecast evaluation. Observed Yes Forecast No Yes A B No C D 2. When an event is predicted not to occur (forecast non-occurrence) and in reality it does occur (observed occurrence), then it is classified as B, otherwise (observed non-occurrence) it is classified as D. 3. A + B: Total number of cases of occurrence of precipitation as observed. 4. C + D: Total number of cases of non-occurrence of precipitation as observed. 5. A + B + C + D: Total number of forecasts. For a best/perfect forecast series: B = 0andC= 0 and hence POD = 1, FAR = 0, MR = 0, C-NON = 0, Bias = 1, CSI = 1, TSS = 1, HSS = 1, PC = 100% Appendix B Table BI. Categorical verification of forecasts (four category events). Observed Forecast I II III IV Total I a b c d J II e f g h K III i j k l L IV m n o p M Total N O P Q T Probability of Detection (POD) POD = A A + B False Alarm Rate (FAR) FAR = C C + A Miss Rate (MR) MR = B B + A Correct non-occurrence (C-NON) C NON = D D + C Critical Success Index (CSI) A CSI = A + B + C True Skill Score (TSS) TSS = A A + B + D D + C 1 Heidke Skill Score (HSS) 2(AD BC) HSS = B 2 + C 2 + 2AD + (B + C)(A + D) Bias (BIAS) for occurrence BIAS = A + C A + B Percentage Correct (PC) PC = A + D A + B + C + D 100% (A1) (A2) (A3) (A4) (A5) (A6) (A7) (A8) (A9) (Category I: cm; Category II: cm; Category III: cm and Category IV: 48.1 cm) Total number of observed events in category I is J = a + b + c + d Total number of forecast events in category I is N = a + e + i + m (B1) (B2) In the similar wayo,k,p,l,q and M are computed. Then the total numbers of events are T = J + K + L + M = N + O + P + Q Percentage Correct (PC) (B3) PC = a + f + k + p 100% (B4) T Critical Success Index (CSI) CSI = Heidke Skill Score (HSS) a J + N a, f K + O f, k L + P k, p M + Q p (B5) JN + KO + LP + MQ a + f + k + p HSS = T JN + KO + LP + MQ T T (B6) References Accadia C, Mariani S, Casaioli M, Lavagnini A Sensitivity of precipitation forecast skill scores to Bilinear interpolation and

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